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NUMERICAL SIMULATION OF WEAR FOR BODIES INT OSCILLATORY CONTACT
SAAD M. MUKRAS
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
Saad M. Mukras
To my parents, Professor Mohamed Mukras and Bauwa Mukras, and to my siblings,
AbduRahman, Suleiman, and Mariam
I express my humility and utmost gratitude to Allah for his blessings in my life. Verily no
success would have been achieved without his grace and mercy. I would next like to thank my
parents for their support in my educational pursuits. I owe them much more than I can ever give
I would like to acknowledge Dr Nam-Ho Kim, my adviser, for the support that he has
provided. Because of his advice and challenges, I have matured as a student and as a researcher. I
would like to thank my colleagues, friends and members of the university staff that have also
Indeed, it would be negligent not mention the support that I have received from the
members of the Masaajid in Gainesville who have enabled me to feel at home while away from
TABLE OF CONTENTS
ACKNOWLEDGMENTS .............. ...............4.....
LIST OF TABLES ................ ...............7............ ....
LIST OF FIGURES .............. ...............8.....
AB S TRAC T ............._. .......... ..............._ 10...
1 INTRODUCTION ................. ...............11.......... ......
Background ................. ...............11.................
Scope and Objective ................. ...............14................
Thesis Organization ................. ...............15.................
2 WEAR-PREDICTION METHODOLOGY FOR BODIES INT OSCULATORY
CONT ACT S .............. ...............16....
Introducti on ........._... .. ....... ...............16...
W ear M odel .............. ...............16....
Simulation Procedure........................ ...........1
Pin-Pivot Finite Element Model ........._. ........_. ...............21...
Geometry Update Procedure .............. ...............22....
Conclusion ........._ ........_. ...............25....
3 EXTRAPOLATION SCHEME S............... ...............30
Introducti on ................. ...............30.................
Constant Extrapolation .............. ...............3 0....
Adaptive Extrapolation Scheme .............. ...............33....
Conclusion ............ ...... ._ ...............34....
4 PARALLEL COMPUTATION INT WEAR SIMULATION FOR OSCILLATORY
CONT ACT S .............. ...............36....
Introducti on ................... .. ................ ...............36.......
Cycle- and Intermediate Cycle-Update .............. ...............36....
Parallel Computation .............. ...............38....
5 WEAR-SIMULATION PROGRAM............... ...............43
Introducti on ................. ........... ...............43 .....
Wear-Simulation Program Format .............. ...............43....
Ansys Input Code .............. ...............43....
Contact analysis............... ...............44
Output of results ..........__._ .... .___ ...............44....
Simulation Managing Code ........._.___..... .___ ...............45....
6 EXPERIMENTAL VALIDATION OF THE WEAR-SIMULATION PROCEDURE......... 48
Introducti on ............... ......._ ...............48....
Wear-Simulation Validation............... ...............4
Step-Update Simulation Test............... ........ ............4
Intermediate Cycle-Update: Parallel Computation .............. ...............50....
Conclusion ............ _...... ._ ...............51....
7 WEAR-SIMULATION EXAMPLE: ESTIMATION OF BACKHOE BUCKET TIP
DI SPLACEMENT ............_ ..... ..__ ...............58...
Introducti on ............... ... ..__ ...............58...
Estimation of Tip Displacement ............_ ..... ..__ ...............58..
Conclusion ............ _...... ._ ...............60....
8 CONCLUDING REMARK S............_ ..... ..__ ...............65..
9 RECOMMENDATIONS FOR FUTURE WORK .............. ...............67....
LIST OF REFERENCES ............_ ..... ..__ ...............68...
BIOGRAPHICAL SKETCH .............. ...............71....
LIST OF TABLES
6-1 Wear test information for the pin and pivot assembly............... ...............53
6-2 Simulation parameters for the pin in pivot simulation test. .....__._.. ........_._ ...............53
6-3 Comparison of results form the simulation tests and actual wear tests for the pin in pivot
assem bly .............. ...............53....
7-1 List of loads and relative rotation angles at the j points of the backhoe ................. ................61
7-2 Summary of the wear depth at the j points after 20,000 cycles as well as the extrapolated
wear depth at 90,000cycles............... ..............6
7-3 Displacement of the boom component parts from the center line ................. ................ ...61
LIST OF FIGURES
2-1. Oscillatory contact for a pin-pivot assembly. .............. ...............26....
2-2. Wear simulation flow chart for the 'step update' procedure. ................ .......................27
2-3. Pin-pivot finite element model. ................ ................ ........ ......... ....__ .28
2-4. A three-node contact element used to represent the contact surface .................. ...............28
2-5. Geometry updates process. .............. ...............29....
2-6. Surface normal vector for the pin-pivot assembly prior to update ............... ............._..29
3-1. Contact pressure distribution on a pin-pivot assembly............... ...............35
3-2. Extrapolation history for a pin-pivot assembly. ............. ...............35.....
4-1. Wear simulation flow chart for the 'cycle-update' procedure ................. ......................40
4-2. Wear simulation flow chart for the 'intermediate cycle-update' procedure. ......................41
4-3. Wear simulation flow chart for the parallel implementation of the 'cycle-update'
proce dure ................. ...............42....... ......
5-1. Interaction between the C code and the Ansys input code .................... ............... 4
5-2. Function of the Ansys input code. ................. ....__ ....__ ....__ ..............46
5-3. Structure of the wear-simulation program ................. ...............47...............
6-1. Pin-pivot assembly for the wear test ................. ...............54........... .
6-2. Cumulative maximum wear on pin and pivot. ............. ...............54.....
6-3. Contact pressure distribution on the pin and pivot during wear analysis.. .................. ..........55
6-4. Extrapolation history plot for the step updating simulation procedure. ............. .................56
6-5. Cumulative maximum wear on pin and pivot for the intermediate cycle updating
procedure and the parallel implementation ................. ...............56........... ...
6-6. Extrapolation history plot for the intermediate cycle update procedure and its parallel
implementation. ............. ...............57.....
7-1. Pin-pivot assembly for the wear test ................. ...............62........... .
7-2. Joint consisting of a pin and pivot. .............. ...............62....
7-3. Wear on the pin and pivot at the backhoe Joints ................ ........... .....................63
7-4. Backhoe component displacement from the vehicle centerline. ............. .....................6
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
NUMERICAL SIMULATION OF WEAR FOR BODIES INT OSCILLATORY CONTACT
Saad M. Mukras
Chair: Nam-Ho Kim
Major Department: Mechanical and Aerospace Engineering
When bodies are in contact and in relative motion, wear becomes an important aspect that
should be considered during design. In mechanisms, wear is experienced at connections such as
joints. A particular type of contact condition, known as oscillatory contact, exists at these
connections and is partly responsible for wear. The obj ective of this study is to develop a wear-
prediction procedure for bodies that experience this type of contact condition.
A prediction procedure for wear occurring in bodies that experience oscillatory contact is
proposed. The methodology builds upon a widely used iterative wear-prediction procedure. Two
techniques are incorporated into the methodology to minimize the simulation computational
costs. In the first technique, an extrapolation scheme that optimizes the use of resources while
maintaining simulation stability is implemented. The second technique involves the parallel
implementation of the wear-prediction methodology. The methodology is used to predict the
wear on an oscillatory pin joint and the predicted results are validated against those from actual
Mechanical systems employ mechanisms that are used to convert one type of motion into
another. These systems consist of connections such as j points where two components of the
system establish contact and are in relative motion during operation. Depending on the
kinematics of the mechanism, either of several contact conditions may exist at the connection.
One particular contact conditions that is widely encountered is the oscillatory contacts. This
contact condition coupled with other factors give rise to wear which could cause the system to
fail. The importance of wear and the need for its consideration in design is dependant on a
number of factors which may be either technical or economical or both. An example in which
wear is of great concern is at the j points of heavy equipment such as backhoes. The j points of such
equipment experience considerable amounts of wear while in operation. In order to minimize
the wear occurring is such joints designers have implemented several techniques such as select
materials based on material ranking or using wear resistant coating on the contacting surfaces.
