Astm stp 1105 1991

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Tribological Modeling for

Mechanical Designers

Kenneth C Ludema and Raymond G Bayer, editors

As M

1916 Race Street Philadelphia, PA 19103

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T r i b o ] o g i c a ] m o d e l i n g f o r m e c h a n i c a l d e s i g n e r s / K e n n e t h C Ludema Raymond G B a y e r , e d i t o r s

(STP ; 1105)

P a p e r s from a symposium h e l d in San F r a n c i s c o on May 2 3 , 1990,

s p o n s o r e d by ASTM C o m m i t t e e G-2 on Near and E r o s i o n

I n c ] u d e s b i b l l o g r a o h i c a ] r e f e r e n c e s and i n d e x e s

ISBN 0 - 8 0 3 1 - 1 4 1 2 - 5

1 T r i b o ] o g y - - R a t h e m a t i c a l m o d e l s - - C o n g r e s s e s

G-2 on E r o s i o n and Wear I V S e r i e s : ASTH s p e c i a l

t e c h n i c a l

9 1 - 8 2 3 8 CIP

No part of this publication may be reproduced, stored in a retrieval system, or transmitted,

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N O T E The Society is not responsible, as a body, for the statements and opinions advanced in this publication

Peer Review Policy

Each paper published in this volume was evaluated by three peer reviewers The authors addressed all o f the reviewers' comments to the satisfaction of both the technical editor(s) and the A S T M Committee on Publications

The quality o f the papers in this publication reflects not only the obvious efforts o f the authors and the technical editor(s), but also the work of these peer reviewers The A S T M Committee on Publications acknowledges with appreciation their dedication and contribution o f time and effort on behalf of ASTM

Printed in Baltimore October 1991

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This publication, Tribological Modeling for Mechanical Designers, contains papers pre-

sented at the symposium of the same name held in San Francisco, CA on 23 May 1990 The

symposium was sponsored by ASTM Committee G-2 on Wear and Erosion Professor Ken-

neth C Ludema of the University of Michigan in Ann Arbor, MI and Raymond G Bayer of

IBM in Endicott, NY presided as symposium chairmen and are editors of the resulting

publication

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Overview K c LUDEMA AND R G BAYER

WHAT MECHANICAL DESIGNERS NEED IN TRIBOLOGICAL MODELING

Comments on Engineering Needs and W e a r M o d e l s - - R G BAYER

Design of Plain Bearings for Heavy M a c h i n e r y - - w A GLAESER

WHAT IS AVAILABLE IN TRIBOLOGICAL MODELS

(MOSTLY FOR WEAR) The Structure of Erosive Wear M o d e l s - - s BAHADUR

Success and Failure of Simple Models for Abrasive W e a r - - J LARSEN-BASSE

Wear by Chemical Reactions in Friction Contacts J L LAUER

Tribological Models for Solid/Solid Contact: Missing L i n k s - - s L RICE AND

F A MOSLEHY

DATA BASE AND SIMULATION ISSUES FOR TRIBOLOGICAL MODELING

Friction in Machine Design K G BUDINSKI

Considerations on Data Requirements for Tribological Modeling A w RUFF

Classification of Metallic Materials from a Viewpoint of Their Antiwear

Behavior T SASADA

W e a r Transition Surfaces for Long-Term Wear E f f e c t s - - c s YUST

PRINCIPLES OF MODEL MAKING AND USE

IS Modeling in Tribology a Useful Activity? J R BARBER

Wear Modeling: How Far Can We Get With Principles? M GODET,

Y BERTHIER, J LANCASTER, AND L VINCENT

Cultural Impediments for Practical Modeling of Wear Rates K C LUDEMA

vii

3 t2

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Purpose

The symposium for which the following papers were written was organized out of the recognition that those tens of thousands of mechanical designers who design consumer products need far better information than they now have when they design mechanical components for wear life They have equations (tables, graphs, guidelines, etc.) for the analysis of stresses, for vibration modes and natural frequencies, for rates of heating and cooling, and for most other phenomena - but very little for the wear life

