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HIGH SPEED SPINDLE HEAT SOURCES, THERMAL ANALYSIS AND BEARING PROTECTION By WEIGUO ZHANG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY ACKNOWLEDGEMENTS author wishes express sincere appreciation to Dr. Tlusty, chairman of the supervisory committee, for his guidance and assistance in this study and in the preparation of this dissertation. Genuine thanks are extended to Dr. Scott Smith, member of the supervisory committee, for his help and advice. The author also wishes to acknowledge the help and assistance from C. Bales, W. Chau, C. Chen, Y. Chen, W. Cobb, D. Smith, and W. Winfough, members of the Machine Tool Research Center (MTRC); Thomas Delio John Frost, engineers at Manufacture Laboratories, Inc.; and Dr. Carlos Zamudio and Chris Vierck, former members of MTRC. Special thanks and appreciation are extended to his wife, Aiyu Li, for her constant support, encouragement, and understanding throughout the length of his program. TABLE OF CONTENTS ACKNOWLEDGEMENTS ABSTRACT CHAPTERS INTRODUCTION ...... Scope of the Problem Historical Review and C Tasks and Methodology contemporary Studies .. of this Study . . . . . . . 2 SPINDLE MODELING Spindle Structure .. High Speed Bearing Load . Bearing Heat Generation . . Internal Motor Heat generation Heat Transfer . .. Other Considerations. ... * a S . S S S S S S S S S . . S S S S S S S C S S S S S S S S 4 5 5 . . . . S S P S C S S S U . * U. S *. . . . ..S S S S S S S. . S *. U . .S S . 6 .* S .S .S . * U S S S S S S S C S 0 S S S S . 3 FINITE ELEMENT ANALYSIS (FEA) ......... Finite Element Analysis of Heat Transfer Problems Generation and Solution of Spindle FE Thermal Mod Calculation of a Spindle with Bearing Heat Sources Calculation of a Spindle with Bearing and Internal Motor Heat Sources ..... ....... 4 SPINDLE TEMPERATURE FIELD MEASUREMENT Thermoelectricity and Thermal Radiation .... Measurement of a Spindle with Bearing Heat Sources Measurement of a Spindle with Bearing and ]Paii * S S S S S S S S S S U S S S U S S S S S S S . S . S S S S S . S S S S S U S S C S . S S LIST OF TA]BI~S IJIST OF FIGURES ................... ................... ..... 5 HIGH SPEED SPINDLE DESIGN WITH THERMAL CONSIDERATION .... ..... Spindle Static and Dynamic Properties .... Effect of Forced Cooling on Spindle Temperature Effect of Spindle Heat Source and Bearing Axial Load .. ...... .. . Spindle Bearing Catastrophic Failure Temperature 6 SPINDLE BEARING THERMAL PREDICTION MO BEARING CONDITION DIAGNOSIS .... .... Bearing Defect Frequencies and Detection .. .... Using Thermal Model for Bearing Monitoring . Bearing Monitoring through Measuring Acoustic Emission and Signal Demodulation 7 CONCLUSION AND FURTHER Conclusions . Areas of Further Research . APPENDIX A APPENDIX B * S S S S S S S S S S S S * S S S S S S S S S S S S S * S S S S S S S S S S S S C S * S S S S C S S S S S S S S * S S S S S S S S S S S S S DEL AND . S S S S S S S S S . S S S S S S S . . S . S C S S S S S S S S S S S S BEARING CALCULATION PROGRAM ......... MOTOR LOSS MEASUREMENT REFERENCES WORK . . . . . . I3IOGRAIP~C S~TC~EI LIST OF TABLES Table 2.1 Coefficient f, for Angular Contact Ball Bearing 2.2 Inductive Power Loss Distribution . . . . . . . Page 25 29 2.3 Motor Drive DC Power Measurement @ Idling 2.4 Surface Characteristic Length for Free Convection ............... 3.1 Spindle Surface Classification . . . . . . . . 3.2 Spindle A Simulation Conditions .. .. .. .. ... .. .. . . 3.3 Spindle A Heat Generation Rate 3.4 Spindle A Surface Convection Coe: * S enSS S S S S S S S S S S S S S 3.5 Spindle A Temperature From Simulations ........ ....... 3.6 Spindle A Time Constants From Simulations ............. 3.7 Spindle Bearing and Motor Heat Generation Rates .... 3.8 Spindle B Convective Coefficients .. . . 4.1 Spindle A Measured Time Constants ... 4.2 Spindle A Measured Temperature .. ..... 5.1 Bearing Heat Dissipation at Seizure ....... 6.1 Curve Fitting Results of Bearing Failure Cases 6.2 Curve Fitting of Normal Cases ... . S S a a . S S . S. S S S S S S S S S S S . 5 0 5 5 S S S S S S S S S S S S S S S LIST OF FIGURES Figure 1.1 Bearing Thermal Condition Diagram 2.1 High Speed Spindle . . .. .. . . 2.2 Angular Contact Ball Bearing .. . . . . . .. 2.3 Bearing Ball Gyroscopic Moment .. .. 2.4 Differential Slipping 2.5 Heat Generation: Measurement and Calculation, Bearing 2MMV99120 .... .. .. ... 2.6 Heat Generation: Measurement and Calculation, Bearing 2MM9117 7 Bearing Heat Generation Calculation and Result from Temperature Measurements 3.1 Structure of Spindle A .... ........ 3.2 Simplified Structure of Spindle A . . . . .. 3.3 Meshes of Thermal Model of Spindle A ........ 3.4 Temperature Field and Time Response at Ii: a. Case 1, b. Case 2, c. Case 5, d. Case 6 . . . . . . 51 3.5 Different Convection Situations . . . . . . . . 3.6 Simplified Spindle B Structure .. 3.7 Meshes of Spindle B . . .. Page 3 4.1 Infrared Sensor Assembly and Arrangement 4.2 Sensor Arrangement for Temperature Measurement 4.3 Temperature Measurement for Case 1, Case 2, Case 3, Case 4: a. Case 4.4 Sensor Arrangement for of Spindle B .. b. Case 2, c. Case 5, d. Case 6 Temperature Measurement 4.5 Measured Temperature Field at 15,000 rpm and a. 15,000 rpm, b. 25,000 rpm .... ,000 rpm 4.6 Measured vs. Calculated Temperature for Spindle B 4.7 Transient Temperature Response, 8000 rpm 5.1 Temperature Fields (for Bearings with Water Cooling) at 15,000, 25,000, 35,000 and 45,000 rpm Temperature in Bearing Races 5.3 Temperatures in Bearing Outer Rings 5.4 Temperatures at Spindle Arbor Inner S Surface . . . . . Measured Temperature with Different Bearing Preloads .6 Bearing Heat Generation Calculation with Different Axial Load .. 5.7 Measured Bearing Seizure Temperature 5.8 Bearing Heat Generation a. Bearing Heat Generation Change at Seizure b. Bearing Heat Generation vs. Speed without Seizure 5.9 Increase of Bearing Axial Load at Seizure .... 5.10 Bearing Temperature Change at Contact .... C 1 1 'oI', , /, "n, ,n,,S.. 1... n n ^ a a C  / A 1r 1 S. . . . . . 89 . a a a a a S S S S . . S S S a a a * a a a . a a a a a . p 6.2 Measured Temperature (Normal & Failure Cases) 6.3 Curve Fitting Results for Cases in Figure 6.2 . 6.4 AE Signal and Signal Processing a. Pattern of AE Signal of Bearing b. AE Signal after Rectification c. Rectified AE signal after Low Pass Filter d. AE Signal Processing Diagram ..... 6.5 Measured Bearing Vibration Signal @ 15,000 rpm .. 6.6 Demodulated Bearing Vibration Signal in Figure 6.5 A.1 Program Flowchart A.2 Ball Contact Geometry and Deflection under Load ............... A.3 Deflection of Racecurvature Centers and Ball Center ............. A.4 Ball Force, Moment and Motion Vectors Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy HIGH SPEED SPINDLE HEAT SOURCES, THERMAL ANALYSIS AND BEARING PROTECTION By Weiguo Zhang May, 1993 Chairman: Jiri Tlusty Major Department: Mechanical Engineering thermal modeling high speed spindles analysis their temperature fields, thermal characteristics, and bearing defect signals are presented. The results provide an understanding of the thermal situation of high speed spindles and introduce practical methods for assisting in the analysis and design of high speed spindles. this study thermal modeling technique based on the finite element method was developed for the high speed spindles. The bearing loads, the bearing heat generation properties, spindle structure meshing, spindle thermal conduction and convection, and the bearing defect characteristics were investigated. An improved heat generation model of high speed angular contact ball bearings was _ ... .. 1 t 11 .. ...... ... A i J ... ___ 1 1__   .. j agreement between the computational and experimental results was found. infrared temperature measurement technique was developed for the measurement inside the cavities of the rotating components. temperature Additionally, the effect of spindle speed, bearing preload, water cooling of the spindle bearings, oilair lubrication drop rate, supply pressure were investigated. Model evaluation based on the measurement of a real bearing seizure yielded bearing catastrophic failure load and temperature and showed the large value of the transient thermal load. Bearing defect monitoring through measuring bearing vibration spectrum, bearing temperature variation and acoustic emission was also investigated in this work. An acoustic emission signal demodulation method was implemented. measurement of bearing vibration signal shows method is effective bearing monitoring under condition of strong background noise. CHAPTER 1 INTRODUCTION Scope of the Problem High speed, high power and high accuracy spindles are important m efficient use of machinery and labor resources and in the making of high quality parts. The design of these spindles is a difficult task in the machine tool industry. Such spindles have desirable characteristics, such as high power and high stability, but they also have some limitations. One of these limitations is that when bearings undergo very high dynamic load, they generate a large amount of heat and then are subject to sudden failure due to heavy inertia load and improper lubrication. One of the most important factors affecting high speed spindle performance and bearing life is the spindle thermal condition, which is a combined result of heat generation, heat dissipation, temperature, thermal load and stability. study spindle thermal condition related factors were investigated. Also included are analyses spindle structure material properties, heat source properties, and finite element thermal modeling and analysis. This study provides an understanding of high speed spindle thermal situations and will be useful for the design and analysis of high speed spindles. Tlusty et al [1] investigated the stability lobes in milling and demonstrated the high speed milling. The application greatly improved milling productivity and quality. Currently, research conducted in the Machine Tool Research Center at the University Florida Manufacturing Laboratories, Inc., achieved significant increases in metal removal rate (MRR) with a highspeed, highpower spindle. The research revealed that highspeed highpower spindles will play an important role in improving the manufacturing processes. Since spindles contain heat generation components (for example, bearings and the motor), the thermal condition is a major concern in designing and operating high speed highpower spindles. Any increases in bearing speed or bearing load are always accompanied an increase of bearing heat generation. Bearing heat generation affects the spindle thermal situation and bearing lubrication, which again affects bearing heat generation. This process, displayed through the block diagram in Figure 1.1, greatly influences the bearing life and limits spindle speed. Bearing speed and size both restrict maximum bearing speed, and a DN number (where D is the bearing bore diameter in millimeter, and N is the bearing speed in rpm) can represent these effects. Currently, commercially available high precision bearings with steel balls can be run at speeds up to DN = 1.5x106 and with ceramic balls DN = 2.2x106 [3]. It has been understood for some time that the bearing heat generation, heat dissipation and bearing thermal load are important in designing high speed bearing assemblies [4, 5]. Therefore, many measures have been taken to improve bearing thermal condition. design of bearing assemblies, especially with respect to machine tool spindles, many measures to improve the spindle thermal process was limited. For example, it is wellknown that the spindle arbor has a high temperature, but the true value and distribution are poorly known. Frequently, design, a conservative estimation made, or experience followed. The bearing thermal condition and thermal load are not evaluated. significance of understanding the spindle thermal situation is obvious: knowledge of the temperature field and the thermal expansion allows measures to be taken to limit the temperature and thermal load, and to maintain bearings in a stable working condition. SPINDLE SPEED INERTIA LOAD HEAT TEMPERATURE EXTERNAL LOAD THERMAL LOAD  Figure 1.1 Bearing Thermal Condition Diagram In this study a spindle thermal model was established. The spindle structure treatment, the bearing and motor heat generation, the spindle heat transfer, and the finite element method were used in the modeling process. This model was used to calculate the spindle temperature fields and to predict the temperature at different speeds. Real temperature profile measurements were made and good agreement was BEARING HEAT GENERATION MECHANISM BEARING BALL CENTRIFUGAL FORCE SPINDLE THERMAL SYSTEM FRICTION EFFECT AND THERMAL EXPANSION 4 from measured spindle temperature field. Spindle bearing temperature and vibration were also investigated. Historical Review and Contemporary Studies Jones' Bearing Load Theory In the 1940s, Jones [6] carried out a load analysis on deep groove and angular contact ball bearings and presented a method, based on bearing geometry, material strength and elasticity theory, to obtain bearing load distribution. proposed the race control theory to describe the ball spinning phenomenon. His later work included the investigation of ball motion and bearing friction[7]. Some of his theory is still used in bearing applications today. LundbergPalmgren's Bearing Life Theory and Palmgren' Work in Bearing Application Lundberg and Palmgren [8] performed their bearing fatigue life study in the early 1930s. This study related bearing life to bearing load and bearing structure through the famous bearing life formula and through the bearing basic dynamic load rating. This theory, called LundbergPalmgren's bearing fatigue life theory, is still the major tool in estimating bearing life. While evaluating bearing friction and temperature, Palmgren [4] analyzed bearing mechanics and pointed out that interfacial slipping friction between the rolling element and raceway was an important part in bearing mechanical friction. However, due to the complicated nature of bearing friction, when he formulated bearing mechanical friction torque, he adopted experimental data instead to lubricant shearing. These friction equations made it possible