Although these procedures are widely used, they do not give sufficient insight or quantitative
information on how a system may fail due to wear. It would thus be advantageous for designers
to have the ability of predicting the wear beforehand. One way that has been used to achieve this
has been the use of accelerated design verification procedures on prototypes. The procedures are
generally expensive and destructive in nature but provide an abundant amount of information
regarding the wear as a mode of failure.
An enormous amount of effort and resources has been placed into developing techniques
that utilize computer simulations in the prediction of wear. Use of simulations for wear
prediction has a number of benefits, one of which is its potential to reducing or eliminating
costly tests that may be required when considering wear in design. Simulations for wear
predictions are also a versatile alternative, allowing for rapid changes in the simulation
conditions with little effort.
A number of papers have been written dealing with the subj ect of wear prediction. A
general trend that that has emerged is the use of numerical methods together with variations of
Archard's wear model in predicting wear. Padra and Andersson  used finite element method
(FEM) in an iterative procedure to determine the wear on a pin placed over a moving disk. The
simulation yielded results similar to those of an analogous experiment. In a separate paper, Padra
and Anderson  discuss the use of finite element analysis in wear simulation of a conical
spinning contact. They compared simulation results to analytical results which showed good
agreement. Padra and Andersson  also used the Winkler surface model, to compute contact
pressure instead of the finite element method, to simulated wear. They reported results that
showed close agreement with simulations in which the finite element method was used. Yan et
al.  predicted the wear resulting form a loaded pin contacting a rotating disc, by noting that the
center of the disc wear track may be approximated as a plain strain region. They showed that the
prediction results were consistent with experimental measurements. Wear simulations for a pin
on disk problem were performed by Gonzalez et al.  using finite element method in
conjunction with an incremental wear-prediction technique. In their simulation procedure, the
geometry was updated at the end of each iteration. This was done to account for the worn out
material. Telliskivi  preformed simulations to predict the wear on a disc-on-disc assembly
using the Winkler mattress model. Good agreement between experiment and the simulation
results were reported. Dickrell and Sawyer  developed a model to study the evolution of wear
for a shaft and bushing assembly and ran experiment to validate the model.
A number of papers dealing with wear prediction of more complicated geometries have
also been written. Flodin and Andersson , simulated the wear on spur gears using the Winkler
model. They used an incremental wear-prediction approach in which the geometry was allowed
to evolve as the simulation progressed. Flodin and Andersson  later extended their
methodology to helical gears. They treated the helical wheel as several thin independent spur
gear teeth. Brauer and Andersson  conducted wear simulations for gears using a combination
of finite element method and an analytical approach based on Hertz theory. The FEM was used
to determine the loads resulting form gear teeth interaction which were in turn used to determine
contact pressure using the analytical expressions. In one paper Hugnell et al. [l l] simulated the
wear resulting from a cam-follower contact and in another paper  they simulated the mild
wear in a cam-follower contact with follower rotation. They also used an incremental wear-
prediction procedure and allowed the geometry to change after every simulation step. Nayak et
al.  predicted the wear on a cam-follower and presented a guideline on designing cam
followers for low wear. Fregly et al.  performed wear analysis to simulate mild wear on a
tibial insert model. They reported close agreement between the simulation results and damage
observation on actual tibial insert. Wear predictions on total hip arthroplasty were performed by
Maxian et al. . Bevill et al.  also performed simulations to determine the damage on a
total hip arthroplasty due to wear and creep.
Depending on the complexity of wear mechanisms, wear predictions using computer
simulations have yielded relatively reasonable results [1-3, 17-18]. The simulations, however,
have been found to be quite computationally expensive. Several ideas have been implemented in
an attempt to reduce computational costs associated with the wear-simulation process. Padra and
Andersson  attempted to minimize the computational cost by using the Winkler model to
determine the contact pressure distribution. The Winkler model was used as an alternative to the
more expensive but relatively accurate FEM. Although the method was found to be less
expensive it can be argued that the benefit of using more accurate results from the finite element
technique outweigh the gains in computational efficiency when complicated geometries are
considered. Padra and Anderson  also employed a scaling approach to tackle the problem of
computational costs. In this approach the incremental wear at any particular cycle of the
simulation was scaled based on a predefined maximum allowable wear increment. The scaling
factor was obtained as a ratio between the maximum allowable wear increment and the current
maximum wear increment (maximum wear increment of entire geometry). They found that this
procedure was more computationally effective. Kim, et al.  used a constant extrapolation
technique to reduce the computational costs for the oscillatory wear problem. In their technique
one finite element analysis was made to represent a number of wear cycles. Through this
extrapolation, they were able to reduce the total number of analyses needed to estimate the final
wear profile. A similar procedure was done by McColl, et al.  as well as Dickrell et al. .
In another paper , the computational costs of simulating a pin on a rotating disc was reduced
by approximating the state of strain on the center of the wear track as plain strain. A less costly
two-dimensional idealization was then used in place of the more expensive three-dimensional
Scope and Objective
As is apparent from the literature, a number of procedures have been proposed to simulate
wear. In addition several procedures have been proposed to simulate wear in more specific
assemblies such as gears and cam-follower systems. One type of assembly that is encountered in
numerous applications is one in which the oscillatory contact is experienced. These types of
assembly are commonly found at the connections of mechanisms. Due to the nature of relative
motions at such assemblies, wear is inevitable. In this research, the obj ective is to develop a
simulation framework for wear prediction in bodies that experience oscillatory contact. In
addition to developing the prediction procedure, emphasis is made on incorporation techniques
that minimize the overall computational costs and enable stable simulations.
In Chapter 2, the details of the wear model used in the prediction procedure are discussed.
The simulation prediction procedure specific to bodies experiencing oscillatory contact will then
be presented. A representative model to be used to demonstrate the procedure is introduced and
discussed in Chapter 2. Chapter 2 will close with a discussion of a geometry updating technique
that minimizes the mesh distortion.
Techniques to minimize computational costs will be presented in Chapter 3 and 4.
Discussions in Chapter 3 will focus on the use of extrapolations to minimize costs. The issue of
instability when extrapolations are used as well as a proposed solution is included in Chapter 3.
In Chapter 4, the implementation of parallel computation as a way to reduces computational
costs is discussed. In order to implement the wear-prediction procedure, a simulation program
was written. The details of the program are discussed in Chapter 5.
Validation of the wear-prediction procedure is discussed in Chapter 6. Results from
experiments are compared to results from the wear simulation. In Chapter 7, an example .that
demonstrates how the wear-simulation program can be used to evaluate the effect of wear on the
performance of a system is presented. Finally conclusions about the wear-prediction procedure
will be drawn in Chapter 8 and suggestions for future research will be made in Chapter 9.