of products

The needs of designers may best be seen in the dichotomy between the mechanical sophistication of machines and devices, and the fact that these devices are most often discarded because of mechanical wear Tribological adequacy seems to be one of the last considerations in the design process

if it is explored at all, and probably for good reason - it is very complicated Tribological design requires knowledge of materials (including lubricants), surface making processes, running-in procedures and assembly procedures The designer is handicapped because neither friction nor wear are intrinsic properties of material in any form, but rather are highly dependent on the mechanical system and how it is run Most designers have been caught in attempting to upgrade products only to find that the new product fails too often Some then attempt a test program, only to find that there is no correlation between test results and the functioning of production items

Proaress in wear modeling

The impetus for developing useful information on the wear properties of material comes mostly from those in research, referred to here as research tribologists Their first priority Is to maintain research activities and write scholarly papers By the nature of their work tribologists select relatively impractical materials and experimental parameters, and interact mostly with others who do the same However, some tribological concepts have diffused into general design practice The most common are equations for designing fluid film bearings Further mature concepts have made their way into the design of rolling element bearings, belts, gears, pumps, etc such that predictions can easily be made of functional product life Whereas many mechanical devises can be built up with such components, many consumer products can not, because they must sell at the lowest cost The majority of designers are connected with consumer products

This is the third symposium on modeling for wear resistance, each with different sponsors The first was held at Columbia University in New York City, December 17-19, 1986 (1) and the second was held at Argonne National Laboratories (2) These were attended mostly by researchers, and

by invitation These were serious efforts and much good information was exchanged It may be seen from the proceedings of these symposia that each of the specialties in tribology communicates in very different and esoteric language, compared with the needs of designers

vii

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how the great chasm between research language and designers needs could be bridged Perhaps the extent of the chasm may be seen in that only two authors from industry submitted papers The great majority of the papers were written by research tribologists The latter were written from the perspective of a physicist, a chemist, several in materials engineering,

on specialist in solid mechanics and five mechanical engineers The latter are "near" the design process, but do not often design consumer products

Overview of the papers of the symposium

To a great extent the authors report that they have a long way to reach in order to reach designers Designers have an equally long reach, but they have no better idea than do research tribologists which direction to reach Our authors made a valiant effort to propel us toward sensible wear models Most authors agreed on the nature of the problem and some offered specific improvements in the understanding of wear In particular, some of the points made were the following, with editorial comment:

1 Research papers in tribology contain information that is rarely applicable to practical problems The reasons may include:

a Terminology is a major point of confusion in the field This is probably a consequence of the presence of several very different academic disciplines in the field

b Research papers focus on very few of the operating variables and phenomena in real machines that control wear Research papers range from the "near applied" to the fundamental, the latter often from the point of view of the atomic and molecular structure through the sliding interphase region

c Attempts to harmonize the methods in the various specialized areas in tribology are largely philosophical and not well directed

d Research results as presented seem to imply that the dual phenomena of friction and wear are uncoupled from each other and from considerations of the mechanical properties of the machinery holding the sliding pairs

e Research results rarely provide information on the changes that occur at interfaces (debris formation and migration, eg.) over time

2 The greatest advances in tribology have been made in capital products and machinery that are expected to last for a long time The design of consumer products involves minimum cost for material and manufacture, which involves variables (surface roughness, materials variation, etc.) that have been inadequately studied

3 Several wear models do exist but these are extremely limited in scope and applicability Unfortunately, the limits of applicability of these models are rarely published In fact, the literature would suggest, by virtue of the lack of comment, that the available models are universal

in application This is particularly misleading in designing weal" tests when only those variables that appear in simple models are thought to

be the controlling variables in all sliding systems

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decade This is so because it is not reasonable to expect the many relevant and disparate variables in wear to be rationalized in the next decade, whether in the form of broadly applicable equations, models, algorithms or handbook entries The same applies to wear tests as well as to the selection of materials