to calculate average bearing temperature (bulk temperature) balancing heat generation convection of the bearing assembly [4]. Because of the complexity of the rolling element bearing friction[8], Palmgren' empirical equations are still popular estimating bearing friction, particularly at low speed. Other Bearing Heat Generation Formulae Astridge and Smith [9] investigated the heat generation of roller bearings and found VISCOUS friction is a major source of heat generation Palmgren's empirical formulae overestimated bearing heat generation. Ragulskis [10] systematically analyzed all friction torque components in a general sense. formulae will be further analyzed later in this work. Tallian's Generalized Bearing Life Theory When Tallian analyzed the endurance data from a large group of bearings of different types and load conditions, lubrication, maintenance and application, he confirmed that Weibull distribution fit the test data in the most used cumulative failure probability region (failure probability from 0.1 to 0.6) [11], and presented a more general rolling contact fatigue life theory [12]. He systematized the effects of material properties, lubrication, surface roughness, load properties other operating conditions and presented life correction factors [13, 14]. Since tests should be carried out on all types of bearings to obtain the values of those correction factors, this method has rarely been seriously applied in bearing applications. Harris's Work on Bearing Load and Application 6 distribution and high speed bearing load distribution, bearing deflection, fatigue life and friction. He used a node system method to calculate the temperatures of the bearing and bearing assembly. He also investigated the gross sliding motion, i.e., skidding between the balls and inner raceway, and developed a method to predict the skidding [15, 16], which is important in high speed bearing operation. Dowson and Hamrock' Contribution to Bearing Lubrication Theory For many years before 1950, the lubrication of rolling element bearings was analyzed through hydrodynamics, i.e., the bearing was considered to be lubricated by generated movement pressure lubricant. Accordingly, at high load, low speed, and low conformity, the hydrodynamic pressure was not high enough to maintain film, surface contact would occur. However, the study of hydrodynamic lubrication could not explain many of the rolling contact lubrication phenomena. In 1949 the initial elastohydrodynamic lubrication (EHL) concept was introduced by Grubin, and it was rapidly developed in the 1950s and 1960s by many researchers, particularly Dowson and Higginson [17]. A complete analysis on EHL of point contact was not made until 1976, when Hamrock and Dowson [18] presented their calculation method, results and formulae for central thickness and minimum thickness of EHL film. Since then, much research has been conducted using this theory in the friction and failure analysis of the rolling element bearings and other point contact mechanisms. Other Studies on Bearings and High Speed Spindles In 1979, Gupta [19] presented a rolling element bearing dynamic model giving torque and bearing bulk temperature. The study conducted by Zaretsky et al. [20], posted some practical limitations on high speed jetlubricated ball bearings and compared the jetlubrication and the oilmist lubrication. This work provided a good reference for the practical use of high speed bearings and lubrication. Based on LundbergPalmgren's bearing fatigue life theory, loannides and Harris [21] proposed an improved bearing life model. It introduced a "fatigue limit stress" concept to describe the initiation of a fatigue crack and used the integration computed element stress volumes for the prediction. Their application showed improvement in the life prediction of high speed bearings[22]. At high speeds, the bearing outer race will undergo a very high ball centrifugal force. There was an attempt to reduce this load by changing the single outerrace ball contact into two contacts through the use of an arched outer race (the outer race arc consists of two pieces of curves such that the balls will have two contacts with each raceway). Coe and Hamrock [23] conducted tests on this type of bearing and no improvement of performance was concluded. Boness [24] developed an empirical equation that determined the minimum thrust load to prevent skidding improve bearing' high speed performance Kingsbury presented an experimental method measuring the ballrace slip which was important in evaluating the bearing lubrication and friction. Jedrzejewski [26] studied a way to reduce the bearing temperature and power loss by inserting a layer of insulating material between the bearing inner ring spindle journal, showed some very good  .. 0 results on a spindle. w ram 8 rate, and housing thermal conditions, on preloaded ball bearing transient and steady state behavior. Their study was done on conventional spindles. Tlusty et al. [28] studied dynamic and thermal properties of high speed spindles with roller bearings, and concluded that the use of roller bearings at DN = 1x106 and over was possible. Shin [29] investigated high speed spindle bearing stability and predicted that, at a high speed, bearings will present different dynamic characteristics, and stability lobes will be seriously affected. Stein and Tu [30] analyzed a similar spindle and obtained a model which predicted high speed bearing thermal load from temperature, speed, external load, and material properties, which could be used to prevent the bearings from being thermally overloaded. However, above analyses on high speed bearings and spindles have concentrated on those be bearing axial load could not be constantly maintained. daring assemblies where Most industrial high speed spindles have been designed so that their bearing loads have been preset at some certain high speed range which will yield good bearing performance. In contrast, a springpreloaded constant axial bearing load mechanism has been successfully used research under Tlusty at the University Florida Manufacturing Laboratories, Inc.,[31]. 35,000 rpm (DN It was used in a spindle with a speed range of over 0 to = 2.273x106, ceramic ball), and in a modified spindle to increase the speed range from 0 to 6300 rpm (DN steel ball). = 6.3x105), to 0 to 12,000 rpm (DN It proved that, with good understanding of high speed spindle/bearing thermal behavior, high speeds above 2.25x safely achieved. Although there are many general rules in the spindle design temperature estimation 9 Bearing Condition Monitoring and Prediction Since the 1970s, frequency analysis techniques have been used to diagnose bearing condition machinery. Many methods have been developed monitoring and diagnosing of rolling element bearings. Some examples are the fiber optic bearing monitors for displacement vibration analysis, introduced by Philips [33], proximity monitors mentioned Sandy [34], velocity transducers suggested by Berry [35]. These techniques use the noise signal produced when the defected component passes the contact as an indication of bearing defect. They are usually effective in measuring the current physical condition of the bearing without strong background noise. Using these techniques one can possibly show how long one damaged bearing can one cannot identify bearing lubrication condition and load condition. In high speed bearing applications, however, lubricant starvation and seizure are among the major causes of bearing failure. Tasks and Methodology of this Study Heat Source Modeling The equations of bearing heat generation developed by Palmgren are popular in application. However, since these equations were based on data gathered from bearings running in lower speed ranges, and with the bearing quality and lubrication methods of almost 40 years ago, bearings has not been studied. H; the accuracy of these equations for high speed arris [5] presented a method that included the ball spinning torque in the mechanical friction torque equation in order to take some high into Palmgren's empirical formula of mechanical friction torque. For this study, the bearing heat generation was based on Ragulskis' general equation with special modifications for high speed angular contact ball bearing. Friction estimation was verified against measured spindle power loss data and finite element analysis results. Estimation of the internal motor heat generation could have been made through measurement or calculation. Based on inductance motor loss analysis [36], the motor heat generation was mainly from power loss, I2R, and magnetic loss, which account for more than 75% of the total loss. percentage of the total loss. Bearing friction loss was only a small If the resistances of the stator winding and of the rotor conductors could be obtained, a good estimate of the motor heat generation could be calculated. The power loss measurements of the available motor were used in the spindle modeling of this study. Spindle and Bearing Models In this analysis, bearings were considered as part of the spindle, and the moving heat generation points were considered as a fixed heat generation circle. balls were simplified as a fixed ring that connected the outer ring and inner ring of the bearing. bearings, internal motor, arbor structure were symmetrical components, and all the heat generating sources were symmetrically distributed to the spindle center line. The thermal field was also essentially symmetrical. spindle housing was usually a rectangular or cylindrical block with a flat mounting surface. As a whole, its structure boundary conditions (BCs) are close a 2D structure was developed instead of a 3D model in order to eliminate the complexity of modeling and computation without a great loss of accuracy. Heat Transfer and Calculation Heat conduction was taken as conduction in homogeneous materials. interface (joints of the contacting parts) thermal resistances were not considered separately from the material properties. Since many spindle structures are similar, interface locations sizes are comparable spindle size. This simplification did not limit the model generality. However, because the materials were not consistent, the actual thermal conductivity was not taken from a material property table, but rather was modeled to match the measured temperature. Another important factor was that air inside the spindle had a much higher ability to convey heat from higher temperature surfaces to lower ones. considered in the model. This was also Heat convection depends on the convective coefficients, surface area and free stream temperature. Here the coefficients were calculated based on the heat transfer theory, and the free stream temperature was considered as the surrounding temperature. Since the spindle speed affected the convective coefficients, the coefficients actually used were corrected for spindle speed. The calculation of both steady state and transient thermal responses were made using Finite Element Analysis (FEA) technique. A PCbased FEM software (COSMOS/M) was used to realize the model meshing and to conduct all the calculations. COSMOS/M can be used to build the model mesh, attach boundary conditions, compute the temperatures, the temperature gradients, and the heat flux 12 Temperature Field Measurement The temperature measurement was made on both nonrotating components and rotating components. The measurement of the nonrotating components was done by using thermocouples. The measurement of the temperatures of the rotating components could not be made by contacting methods since, in rotation, any sliding contact would produce significant heat and greatly distort the measurement. Rather, a noncontact temperature measurement was preferred. Since infrared temperature probes can measure temperatures over a wide range accurately without contact, and, since they made very small, rotation component temperature measurement was made by using an infrared technique. Modeling and Verification The thermal model was spindles. built based on measurements of several different First, the model was built from the spindle structure and the calculated heat generation rates and convection coefficients. The convective coefficients and some material properties were varied to make the calculated temperature field match the measured result. From the result of the modeling and measurement of several spindles, the model parameters could be accurately determined and temperature field prediction become possible. Thermal Prediction Model The purpose of thermal prediction is to use the thermal signal to forecast the bearing working condition and issue the necessary warning to protect the bearing. The thermal prediction is based on the fact that the temperature of any part of a performance, load and speed, and, perhaps, the motor load. In the prediction, the measured temperature signal could be compared with the temperature generated by the spindle thermal model so that any difference would suggest a change of the spindle thermal condition. Through model simulation, bearing heat generation, and the bearing load, could be estimated. It also could use certain criteria to check the measured temperature which would determine bearing situation without model simulation. In this study, the proposed criterion was the first derivative of the bearing temperature signal, which was proportional to the change of the bearing heat generation rate. For example, if the bearing temperature slowly rose over a long period of time, this usually meant that the bearing lubrication was deteriorating or the bearing was gradually failing. However, if there was a significant increase of the bearing temperature in a short period of time, possibly under too heavy a thermal load. then the bearing was Another use of the model was to match the measured temperature with the thermal model simulation result, and then one could estimate the bearing load corresponding to the temperature. Bearing Diagnosis Spindle vibration signal acoustic emission (AE) signal can serve indicators of the bearing health and operation condition, in addition to temperature. Several widely used defect frequency formulae can be used to locate defects of the bearings in signal power spectrum and intensity. show the bearing