WEAR-PREDICTION METHODOLOGY FOR BODIES INT OSCILATORY CONTACTS
When two bodies are in contact and are in relative motion with respect to each other, wear
is expected to develop on the regions of contact. The type of contact that the bodies experience is
dependent on how the bodies move relative to each other. One type of contact condition that is of
interest is the oscillatory contact. This type of contact condition is characterized by an oscillatory
relative motion between the bodies that are in contact. The contact between a pin and a pivot in a
center-link pivot joint is an example of this type contact. This example is shown in Figure 2-1
where the pin oscillates between two extreme angles. In this Chapter a procedure to predict the
wear occurring in this type of contact is discussed. In this work, the assembly shown in Figure 2-
1 will be used as a representative case of the oscillatory contact to illustrate the wear-prediction
In developing the wear-prediction methodology it is assumed that all the wear cases to be
predicted fall within the plastically dominated wear regime, where slide velocities are small and
surface heating can be considered negligible. Archard's wear law  would thus serve as the
appropriate wear model to describe the wear as discussed by Lim and Ashby  as well as
Cantizano, et al. . In that model, first published by Holm , the worn out volume, during
the process of wear, is considered to be proportional to the normal load. The model is express
mathematically as follows:
where V is the volume lost, s the sliding distance, K the dimensionless wear coefficient, H
the Brinell hardness of the softer material, and F, the normal force. Since the wear depth is the
quantity of interest, as opposed to the volume lost, Eq. 2-1 is usually written in the following
= kF,, (2-2)
where h is the wear depth and A is the contact area such that V = hA The non-dimensioned
wear coefficient K and the hardness are bundled up into a single dimensioned wear coefficient
k (Pa )~. It should be noted that the wear coefficient k is not an intrinsic material property but is
also dependent on the operating condition. The value of k for a specific operating condition and
given pair of materials may be obtained by experiments . Also worth noting, is that measured
values of wear coefficients usually have large scatter and may affect wear predictions
significantly. Care should thus be taken in obtaining these values. Uncertainty analysis for
measured values of wear coefficients, such as those presented by Schmitz et al. , may be of
Equation 2-2 can further be simplified by noting that the contact pressure may be
expressed with the relation p = F,/A so that the wear model is expressed as
= kp (2-3)
The wear process is generally considered to be a dynamic process (rate of change of the
wear depth with respect to sliding distance) so that the first order differential form of Eq. 2-3 can
be expressed as:
= kp(s), (2-4)
where the sliding distance is considered as the time in the dynamic process, and the contact
pressure is a function of the sliding distance.
A numerical solution for the wear depth may be obtained by estimating the derivative in
Eq. 2-4 with a finite divide difference to yield the depth as follows:
h, = h~,_+kpAs, (2-5)
In Eq. 2-5, hi refers to the wear depth at the jth iteration while hi,_ represents the wear depth at
the previous iteration. The last term of Eq. 2-5 is the incremental wear depth which is a function
of the contact pressure and incremental sliding distance (As, ) at the corresponding iteration.
If information about the wear coefficient k, the contact pressure p, and the sliding
distance As, is available at all iterations ( j), the wear depth on a contact interface for a specified
sliding distance s can be estimated using Eq. 2-5. Here the sliding distance is an accumulation
of the incremental sliding distance for all iterations (n iter ) as is expressed in Eq. 2-6.
s = As (2-6)
The contact pressure ( p) may be obtained through numerical methods. The finite element
method appears to be the most widely used method. This is probably due to its accuracy. Several
papers [3, 6, 27-28] have been written in which an elastic foundation model has been used in
place of the finite element method. The wear coefficient can be obtained through experiments
such as this explained by Kim et al. [18, 25] where as the incremental sliding distance may be
obtained from the finite element analysis or can be specified by the user.
The most widely used procedure to simulate wear occurring at a contact interface is an
iterative procedure describe by the numerical integration in Eq. 2-5. A number of papers [1,2, 17-
19,25,29], that demonstrate the implementation of Eq. 2-5 in predicting wear, have been written.
Although the details of the various procedures differ, three main steps are common to all of
them. These include the following:
* Computation of the contact pressure resulting from the contact of bodies.
* Determination of the incremental wear amount based on the wear model.
* Update of geometry to reflect the wear amount and to provide the new geometry for the
The procedure developed for predicting wear on oscillatory contacts incorporates the
As was mentioned earlier the pin-pivot assembly shown in Figure 2-1 will be used to
illustrate the simulation procedure. In this assembly the pin is fixed so that it does not translate in
any direction but is allowed to oscillate (in an axis perpendicular to the paper) from one extreme
to another (bounded by specified amplitude). Contrary to the conventional definition of a cycle,
in this work a cycle is defined as a rotation of the pin from one extreme angle to the other
(e.g.+60O). The goal is to develop a procedure that can predict the wear over several thousand
cycles. It is worth noting that most of the work present in the literature dealing with wear
simulation does not address this type of motion but rather, that which is of a continuous nature
such as in rotational contacts.
The simulation of wear at the contact interface of the pin-pivot assembly is achieved by
considering each cycle separately. The wear in any cycle can be obtained by discretizing the
cycle into a number of steps and thereafter applying Eq. 2-5. The discretization is such that each
step corresponds to a specific pin angle between the two extremes. In the application of Eq. 2-1,
the wear coefficient k and the incremental sliding distance As~ are taken to be constant where as
the contact pressure p, is computes by the finite element method. The pin-pivot finite element
model used to illustrate the simulation procedure will be described a later subsection.
At each step a finite element analysis is performed to determine the contact pressure over
the contact region. The wear depth during any cycle and at any point on the contact surface can
then be determined by Eq. 2-7 which is a modification of Eq. 2-5.
h,,l,,= h,,, ,+kpg,,As, (2-7)
In Eq. 2-7, n refers to surface nodes number (of the finite element model) which may or
may not establish contact with the opposing surface. The sub script i and j indicate the current
step and cycle, respectively. All other terms are as defined previously.
The geometry is then updated to reflect the amount of wear and to prepare the model for
the next step. Details of the geometry update procedure will be discussed in subsequent
subsection. At this point the simulation progresses to the next step and the oscillating pin
assumes a new position. This involves a rotation through an angle corresponding to the
incremental angle. The previously described processes are repeated up until all steps in a cycle
are completed. The direction of pin rotation is reversed and the simulation of the next cycle
commences. The term 'step update' is adopted for this procedure since the geometry is updated
after every step. The simulation process for the step update procedure is summarized in the
flowchart shown in Figure 2-2.
Pin-Pivot Finite Element Model
Two methods that have been used in the literature to calculate the contact pressure at the
contact surface were mentioned as the elastic foundation and the finite element method. The least
expensive of the two methods, in terms of computational costs, is the elastic foundation method.
This method is, however, the least preferred due to its level of accuracy especially for
complicated geometries. To illustrate the simulation procedure the finite element method has be
The diagram of the 2D Einite element model for the pin-pivot assembly is shown in Figure
2-3. As can be seen from the diagram, three kinds of elements have been used. The eight-node
quadrilateral elements were used to model the pin and the pivot. Three-node contact elements
were used to represent the contact surface. It is worth noting that the contact elements coat the
outer and inner surface of the pin and pivot, respectively. It should also be noted that the contact
element do not add any new nodes to the model. Instead, the nodes of the quadrilateral elements
that appear on the surface make up contact elements. The third type of element that was used is
the link (truss) elements. This element was used to prevent rigid body motion (RBM). It was
mentioned earlier that the pin is Eixed from translating but allowed to rotate in a controlled
manner. Specifically the rotation is allowed only once the finite element analysis has been
completed. This means that the pin will not experience RBM. The pivot, however, is Eixed along
its lower edge to prevent any horizontal translations as well as rotation in any axis but is allowed
to translate in the vertical direction. This is also the direction of loading as is shown in Figure 2-
1. There is thus a potential for RBM to occur. The link element is used to eliminate this
possibility. The effect of the link element is reduced by assigning it a very small elastic modulus.
Geometry Update Procedure
The process of geometry update is necessary in order to correctly simulate and predict the
wear occurring at the contact interface. Indeed material removal changes the contact surface and
causes a redistribution of the contact pressure resulting from the contact. These changes can only
be captured if the surface is altered through a geometry update. Estimation of wear through an
extrapolation which is based on the original surface has been shown to produce erroneous
predictions . It is therefore becoming as standard, as is evident in the literature [1-2, 17-19,
25, 29, and 3 1], that geometry updates are included in the process of wear simulation.
The procedure proposed to update the geometry in this research involves two steps. These
steps are outlined below:
* Determine the normal direction (vector) of the contact surface at the location of each
surface node (contact node).
* Shift the position of the surface nodes in the direction of the normal vector by an amount
equal to the wear increment.