The empirical method includes:

a Gathering data from practical sliding elements over a reasonable range of controllable variables The entire system, including the machinery surrounding the sliding surfaces, must be thoroughly characterized

b A data base of research results, for equally well characterized laboratory systems should be (and is being) gathered

c Bench wear tests should be done but only after the results of the bench test are known to correlate very well with the results from the practical system being simulated

d Special attention should be paid to wear debris and other residue

- the manner in which sliding systems retain or flush out debris, which will depend on, among other things, specimen shape, vibration characteristics and duty cycles Efforts should be made

to trace the chemical and mechanical "pathways" by which the debris and residue was formed, transformed or ejected

A significant fraction the efforts of research tribologists should be devoted to such empirical work

Overall, tribology is seen to be a very broad and complicated topic There is a major problem in communication across the field which should

be addressed in the next decade Research tribologists should devote some of their efforts to making their results useful, but designers should indicate what they need from research tribologists Many more symposia

on wear modeling must be held

1 Approaches to Modeling of Friction and Wear, Proc Workshop on the Use of Surface Deformation Models to Predict Tribology Behavior , Eds FF Ling and C.H.T Pan, Springer-Verlag

2 Proc of the International Workshop on Wear Modeling, June 16 and 17,

1988, Eds, F.A Nichols, A.I Michaels and L Northcutt,

DOE-Conf.-8806370, June 19,1989)

Ken Ludema University of Michigan, G.G Brown Building Ann Arbor, MI 48109-2125

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COMMENTS ON E N G I N E E R I N G NEEDS AND WEAR MODELS

and Wear Models, = Tribolo~ical Modelin~ for Mechanical

Philadelphia, 1991

tribological considerations other than the ranking and

assessment of the, significance of a variety of design

parameters, determination of tolerances for these parameters,

these are illustrated in terms of actual situations

encountered by the author, along with the methods used to

such applications of tribology are identified, and current

approaches in wear modeling and wear testing are compared to

differences between a material engineering and a more general

design approach to engineering problems are identified, and

the significance of these in terms of modeling ~ n d testing

are discussed

prediction, wear transitions

INTRODUCTION

The subject of wear models is one of current and perhaps perennial

More recently there have been informal and formal meetings sponsored by

various technical and governmental agencies of wear models (1,2,3)

This volume on the proceedings of ASTM's Symposium on Tribological

Modeling for Mechanical Designers reflects the current interest in this

engineers regarding wear models, a variety of meanings for the term

"wear model" can be found along with a v a r i e t y of expectations for

Raymond G Bayer is a senior engineer at International Business

co-chairman for this year's Symposium on Tribological Modeling for

M e c h a n i c a l Designers

C o p y r i g h t 9 1991 b y A S T M I n t e r n a t i o n a l w w w a s t m o r g

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models In some cases a p h e n o m e n o l o g i c a l description of the w e a r

r e l a t i o n s h i p for a p h y s i c a l mechanism Still in others it is

specifically a q u a n t i t a t i v e r e l a t i o n s h i p b e t w e e n design parameters and

description of w e a r behavior and a resulting set of design guidelines

is interesting to note that these concepts of w h a t constitutes a wear

example, an empirical p h y s i c a l scientist would tend to the first

interpretation A t h e o r e t i c i a n w o u l d t e n d to think in terms of the

second, while with a cut-and-dry engineer the last i n t e r p r e t a t i o n might

be found

The uses of or expectations from a m o d e l also v a r y with the type of

involvement with tribology With the f u n d a m e n t a l i s t the u n d e r s t a n d i n g

the mechanical or design engineer the m o d e l should provide guidance in

scientists, on the other hand, w o u l d expect a m o d e l to guide them

either in the selection or the development of materials by p r o v i d i n g an

u n d e r s t a n d i n g of the m a t e r i a l parameters which affect wear behavior