condition. The intensity of these signals will Since there are strong background noises in a high speed spindle operation, the signal spectrum may not show the bearing condition with CHAPTER 2 SPINDLE MODELING Spindle Structure Spindle Housing and Shaft Two spindles were investigated in this study (Spindle A and B). in Figure Illustrated 1 is Spindle B, which has four bearings and an internal motor. Spindle A larger bearings than Spindle B and does have motor. internal Spindles are 3D objects consisting of many parts of different shapes dimensions, made different materials; detailed Figure 2.1 High Speed Spindle structures very complicated. For the purpose of modeling, the detailed structure can be greatly simplified. This process can reduce the number of the model elements and still produce acceptable accuracy. Otherwise, a large number of elements will build a 15 overshadowed by the inaccuracies of the material properties and heat convective coefficients. In this process, the following aspects were considered: Since most parts in a spindle are cylindrical and symmetrical about the spindle center line, the spindles were considered as a cylindrical object and therefore modeled as 2D structures. In each case the outer diameter of the cylinder was calculated so as to make the ratio of the housing perimeter to sectional area unchanged. In this way, the time constant is approximately unchanged. plane stress, plane strain, body revolution element, which represents a 3D solid portion in a cylindrical object covering a center angle of one radian, was selected for the model. All the adjacent parts (either tight fit or loose fit) were considered as one continuous part. For example, the bearing inner rings were part of the shaft and the bearing outer rings were part of the housing, etc. Subsequently, some special thermal resistances in the interfaces were neglected in the geometry but were compensated for by adjusting the material properties. Small structures and details were neglected if their dimensions were significantly smaller than the expected element size. small shoulders in the shaft were disregarded. By i Chamfers, tiny holes and making the simplification, the object became a 2D object consisting of several simple parts. Bearing Since bearing rings were taken as a continuous part of the shaft housing, only bearing balls and cages (ball retainers) were discussed here. Compared surface area, the heat capacity is negligible, and the heat transfer ability, or heat dissipation ability, is limited. Therefore, bearing balls were simplified as a thin ring between outer and inner rings in the 3D model, and they have a rectangular cross section in the 2D model. The thickness of the ring was chosen so as to make the volume of the ring close to the volume of the balls. For example, the front bearing of a spindle has 31 balls, pitch diameter t 125 mm, ball diameter db = 10.3124 mm, then the total volume of balls is = 31 *73* 4,3/6 = 17800 mm3 The total surface area  31 * ,r* db = 10357 mm For the ring with a thickness of 2 mm, the total volume is =2* + db)2  db)2]/2 = 16198 mm3 and the total surface area is =%* + db)2  db)21/2 + = 8884 mm2 After simplification the surface area and volume will be those of the balls respectively. 10% less than The heat conduction error cannot be easily calculated since the actual contact area is small and load dependent. However, comparing the result of the FEA and that of the measurements, it was found that only a small error had resulted since the ball did little in the total conduction and convection. In the model the cage was neglected. should be very small. The error caused by neglecting the cage This was because the cage is made of very light material (usually phenolic for high speed) with very low heat capacity and conductivity. Also, n*[(t conduction between the cage and other parts is very small. Consequently, the cage has very small effect in the bearingspindle thermal condition. Material Proverties Since there exist "impurities" in the spindle parts, for example, joints, cavities, and different materials, the variance of a material's physical properties is inevitable. The parts in a spindle were classified into three basic groups according to their physical characteristics: (1) solid and uniform materials; (2) porous parts with or without interfaces and consistent materials; same as group 2 of inconsistent materials. For group 1, the material properties were selected directly from a standard material property table with little adjustment. group 2 were obtained by adjusting the values from the mate; The properties of rial property table. Measured temperatures were used to check values. For group material properties were obtained by trialanderror; example, rollercage spindle rear bearing assembly consists of a porous aluminum cage and many small steel rollers, and the rollers have limited contact area with their tracks; therefore, the heat capacity and conductivity of the rollercage were obtained by adjusting the material property values to match some known results. High Speed Bearing Load Ball Motion Figure 2.2 illustrates the cross section of an angular contact ball bearing. When the bearing inner ring rotates with the spindle shaft, the balls will roll on both at inner race and outer race are almost BEARING OUTER RING equal, and the ball will have only one possible spinning axis. At high speed, in rotation, significant mass centrifugal generates force, the outer race contact angle will decrease and the inner race contact angle will increase in FREE ANGL / SHAFT AXIS order to maintain the equilibrium of the ball. moment, BEARING INNER RING possibly purely roll on either the inner raceway or the outer raceway. In either case, ballraceway sliding will occur at Figure 2.2 Angular Contact Ball Bearing one contact area. Since the two rotations of a bearing ball are not parallel to each other, a gyroscopic moment will be produced. This moment intends to give the ball a third rotationgyroscopic motion (see Figure 2.3). This motion will cause sliding and possibly damage the bearing [4]. To prevent the gyroscopic motion, an angular contact bearing should always be preloaded. High Speed Bearing Loads External loads acting on a bearing can be combined as an axial load and a radial load. A ball inside a rotating bearing has several loads, namely, inner race and outer race contact forces, centrifugal force, gyroscopic moment, friction forces /_ INNER RACE " *  ~~     A W I " '/  ^___ _ OUTER RACE CONTACT LOCUS CONTACT LOCU CONTACT LOCU Figure 2.3 Bearing Ball Gyroscopic Moment through deflection load relationship at each ballrace contact equilibrium of bearing. Since there are many balls in a bearing and normally every ball has different load, motion and deflection, the solution of loads is a very tedious process. A computer program for the solution of an angular contact ball bearing under general load and rotation condition was developed in this study (Appendix A). Bearing Heat Generation General Friction Toraue Formula Ragulskis summarized many researchers' results and stated friction torque in bearings consists of the following components: (St srgy 'hys + dCv +Ta ca + T + T + T)K lub med temr (2.1) 1  friction torque arising from gyroscopic spin of rolling bodies;  friction torque due to losses on elastic hysteresis in the material of bodies in contact;  friction torque due to deviations of bearing elements from the true geometric shapes and due to microasperities on the contact surfaces; Ta sliding friction torque along the guiding rims orienting the cage and torque arising from the contact of rolling bodies with the cage cavities; Tb friction torque due to shear and shifting of the lubricant; Trd friction torque due to the working medium of the bearing (gas, air, liquid, vacuum);  friction torque arising from the change of temperature; K correction coefficient taking into account all other unconsidered factors. Since some factors in the above equation have not been carefully studied yet, some components are insignificant in common spindle bearings, others important but not stated, and we could not use this equation directly. Empirical Formulae In Palmgren's empirical formulae bearing friction torque T is considered as mainly consisting of two components: the bearing load related friction torque T, and the lubricant viscous friction torque T,: (2.2) and according to Palmgren [4] and Harris [5], T, and T, can be calculated from = f, 107(v n)~t3 vn l 2000 (2.4) where S load dependent friction torque, (Nm);  friction coefficient, which can be obtained from experimental data or the following empirical equation; F C  bearing static equivalent load, (N);  bearing basic static capacity (static rating), (N);  bearing structure dependent values;  viscous friction torque, (Nm); f, coefficient depending on lubricant and lubrication method; v lubricant viscosity in centistoke (mm2/sec); n bearing speed in rpm; t bearing pitch diameter, (m). Because the coefficients of the above formulae are selected from many values experience, and natures of some important friction torques (ball sliding, gyroscopic sliding) are not represented by the formulae, these empirical formulae are not accurate. Particularly, for high speed bearing application, since the load related friction toroue formula cannot reflect the effects of the nreloading mechanism and cannot be simply applied to high speed bearings. The viscous friction torque can well represent the nature of the lubricant shearing friction for a wide speed range. Improved Formulae The bearing friction torque formulae used in this study include differential slippage friction torque, the ball sliding friction torque due to uneven contact angles (gross sliding), the ball gyroscopic spin friction torque, the lubricant shearing friction torque and the friction torque arising from ballcage contact and cagering contact. = T 7 +r T Each of the friction torque terms are discussed below. Differential sliding friction torque T. When rolls over bearing raceway surface, contact curve Ut contact 'center area is an ellipse. Since the ball and raceway have different curvature radii and the elastic deformations of the ball and the raceway are different, pure rolling will occur only along two lines (Figure small local S lines with no differential slip Figure 2.4 Differential Slipping displacement will occur anywhere else. The work done for one ball by this slippage can be expressed by Ani (9M NW ..t (2.5) + TV + TS + Te t' 23 in a unit of time by the point of contact of the ball with race; subscriptj refers to the jth ball, i and o refer to inner race and outer race respectively. Friction force F can be expressed by the product of normal force and friction coefficient, and the slipping distance can be expressed by = t(1 2 d2  cos2 a)n t2 and then the friction torque Tr is "b 12n 27rnI (2.8) where a is the contact angle, a different value applies at the inner race and the outer race, db is ball diameter, and nb is the number of balls in the bearing. Ball gross sliding friction torque T, When an angular contact ball bearing starts to rotate, have different contact angles at the inner race and the outer race. the larger the difference. The higher the speed, Mainly because of the unequal contact angles, the balls in the bearing will slide either on the inner raceway or the outer raceway or both. order to distinguish this sliding from differential slipping, it is called gross sliding. If gyroscopic spinning can be prevented, the ball will slide ball gross sliding friction on one race only, and the torque can be estimated through the following equations. At first, the sliding torque acting on the ball, Tb is = fFaEz 8 (2.9) Tas s (2.10) where fs is coefficient of sliding friction, F is contact load, a is the semimajor axis of contact ellipse, E2 is the elliptic integral of the second kind, ', is the ball spinning speed on one race (2.11), and wc, is the ball orbital rotation speed (cage speed). + y cosca)tan(a +* ysinac (2.11a) (as ~0Oi  ycosa,)tan(a + ysma, (2.11b) where ror, is the ball rolling speed on the race, p is the ball altitude angle, ratio of the ball diameter and the bearing pitch diameter y is the and the subscripts o and i refer to spinning on the inner race and the outer race. Ball gyroscopic spinning friction torque T, If the ball gyroscopic moment can overcome the ballrace friction force, ball will spin, and the friction torque generated on a ball is its gyroscopic moment: (2.12)  I,(0b(Jt srnC where I, is the mass moment of inertia of the ball, ob is the ball spinning speed, wc is the bearing cage rotation speed, and C is the angle between vector ob and vector can also be converted to a torque acting on the bearing, T, as below: (2.13) agTg This conversion can not be expressed in a direct form since the ball spinning speed under  can not be obtained. The conversion factor K. depends on the (0, I Lubricant viscous friction torque T, The lubricant viscous friction torque is computed according to (2.4) = f (v n)2/3 t 3 90 (2.14) Here f, is a friction coefficient depending on lubrication (from Table 2.1). Table 2.1 Coefficient f, for Angular Contact Ball Bearingt Lubrication Type Coefficient f, Oil Mist & Air/Oil 1.0 Oil Bath and Grease 2.0 Vertical Mounting Flooded 4.0 Oil and Oil Jet Lubrication t: Coefficient values adopted from Harris [5]. Bearing cageball and cagering friction torque Tc Cage related friction torque Tc consists of the friction torque between rolling elements and cage, Tc,, and the friction torque between cage and bearing ring guiding rim, T2,. From Ragulskis [10], = (1 4 d2 .dsina  cosa)sin[a+tan(d( 2i )] Gfn, t2 2 R, (2.15)  dbcosa 2 b s (2.16) where Ri is the radius of the race on the inner ring, G, is the mass of the cage, fc the friction coefficient, k is a conversion factor depending on which ring the cage is guided, D, is the diameter of the cage guiding rim, and E is the eccentricity of the =R Gf, n2D, E( 26 Comparison of Empirical Formulae and Improved Formulae Spindle power consumption were measured on Spindle A and the results are plotted in Figure and 2.6 against the calculation results with empirical formulae and improved formulae. In Figure 2.5 and 2.6, all cases were measured with constant axial load. Case A1S refers to