The normal direction of the surface nodes at the location of the contact nodes can be
obtained by considering the locations of the contact elements. The contact elements at the
surface have three nodes each. This element is illustrated in Figure 2-4. The corresponding shape
functions for this element may be written as follows:
N, = (t -1) t
N2 = -(t -1)(t +1) (2-8)
N3 = ~(t +1) t
where t is the local coordinate parameter. The surface of an element can then be described in
terms of the nodal coordinates and as a function of the local coordinate. The expression for the
surface is given in Eq. 2-9.
Tx N 0 N, ON,O x1 ,X
y 0 N, O N, O Ni y,-9
where xk and yk are the coordinates of node k (k = 1, 2, 3 )for the element of interest. If the
vector tangent to the surface (contact element surface) is denoted as vt then its value for the
element can be obtained as follows:
vt = -i+ j+0 k (2-10)
where the partial differentials is given in Eq. 2-11 or 2-12.
dt dt dt dt x,
Sy 8N, 8N, dN, y,
0 0 0
dt dt dt dt Ix,
dt ,= t
dt ,= dt
The vector normal (v ) to the surface (depicted in Figure 2-4) can be expressed as a cross
product of the tangent vector ( v,) and the vector perpendicular to the plane of the surface
(v, = (0, 0,1)). This cross product is expressed in Eq. 2-13.where n2 denotes the node number.
von=tn p. (2-13)
The resulting unit normal vector then appears as follows:
(y 8x .
v = t Bt(2-14)
ax"t I B9'tl
vo,n = vnorm~x,ni + vnorm~y,nj (2-15)
where v and v are the components of the vector normal to the surface. Once the
contact pressure distribution and normal vectors at all the nodes on the surface have been
determined, the geometry can then be updated. The update is done by moving the surface nodes
in the direction of the unit normal vector. The coordinate of the new node position at any step of
any cycle can be written as follows:
n,2, n,2 1, n Lz norm~x,n .(2 -16 )
n,, n,-,Jnr x,n
The process of the geometry update is shown in Figure 2-5. In this diagram the wear depth
is grossly exaggerated to illustrate the concept. The procedure for the geometry update has been
used successfully in the wear-simulation process. A possible problem that could be encountered
during model updates is mesh distortion. In the pin-pivot model, mesh distortion during model
update is minimized through a carefully created finite element model. The FE model is initially
created in such a way that all normal vectors at surface nodes, before any update is performed,
will be in a direction parallel to the element edge. This idea is illustrated in Figure 2-6. After
several geometry updates it can be expected that the vector will no longer be parallel to the edge.
The deviation is however small to be of any maj or consequence.
The procedure discussed was used to predict the wear occurring at the interface of the
pin-pivot assembly. Although this was a specific problem, the general framework outlined can be
extended and used to predict wear in other 2D oscillatory contact problems.
< I l l i f i I I /~ ,
.1II Ir ~ I II PiVOt
Pressure .-]... Pi ..1~ 111 0th
Figure 2-1. Oscillatory contact for a pin-pivot assembly.
Figure 2-2. Wear simulation flow chart for the 'step update' procedure.
8-n~ade t:~ ':;i-:-l i
Figure 2-3. Pin-pivot finite element model.
Figure 2-4. A three-node contact element used to represent the contact surface.
Figure 2-5. Geometry updates process.
Figure 2-6. Surface normal vector for the pin-pivot assembly prior to update
The procedure discussed in Chapter 2 provides a way to simulate the wear resulting from
oscillatory contacts. However, the process can be quite expensive. For instance, if one desires to
simulate 100,000 oscillatory cycles for a case in which each cycle is discretized into 10 steps
then 1,000,000 finite element analyses (nonlinear) as well as geometry updates would be
required. Clearly this may not be practical and the need for techniques to combat the
computational cost becomes immediately apparent. Techniques to tackle the problem of
computational costs will be discussed in the current and following Chapters.
Extrapolations have been used in various forms with the goal of reducing computational
costs. In this work an extrapolation factor ( A) is used to proj ect the wear depth at a particular
cycle to that of several hundreds of cycles. Essentially, the extrapolation is the total number of
cycles for which extrapolation is desired. Thus according to this definition, the extrapolation
factor can only take on positive integers values.
The equation used to determine the amount of wear at a particular node during any step in
a cycle was expressed in Chapter 2 as;
Equation 3-1 can be modified slightly in order to incorporate an extrapolation factor. It is
first noted that the first term on the right hand side (R.H. S.) of Eq. 3-1 refers to the cumulative
wear depth from previous cycles whereas the last term refers to the incremental wear depth at the
current step and cycle. As way to minimize computational costs, it is assumed that the next A "
cycles (as many cycles as the value of the extrapolation) will have the same amount of wear
depth as that of the current step and cycle. The total incremental wear depth for those many
cycles may then be obtained by multiplying last term of Eq. 3-1 with the extrapolation factor.
The resulting expression is shown in the following equation:
hn,l,J+A hn,2-,l, + kApl~n~s, (3 -2)
Utilizing the same concept, a new expression can be written to describe the position of the
contact nodes during the wear-simulation process. This expression is as follows:
yn,l,J+A n,21, norm x,n 3)
Extrapolation and stability. As may be expected, the level of accuracy of the wear
simulation is reduced when extrapolations are used. This is directly related to the assumption that
the same value of incremental wear depth is maintained for several cycles. This is, however, not
the case since in reality the geometry would constantly evolve which in turn would lead to a
continuous redistribution of the contact pressure and thus a change in the incremental wear depth
at each cycle. However the difference is small enough that it may be neglected as is evident from
the overall error of simulation results.
Use of extrapolations may also cause problems in simulation stability. Here stability is
defined with regard to the contact pressure distribution and hence the wear profile. An ideally
stable wear simulation would be defined as one in which the contact pressure distribution
remained smooth (with no sharp or sudden changes in the distribution) for the entire duration of
the simulation. It is however unlikely to have smooth pressure distribution throughout the
simulation process. As a result a more relaxed definition of stability is adopted where by sudden
changes in the pressure distribution are allowed to occur. In Figure 3-1A, the contact pressure is
seen to vary smoothly over the contact region except for small peaks at the contact edges. The
peaks are attributed to the transition form a region of contact to a region of no contact. This
transition occurs at a point which can not be represented by a discrete model. The result is that
there is an abrupt change in the surface curvature which causes high pressure. If such contact
pressure distribution is maintained through out the simulation, the simulation can be referred to
as stable. On the contrary, the diagram in Figure 3-1B is representative of contact pressure
distribution that would constitute an unstable wear simulation. The two diagrams show the
contact pressure distribution for a stable and unstable wear simulation consistent with the
adopted definition of stability.
When very large extrapolation sizes are used, wavy pressure distributions (Figure 3-1B)
are observed and the simulation becomes unstable. The shift to instability due to the use of large
extrapolation sizes can be explained as follows. The contact pressure distribution (obtained from
the finite element analysis) is generally not perfectly smooth. This may be due to the
discretization error stemming form the finite element analysis. The use of an extrapolation factor
magnifies these imperfections so that when the geometry is updated the contact surface
smoothness is reduced. If large extrapolation sizes are used, the regions that experience high
contact pressure in a particular step of the simulation are worn out excessively so that in the
following step these regions experience little or no contact. On the other hand, the regions that
did not experience high contact pressure will be worn out less and thus will experience greater
contact pressure in the next step. This behavior will repeat in subsequent steps causing the
surface to become increasingly unsmooth. The simulation will then become unstable. If,
however, smaller extrapolation sizes are used the wearing process acts as an optimizer to
smoothen the surface.
A smooth contact surface is critical for two reasons. The first reason is that a smooth
contact surface is consistent with the actual case that is being simulated, and the second is that a
non-smooth surface would affect the solution of the finite element problem. Due to these
reasons, a condition is placed on the selection of the extrapolation size such that the selected size
would not severely affect the smoothness of the pressure distribution.