These observations imply that in any discussion of wear m o d e l i n g it

is appropriate to identify from w h o s e p e r s p e c t i v e the subject is being

the p e r s p e c t i v e will be from a mechanical design engineer who wants a

model to relate wear performance in his a p p l i c a t i o n to design

variations in the uses of models or the type of model required, there

g e n e r a l aspect of this type of u s e of m o d e l s w i l l be illustrated in

state of tribology and t r i b o l o g i c a l m o d e l i n g will then be reviewed w i t h

the r e l a t i o n s h i p of wear testing to these needs and m o d e l i n g also will

be made Then, in c o n c l u s i o n ~ s o m e suggestions for future w o r k and

m o d e l i n g development will be made

E N G I N E E R I N G A P P L I C A T I O N

A case study involving a p r i n t e d circuit edge connector system c a n

be used to illustrate the type of concerns w i t h wear that can arise in

are composed of two or more e l e c t r o p l a t e d layers, the outermost layer

being Au or some other noble metal to resist corrosion and p r o v i d e

exposure of the base metal, which w o u l d allow corrosion to take place

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METALIZEDI

LAYER

INSERTION/EXTRACTION

CONTACT SPRINGS

Figure 1 View of Card Edge Connector System

Motions Due to Vibration Can Occur in A n y Direction

M e t a l i z e d layer consisted of a surface layer of Au or Pd-Ni

In the original a p p l i c a t i o n of this connector system, the only source

of relative motion b e t w e e n the tab and the spring was during insertion

the tab during the engagement of the contact is a design feature

range of the load b e t w e e n spring and tab u s e d in the design is also

the contact system was expected to experience only several dozen c a r d

insertions and actuations over life, wear evaluations were handled

As frequently happens in an industrial environment, an additional

used increased by a p p r o x i m a t e l y seven times from those considered in

relative m o t i o n b e t w e e n the tab and the spring during shipping and

m a c h i n e o p e r a t i o n h a d to be considered In fact, some vibration

testing with actual hardware showed v e r y q u i c k l y that not only could

such motions occur but that they could also p r o d u c e a significant

questions, such as the following:

How m u c h m o t i o n can the p r e s e n t design tolerate?

How m u c h improvement in the w e a r resistance is needed?

What improvement will different m e t a l l u r g i e s provide?

How does insertion w e a r interact w i t h v i b r a t i o n wear?

Is lubrication adequate for the vibration situation?

Is there a better lubricant?

What are the effects of design tolerances on this wear?

Do the v i b r a t i o n tests u s e d in c o m p a n y q u a l i f i c a t i o n s p r o v i d e

adequate simulation of this type of wear?

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r e s u l t i n g data In t h e s e tests, loads r a n g e d f r o m 125 to 250 gm;

cycles, 1 to i0~; s t r o k e length, 35 to 6 ~m; r e p e t i t i o n rate,

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hi

Ki = ( D N i ) 2 pn

Figure 2 Method for D e t e r m i n i n g Wear Coefficient

In the design situation, the general advantage of this type of

model and associated data is that d e v e l o p m e n t time is reduced, h a r d w a r e

cost for tests with prototypes or in simulations is reduced, various

design options and needs can be addressed analytically, and wear

considerations can be factored into the design process at the

beginning, not after hardware is built and tested

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This specific example illustrates some of the general features

1 - a completely defined analytical e x p r e s s i o n relating wear to design

parameters and application factors; 2 - a data base for material wear

with the advances in computational and evaluation capability, e.g., FEM

and CAD techniques, this is p r o b a b l y not a necessary requirement

W E A R T H E O R Y AND M O D E L S

To the designer, the ideal situation w o u l d be to be able to go

directly to some reference source, e.g data base, book, or expert

system, and find the engineering model that is applicable to the

specific situation, along with relevant data for different materials

The next best situation is that the designer can contact tribologists,

w h o in turn can identify the needed model, or perhaps reduce a more

general m o d e l to this specific case, and identify the associated data

p r o v i d e d a n a l y t i c a l l y with, perhaps, some short, simple wear tests to

either the designer or the tribologist finds when this is attempted

In the wear literature and information, some engineering types of

the more specific models the range of a p p l i c a b i l i t y appears limited and

specific information related to engineering models, there is

considerable information available regarding wear p h e n o m e n a and wear

are not directly relatable to an application for a variety of reasons

For example, the conditions of the wear test associated with the

information could be significantly different than the condition in the

p h e n o m e n o l o g i c a l l y oriented, or the q u a n t i t a t i v e data taken may be