newly installed bearings and short spindle running time. Case AlL refers to the same bearings and long spindle running time. Cases A2S and A2L indicate the same bearing cases A1S and A1L with more than a thirtyhour running time. Also in the figures, "Old Formula" refers to the calculation result from the empirical formulae (2.2 to 2.4) and "New Formula" refers to the improved formulae (2.5 to It can be seen that the empirical formulae underestimated the bearing friction torque in the high speed range and the improved formulae better estimated the bearing friction torque. Another comparison was made on Spindle B by using the calculated bearing heat generations to compare with the values obtained through matching spindle temperature profiles with temperature measurements, as shown in Figure . The smoother curve was obtained from equations (2.5) to (2.16) and represents estimation of bearing heat generation. second curve represents actual bearing heat generation. On the second curve, the first part between 0 and 25,000 was obtained through finite element calculation to match measured temperature field, and the part between 30,000 and 50,000 rpm was a curvefitting extension of the first part. real bearing heat generate It can be seen that the calculation result was close to the on. Because there were flaws on the ballrace contact POWER, FRONT BEARING SPEED (rpm)  OLD FORtULA  AS A1L  A2S XE A2L NEW FORMULA Figure 2.5 Heat Generation: Measurement and Calculation, Bearing 2MMV99120 POWER REAR BEARING 20I 0 SPEED (pm) ,OL3 FORML.A + A1 S AIL  A2S 4 A2L  NEW FORMULA Figure 2.6 Heat Generation: Measurement and Calculation, Bearing 2MM9117 Bearing Heat Generation (Watt) Calculation Result from improved bearing friction formulae Result from matching finite element calculation to spindle temperature measurement Bearing Speed (X1000 rp 0 5 10 15 20 25 30 35 40 45 50 Figure 2.7 Bearing Heat Generation Calculation and Result from Temperature Measurement Internal Motor Heat Generation Spindle Internal Motor Structure In order to reach very high speeds, almost all internal spindle motors on high speed spindles are variable frequency, inductance motors. This type of motor has a stator winding and a silicon steel laminate rotor with aluminum bars (cage) fitted into laminate slots. The stator winding and rotor aluminum conductors generate most of the heat. Inductive Motor Losses From the statistics provided by Andreas [36], the standard NEMA (National loss distribution as shown in Table 2.2. The motor full load efficiency is 89 to 92 for this type of inductive motor with the power between 25 and 100 HP. Since a spindle will have more and larger bearings than an inductive motor of the same power, there will be greater frictional loss. In this text, "motor loss" or "motor heat generation" does not include loss or heat generation in spindle bearings. Table 2.2 Inductive Motor Loss Distributiont Motor Component Loss Percentage of Total Loss (%) Stator Power Loss I12R 37 Rotor Power Loss I22R 18 Magnetic Core Loss 20 Friction and Windage 9 Stray Load Loss 16 T: Data adopted from Andreas [36]. Motor Heat Generation Estimation no measurements made on the motor no motor design parameters are known, motor loss can be roughly estimated through motor power, efficiency and loss distribution. For a motor without an external load, motor power can be found by measuring the motor voltage, current and phase angle at different speeds. From this measurement, the total power consumption can be calculated, and this total power minus the calculated bearing friction power will be roughly the motor power loss, and Theoretically, when motor design parameters (winding rotor conductor resistance, inductance, phase angle) are provided, the motor loss can be calculated. For example, the friction torque can be expressed by T = K, i, where Ki can be estimated by known motor parameters, i can be calculated from the stator winding resistance, inductance and motor speed. the torque and the motor speed. The motor loss is the product of In most situations, however, accurate motor loss data can only be obtained from measurement. Motor Loss Measurement The motor loss was measured for the test HS spindle through the accessible circuitry of the frequency inverter (motor drive) of the motor (Appendix B). Two methods were used and the measured results are listed in Table Table Motor Drive DC Power Measurement Idling RPM IDC (A) V DC(V) PDC(W) Pload (W) 2500 3.0263 42.857 129.7 103.8, 100.0/119.5 5000 3.1579 85.714 270.7 216.6, 159.4/200.0 7500 3.4211 128.571 439.9 351.9, 227.7/269.7 10,000 3.6842 171.429 631.6 505.3, 321.1/359.2 12,500 4.0789 214.286 874.1 699.3, 438.7/499.0 15,000 4.3684 257.143 1123.3 898.6, 598.9/778.5 17,500 4.7895 300.000 1436.9 1149.5, 839.7/1047.4 20,000 5.0526 342.857 1732.3 1385.8, 1021.4/1276.7 22,500 5.5263 385.714 2131.6 1705.3, 1294.6/1526.5 25,000 5.8421 428.571 2503.8 2003.0, 1517.0/1897.3    power. Since there was no external load, the load is the motor loss and bearing friction loss. The values on the left were obtained by subtracting 20% loss of the drive circuit from Pnc The values on the right were calculated from the measured motor "load current" (not DC current, two values here are due to two ways to read this current, see Appendix B). Heat Transfer Conduction Conductive heat transfer mainly occurs inside spindle parts and other non convection areas, such as enclosed spaces with no opening and no air movement. Outside the spindle, although significant conduction exists, as the heat is conducted between the spindle and machine mounting surface, conductive heat transfer cannot be accurately calculated, since the cannot be calculated. heat conducted between spindle and machine This amount of conductive heat transfer is then compensated through convective heat transfer. Since most spindles have a ratio of mounting area to their total surface area ranging from 0.15 to 0.3, convection is the major mode of the spindle surface heat transfer. Convective Heat Transfer There are many formulae for convective heat transfer coefficient calculation, but they always are subject to certain conditions (surface shape, orientation, and fluid situation). Those conditions can hardly match those of the spindle convection surfaces. Therefore in the modeling the coefficient calculation is based on the spindle parts. Consequently, the calculation will be more closely related to individual surface, and, for each type of surface, a relationship between the flow speed, characteristic length and surface orientation can be established and used for general spindle modeling. There are two basic types of convective heat transfer: forced and free (or natural) convection. Forced convection was produced by the rotating spindle and can be analyzed by the conductive heat transfer in the thermal boundary layer and the flow of fluid outside this layer. The analysis can be found in many heat transfer textbooks, e. g. Holman [37], and only the result is presented here. The resultant averaging convective heat transfer coefficient is = 0.664 R,' where /2 pr/3 (2.17)  Reynolds number:  Prandtl number: V CkF a k (2.19)  fluid heat conductivity;  surface characteristic length; fluid properties are not constant m most cases), they calculated at the film temperature Tp I snl Ijrf Ah n\ 33 Although generally the convective heat transfer of a spindle surface is forced convection, at low spindle speed with surrounding air not sufficiently disturbed to produce forced convection, natural convection prevails. It is said that natural convection is of primary importance if > 10 (2.21) where  Grashof number, which may interpreted physically as a non dimensional group representing the ratio of the buoyancy forces to the viscous forces in the convection flow system. gp ( T  gravity;  volume coefficient of expansion of the fluid;  surface characteristic length. (2.22) If freeconvection is dominant, a simple flatsurface formula will be used for the convection coefficient calculation =cC(T) (2.23) providing that the fluid flow is laminar and L is properly chosen. Factor C ranges from to 1.42, only when plate surface horizontal 0.59. Characteristic length L can be chosen according to Table 2.4. T,)L 34 Table 2.4 Surface Characteristic Length for Free Convection Surface Orientation L value Plate Vertical Plate vertical dimension Surface Horizontal Plate horizontal dimension Cylinder Vertical Cylinder length Surface Horizontal Cylinder diameter Convective Conduction There is a special case in the spindle heat transfer which is the heat transfer via the moving air enclosed in the spindle housing. Since inside the spindle the air is moving very fast and the convection coefficient between surfaces and moving air is very high, heat can be considered to be quickly removed from high temperature surfaces and transferred to low temperature surfaces. This phenomenon is a two stage convection but cannot be easily applied in the FEA model. In this study, the fast moving air was considered as a medium with low heat capacity and high heat conductivity, and its conductivity depends on spindle speed the size spindle. The experimental work of Davis et al. [38] has shown that in this situation better internal heat transfer can be expected. Other Considerations Internal Convection Since the internal cavities of spindles are not totally isolated from the outside, and oilmist or oilair lubrication supplies air to the inside of the and causes an air 35 small and since the air has very low heat capacity, this air flow does not contribute much to spindle heat dissipation. study, forced convection with small coefficients was used to emulate this phenomenon in the FE analysis, and it was seen from the results that the heat transferred by this internal convection was very limited. Nonlinear Heat Source In the bearing seizure cases which occurred in the study, it was observed that bearing heat generation increased with time when spindle speed was constant (Chapter 5). This type of heat generation sources is called nonlinear heat sources. This increasing heat generation occurred since the bearings were fixed in the spindle and the constant axial load mechanism could not relieve the bearing load. Then when bearings were running, bearing heat generation would cause high temperature on the shaft than on the spindle housing. and housing expansions resulted in higher bearing load. The difference of the shaft Consequently, higher load resulted in more bearing heat generation and more difference in shaft and housing expansions, and this process continued until the bearings were seized. Similarly, for spindles without constant bearing axial load mechanism, different expansions of the shaft and the housing can cause an increase of bearing load and limit maximum spindle speed. External Heat Sources A cutting tool under working conditions will generate substantial heat and some of this heat may be conducted into the spindle. In a high speed spindle, especially in high speed milling, in order to eliminate flexibility, tools are mounted to spindle shorter more heat conducted spindle. Generally, this amount of heat is small compared with the heat generated from the bearings and/or motor. The external heat sources were not considered further in this study. Bearing Condition Monitoring Conventionally, the bearing thermal condition is monitored by measuring the maximum temperature of the bearing. If the temperature is beyond a preset limit, it is said that the bearing assembly needs to be serviced. This criterion has some problems. cannot identify bearing condition before bearing temperature becomes high. If the temperature is due to a failing bearing, the bearing will possibly already be damaged when the temperature reaches its limit, especially in the high speed case. If the temperature limit is set sufficiently low to avoid damaging to the bearing, the bearing capacity will be restricted. There was a bearing seizure in this study, and although the monitored temperature did not reach the limit (80 C), the bearings were already damaged. Bearing temperature change is another indicator of bearing health. bearing failure cases observed in this study all were accompanied with abnormal temperature increase before failure. seems temperature change monitoring may be a good method for bearing catastrophic failure (unstable thermal load, lubrication failure). Bearing vibration (noise) analysis is a method for detecting a bearing with defective components, but there is very strong noise in high speed bearing vibration signal. The use of bearing acoustic emission can eliminate the CHAPTER 3 FINITE ELEMENT ANALYSIS (FEA) Finite Element Analysis of Heat Transfer Problem The finite element method consists primarily of replacing a set of differential equations in terms of unknown variables with an equivalent but approximate set of algebraic equations where each of the unknown variables is evaluated at a nodal point. Normally, there are seven steps in the FEA technique: formulate governing equations and boundary conditions; 2. divide the analyzed region into finite elements; 3. select the interpolation functions; 4. determine the element properties; 5. assemble the global equations; 6. solve the global equations; and 7. verify the solution. Several different approaches may be used in the evaluation of the governing equations. Three of the most popular methods are the direct, the variational, and the residual methods. In the direct method, the unknown variables are expressed as a set of equations for each of the structural members or elements. The equations are converted into element matrices, and those matrices are assembled together to be used to solve for the variables. Although it is straightforward, this method is difficult to apply to two and threedimensional problems. The variational method involves a quantity called a functional, and minimizes the value of the functional with respect to each of the nodal values. The solution to the problem is approximated by finite element function such I T~ where represent temperature of an element and T is the actual value. The approximate solution is defined as the sum of a set of local functions, one for each element: e r (3.1) e=1 An advantage of the variational method is the easy extension to two and