Extrapolations provide a solution to the computational cost problem but as has been
discussed its use may introduce other problems. The accuracy and stability of the simulation may
be jeopardized by using extrapolation sizes that are too large. Using small extrapolation sizes
will produce more reliable solutions but will result in a less than optimum use of resources. It
may also be argued that even if an appropriate extrapolation size was selected at the beginning of
the simulation it may be that at a different stage of the simulation a different extrapolation size
would be required to provide optimum use of the available resources. In the next subsection a
procedure is described that seeks for the largest extrapolation sized while maintaining stability
during the entire simulation process.
Adaptive Extrapolation Scheme
The adaptive extrapolation technique is an idea proposed as an alternative to the constant
extrapolation scheme. The idea behind it is to seek for the largest extrapolation size while
maintaining a state of stability (smooth pressure distribution) throughout the simulation process.
The scheme is a three-step process. In the first part an initial extrapolation size ( A,) is selected.
The selection is based on experience.
In the second part of the adaptive extrapolation scheme, a stability check is performed. A
single check, preferably at the center step of the cycle, is sufficient for an entire cycle. The
stability check involves monitoring the contact pressure distribution within an element for all
elements on the contact surface. This essentially translates to monitoring the local pressure
variation. If the contact pressure difference within an element is found to exceed a stated critical
pressure difference Apont then a state of instability is noted and vice versa. In the final step of the
adaptive scheme, the extrapolation size is altered based on the result of the stability check. That
is, the extrapolation size is increased for the stable case and a decrease for the unstable case. This
process can be summarized as follows:
SAi i + MAmr if Apele < Apcnt
A = (3-4)
It must be mentioned that in order to maintain consistency in the geometry update as well
as in the 'bookkeeping' of the number of simulated cycles, a single extrapolation size must be
maintained through out a cycle. That is, every step in a cycle will have the same extrapolation
size while different cycles may have different extrapolation sizes. Figure 3-2 shows a graph of
the extrapolation history for the oscillating pin-pivot assembly. From the graph, it can be seen
that the extrapolation took on a conservative initial value of about 3900 and increased steadily up
to the 12th cycle (actual computer cycles not considering the extrapolations). Thereafter the
extrapolation size oscillated about a mean of about 6000.
The use of extrapolations is an efficient way to cut down on computational costs. Even
though no way of accounting for the error involved has been developed, the results observed
from simulation runs have shown acceptable error ranges. An adaptive extrapolation scheme was
proposed to govern the selection of the extrapolation size during the simulation. The scheme
ensures that the largest allowable extrapolation size is used during the simulation. The scheme
thus provides for a way to minimize computational costs while maintaining a stable simulation.
Extrapolation Vs Cycles (E=207Gpa & Pivot thikness t=19mm)
5 10 15 20 25
30 35 40
Figure 3-2. Extrapolation history for a pin-pivot assembly.
Figure 3-1. Contact pressure distribution on a pin-pivot assembly. A) The case of a stable wear
simulation. B) The case of an unstable wear simulation.
PARALLEL COMPUTATION INT WEAR SIMULATION FOR OSCILLATORY CONTACTS
Although the use of extrapolations is probably the most effective way to reduce the
computational costs, other ways are also available. A parallel processing implementation of the
simulation procedure is proposed as an additional way to remedy the problem of computational
costs. This technique may be used in conjunction with the extrapolation scheme to further reduce
computational costs. The discussion of parallel computation will be preceded by an introduction
to the concept of 'cycle-update and intermediate cycle-update' which are central ideas in the
parallel computation procedure.
Cycle- and Intermediate Cycle-Update
The wear-simulation procedure that was discussed earlier was termed as the 'step-updated'
for the reason that geometry updates were preformed after every step. An alternative to the step
update procedure would be to exclude all geometry updates during the entire cycle and perform a
single update at the end of the cycle. We term this procedure as the 'cycle-update'. The cycle-
update is a modification of the step-update where updates are performed at the end of each
step/analysis. For the cycle-update, information from each analysis performed at each step is
stored and later used to update the model at the end of the cycle. The equation for the wear depth
at the contact interface for the cycle-update is expressed as follows;
h2,J+A -h,,,_z+Ml C pl_,,s;, (4-1)
where n step is the total number of steps in a cycle. All other terms are as defined previously.
The cycle-update procedure can be summarized in the flowchart shown in Figure 4-1.
It should be noted that in both the cycle- and step-update techniques, the material
removal is discrete which is at variance with the actual process of wear in which the material
removal is continuous. The situation is, however, worse for the cycle-update since the frequency
of material removal is much less than in the step-update procedure. The step-update therefore has
a closer resemblance to the to the actual wear process. It would therefore be expected that the use
of the cycle-update procedure in wear simulations would yield less reliable results in comparison
to the step-update counterpart. Indeed this is what is observed when the procedure is tested.
More specifically the smoothness of contact pressure distribution during the simulation is
severely affected by the cycle-update than is by the step-update. A simplified explanation for this
phenomenon is that the step-update, performed at each step, closely captures intermediate
geometry changes within a cycle and hence the contact between two mating surface is
approximately conforming throughout the simulation. The result is that the pressure distribution
remains reasonably smooth. In the case of the cycle-update, the geometry is updated once in an
entire cycle. This dose not allow for the contacting surface to evolve smoothly throughout the
cycle and hence resulting in a less conforming contact between the mating surfaces. In this case
the pressure distribution would be less smooth, putting the accuracy of the results to question.
Although the cycle-update technique may yield less than accurate results, the technique
may still be used with caution. A general observation can be made regarding the accuracy when
using the cycle-update procedure. It has been observed that for a fixed extrapolation size, as the
total sliding distance covered through a complete cycle increases, the smoothness of the pressure
distribution is affected and hence the stability and accuracy of the simulation. Based on the
observation, a critical sliding distance so, is defined which if exceed, during sliding, geometry
update must be performed. Determination of the critical sliding distance is unnecessary since
short simulation runs can determine if the cycle-update is the appropriate produce. Thus the
mention of the critical sliding distance is purely for academic reasons rather than for practical
reasons. It is concluded that the cycle-update is best suited for cases in which the total oscillation
angle is small so that the sliding distance in a single cycle is less than sent .
In the event that the total sliding distance for a complete cycle is larger than sent we may
still take advantage of the idea behind cycle-update procedure. Instead of performing a single
update at the end of the cycle we may perform several equally spaced updates within the cycle.
This can be considered to be a hybrid of the step- and cycle-update procedure and the name
intermediate cycle-update is used for the procedure. The advantage of this idea is that the number
of updates in a cycle is reduced without affecting the stability of the simulation. The intermediate
cycle-update procedure can be summarized as is shown in Figure 4-2.
Computers may be configured to operate in parallel mode with the advantage that results
can be produced at a quicker rate. The idea proposed as a cost cutting means is a direct parallel
implementation of the cycle-update and the intermediate cycle-update procedures. Since the
implementation of the two procedures is similar, only the parallel implementation of the cycle-
update is discussed.
The cycle-update procedure is centered on the idea that no update is performed on the
geometry during the entire cycle. This means that all the analysis performed at each step within a
cycle is done on same geometry. The difference between any two analyses within a cycle is the
angle at with the two bodies contact during the analysis. This information may be exploited to
construct the parallel computation equivalent of the wear-simulation procedure.
The parallel implementation works as follows. Several processors are dedicated to the
wear analysis simulation. One of these processors is assigned the duty of a master processor.