the information is frequently not addressed nor is the relevance of

descriptive and some are c h a r a c t e r i z e d by analytical relationships

However, their relationships to design parameters are u s u a l l y not

out that wear is a system property; that there are many mechanisms b y

which materials wear; that there are transitions in wear behavior; that

the individual wear mechanisms can exist in parallel and interact in a

sequential, as well as in a parallel, manner

This complex, confusing (to the non-tribologist), and often

incomplete condition of wear knowledge typically results in the

tribologists p e r f o r m i n g a study, which involves testing, to develop or

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select the model and the needed data base Occasionally, one does find

the desired model and data in the literature, but this is rare

For engineering needs, the model should focus on the operative

design elements, which are the loading, motion, geometry and

types of devices, like cam followers, gears, journal bearings, or more

general models, such as small amplitude sliding wear, or rolling wear

Models for wear mechanisms, such as adhesive wear, abrasive wear, or

surface fatigue wear, are not p a r t i c u l a r l y useful unless the engineer

there is the need to develop quantitative, analytical models for wear

engineering models which focus on applications and design parameters

The former models can provide the b u i l d i n g blocks and elements of the

etc., of the individual physical wear m e c h a n i s m s have to be studied in

combine differently under dry and lubricated sliding? under low and

debated as to whether or not it is adequate to treat wear as a "black

approach, some knowledge and information relative to the p h e n o m e n a

occurring has to be factored into the development of such a model

With any of these models, the engineering needs also require that

the range of a p p l i c a b i l i t y of these models and associated wear

coefficients be p r o v i d e d so that the appropriate m o d e l and values can

supporting that m o d e l is needed, as well as s o m e test m e t h o d which can

provide such data

WEAR TESTS AND M O D E L I N G

As indicated in the above comments on the development of

engineering models, wear testing cannot be separated from wear

p r o c e d u r e s used for the determination o f the wear coefficients used in

indicates that appropriate testing is required to develop valid models

The testing is needed to identify and characterize the wear p h e n o m e n a

involved and the influence of various factors on the wear and to v e r i f y

that is performed is p h e n o m e n o l o g i c a l in nature and b i a s e d towards

testing should be done completely enough and in a sufficiently

quantitative fashion that w o u l d allow the formation of analytical

expressions for wear in terms of the p a r a m e t e r s of the test and p r o v i d e

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to be extended to s p e c i f i c a l l y address design parameters For example,

the effects of shape or size are not u s u a l l y addressed in current tests

b u t have to be a d d r e s s e d in e n g i n e e r i n g models

The m a j o r i t y of the standard tests and test procedures u s e d today

are generally aimed at p r o v i d i n g a single number to evaluate materials

are run to a region of stable w e a r b e h a v i o r before data is obtained,

m o r e fundamental type, is done in regimes or under conditions which do

fundamental studies under dry conditions or at high w e a r rates

Contrary to this, m o s t applications u t i l i z e lubrication and m a n y can

p e r i o d of these tests can correspond to the m a j o r p o r t i o n of the useful

w e a r life, e.g., where failure is associated with a few mils of wear

One m a j o r change in wear testing that is needed to support

e n g i n e e r i n g m o d e l development is the generation, use, and reporting of

wear curves which plot wear as a function of the amount of sliding,

attempt to u n d e r s t a n d and q u a n t i f y all aspects of the test, not just

b e h a v i o r in the p e r i o d of stable wear behavior, or of m a t e r i a l

properties The w e a r test c o n f i g u r a t i o n itself can be viewed as a

u n d e r s t a n d and q u a n t i f y the total wear p e r f o r m a n c e of the two members

in the test is equivalent to b e i n g able to u n d e r s t a n d and quantify w e a r

control w i t h the application

S U M M A R Y A N D R E C O M M E N D A T I O N S

W e a r models for engineering purposes need to account for all the

design parameters, not just m a t e r i a l parameters, and be addressed to

addition, ranges of a p p l i c a b i l i t y of the m o d e l should be provided, as