threedimensional problems. The disadvantages include the lack of a functional for certain classes of problems and the difficulty of finding them for other problems even when they exist. Therefore, other methods, such as the residual method, sometimes used. The residual method usually starts with a governing boundary value problem. The differential equation is written so that one side is zero. Then some approximation of the exact solution is employed and substituted into the equation to generate an error r, rather than zero. The error r is then multiplied by a weighting function W, and the product is integrated over the solution region. The result is called the residual R and is set equal to zero. Actually, there is a weighting function W and a residual R for each unknown nodal value, so the result is a global set of algebraic equations. There are many FEA packages on the market, such as NASTRAN, ANSYS, depends on suitability and cost. In this study, COSMOS/M was used. It is capable performing linear/nonlinear static, linear/nonlinear dynamic, buckling, heat transfer, fluid flow, and electromagnetic steady and transient state analysis on one, two and threedimensional models with full doubleprecision accuracy, which leads to results comparable with those obtained from major FEA packages on mini computers and mainframe systems. Although the cost of the software is an important concern, COSMOS/M has certain advantages. For example, it can perform transient heat transfer analysis which some other programs (such as CAEDS) cannot, and COSMOS/M has a comprehensive element library. It can handle and 15,000 nodes in one model and can be used in a microcomputer. Heat Transfer Governing Equation and FE Formulation 15,000 elements Heat transfer analysis a boundary (field) problem governing classical equations consist of the equations governing the heat flow equilibrium in the interior and on the surface of the body: (k, ao+_(k ao)+ ax kx ay Y ay aO) 8z' =4 (3.2) (3.3) (3.4) where ki is the conductivity in i direction, O is temperature, S is the surface of the object, and q is the heat quantity transferred. There are three basic assumptions for Sif=a kan an 40 1. the body of heat transfer is at rest; 2. heat transfer can be analyzed decoupled from the stress condition and 3. no phase change and latent heat effect. Our case satisfies these assumptions. A variety of boundary conditions are encountered in heat transfer analysis: 1. temperature conditions, as expressed by (3.3); 2. heat flow conditions, as expressed in (3.4); convective conditions, which are generalized as ( 4) and expressed by: =h(Q SOS) (3.5) radiation boundary conditions with its general form as (3.4): =K(Or  es) (3.6) = hr(O2 + (e)(e, +O s) (3.7) where h is convection coefficient, K is heat quantity transferred through radiation, subscript r and e refers to heat source and element, and superscript s refers to the surrounding. For the development of a finite element solution scheme, either the direct, the variational or the residual formulation can be employed. For a general threedimensional heat transfer problem often the variational method is used and a variational functional can be expressed as 2 ax a8 +k( )y ay ao )dv +k() Qz'z Oq qdv O q dS zoios 1f s . rr n\ (3.9) in matrix form S eTk edV Sq BdV+ f .S2 60Sq Oi Q S I x (3.10) where   ax ay kO (3.11) (3.12) denotes "variation This equation expresses heat flow equilibrium at all times of interest. The stepbystep incremental equations can be developed by a systematic procedure and finally discrete equations will be produced for each different heat transfer case (linear, nonlinear, steady and transient state). All the abovementioned procedures can be found in many finite element textbooks, such as Bathe [39], and will not be discussed further. Spindle Heat Transfer Model A spindle is a multicomponent threedimensional object with a complicated physical profile, load and boundary conditions. There are many intercomponent joints which usually have temperaturedependent properties, spindle' internal heat generation is also dependent upon its thermal condition and some random variables. Spindle heat transfer has many nonlinear factors. It is impossible dS + properties are taken into consideration in the model. In order to overcome the difficulties mentioned above and to get a general spindle thermal model, many generalizations simplifications were made, such as those mentioned in Chapter 2. Ignoring the existence of physical joints may introduce errors in the temperature profile (there is normally a temperature discontinuity in a joint), and assuming a twodimensional symmetric model will generate other inaccuracies in the resultant temperature field. However, the joint temperature discontinuity can be compensated for by adjusting material properties, and the 2D model can represent a 3D object if the average BCs are used and the boundary dimensions are properly chosen. Generation and Solution of Soindle FE Thermal Model Generating Spindle FE Model After the spindle structure has been modified for modeling purpose, meshes can be generated following the steps below: Enter coordinates (may use different methods) of important points which represent intersection points in the simplified 2D structure. Connect corresponding points to form lines of the spindle profile. each closed line loop a contour can be defined, and if a contour encloses none or some other contours but is not enclosed by any other contours, this contour and its enclosed contour(s) can form a region. A region is a basic unit for automeshing. Define element groups (type of elements) and material groups (material elements will be of the current active element type and have active material properties. the current The selected element type is PLANE2D in our study since it supports the axial symmetric property. d. Meshing. COSMOS/M. Automeshing, manualmeshing are two meshing methods in Automeshing is faster and can be applied to a defined region to generate most of the elements, while elements from automeshing of a very irregular region will be distorted and further refining should be used in order to yield evenly shaped elements. extent element distortion measured by the element aspect ratio. Generally, the refining process will consume more time than that spent on automeshing if the region is uneven, and will generate more elements. in the space. Manualmeshing can be applied to any part It is a slow process but the element shape from manual meshing can be fully controlled. Since the regions defined from a spindle usually are very uneven and complicated, and the number of elements does not have to be very large, manual meshing may be used for most of the cases. Before meshing, corresponding element group material group should activated. In our case, since COSMOS/M does not support automeshing of axial symmetric 2D elements, automeshing could not be used. e. Merging nodes which are located too close to each other and elements which are overlapping, and compressing nodes and elements so all the nodes and elements will be numbered in a continuous order. All elements should be connected through nodes. The element shape should be as close to square as be less than five times. The connectivity and element shape can be checked automatically by executing the CHECK command in COSMOS/M. Applying Load and Boundary Conditions In COSMOS/M the thermal load can include a nodal heat source, node and element heat flux, and an element heat source. Since bearing heat generation is located at the ballrace contact and the contact area is very small, it was considered as a nodal heat source. Internal motor heat is generated from the stator winding and rotor conductors and was represented by element heat sources. In the analysis of an individual component or assembly, heat flux was used to describe heat flow between the contact surfaces of components. Only convective boundary conditions are applied to boundary elements. values of node heat, element heat and convection coefficients were calculated through the formulae in Chapter 2. and were modifi by matching the FEA result to measured temperature fields. Analysis Steady state analysis was made after the BCs were added to the model and the maximum number of iterations and convergence tolerance were specified. the transient state analysis, a time step and a time range were given before starting the analysis. Since many machine tool spindles have similar operation conditions, convective coefficients have a relatively general meaning. The verified coefficients in this model can be applied to corresponding elements of another spindle model if there are no measurements available. Many pilot cases were analyzed in this study and the convective coefficients and material properties were tuned to make the FEA 45 Calculation of a Spindle with Bearing Heat sources Modeling Spindle A Figure illustrates original physical structure Spindle After simplifying the complicated details neglecting the small structures, such lubrication orifices and screw holes, a 2D object was developed, as shown in Figure Then manualmeshing was used to create nodes and elements. element size was chosen as The nominal 10 mm comparing the overall length 960 mm of the Figure 3.3 illustrates the final mesh for Spindle A. Fig. 3.1 Structure of Spindle A Fig. 3.2 Simplified Structure of Spindle A S1.IIzFI 1 IIIrI~Jz ItlZ spindle. r trI tit _ i. I I I I thermal load condition for Spindle was frictional heat at bearing contacts. There are two bearings in the spindle, and correspondingly in the 2D model, there are 4 contact points, or 4 node heat sources. All the surfaces are convection surfaces except the interface surfaces. The meshing is valid for all of the simulation cases (different speed, lubrication). different cases, heat generation rate and surface convection coefficients were different and were evaluated accordingly. In order to investigate the convection property of different surfaces, the spindle surfaces were classified into seven categories, as shown in Table 3.1. classification is based on the surface air flow velocity. Calculation Cases Spindle speed, cooling lubrication, were considered to be most important factors in spindle model for designated spindle structure and bearings. Hence Table 3.2. , spindle thermal analyses were conducted under the conditions as listed in The speeds were 4000 and 8000 rpm, airoil producer inlet pressures were 35 and 75 psi, and two cooling conditions were the shaft center hole with both ends open and with only one end open. In Table 3.3, bearing heat generation rates are listed for the different cases. These values were obtained from the improved bearing heat generation formulae (equation to 2. Since there were two contacts per bearing and the model was built for one radian center angle, these values were divided by 41r before being applied to the model. Table 3.4 lists surface convective coefficients obtained from 47 Table 3.1 Spindle Surface Classification Surface Location Symbol Surface Characteristics(V,,L)t Both Ends V = 0.025V, Open L = Hole Length S1 Shaft Center Hole & One End Open V = 0.01 Vt Sla L = Hole Length Both Blocked No Convection Housing Outer Wall S2 V, = 0.167 V,, L = (Length + Width)/2 Housing Outer Surface, Top S3 Same as S2, if with mounting and Bottom conduction, use same value as that of S2 Shaft Outer Surface, Outside S4 V~ = 0.0667 Vt; Housing, Small Diameter L = Average Diameter. Shaft Outer Surface, Outside S5 V, = 0.1 Vt; Housing, Large Diameter L = Average Diameter. Housing End Walls S6 V, = 0.2 Vt; L = (Length + Width)/2. Convective Surface Inside S7* Vs = 0.025 V,; Housing L = Average Diameter. the calculation, surface wall temperature T, and fluid stream temperature Twere needed. Twas taken as estimated wall temperature, and T, was the incoming air stream temperature under normal condition; Considering lubrication effect convection, following suggested coefficients should multiply the convection coefficient obtained: Lubrication Coefficient Lubrication Type Coefficient Air: <30 psi 1.0 OlAir Air: 3060 1.2 Air: 60120 1.4 0"4. __ inf 48 Table 3.2 Spindle A Simulation Conditions Cooling Condition (Shaft Center Hole) Speed (rpm) Lubricantt 10 DPM Air Pressure* 35 psi Lubricantt :10 DPM Air Pressure*: 75 psi Both Ends Open 4000 1 (SA4B) 5 (SA4D) 8000 2 (SA8B) 6 (SA8D) One End Open 4000 3 (SA4BN) 7 (SA4DN) 8000 4 (SA8BN) 8 (SA8DN) Airoil lubrication was used in the study. The lubricant was VISTAC oil ISO 68 for all cases. 10 DPM is 10 drops per minute, equivalent to 1.0 cm3/hr; Air pressure was measured pressure at airoil producer inlet. Tabl 3.3 Spindle A Heat Generation Ratet Front bearing was 2MMV99120, 31 balls, rear bearing was 2MM9117 21 balls, 15 15" contact angle and steel ball, contact angle. Table 3.4 Spindle A Surface Convective Coefficients (W/m2/' *C) S case 1 2 3 4 5 6 7 8 1 55.2 65.2 10.2 18.2 55.2 65.2 10.2 18.2 la 35.3 40.3 1.28 1.30 35.3 40.3 1.28 1.30 43.3 40.3 0.31 0.22 43.3 40.3 0.31 0.22 54.2 55.2 0.20 0.03 54.2 55.2 0.20 0.03 2 8.01 10.5 8.01 10.5 8.01 10.5 8.01 10.5 3 8.01 10.5 8.01 10.5 8.01 10.5 8.01 10.5 4 7.32 10.2 7.32 10.2 7.32 10.2 7.32 10.2 5 8.22 11.3 8.22 11.3 8.22 11.3 8.22 11.3 6 8.47 11.5 8.47 11.5 8.47 11.5 8.47 11.5 Case Front Bearing (Watt) Rear Bearing (watt) 1, 3, 5, 7 50 43.75 2, 4, 6, 8 113.5 82.38 49 Table 3.5 Spindle A Temperature From Simulations Temperature ( C) Location 1 2 3 4 5 6 7 8 I1 33.6 44.5 38.5 50.5 31.8 42.2 34.5 45.95 12 32.7 42.2 37.9 49.6 30.8 39.3 33.2 44.86 13 30.9 39.0 35.6 44.0 28.8 35.1 31.2 38.97 14 30.6 36.8 35.3 43.1 28.5 34.8 30.9 38.05 15 33.3 41.6 37.5 46.5 31.1 38.2 33.4 41.83 16 35.1 43.9 39.1 49.2 33.9 42.7 35.2 44.83 17 33.9 39.1 37.9 44.5 31.9 36.2 33.5 42.84 18 30.7 35.1 34.8 41.1 29.1 32.7 31.5 37.41 19 33.0 41.2 37.9 49.4 31.2 40.0 34.0 44.87 K1 32.5 39.3 33.7 41.0 30.6 36.7 31.1 38.01 K2 32.8 39.9 33.9 41.6 30.9 37.0 31.4 38.65 K3 33.2 41.1 34.5 42.9 31.3 37.1 31.9 39.84 K4 32.4 39.1 33.6 40.7 30.4 35.5 31.0 37.74 K5 31.0 36.0 32.0 37.2 29.1 33.6 29.5 34.43 K6 30.9 35.8 31.9 37.1 29.1 35.1 29.5 34.37 K7 30.5 34.9 31.4 36.1 28.7 30.8 29.0 33.33 K8 29.9 33.5 30.8 34.5 28.1 32.8 28.5 31.96 K9 30.3 33.5 31.1 34.5 28.3 33.5 28.6 32.20 K10 35.2 42.6 36.8 44.9 31.4 39.9 33.7 41.49 K11 31.1 34.7 32.5 36.0 29.2 32.7 29.6 33.53 Figure 3.4 illustrates the spindle temperature profiles and the temperature transient responses at a node on the shaft's inner surface at the front bearing location (corresoonding to the thermal sensor measuring noint 11 as shown later in Figure 4.21 50 made with the spindle speed quickly increased from zero to the calculation speed in order to simulate the step input used in FEA calculation. 