This will be the processor responsible for distributing tasks to other processors as well as
consolidating the results from other process. The remaining processors will be the slave
processors. Each of the processors, both slave and master processors, will represent a particular
step within a cycle. In the beginning of any cycle, the appropriate model of the assembly to be
analyzed for wear is fed into the master processor. The master processor then distributes the
same model to the remaining processors. The master processor also allocates contact angles
(each slave will have a different contact angle corresponds to a specific step in the cycle) and
corresponding analysis conditions to each of the slave processors. At this point the master
processor instructs the slave processor to solve their corresponding contact problem. Once the
analysis in the different slave processors is done the master node collects the results and
computes the wear amount for that cycle. The model geometry is then undated and thereafter a
new cycle commences. The parallel implementation of the cycle-update procedure is
summarized in the flowchart shown in Figure 4-3.
From the flowchart it can be seen that considerable amount of time is saved by using the
parallel computational in comparison to the cycle-updating procedures. If the number of
processors available is equivalent to the number of steps selected for a cycle, then the time
required to complete a single cycle while using the parallel procedure is approximately equal to
the time required to complete a single step in the step and cycle updating procedures.
Figure 4-1. Wear simulation flow chart for the 'cycle-update' procedure.
Figure 4-2. Wear simulation flow chart for the 'intermediate cycle-update' procedure.
Solve Contact problem
(Obtain Contact Pressure)
Step 1 Step 2 Step 3 ..
Figure 4-3. Wear simulation flow chart for the parallel implementation of the 'cycle-update'
A simulation program was written in order to execute the wear-simulation procedure that
has been discussed in Chapters 2-4. The programming language used was "C" and the Finite
Element Analysis software used was Ansys. Ansys Parametric Design Language (APDL) was
used to write the commands necessary for the analysis. It should be mentioned that the choice of
language and software for this task, was based on convenience rather than limitation. Other
languages and analysis software may be used. In this Chapter the basic structure of the program
will be discussed.
Wear-Simulation Program Format
The wear-simulation program is composed of two parts. The first part of the program is a
C-program responsible for managing the simulation process and the second part is an Ansys
analysis input file, written in APDL, consisting of a set of commands related to the finite element
analysis. There exists an interaction between the two programs in which information is
exchanged. The interaction is managed by the C-program. A representation of the interaction is
shown in Figure 5-1. These two parts will be discussed in the following subsections.
Ansys Input Code
The Ansys input code is composed of a set of commands necessary to perform an analysis
on the finite element model and output analysis results. The input code has two main functions
which include performing contact analysis and extracting results from the analysis. These will be
discussed in the following sub sections.
When the simulation program is launched, the C- program invokes Ansys and the Ansys
input code is read. This will be the beginning of a step within the current cycle. The C-program
also sends information to Ansys which will be read-in by the input file. This information may
include the orientation of the oscillating body, the current step and cycle. Based on the
information from the C-program, the input file instructs Ansys to read-in the corresponding
model (the model is in a file format with extension "CDB") and prepare it for analysis. The
preparation includes reorienting the oscillating body into a position consistent with the current
step. Any gaps occurring due to wear in the previous step are also closed. This essentially means
that contact is established between the bodies before the analysis begins. This is a necessary step
since any gap may result in rigid body motion (RBM). At this point, the input code instructs
Ansys to solve the contact problem.
Output of results
The solution of the contact problem yield an enormous amount of information, most of
which is not of interest in the wear problem. The second task of the input code is to extract the
necessary information for the wear analysis. Specifically, the contact pressure at each node is
extracted from the contact analysis results. The input code also extracts the coordinates of the
contact node and computes the normal vector at each contact node. This information is required
for the model update.
The data extracted from the analysis as well as the model is written onto a text file in a
predefined format that is readable by the C-program. Creating the text output file serves as the
end of the step. Ansys software then shuts down and the C-program resumes command. A
summary of the work done by the input code is shown in Figure 2-2.
Simulation Managing Code
The other part of the wear-simulation program, written in C, act as the simulation manager.
The codes' main functions are to coordinating all the analysis performed by Ansys as well as
performing the wear calculations.
Once the simulation program is launched the C-program reads in a set of user defined
parameters that describe the desired simulation. These parameters include information such as
the value of the wear coefficient, the number of steps per cycle, the total cycles to be simulated
and the oscillation amplitude. The C-program then invokes Ansys, as describe in the previous
section, and stays dormant until the contact analysis is done. Results from the contact analysis
stored in the text output file are then read in by the C-program. Stability check and extrapolation
modifications are then performed as was outlined in Chapter 2. The wear rule is then applied.
This determines the amount of wear increment at each node consistent with the contact pressure
form the analysis and the wear coefficient. Base on the incremental wear depth geometry update
is updated and a data file in text format is created. Information such as the contact node number
and the corresponding contact pressure and wear depth are appended to the file as the simulation
progresses. At this stage a cycle is completed and a new cycle commences. The structure of the
simulation program is depicted in Figure 5-3.
rsesults to C-fle~
Figure 5-2. Function of the Ansys input code.
Su~pply analdysis inafo.
e. g Chrrent cycle, stp etc
Cont~act Prs. NoJrmdal direction. etc.
-Stability C control
-Up date Ge ometry
-Create Data File
... .. +0.
- I- *:1. I-'lls
.1 I rj I
-1..:.n .:1 anal 1:
-E::Ir .:IF e:- 11:
-1 i.:.rnail clare.:1l.:.n il.:
Figure 5-1. Interaction between the C code and the Ansys input code.
Info fromb C0-}le ~
... .I ..
.~ ~ ~
..~ :. :
r ~. ..?.
-- CDB F)1 -
in Fe *. us .E-E Fl e
Figure 5-3. Structure of the wear-simulation program.
EXPERIMENTAL VALIDATION OF THE WEAR-SIMULATION PROCEDURE
Probably the most convincing way to validate the results of a simulation is to compare
them against those from an actual experiment. In this work the simulation procedure is validated
by comparing simulation results to results from a wear tests performed on an oscillating pin in
pivot assembly. The simulation procedure is then used to simulate the wear occurring at the pin
j points of a backhoe (construction equipment). The effect of wear on the performance of the
backhoe is then demonstrated.
The wear simulation is validated through a comparison of simulation and test results. The
wear test consisted of a fixed steel pin inside an un-lubricated oscillating steel pivot. The pivot
was set to oscillate with amplitude of 30 and was loaded in the direction of its shoulder as shown
in Figure 6-1. The resulting pressure at the cross-sectional of the pivot was 601VPa. The pressure
was kept approximately constant through out the test. A total number of 408,000 cycles were
completed during the test to yield a maximum wear depth of about 2mm. It should be noted, for
the sake of comparison, that the definition of the test cycles is different from that of the
simulation cycles. Here a test cycle is defined as a complete rotation from one extreme to the
other and then back to the starting position (in this case -30 to 30 and back to -30). The test
information is summarized in Table 6-1 for convenience.
Three simulation experiments were performed to mimic the actual tests performed on the
pin and pivot assembly. The three simulations experiments were as follows:
* step-updating procedure
* intermediate cycle-update procedure
*parallel implementation of the intermediate cycle-update procedure
All three simulation tests were performed with the model shown in Figure 6-1. A wear
coefficient of 1.0 x 105 mm3/Nm (typical on un-lubricated steel on steel contact) was used. This
value is obtained from pin-on-disk tests results reported by Kim et al. . In all three cases the
cycles were discretized into 10 steps. Both the step- and intermediate cycle-updating simulation
tests were performed on the same computer (for time comparison), however, the parallel
implementation was performed on a parallel cluster. The following is a brief discussion of these
simulation test and the corresponding results.
Step-Update Simulation Test
The step updating simulation test was performed with oscillation amplitude and loading
identical to that of the actual wear test. The simulation test was run for 100,000 cycles
(considering the extrapolation). The simulation test parameters are summarized in Table 6-2
below. In Figure 6-2, the history of wear for the pin and pivot nodes that experienced the most
wear is shown. From the figure, a transient and steady state wear regime can be identified as
discussed by Yang et al. .