m e t h o d should also be p r o v i d e d so that value of w e a r parameters needed

for that model can be determined when they're not available in a data

parameters, the development of p h y s i c a l models for w e a r p h e n o m e n a and

mechanisms are essential b u i l d i n g blocks for these higher level models

The development of engineering models is an achievable goal

There are examples in the literature d e m o n s t r a t i n g this, b u t these

on a g r a n d e r scale requires some changes in wear research and study

M o r e emphasis has to be p l a c e d on q u a n t i f y i n g w e a r behavior; the

i d e n t i f i c a t i o n of parameters affecting various p h e n o m e n a and transition

need to be identified; boundaries for the o c c u r r e n c e of these need to

be established; there needs to be a change in w e a r testing practices,

m a k i n g it less materials o r i e n t e d and m o r e system-oriented

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REFERENCES

Prediction in Mechanical Components, G M Research

Laboratory, Warren, MI, 1/22-23/85

Deformation Models to Predict Tribologies Behavior, Columbia Univ., NY, NY, 12/17-19/86

on Wear Modeling, Argonne National Laboratory, Argonne, IL, 6/16-17/88

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DESIGN OF PLAIN BEARINGS FOR HEAVY MACHINERY

Machinery," Tribolo~ical Modeling for Mechanical Designers,

ASTM STP 1105, K C Ludema and R G Bayer, Eds., American

Society for Testing and Materials, Philadelphia, 1991

ABSTRACT: A design system for heavily loaded, slow

moving, grease lubricated plain bearings has been

developed The system is based on frictional input and

dissipation analysis combined with experimental data P-V

design charts have been developed which show regions of

high f r i c t i o n , excessive bearing temperature, high wear,

and moderate wear The information presented in the

design charts compares well with f u l l bearing test

results

KEYWORDS: Plain bearings, bearing design charts,

P-V c r i t e r i a , bronze bearings, wear, f r i c t i o n

INTRODUCTION

Heavily loaded, slow moving (usually grease lubricated) plain

bearings are a class of bearings that perform within rather narrow

limits and make an ideal subject for modeling Construction

machinery such as back hoes, graders, bulldozers, and cranes use

numbers of these bearings Mining machinery such as drag lines,

hoists, and power shovels also have many grease lubricated plain

bearings

The bearings, often made of bronze, cover a size range of from

2 inches O.D to as much as 12 inches O.D Typical bearing loads

are 1,500 to 5,000 psi (bearing stress, based on projected bearing

area) Sliding speeds are 10 to 50 fpm I t is assumed that the

bearings operate under boundary lubricated conditions and a

lubricated wear process eventually causes wear-out These bearings

are not cooled by lubricant flow used on pressure-lubricated

hydrodynamic bearings Frictionally generated heat is dissipated

through the shafting and the bearing housing

William A Glaeser is a Research Leader at Battelle, 505 King

Avenue, Columbus, Ohio 43201-2693

12

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About 20 years ago, the bronze bearing industry initiated research to develop design methods for large, slow moving plain bearings Prior to that time there were no standards for design of this type of bearing Design was based on rule of thumb and

experience of the particular industry using them I t was f e l t that bearing design was overly conservative and that bronze plain

bearings were not being used as widely as they could be

To i n i t i a t e the program an extended series of bearing tests were conducted to determine operating characteristics over a wide range of load, speed, and bearing material combinations Data from these tests were intended to be used for the development of design charts for bearing designers

The method used to reduce bearing test data to a series of bearing design charts, combining both analytical and empirical

methods will be explained These data have since been reexamined and the significance of the P-V trend lines related to recent

efforts to model wear by the use of wear maps

Recent reduction of the design charts to a computer program will be discussed

a I/4 inch wall thickness

The test bearing was mounted in a steel link which was pinned

to a hydraulic loading system The link was held between two

support r o l l e r bearings as shown in Figure 2 The shaft was coupled

to a drive system with a variable speed prime mover

Operating conditions were as follows: [2]