2 are illustrated in Chapter 4. The results for case 1 and All calculations and measurements show very good agreement. Most differences between measured calculated temperatures are within 1 to Calculation Analysis Table locations correspond to the temperature measurement locations in Figure 4 (shown later). Table 3 lists the steady state temperatures at those locations. It can be seen that the spindle speed is a major factor influencing bearing/spindle steady state temperatures, and that lubrication air pressure has a significant effect on reducing the temperatures. This can be understood since higher pressure forced more compressed contact neighborhood. Therefore,the heat convection was improved, the contact temperature was reduced, and the oilfilm thickness and strength were increased. means higher air density and larger heat capacity. More air inside the spindle Iore air also causes a more violent turbulent air flow, results in better convective heat transfer. The size of the opening of the spindle shaft center hole had a very important influence in local (shaft inner surface) temperature. This is because the two ends of the shaft have different diameters, and since the centrifugal force causes air flow radially at the shaft ends, the end with the bigger diameter can throw more air into the surroundings, generating an air flow from the small diameter end to big end, as t ., 2 2.  TC a a. Znl t1 nta ttn nZ,.nt~ :nn.nn12 2 *+ *"e+^ i 4w  ^eems .w +ews e s + > e ^ @e< @**., +,, +ef we ++em .*e # ^ i . .  ,,. ^^ ^,. + 1 1 : i : ; ; * *****  e ** 4 ** pW' m *. i. k r w +'e i s fwrek i +@me 4** a w.  **, .* .. .Sa, ., + ,* ,,. ~ ~ ft ft ftt .f ..ft @a 6 4 fte4 w +g  ft .if ft  ftf ftf  e + e** e la : i > F a : a m e ftf 4 f .,tft^,, ft **S* ** " ft ft  f  . ft. ." ft a * ft f t e * i**** a # I 4, ft.f f. .f b ft * ft .ift * ft * ft~m 4 * ft , * t,, i .; * f + se .4& ^~n i 4  * t* i a j..,,, ,,. ,, . ** ** **     A i . f de 'ye +wm > 4r  p I * e ft ftw nd f t.  f ft_ f * ftI **  ,. .* . t ft f* ft * ftf ftftfft t.*t f ft  .,  *.., ;, f* I  K r * f ft,.   ft* /. , ft;.. f*  *f f **)** om r   ft.. f. i m w m a *# *y# e g s + m  ft . "^:N * *i *'* .tl............. a e i **,**, ,.t  eft i fff tt .   m "' ,.. 4hBm *^ m a ^ fl.t e + ^ f ft ft r!ft * ft * S  * ft f ft,, ft,   t InE TIS TIME 42.2 39.0 36.8 I f t i4 * a ft ft ft f i j ft tft   ~~ ~ ~ f ft,, ,.., ^ , ~I:  .  .,1,. .. ^. ee ff**f fm f tfff f I ft ^~ * i S** ft ft 1 i ff tt t ff t tf t f ff.t*.f..t ftftt**ft* ft f f ft ft ft ft fta ft t  Figure 3.4a Case 1 3.5 33.5 41.6 43.9 ^t...............f .. .     ...... .... .... ,....., ., : : : I I $6< . .... ... ... eN .,,^,,,~~~~ i ff...  s  i * i_^ ^f, , ,...... .,, ,,,. ,. ,. ^,,_. ,.** ,^ i. .*.. .j .^. . !... .. ., . , .. . , .. i .,.. .. . f f f f ft a,^.... ,.,..., <, >, .:..... .. ,,....,,. .,,.,,,', .,. > ,    ft ft fta ft 4 fta * *f f f tf tf tf f tf tf tf i i :   ,    , .**, **.. ..*. . ft ft ft ft ft ft ft ft ft ft ft ftfttftt*t**fftf ,ftt*ffttfff*ftff , ., ,I .** 4. ft;. ft ft ft ftf tf f t* ftftftftf .ftf f ftt.f.ttfttt tf.. ... ft*ftftftftft ftft* ftff .ftf.f f.f.ftftlftf t,. ff  .^,. 4  ,f , .j ftf. ,,.< ,t _ ..  ,f .ft * ft ftf tf tf t tf tftf JISa SO S 91 1202 f7Q 95 116 TI K tie 31 30.8 2.8 28.5 31.1 33.9 31.9 29.1 26.3 25.4 tf .__ ^, t * * ;  ft * f f  *...... * * * 'ft. _,.4  .. ft ft. ft * * * * ftfttft .4ft ft.  .5rft. ft .4 ft * *,^",. .*@* wn *  , ft ft ::.^. : .. k * *twe f v tg wfty 4 am ...,. .... .= ... . .., ft ft ^* ^ TT n lT .BTlrrT rr TT,....  > ,  * ft ft *# ~ fnm t fmt9 wk w s , , f .t +, ,,  ,. ,@@ ++ amqg+4gma  * M. s w,m^, .+ xmw m. ,,  * ftf ft.f f tf ii l l * ft ft ftf tf **f f f f f f ft i f * *ft. ft ft.. ft ftr i f * ft ft ft ft ft ft ft * + + .* fm ft*m 4 v4 *',4  ,4 <, ,**,_***,,**j.^** *v m *w .k o.ed m w ~ n w s se e e H m y w e n p mp n P e n e u s ~ e m ft 4 f ** * ftf t t ,,. >. .* > .** ***   ^  , >, > .ag .n g .. _.,,^.., .. ...~....*. ...d....i..... .,. i.......,.l.~. ... ..a...s......... ft **f t fttt t ft t * t t ftft .* .* ft tf Si i * * * ft f t ft t. ft * 4 f f ft Aft@9 4 9 M H M W f~twy 4WM ftwe ftsh mfmm fmt@ + ft ft fm ft + t ft I* t ft tf t t * f ftf f tf * t ftf t, t ft ft ft It * 4 ft tf *. ft ., .. ,,. * ft ft t t.f  ft, .  . * ft ftf tf * ft Itf tf tf tf tf ft ft t f .  .4t  ,,_ ft I * 4: N: * * t* 44 psedarg LEW4 mm m. emea.mm * .. *  ,,..,~...,,  r.. ,,  4 I 4 4 . ,....,>;,,,,  i* i ft * ft ft ** * ** i i * ft ft *e ftm ftnu p ftw x ft:f f  ft fwte fm t ftm e ft ftw a f+t9@ We Figure 3.4c Case 5 4"d 39.3 35.1 34.8 38.2 42.7 36.2 t. ? * . W. t  . f . . I r E a I 5 . ... , ;. .*. ,__  . #. I I +4ftft ftmt 4 *or$ft................4sm@ ftftft**m*I~ S * .. . ft ft ft ,ftf *t^  .f . .^,,.f  ftm 4 ft ft  ft? 1 4 fta * # * a__ a a fr mh +H mm h m pi menf : r **r + ^r +H* f in ih i :^h gaAng h a m M A & ^ ^ k U ^ A mMdmS :^i^ +Hf^^i ^ t . i e i ie i fftJ f 4 f ........ . I.....4ffff ~ fff *itttff ftttfff f.. tfft.. i .....fti f t ft f t I "1' S ............... ~i fft~g~~' 3 4 > a T a a s s 4 e *^^' * f f f i n i V . .4*fftftft>,., >^ ,i rt ft$. ftfftf *. ft.1.4 ~ ft , j. ft < ftfft . *ff.^. ......... ~ t ft> ..f. ,ft ft f ^ ^ ^ 'S1t ft  f* f f t * 4 3 a * 1I 'tVII $L 1l !1 :1?ll;. 11~il* 1 1 3 t ft ft 1... ft ft ft ft f , . . ...4...I ..s.. .. ....., 4..   i ,. . I r I I I I 1 i _ ...*.6 .....,,I ,        *     2s 4 ft 't fte 2 3 1 e 2t f t f I I t I * r i i '1 ' A1 *SW "F SA *SA _g 15 1 i t f fT E f * *t ftf 4 ft ft ftf tf*tf tf cm 16 In 4 OS15 * 1* 6 50 7 SO it 3*s 7 s ~~~T #C ; rs 27.5 I I riTT 53 the centrifugal effect will cause a surface air flow (or boundary layer flow) from inside toward the ends. In order to compensate for the air loss there, the air flows in from the hole center to supply this flow (Figure 3.5c). It can be seen from Figure 3.5c and d that a shaft with both ends open will have double the amount of air passing its center hole, and the air will travel only half the distance as that in a shaft with one end blocked, so a shaft with both ends open will have better hole convective heat transfer than the shaft with one end open. In addition to the increased air flow, the spindle speed also causes better convection inside the shaft hole. Warm Air Warm Air Warm Air Cold  Air Warm Air Cold Air old Air Warm Air Warm Air Warm Air Worm Air \Cold Air Cold Air C. a. Fig. 3.5 Different Convection Situations Table 3.6 lists the time constants for different cases at the front bearing shaft inner surface. time constants were obtained from local transient temperature responses of different cases. lnnTlll&nnc' mt r hia mon From the time constants the following 1 'c c chnoFft rnntnr hnlar\ hioc o nnnaiTt? cdnnflrKnont 1 response. 2) An increase of airoil lubrication air supply pressure from 35 psi to 75 psi results in a 15% to 50% reduction in time constant. 3) High spindle speed causes high bearing heat generation as well as large convection heat transfer. As a result, although the spindle will have a higher steady state temperature, the transient occurs over a shorter time. This is because time constant is dictated by the heat capacity and convection ability. 4) The calculation results show that the spindle internal contact surfaces (between the bearing ring and the housing hole and the shaft surface) have a large heat conduction resistance, which is an important factor affecting the spindle temperature temperature distribution. The spindle material incongruity and physical cavities reduce heat capacity and reduce transient response time. The material properties also influence the transient temperature response. Steady state temperature fields show that this spindle can be thermally stable at speeds over 8000 rpm, and that the spindle is naturally convected. Table 3.6 Spindle A Time Constants From Simulations Case Time Constant Comment 1(Min) 1 49.40 2 27.90 High speed, fast response 3 56.47 Shaft hole partially open 4 38.85 5 24.71 High air pressure 6 24.64 55 Calculation of a Spindle with Bearing and Internal Motor Heat Sources Modeling Spindle B The structure of Spindle B is illustrated in Chapter Figure It can be seen that there is an integral AC motor and there are four angular contact ball bearings. The spindle is more complicated, smaller and faster in rotational speed than Spindle A. The simplification process wa result was more sensitive to the simplification. is more difficult because the analysis Figure 3.6 illustrates the simplified spindle structure and Figure 3.7 illustrates the meshes of this spindle model. spindle was about 510 mm long and 280 mm tall. Manual meshing and PLANE2D element were used and the nominal element size was 6 mm.   ..  .. .      Figure 3.6 Simplified Spindle B Structure II     II [I t+F ji izzUikEII Il U   I  lz, tIl 1i i I t IHI HRH~    rn  iLl I4fl~ 1r, I lxi pp~zj = = z: : jjj44~ix~i II~It~    ~  riu ~Ti Spindle B has both bearing heat sources and a motor heat source. thermal load includes both nodal heat and element heat. Thus, the The spindle speed range of interest is well over 5000 rpm, and both computational and experimental results indicate that spindle speed influence on the convective coefficients of Spindle B is not as important as that in Spindle A. Calculation Cases In the calculation of spindle the variables studied were spindle speed, cooling effect and spindle axial preload. The calculation was done for spindle axial preload of 100 lbs, 150 ibs, 170 ibs, and 220 ibs, spindle speed every 5000 rpm from 5000 rpm to 50,000 rpm, and with and without water cooling of the bearing outer ring. The results discussed in this text are from the calculation with 150 lbs preload unless otherwise specified. In Table 3.7 the bearing heat generation rates for the calculation cases and the estimated motor heat generation rates are listed. motor heat generation rates were obtained from the AC motor power measurement for the speed from 5000 rpm through 25,000 rpm (Appendix B). For speed from 30,000 rpm to 50,000 rpm, motor heat generation rates used were from extrapolation (polynomial curvefitting) measured result. Table convective coefficients are listed. aircooling surface convection, smaller coefficients correspond to lower spindle speeds and large coefficients correspond to higher spindle speeds. For watercooling surface convection, larger coefficients were selected for low water temperatures and high flow rates. Figur< cnindle tpanductteP tPmnPertllrP nrnfilPQ fnr thp fnllnwnano cneepd e 3.8 shows the 1 0nn0 9S nn1 57 (the temperature at the bearing race contacts, outer ring surface, spindle arbor and rear bearing rollercage) are illustrated in Figure 3.9. In that figure, "F# 1" and "F are front first and second bearings, and "R#1" and "R#2" are rear first and second bearings, "inner" and "outer" designate the innerrace and outerrace of the bearings. The corresponding measurements will be shown in Chapter 4. Table Speed xl000) (rpm) 3.7 Spindl Bearing and Motor Heat Generation Ratest Bearing Heat Generation Rates (Watts/bearing) (front/rear) 100 lb 150 lb 170 lb 220 lb Motor Heat Rate (rotor/stator) (Watts) Front bearing RHP B7012, 18 bearings had silicon nitride ball balls, rear bearing RHP B7909, 20,balls, all s and 20 contact angle. 5 13.87/5.03 13.94/5.53 14.36/5.91 14.73/6.66 82.4/142.1 10 23.79/7.92 29.81/12.9 30.10/13.6 33.26/16.7 173.5/299.2 15 85.7/25.26 76.43/26.0 77.2/27.27 70.0/29.41 274.9/474.2 20 99.7/29.91 89.57/37.2 90.73/39.0 95.5/40.21 386.6/666.9 25 152.6/56.8 135.3/56.7 137.2/59.6 141.1/66.1 508.7/877.4 30 183.1/71.3 188.4/78.9 191.0/82.7 196.2/91.2 641.0/1106 35 235.4/100 242.8/110 246.2/115 252.8/126 783.7/1352 40 307.6/133 317.7/147 322.2/153 330.9/167 937.0/1616 45 388.6/184 402.0/201 407.8/210 418.7/226 1100/1898 50 490.5/258 508.1/279 515.5/289 529/309.1 1273/2197 40 4 38  .   32.5 43.5 40 I    .14 z5B. .i. 4 .7 62. .58.... a. 15,000 rpm 57 37 6 8 4 6 1 / . .f.  . .5 . b. 25,000 rpm 83  __ I  52 87 101 m 1 ii l1 .  1. 1.0 1 _~5.fi....... ._ c. 35,000 rpm 59 145 128 132 JTh 77 142 110 176 166 151 .... .. ....L 2_ _J 3 o .. .... ... ... ... ... ... .. 