The transient wear regime corresponds to the beginning of the simulation until the
contact between the pin and the pivot is conforming. Thereafter the wear transitions to the steady
state wear regime. The steady state wear regime in marked by an interesting phenomenon where
by the contact pressure distribution is observed to be approximately constant over the region of
contact. This is in contrast to the transient wear regime during which a range of contact pressure
values is observed over the contact region. This concept is illustrated in Figure 6-3.
Within the steady state wear regime, the wear is approximately linear with respect to the
cycles as can be seen in Figure 6-2. This information may be exploited to determine the wear on
the maximum wear nodes after 408,000 cycles. Noting that one test cycle has twice the sliding
distance in comparison to that of the simulation test, an extrapolation within the steady state can
be made to predict the wear depth at the 408,000th cycle. The expression for the predicted wear
depth is a follows;
h =21 (hm hFer[ ~,m ) e~st"'" m, hJ (6-1)
where, h is the predicted wear depth, ns,,, and ns,,,z are the total simulated cycles at two points
within the steady state regime whereas hFhi and h,, are the corresponding simulate wear
depths at these cycles. In this equation the experiment test cycles is denoted by neest .
A value of 1.867mm was predicted as the maximum wear depth on the pin. Although this
value underestimates the wear depth it is a reasonable prediction considering that the wear
phenomenon is a complex process. The variation of the extrapolation size is depicted in Figure 6-
4. The simulation took approximately 206 minutes.
Intermediate Cycle-Update: Parallel Computation
The Intermediate cycle-update procedure and its parallel implementation were performed
with the same parameter values as were used in the step-updating procedure (see Table 6-2).
However, in this procedure, the update was performed after every 3 steps so that 3 updates were
performed in each cycle. This is in contrast to the step-update procedure where 10 updates were
performed, one at the end of every step. The result for the intermediate cycle-update and the
corresponding parallel implementation are identical. The plot of the wear on the pin and pivot
nodes that experience the most wear is shown in Figure 6-5.
A maximum wear depth (on the pin) of 1.854mm was obtained from the intermediate
cycle-update procedure and its parallel implementation. A plot of the extrapolation during the
analysis is shown in Figure 6-6. A simulation time of 450 minutes was noted for the intermediate
cycle update procedure. This is slightly more than twice the time it took to complete the step-
update simulation test. This time difference can be explained by examining the extrapolation
history plots (Figure 6-4 and Figure 6-6) for the two procedures. The average extrapolation for
the step update is slightly greater than twice that of the intermediate cycle update procedure. This
is because the step update is a more stable procedure than the intermediate cycle updating
procedure. The stable characteristic of the step update allows for the use of larger extrapolation
and thus few simulations cycles are required to predict the wear depth. In the present case, only
19 cycles were required to complete the step-update simulation test whereas 49 cycles were
required to complete the intermediate cycle update simulation test. The parallel implementation
of the intermediate update procedure only took approximately 13 5 minutes to complete. Clearly
this procedure provides a time advantage. A comparison of the results form the simulation tests
and the actual tests are shown in Table 6-3.
The discussion in this Chapter focused on validating the wear-simulation procedure that
was presented previously. The validation is done by comparing the results from the simulation to
that of an experimental counterpart. The wear occurring at the contact interface of an oscillation
pin-pivot assembly was simulated. The predicted wear depth deviated from the actual
experimental wear depth by approximately 7%. Even though this deviation appears to be large
the predicted results is able to give a good insight into the wear occurring at the interface.
Indeed like any other approximation technique, errors are inherent. A number of factors
contribute to this discrepancy including the wear model, which is not an exact representation of
wear and the finite element analysis, which is an approximation technique.
Another contributor is the wear coefficient. The wear coefficient is obtained
experimentally and as was mentioned has a large scatter. Errors in the wear coefficient
considerably affect the results of the simulation. For instance, if instead a wear coefficient of
1.2 x 105 mm3/Nm WaS used the new predicted wear depth would be 2.028mm. The new wear
coefficient, which is still within the range of scatter according to Kim et al. , has a deviation
of about 1.4% from the experimental value. This is indeed a large improvement from the
previous predictions. It is thus concluded that even though the procedure does not accurately
predict the wear the results obtained are of the correct order of magnitude and can be used for
Table 6-1. Wear test information for the pin and pivot assembly.
Test Parameters Values
Oscillation amplitude 30
Load (cross-sectional pressure) 60MPa
Test condition Un-lubricated steel on steel
Total cycles 408,000
Max wear depth on pin ~2.00mm
Table 6-2. Simulation parameters for the pin in pivot simulation test.
Simulation Parameters Value
Oscillation amplitude 30
Load (cross-sectional pressure) 60MPa
Wear coefficient (k) 1.0 x105 mm3/Nm
Total cycles 100,000
Steps per cycle 10
Table 6-3. Comparison of results form the simulation tests and actual wear tests for the pin in
Max. wear depth Simulation
(pin) (mm) time (min.)
Actual test 2.000 --
Step update 1.867 206
Inter. cycle update 1.854 450
Parallel 1.854 135
* acillation Pin
01 23 4 5
6 7 8 9 10
Figure 6-2. Cumulative maximum wear on pin and pivot.
Pressure A-long Pivot WVidth
Figure 6-1. Pin-pivot assembly for the wear test.
Wear on pin & pint (Step Update)
I I I I I
Figure 6-3. Contact pressure distribution on the pin and pivot during wear analysis. A) Contact
pressure distribution in the transient wear regime. A range of pressure values is
observed. B) Contact pressure distribution within the steady wear regime. The
pressure distribution is approximately constant over the region of contact.
Extrapolation History (Step Update)
6000 - -- -
5000 L -
0 2 468 0
14 16 18 20
Figure 6-4. Extrapolation history plot for the step updating simulation procedure.
Wear on pin & pint (Inter. Cycle Update)
1 23 4 5
6 7 8 9 10
Figure 6-5. Cumulative maximum wear on pin and pivot for the intermediate cycle updating
procedure and the parallel implementation.
Extrapolation History (Intermediate Cycle Update)
0 5 10 15 20 25 30
35 40 45 50
Figure 6-6. Extrapolation history plot for the intermediate cycle update procedure and its
WEAR-SIMULATION EXAMPLE: ESTIMATION OF BACKHOE BUCKET TIP
In Chapter 6, the wear-simulation procedure for oscillatory contact was validated through
experiments. It was found that the method can reasonably predict wear occurring at such
interfaces as long as accurate wear coefficients are obtained. In this Chapter, the usefulness of
the procedure will be demonstrated through an example. The example involves determining the
erroneous displacement at the tip of construction equipment due to wear at various joints.
Estimation of Tip Displacement
A backhoe system will be used to demonstrate how the simulation procedure can aid in
determining the effect of wear on the performance of a system. The system is a part of a
construction vehicle used in excavation work. The particular backhoe system to be used in this
example consists of three maj or parts (boom, dipper and bucket) as shown in Figure 7-1. The
sy stem consists of three j points; two connect the three parts together while the third one connects
the backhoe system to the vehicle (not shown in Figure 7-1). Each j oint consists of two
components that are in contact and experience relative oscillatory motion when the backhoe
undergoes a cycle of digging and loading. The contact at these joints can be considered as
oscillatory and as may be expected, large amounts of wear occur at these j points. The goal in this
example is to estimate the amount of control of the bucket tip that is lost due to wear at these
j points. The loss in control is quantified as the magnitude of the unwanted bucket tip displacement
that occurs when the backhoe is rotated about the rotation axis. The tip displacement is shown in
The diagram in Figure 7-2 shows a pivot j oint before and after wear has occurred. In
Figure 7-2A diagram no wear has occurred and the pin sits snugly in the pivot hole. In such a
case the tip displacement is negligible. However, once wear has occurred at the j points, the pin is
able to rotate through an angle as shown in Figure 7-2B. This kind of rotation propagates through
all three j oint and eventually causes a bucket tip displacement. The magnitude of the tip
displacement is dependent on the amount of wear.