10 to 200 rpm Leaded tin bronze (CDA 932) High leaded tin bronze (CDA 520) Aluminum bronze (CDA 954)

Tin bronze (no lead) (CDA 905) AISI 1045, Rc 30 ground and polished

Sun Oil Co Prestige 741EP grease

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X

/

3 / - Double "0" groove,

0.200 ~'010 ] \ (i0 ~m) / i-6 wide x T2 deep

(5.08 +_ 25 ram) ~ \ _ / (4.8 ram) (2.4 ram)

ooi.oo

IA F"

2.005+,0005 - - ~ (50.93 + 01 mm)

- 2.520 + 001

- .000 64.00 ! 03 mm)

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FIGURE 2 Large journal-bearing apparatus

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Operating limits for the bearings were explored by conducting a matrix of increasing load tests at constant rpm Failure was

detected as accelerating bearing temperature, excessive noise, and heavy wear

DEVELOPMENT OF A MODEL

I t was assumed that the principal mode of f a i l u r e would be overheating of the bearing and thermal degradation of the lubricant The absence of forced cooling in the system made this the most

l i k e l y f a i l u r e mode Since the bearings were subject to lubricated wear, wear-out was considered the ultimate f a i l u r e mode for a long

l i f e system Wear-out would be defined as a given increase in bearing clearance that would cause unacceptable degradation of a machine's performance This value would be decided by the designer

I f the designer required a particular l i f e for a bearing, the design program would give him the estimated wear in inches of material loss

amount of wear was tolerable A rather unsophisticated model could

be developed from this set of assumptions

Bearing operating temperature is a function of #PV where:

The operating limits of the bearing could be defined within the

PV bounds as a boundary locating a maximum allowable bearing

temperature and, secondly, a bearing pressure at zero sliding

velocity where compressive yield would occur

I t was assumed that the expression PV = K would be the

in Figure 3 The solid line in Figure 3 defines the PV = K trend line for a maximum bearing temperature of 350F (350 ~ F was selected for the grease used)

Bearing failure data have been added as data points in the

chart was limited to 60 fpm sliding velocity and 5,000 psi bearing

low bearing pressure begins to encroach on hydrodynamic lubrication, while the bearing pressure at which "burn out" occurs is too low to

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data points from bearing tests (Temp = 350 F)

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loads represented in this chart, i t was decided to forgo log - log

plotting system

I t was assumed that flash temperature might influence wear

cause desorbtion or vaporization of the boundary film at asperity

contacts, one might expect a jump in adhesive wear of the contacts

Since flash temperature is roughly proportional to P~V [3], a

c r i t i c a l flash temperature boundary might appear as shown in

Figure 4 The PV chart is now divided into three zones: overheat,

high wear, and moderate wear

Hiqh Friction Zone

I t was noted that f r i c t i o n data from the bearing experiments

appeared to f a l l into two regimes, high f r i c t i o n (#=0.1) and "low"

f r i c t i o n on the design chart was located with data from the

experiments and is shown in Figure 5 The two f r i c t i o n zones are

not as sharply divided as shown in Figure 5, but by locating these

zones in this way, i t was found that predicted bearing temperatures

l a t e r in the finished model were more accurate

Actual Maximum Temperature and Hiqh Wear Isotherms

When the experimental data for maximum operating temperature

were subjected to regression analysis, i t was found that the

boundaries for maximum allowable temperature and for high wear

followed the fuDction PV ~ = K The resulting chart is shown in

Figure 6 The data provided a more liberal area of safe operation

than might be expected for PV = K or the flash temperature criterion

for high wear This difference is i l l u s t r a t e d in Figure 7

I t is suggested that under boundary lubrication, the effect of

mixed film conditions that develop as the sliding velocity increases

may be more powerful than flash temperature in moderating wear

That is, as a thin film takes more of the load support from the

asperity contacts, f r i c t i o n will decrease and contact pressures

would be moderated

The data from experiments for four different bronzes (tin

bronze, leaded t i n bronze, high leaded t i n bronze, and aluminum

charts, taken from a bearing design handbook written on the basis of

bronzes containing lead appear to be more sensitive to increasing

sliding speed Since the lead-containing bronzes have lower thermal

conductivity than the nonleaded bronzes, this s e n s i t i v i t y to heat

generation associated with increases in sliding speed may be

attributed to the differences in thermal conductivity

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FIGURE 6 PV p l o t with zones corrected based on test data