105 ^===TZ  I)~) 001 1 ]I I RACE TEMPERATURE Spindle RACE Speed (K rpm) TEMPERATURE F#2 0 5 10 IS 20 2$ 3O 35 *0 45 50 Spindle Speed (K rpm) RACE TEMPERATURE, R#1 = =^= =:= Spindle RACE Speed rpm) TEMPERATURE , R#2 OUTER OUTER RING RING TEMPERATURE, Spindle Speed (K rpm) TEMPERATURE, FRONT REAR Spindle SPINDLE Speed ARBOR at center hole (K rpm) TEMPERATURE inner surf ace  F F.brg R br g la t Ion locoaton Spindle SPACER Speed (K rpm) ROLLER all at outer TEMPERATURE center surface SPACER REAR ROLLED 61 Table 3.8 Spindle B Convective Coefficients Convection Surface Location Value (W/m2 C) Spindle arbor center hole, near opening 20 30 Spindle arbor center hole, away from opening 8 15 Spindle rotating shaft, outside housing 35 60 Housing wall, near rotating parts) 30 60 Housing side wall, away from rotating parts) 20 40 Surface inside housing 0.5 2.0 Motor water cooling surface 450 550 Bearing water cooling, equivalent surface 150 200 Calculation Analysis From Figure 3.8 it can be seen that the bearings and motor rotor conductors have higher temperatures than the other spindle parts, indicating that the motor and bearing heat generations play an important role in limiting the maximum speed. motor rotor conductors have highest temperature, however motor rotor material can withstand higher temperatures than bearing components. At high speeds, the bearing temperature increases very rapidly with the speed and finally limits the spindle speed. This is because, as the spindle speed increases, the bearing heat generation increases exponentially, as shown in Figure Since the rear bearings were inside the roller cage, which has low heat conductivity, and the rear bearings were close to the motor rotor, the rear bearings had higher temperatures tlhrn thka Frrnnt hnannc spindle speed race temperature is 100 at about 30,000 rpm. This temperature (100 C) was considered as maximum bearing temperature , since higher temperatures would deteriorate the lubricant, or reduce the strength of the bearing cage. The remains of the decomposed oil would stay on the race, further deteriorate the lubrication and cause the bearing to generate more heat. Such temperature related lubrication deterioration was not modeled in this work. Since the rear bearings had very high race temperatures, if higher spindle speed is desired, rear bearing assembly should modified. lower the bearing temperature, motor can be relocated in a position farther from the bearings, or special cooling method can be used to remove more heat from the bearings. To achieve higher spindle speed, the high motor rotor temperature also needs to be reduced. This can be done by using a higher efficiency motor or by increasing the heat transferred from the motor. Since this structure (internal motor is between the bearings) allowed motor heat generation to dissipate through bearing locations, motor power loss directly resulted in the high bearing temperatures. CHAPTER 4 SPINDLE TEMPERATURE FIELD MEASUREMENT Thermoelectricity and Thermal Radiation Thermoelectric theory states that if a conductor is heated at one end, there an electric potential gradient along conductor. This thermoelectric potential varies for different metals and alloys. A thermocouple is a pair of different metal or alloy wires which are joined together at one end to form a junction. When the temperature at the junction is higher (or lower) than that at the other end of these wires, difference potentials other ends indicates temperature junction relative to the other ends. With a temperature reference, the thermocouple can be used for temperature measurement. Since the measurement junction should be at the same temperature as the measured object, there should be good contact between the hot junction and the target. temperature measurement a moving surface usually done radiation thermometry. The thermal radiation from a blackbody can be expressed in terms of spectral radiance L, as used in reference [40]. The spectral radiance is defined as the radiant flux (i.e. rate of energy flow) propagated in a given direction per unit solid angle about that direction and per unit area projected normal to that direction. The spectral radiance also depends on temperature and wavelength, as (4.1) The maximum is at (X7)~ = 2898 pimK (4.2) where LA: Spectral radiance, W *cm2 *m; A: Radiation wavelength, pm; T: Absolute temperature (K); Coefficients. Practical materials follow the same law but on a different scale. application of the radiation theory to temperature measurement, emissivity (e used, which is defined as the ratio of energy emitted by an object to the energy emitted by a blackbody at the same temperature. Emissivity depends upon the material and surface texture. Since, with the same emissivity, the energy emitted from an object depends on the temperature, the temperature can be obtained by measuring this energy. Because the wavelength of thermal radiation covers a wide range, from 0.760 to 1000 electromagnetic spectrum, radiation thermometry can use energy over different frequency ranges to measure temperature. However, the most commonly used wavelength is usually from 5 to 20 pm due to the high spectral energy in this range. The spindle temperature is usually in the range from approximately 300 K to 450 K. Equation (4.2) shows that the radiation peak is between 9.66 to 6.44 pm for = CI 1 51[e  1]' easier to measure higher temperatures. Radiation attenuation through a media is determined by the wavelength, and long wavelength radiation has a high attenuation. For high temperature measurements, since the radiation is strong, the measurement can be done at high frequency, and the radiation loss is small. Then many materials can be used to make the sensor head small and to transmit radiation over a long distance before radiation is converted an electrical signal. temperature measurements on the other hand, the strong radiation peak is in the low frequency range. To avoid losses, the radiation is directly converted into an electrical signal without any media other than air. the sense of thermal radiation, spindle temperature is in the low temperature range. Type K (NiCr/NiAl alloys) thermocouples were used for measuring the temperature of nonmoving surfaces, and an infrared temperature sensor was used to measure the spindle arbor center hole surface temperature. The infrared sensor used was a 3000AH Microducer manufactured by Everest Interscince, Inc.. This sensor has a scale range of C to 1100 with a resolution of 0.1C, and a spectral pass band (wavelength range) from 7.0 to 15.0 pm. The diameter of the spindle arbor center hole is 1.05 inches, and the sensor, claimed as the world smallest infrared sensor in their literature, still has dimensions of p0.625x2.25 square inches. Because of the limited room, the measurement cannot be accomplished by directly aiming the sensor at the surface. Also since noncontact infrared sensors always use an optical window that has a field of view, the measurement should be made at a overcome these difficulties the sensor was assembled as shown in Figure 4.1, where the sensor was in an axial orientation with a front surface goldplated mirror placed in front of the sensor at 45 surface into the sensor window. for infrared radiation. angle to reflect infrared radiation from the measured This mirror has a reflection efficiency of 95 The total distance from target to the sensor window was about 1.5 inches. Measurement of a Spindle with Bearine Heat Sources Figure illustrates locations temperature measurement Spindle A with thermocouples and the infrared sensor. Since there was only one infrared sensor, in the measurement, the sensor was moved between II through 19 locations. Steadystate temperatures were measured for each of these points and the transient temperatures were measured at most of the locations. fields of the cases in Chapter 3 (Table 3.2) were measured. The te The temperature :mperature profiles and transient responses, corresponding to the results in Figure 3.5, are illustrated in Figure 4.3. In Figure 4.3 cases 1 and 2 were measured for lubricator air pressure 35 psi, at 4000 rpm and 8000 rpm respectively. psi, at 4000 rpm and 8000 rpm respectively. Cases 5 and 6 were for air pressure 75 Table 4.1 lists the time constants from the measured transient response and Table 4.2 lists the temperatures measured at specific points for each case. The data in Tables 4.1 and 4.2 correspond to those listed in Tables 3.6 and 3.7. Pt I i cc S l b3 Cd C)3 C 4e CdN 5 C cm) eC) 31 C~ (O THERMOCOUPLE IZ INFRARED SENSOR Figure 4.2 Sensor Arrangement for Table 4.1 Spindl Temperature Measurement A Measured Time Constants Case Time Constant at II Curve Shape (_Min) 1 52 2 41 3 52 4 25, 40 Clear overshoot peak 5 33 6 15 Fast response, Overshoot peak not clear 7 35 8 22, 35 Clear overshoot peak * 31. SI.~ 0 20 40 60 80 100 120 140 160 180 TI nm CMI r Figure 4.3a Case 40.0 38.3 36.6 35.6 35.2 0 20 40 0 40 00 120 140 Iea o80 TlA m CM' n n T7;,, A / L FL, J H nn 29.1 28.9 28.9 28.9 28.6 0 20 40 60 80 100 01B20 40 160 10 T I ms CMsn ) Figure 4.3c Case 5 3 34.4 33.3 57.1   TTmlr CM r" Fionre 4 3d Tl 'pe 6 71 Table 4.2 Spindle A Measured Temperature Temperature ( C) Location 1 2 3 4 5 6 7 8 Il 33.4 42.4 38.8 48.9 31.6 40.4 34.3 45.8 12 33.0 41.1 39.8 50.3 31.0 38.6 34.9 47.6 13 32.4 37.8 38.7 47.6 30.4 36.4 34.0 44.9 14 32.4 37.5 37.8 46.6 30.0 36.0 33.6 44.0 15 34.1 41.2 40.4 49.4 31.4 N/A 35.5 46.6 16 34.6 42.4 40.8 50.6 32.3 39.7 36.4 47.6 17 33.7 39.5 39.3 47.8 31.5 37.4 35.5 44.9 18 N/A 35.2 N/A 41.2 N/A N/A N/A N/A 19 32.7 42.2 36.4 45.3 31.2 39.3 32.2 41.6 K1 29.4 33.3 32.2 35.0 28.5 32.3 29.4 32.9 K2 30.6 40.0 33.3 41.1 29.1 34.4 30.0 35.6 K3 32.8 46.1 36.1 47.2 31.1 39.4 32.2 40.6 K4 32.2 42.2 35.0 42.7 30.0 37.1 30.7 38.3 K5 31.7 41.1 34.6 41.1 30.0 36.6 30.1 37.9 K6 30.6 38.3 32.2 39.4 28.9 33.3 29.4 35.6 K7 31.7 40.0 33.8 41.1 29.6 36.1 30.0 37.4 K8 30.6 36.6 31.6 37.9 28.9 32.7 29.2 34.4 K9 30.6 35.6 31.6 36.6 28.9 32.7 29.2 33.9 K10 34.4 42.8 35.5 43.8 31.7 38.3 32.2 39.4 K11 30.5 35.2 31.2 36.2 28.6 31.6 28.9 33.1 N/A: not available. Measurement of a Spindle with Bearing and Internal Motor Heat Sources The locations of the thermocouoles and the infrared sensor in snindle B are 72 25,000 rpm and the axial preload 100, 150, 170 and 220 lbs. Since this spindle has a much larger speed range than Spindle A, the transient responses were measured by increasing spindle speed in multiple steps. Every time the speed was increased by 5000 rpm transient temperatures were measured. When a steady temperature field was achieved, the speed was increased by another 5000 rpm. Figure 4.5 illustrates two measured temperature fields at 15,000 rpm and 25,000 rpm which correspond to the calculation cases at the same speeds in Figure 3.9. Figure 4.6 illustrates temperaturespeed relationships at different locations, which correspond to the calculation results in Chapter 3. The computed temperatures at the same points are also plotted in Figure 4.6. the plots "f#1" indicates the calculation result of the first front bearing, "r" indicates the calculation result of the rear bearing. The curves symbolized with "f# 1 M" and "test" are from the measurement results. The rest of the curves are the calculation results, which are plotted here to compare with the measured temperatures. Figure 4.7 illustrates a typical transient temperature response for the axial preload of 170 lbs and at 8000 rpm. The temperature was measured at location T9 and the spindle was started from 0 rpm to 8000 rpm. The noise in the temperature signal was due to the interference of the spindle's internal motor. Unlike Spindle A, Spindle temperatures not have an overshoot. curve shows response has three stages, i.e., rapid increasing, slow increasing, and slow decreasing to approach a steady value. Since the curve is not smooth, and the discontinuity could only result from the change of heat sources, it can be concluded that the "f#2 Figure 4.4 Sensor Locations for Temperature Measurement of Spindle B Figure 4.5a 15,000 rpm OUTER RING TEMPERATURE, FRONT 20 25 Spindle Speed (K rpm) FRONT Surface of SPACER spacer bi TEMPER between fi ATURE nner rings Inl 2 3 10 IS 20 3S 30 43 40 '4 S Spindle Speed (K rpm) SPINDLE ARBOR at arbor nner TEMPERATURE surface 0 to 15 20 2S 30 3S 40 45 5J Spindle Speed (K rpm) ROLLER re SLEEVE iar roller SURFACE sleeve outer TEMPERATURE surface 280 240* 220 200 *8 140 g $200 60 40 20 10 D 20 40 60 BO 100 120 140 tirre (mm)n Figure 4.7 Transient Temperature Response, 8000 rpm Comparison with FEA Results and Discussion Spindle A. Comparing Tables 4.1 and 4 with Tables 3.6 and 3.7 it is shown that the FEA results are fairly close to the measured results. It should be noted that the material properties of the rollercage and most of the convection coefficients were adjusted to make the simulation results match the experimental results. convection coefficient adjustments were integrated convective coefficient formulae, and the obtained rollercage properties can be directly used for other similar structures without substantial error, for example, for Spindle B. The effects spindle speeds supply pressures on spindle temperatures time constants behaved like those predicted by FE model (Chapter 3). Since different spindle speeds caused different air flow speeds along spindle housing surface, the rnvPrtivu nPffiientfc 2t rdiffetrent cnpredc E re different Wi ohr ilhihrntnr inlPt nir convection resulted. If we compare the temperatures of case 2 and case 6 (or case 4 and case 8), we can see the change of air pressure from 35 psi to 75 psi caused 2 * C decrease in temperature, which is equivalent to a result from a speed change of about 1000 rpm. The difference between the measured temperatures and time constants and the calculated temperatures and time constants seem to be the result of following three effects. First, the surfaces at different locations had different local convection coefficients that greatly depended upon the local air flow and temperature conditions. local air flow cannot be accurately calculated. The coefficients used in calculation were estimated average coefficients. Second, the spindle material local heat conduction resistance could not be expressed and included in the finite element model at this time. Third, the material properties (heat conductivity and capacity) could only be obtained as approximate values. The major difference between the calculated measured transient temperature responses exists appearances of the transient response curves. The calculated transient responses are all smooth curves, but the measured responses have apparent overshoots, which can be interpreted as the result of nonlinear heat sources. At high heat generation rates and in low convection in the shaft center hole there is an overshoot peak occurring shortly after the spindle is started, occurring at a time very close to the calculated time constant. The peak not only occurred in the infrared sensor measurements inside the center hole of the spindle shaft, but also appeared in the thermocouple measurements in the spindle housing. These temperature overshoots are apparently warmed, the spindle shaft expanded more than the housing, because friction between the spindle housing and rear bearing rollercage slowed the constant axial load mechanism's reaction to compensate for the heat induced axial load, the bearing axial load increased. heat generation continued increase with temperature until the heat induced axial load was large enough to overcome the friction. In the meantime, because the shaft slowed down its expansion while the housing continued to expand, there was a small release of bearing axial load. Then the actual axial load and heat generation became smaller and the area around the bearing contacts had a temperature reduction such that the temperature gradient was changed. In some parts of the spindle the temperatures appeared to stop increasing or to start decreasing until a new thermal equilibrium was achieved. This also showed existence effectiveness bearing constant axial load mechanism are very important. Spindle B. Comparison of the