In this example the tip displacement will be obtained assuming that the backhoe has been
in operation for a period of one year. This corresponds to a total of 90,000 cycles of digging and
loading dirt. This is obtained by assuming that the backhoe executed 60 cycles an hour, 5 hours a
day for 300 days in a year. The tip displacement is obtained by first determining the amount of
wear at each of the j points. In this case the j points are represented by a pin and pivot assembly
similar to that used in the previous Chapters. The loading at each j oint is taken to be constant
throughout the entire cycle. A list of the loads applied at each pivot is shown in Table 7-1. Also
listed in Table 7-1, are the oscillation amplitudes of the each pin at each their corresponding
joint. It is worth noting that an assumption is made that no other factors contribute to the tip
displacement and that the initial tip displacement is zero.
The three joint are assumed to be made of steel and that no lubricant is used. A wear
coefficient with a value of 1.0 x105 mm3/Nm is thus used in the analysis. This choice is
consistent with experiments performed by Kim et al. . A wear analysis is performed on all
the joints for the specified parameters. Only 52440 cycles are simulated and the final results are
linearly extrapolated. The wear depth at the j points obtained from the simulation is shown as a
function of the cycles in Figure 7-3. It can be seen from Table 7-2 that the wear on j oint 3 is
greatest. This is consistent with the fact the oscillation amplitude for the third j oint is the largest.
The maximum wear depth on the pin and pivot at 20,000 cycles and the extrapolated wear depths
at 90,000 cycles for the three j points are reported in Table 7-2. The wear depth at 90,000 cycles is
used to determine the bucket tip displacements of all the component parts from the centerline.
The component displacements as well as the overall backhoe tip displacement are listed in Table
7-3 and are depicted in Figure 7-4.
A maximum bucket tip displacement of 149mm is estimated. This can be interpreted as the
additional distance, from the desired position, that the bucket tip will travel be for coming to a
halt when the backhoe is rotated.
The value of the simulation procedure was demonstrated through an example in which the
erroneous bucket tip displacement, attributed to wear, for a backhoe system was estimated.
Although the input values for the backhoe system and thus the tip displacements are not from an
existing case, the example demonstrates how the performance of a system can be affected by
wear and how the simulation procedure can aid in quantifying the loss in performance.
Boom OBM~ 1.6880 LBMC 73.64
Dipper GD 0.4260 LD 55.34
Bucket GjBU 0.4320 LBU 20.00
Tip displacement 148.98mm
Table 7-1. List of loads and relative rotation angles at the joints of the backhoe.
Load (MPa) Oscillation amplitude
Joint 1 10.75 -150 to 150
Joint 2 10.40 -22.50 to 22.50
Joint 3 12.15 -350 to 350
Table 7-2. Summary of the wear depth at the j points after 20,000 cycles as well as the
extrapolated wear depth at 90,000cycles
Initial diameter Wear depth at e dp a
(mm) 90000 cycles (mm)
Pin Pivot Pin Pivot Pin Pivot
Joint 1 74.47 75.44 0.114 0.128 0.516 0.576
Joint 2 75.13 76.11 0.139 0.168 0.626 0.758
Joint 3 54.48 55.19 0.161 0.216 0.724 0.974
Displacement of the boom component parts from the center line.
Figure 7-1. Pin-pivot assembly for the wear test.
Figure 7-2. Joint consisting of a pin and pivot: A) Joint before wear has occurred on both
components. B) Joint after wear has occurred on both components.
Wear on Pmn & P~vot (Joint 1)
U 05 1 15 2 25 3 35 4 45 5 55
cycles x 104
Wear on P n & Pivot (Joint 2)
105 115 225 335 445 555
cycles x 104
Wear on Pmn & Plvot (Joint 3)
10 05 1 16 2 26 3 36 4 45 6 55
cycles x 104
Figure 7-3. Wear on the pin and pivot at the backhoe Joints. A) Wear at j oint 1. B) Wear at joint
2. C) Wear at j oint 3.
Center lirne ----
Figure 7-4. Backhoe component displacement from the vehicle centerline.
The obj ectives in this work were two fold. One goal was to develop a wear-simulation
procedure to predict wear occurring on bodies experiencing oscillatory contact. The second goal
was to incorporate into the wear procedure, techniques that would minimize the associated
computational costs of the simulation process while ensuring stability through out the simulation
The wear-prediction procedure was developed based on a modified form of Archard' s wear
law. It involves determining wear at incremental steps within a cycle for the total number of
cycles to be simulated. At the end of every step the geometry is updated to reflect the evolution
of the surface and thus account for changing contact conditions. This update procedure, termed
as step update, is a more stable procedure than the cycle and intermediate cycle update
procedures in which updates are delayed to the end of the cycle or after several steps have been
Two techniques were proposed to minimize the computational costs of the simulation. The
first technique was an incorporation of an adaptive extrapolation scheme into the wear-prediction
procedure. The purpose of scheme was to optimize the selection of the extrapolation factor for
the best use of the available resources while ensuring stability in the simulation.
The second technique is a parallel implementation of the cycle and intermediate update
procedures. With no parallel implementation, step update approach is computationally cheaper
than the intermediate cycle update procedure. The reason for this is that the intermediate cycle-
update procedure is a less stable procedure (due to the reduced number of geometry updates in a
cycle) and thus requiring the use of smaller extrapolation sizes. This results in a longer
simulation time. When parallel computation is used, the intermediate cycle update procedure is a
cheaper alternative in terms of computational cost. It is deduced that in the absence of parallel
computing resources, the most reasonable simulation procedure to use is the step-updating
procedure where as the intermediate cycle updating procedure is best when parallel computing is
In the simulation validation process, it was found that the wear depth on the pin predicted
by the simulation procedure was under predicted but within a reasonable range. This under
prediction is largely attributed to the wear coefficient used. The wear model used is a
phenomenological model in which the wear coefficient is determined through experiments.
Hence an inaccuracy in this coefficient has a great effect on the prediction process as was shown
in Chapter 6. Based on the results it is concluded that the procedure is a reasonable way to
predict wear on bodies experiencing oscillatory contact
RECOMMENDATIONS FOR FUTURE WORK
The wear-prediction procedure presented in this work provides a way to determine the
wear occurring on bodies that experience oscillatory contacts. In the procedure, the changing
contact condition or evolving surface was accounted for by updating the surface as the
simulation progressed. This ensured for a more realistic simulation of the wear process.
The prediction process can be made even more realistic by considering how the wear
affects the kinematics and dynamics of a system and in turn how the kinematics and dynamics of
the system affects the wear process. In mechanisms, once wear has occurred at connection, the
initial paths through with components of the mechanism travel are no longer preserved. The
loads involved may also be affected. These changes occur due to the gap or change in geometry
that is introduced at the connections as wear occurs. It should also be noted that the changes in
the motion of the components, as well as the loading, will affect the wear process.
The procedure that has been presented is an idealized case in which the changing system
does not affect the wear process and vice versa. Essentially wear predicted by isolating the
region in which the wear occurs and thus neglecting any changes that the wear would have on
the overall system. A recommendation for future work is to study the effect of a continuously
changing system (changing due to wear) on the wear process itself.
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Saad Mukras was born in Nairobi, Kenya. He was raised in Nairobi and partially in
Gaborone, Botswana, where he completed his secondary education. He then j oined University of
Botswana and then transferred to Embry Riddle Aeronautical University in Daytona Beach,
Florida. There, he studied aircraft engineering technology and received his bachelor' s degree in
2003. He then j oined the University of Florida to pursue a master' s degree in mechanical
engineering in 2004. He worked under the supervision of Dr. Nam-Ho Kim, completing several
research proj ects, earning his masters degree in 2006.