measurements with the FEA results in Chapter 3 shows good agreement. computed temperature fields are close to the measured temperature profiles as compared Figures 3.10 calculated temperatures some important points fairly close measurements as shown in Figures 3.11 and 4.6, the temperatures at bearing outer rings and arbor outer surface). The sources for the remaining differences are the same as those for Spindle A. In Figure 4.6 the first graph displays the computed temperatures for the outer marked outer rings of the rear bearings are not accessible measurement. The second graph plots the temperatures of the spacer between the front bearings (T10), the third graph plots the temperatures of the surface of the rollercage (K17), and the fourth plots the temperatures in the hole of the spindle arbor (T9, T3), all of them as computed and as measured. However the measured data apply only to speeds up to 25,000 rpm, whereas computations were made up to 50,000 rpm. The measurements and computations both show that the bearing outer rings and inner rings have different temperatures and that the differences increase with the speed. transient temperature shows some characteristics similar to those Spindle A. The transient curve is smooth, this suggests that the rear rollercage moves freely. The fast rising portion of the curve is due to the change of the bearing heat generation. next portion, shaft' thermal expansion applied substantial load on the bearings and the heat generation rate was slowly increasing. At this time, the shaft expanded more than the housing. After a certain time the housing expanded more than shaft, bearings were released heat generation rate decreased. In the transient curve, it is shown as a slow decrease in temperature. Since housing expansion was limited, decrease temperature was small and the temperature finally reached a steady value. Since the constant bearing load mechanism was very effective, the above bearing load change was very small. The transient temperature also shows that the spring constant load mechanism ,, N" between the shaft and the housing was large. If the housing has good cooling, such as water cooling, the bearings will have a significant thermal load, and in the design this thermal load should be considered. The bearings were arranged as DF (faceto face) tandem, and a shaft expansion larger than the housing expansion would cause significant bearing load increase if the constant axial load mechanism was effective. Another phenomenon observed in the measurement is the slow temperature increase when spindle speed changed from 15,000 rpm to 20,000 rpm. In contrast to this slow temperature rise, the temperature increase for spindle speed change from 10,000 rpm to 15,000 rpm was quite large. An explanation is that the bearings were previously slightly damaged at 16,000 rpm by bearing seizure. The seizure caused surface flaws in the races of the bearings at the contact angle corresponding to this speed. When the spindle was not running at the speeds around 16,000 rpm, the bearing balls contacted the races in the good tracks, and the friction was moderate. Then when the speed was around 16,000 rpm, the balls contacted the races in the neighborhood of the damaged tracks, the friction became large. This caused the significant high temperature at 15,000 rpm. there were good bearings, temperature change from 10,000 rpm to 20,000 rpm would be smooth. It can be estimated from the plots that the temperature at front bearing was about 8 than the temperature with good bearings. large, * C higher Since this temperature increase was not the damage to the bearing race was not severe. CHAPTER 5 HIGH SPEED SPINDLE DESIGN WITH THERMAL CONSIDERATION Currently in the design of spindles, the stiffness and power are major concerns and can be under the control of design engineers. However, the design of spindle thermal characteristics, which greatly affects the spindle properties at high speed, is largely based on experience. At high speed, the bearing generates more heat, and the spindle has higher temperature and larger thermal expansion. Special thermal design becomes necessary to remove the spindle internal heat from the bearings, and prevent the bearings from being thermally overloaded. Spindle Static and Dynamic Properties spindle stiffness determines static dynamic properties. stiffness can be increased by using larger bearings and larger arbor diameter, and by applying a larger preload to the bearings. The location of the bearings and the structure of the arbor can significantly influence the spindle static and dynamic properties. Most currently available spindles used in various machines and machine centers are designed to operate at speeds below or around 5000 rpm. When the spindle has to be used at higher speed, it will have a higher temperature, both its dynamic properties structure influenced high temperature The purpose of the thermal design is to eliminate bearing thermal load, lubricant deterioration and unacceptable structural distortion, and also to maintain the dynamic properties. After a valid spindle thermal model is established, thermal design can be processed through estimating and eliminating the bearing thermal load, reducing the high local temperatures, adjusting the bearing preload and modifying the lubrication system. Effect of Forced Cooling on Spindle Temperature Spindle cooling is important, commonly used method spindle cooling is the natural convection of the spindle surface. When the internal motor is used in a spindle, a water cooling jacket needs to be used remove heat generated from the motor stator. Forced cooling for a spindle will add structure complexity and service difficulty, and is used when natural cooling cannot satisfy the cooling need. For high speed, high power spindles, natural cooling usually cannot provide adequate cooling to maintain stable thermal condition lubrication condition. Since it is essential for spindle bearings to operate below a maximum temperature, effective cooling of bearings becomes necessary. The water cooling of the bearing outer rings is considered as a good method. The effect of the water cooling of the spindle bearings was analyzed based on the thermal model established in Chapters 2 and 3 for Spindle B. Calculations for the model with water cooling in the bearing outer rings were done in contrast to the Figure 3.10. reduction temperatures around bearings obvious, particularly at high spindle speed. The water was introduced into the cavities near the bearing outer rings. Figure shows the computed temperatures on the races bearings with without water cooling. Figure shows temperatures in the bearing outer rings. Figure .4 illustrates the temperatures at the spacer between the front bearings, the outer surface of the rear roller sleeve and the surface of the arbor center hole. Both the computational and measured results are displayed in Figures 5.3 and 5.4 (water cooling of the bearings and no water cooling bearings). effect cooling bearing outer rings computational result only since cooling was not introduced housing experimentally. The computations show that, for the same temperatures, with water cooling it may be possible to increase speed by about 10,000 rpm. The water cooling of the bearings was done by placing 8 quarterinch diameter holes around the outer rings of the bearings. convective coefficients for the water cooling of the bearings were 150 200 W/ K/m2 as listed in Table 3.9. These values are average values considering total cooling area, water hole area convective coefficients at the surfaces of water holes. The water convection coefficients were obtained under the pressure of regular chilled water supply. Although the highest temperatures in Figure 5.1 are not much less than those in Figure 3.10, the high temperatures in the bearing rings and races are greatly reduced. observed from the temperature curves in Figures This can also be through 5.4. 30.6 40.5 38 40 36 __ 47.5 46.5 54  " __ _... L......._..45.5 47.8 51 45 43 a. 15,000 rpm 35.7 SQ  ~ft    .6 ~flL Jr . __ .5.6._. 74._ _97 69.2 62.6 .. . ..5 .._ ... .. .. _7.. .. ... .. .. .. . b. 25,000 rpm    43.6 77 58 88 92 ___.__._.__.l99128_ 100 90 _LE_ c. 35,000 rpm  .  44.7 II ft. * .107 110 14O 113 1i9 d. 451000 mm (1(1 nrn I ~fi ~79P7~11 _17 i i I RACE TEMPERATURE, Inner I+cot~r Spindle RACE Speed (K rpm) TEMPERATURE F#2 O a 10 is 20 2$ 30 Ms 4o as so Spindle Speed (K rpm) RACE TEMPERATURE, R#1 outer Inner O+~wotr I+watar O tT outer Inner O+wotar l+wactr Spindle Speed (K rprn) RACE TEMPERATURE, R#2  ____ _____inn .r  Oa+'*otar *4.watrr OUTER RING TEMPERATURE, FRONT Spindle Speed (K rpm) OUTER RING TEMPERATURE, REAR a r#1l r#2 r#1 W r#2+W Spindle Speed (K rpm) Figure 5.3 Temperatures in Bearing Outer Rings a fwoter r.woter ftesta f~tnst  & r esT Spindle Speed (K rpm) 'imira C A 'T'nnTnarotlfimac at CnCArl1 A rhn TlnnTar CiirforOa a f 86 Effect of Snindle Heat Source and Bearing Axial Load Another method to reduce the spindle temperature is to reduce the bearing heat generation and to design the spindle structure such that the generated heat can quickly conducted out of heat sources thus an even temperature distribution could be achieved. A uniform temperature field is always good for both eliminating thermal load dissipating heat. it usually cannot easily achieved since the location of bearings will affect the spindle dynamic and static properties more than the spindle temperature distribution. As shown in the Figures 3.10, motor heat generation contributes much to the spindle temperature, especially to the temperature of the rear bearings. Therefore reasonable to relocate the motor to a location away from the bearings such that the bearing temperatures can be reduced. Figure 5.5 shows the measured effects of preload on the temperatures of the outer rings of the front bearings, and of the surface of the hole in the spindle. preload was applied through a spring system that provides constant axial load to the bearings. The adjustment of the preload was made by compressing the springs a certain amount. The results are not very systematic, but they show that an increase of the preload from 100 lbs to 220 lbs (per two bearings) caused a temperature increase about 1015 Figure illustrates calculated bearing heat generations when the bearing axial load varied from 110 lbs to 220 lbs. bearing heat generation was increased by 25% to 40%. In this case, This also indicates that an 87 a) @ Front #1 Bearing Outer Ring 100" 220W Sptndle Speed (x 15 1000 rpm) b. @ Rear #1 Bearing Arbor Inner Surface 0 5 10 15 20 Spindle Speed (x1000 rpm) Figure 5.5 Measured Temperatures with Different Bearing Preloads 0 G 1 0 1 l0 2G SO GG 40 4 Speed (X1000 rpm) 88 Spindle Bearing Catastrophic Failure and Temperature Usually it is relatively easier to detect bearing fatigue failure than to prevent bearing rapid catastrophic failure. It is especially true for high speed bearings. Two cases of bearing sudden seizure failure were experienced in this study, both at 16,000 rpm. Both failures happened when spindle was restricted axially and the bearing thermal load became large. Bearing Failure Below is the investigation of one of the cases. Temperature (Measurement) The bearing rapid failure happened 10 minutes after the spindle speed was changed from 8000 rpm to 16,000 rpm. bearings measured a continuously increasing temperature, however, the bearing outer ring temperatures were below the assumed alarm level Figure illustrates transient temperature responses of bearing failure at the outer rings of the front bearings ("F indicate the first and second front bearings). 1" and "F A spindle temperature profile was recorded once each minute for this case. Firs Fron Bearing; Second Front Bearing. 0 1 2 3 4 5 6 7 8 9 89 Thermal Induced Bearing Heat Generation The above bearing failure was simulated through FEA. Since the spindle thermal model was well established, then in the simulation the variables were bearing heat generation spindle runmng time. nonlinear case, a pseudo nonlinear method was used. For each time period minute) bearing heat generation was held constant so as to use the available FEA software for the transient heat transfer calculation. The bearing heat generation was adjusted to make spindle temperature profile match measured profile at each period. Table lists the increase of heat generation during the bearing seizure. The figure indicates that at the time of the seizure, the bearing heat generation was equivalent to that at 42,000 rpm, far beyond the maximum spindle speed. The estimated bearing heat generation is also plotted in Figure 1 2 3 4 5 78 7 8 9 10 0 10 15 Time (min)eed (x rpm) Speed (x1Ooo rpm) Figure 5.8a Bearing Heat Dissinatinn Chanue at SeiznreT Figure 5.8b Bearing Heat Ilissinatinn vc: Snee.d without S..i7iire 90 Bearing Thermal Load at Failure The axial loads were calculated through the relation between bearing heat generation and bearing axial load. The spindle has a constant axial load mechanism, thermal expansion can be compensated through a set of springs, and so the bearing thermal load can be elimin (1040 N) per two bearings1 bearings was constrained. changed from 8000 rpm tc ated. The spindle was set with an axial preload of 220 lbs . The bearing seizure was because the movement of the It was assumed that at time 0 min., the spindle speed was S16,000 rpm and the bearing axial load was 1040 N per pair, and then bearing axial load was calculated (Table 5.1 and Figure result shows that the axial load at bearing failure could have been four times as much as the preload. Spindle and Bearing Failure Temperature Since bearing failure occurred a short time, spindle housing temperature increase was small, however, bearing components great temperature increases, and Figure 5.10 and 5.11 illustrate these changes. From the figures it can be seen that the highest temperature at the failure was about 105 on the bearing inner race. Bearing Rapid Failure Cause Analysis The above investigated case is a typical bearing rapid failure. The steps for failure were as follows: the bearing friction generated heat and caused the bearing components to expand. Since bearing was axially constrained, hkPrnna rnsc rnmnraccal hr thf thsrml lnrA T Tnsro ti tr h; frrnm lrj 1 ths= henrino 