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FIGURE 8 Bearing design charts for four different bronzes

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THE COMPUTER MODEL

Although the design charts are useful for the bearing designer,

they s t i l l require excessive time i f an i t e r a t i v e process is used

developed The objective of the program was to provide the designer

with bearing operating temperature, total wear, and power absorption

the designer to any o f f limits areas he might be operating in

These include high velocity, beyond the maximum allowable

advise the designer i f hydrodynamic lubrication were feasible

Provisions were also made for analyzing the effect of forced air

cooling of the bearing

In order to meet these requirements, i t was necessary to

develop an equation for estimating bearing operating temperature

developed by combining Crease's equations for heat transfer through

the bearing wail, heat transfer through the shaft and f r i c t i o n a l

= shaft diameter, inches

= equivalent housing diameter, inches (This is the diameter

which w i l l describe a circle with pillow block is the

distance from the top of the bearing cap to the bottom of the

pedestal)

= length of bearing, inches

= total length of shaft from the center of the bearing to the

free end, inches

= shaft, rpm

= load, Ib

= average coefficient of f r i c t i o n

coefficient is influenced by shaft size, velocity of air

moving over the bearing housing and the contribution of

range from 6 at one-inch diameter to 4 at about 10 inches)

housing inner area and outer area)

= thermal conductivity of bearing-housing combination (BTU/ft/F ~

a value of 30 is reasonable for most applications involving

cast iron or steel housings)

= dimensionless factor for shaft cooling (Depends on shaft

diameter)

The bearing size range covered by the three factors f, c, and h

in the equation is shown in Table i

C o p y r i g h t b y A S T M I n t ' l ( a l l r i g h t s r e s e r v e d ) ; T h u D e c 3 1 1 3 : 2 2 : 0 2 E S T 2 0 1 5

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TABLE I - - Range covered by heat transfer factors

Inches

The range shown for the heat transfer coefficient, h, is based on

computer program

One weakness in this analytical approach is the d i f f i c u l t y in

is no reliable model to predict f r i c t i o n coefficient, and f r i c t i o n

is influenced by many uncontrollable factors including the

equation, a PV plot was made for a boundary at 350~ Data from the

bearing tests were then entered into the chart; the results are

found The f r i c t i o n coefficients assigned to the high- and low-

f r i c t i o n zones in the PV charts appear to work f a i r l y well

Fortunately, under boundary lubrication conditions, the scatter in

f r i c t i o n coefficient values is not excessive, which should allow use

of the temperature-rise equation, with caution

Wear rate values were assigned to the various zones in the PV

charts The program was then developed to predict bearing

printout for the program is shown in Figure 10 The input is shown

in the numbered items ( l i f e , hr means the desired l i f e to be input

clearance, maximum bearing temperature, maximum temperature with air

cooling and power absorbed by the bearing,

This program has been exercised considerably over a wide range

been used in the solution of actual bearing problems, including

into the Copper Development Association Computer Aided Bearing

Design Program, [6] providing design systems for both hydrodynamic

and boundary lubricated bearings

DISCUSSION

The bearing design program has been developed by both

analytical and empirical means The i n i t i a l PV chart with the safe

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13 9 Experimental data points

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FIGURE 10 Printout for boundary lubricated bearing design program

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data revealed that the maximum temperature boundaries are more

l i k e l y to follow PV ~ = K Comparing the r e s u l t s with Ashby's wear

developed on the same p r i n c i p l e s he used in developing his well

known metal a l l o y deformation maps He has p l o t t e d on a normalized

P- normalized V chart zones r e l a t i n g to several wear modes including

o x i d a t i v e wear boundary by assuming asperity flash temperature as

conditions, asperity f r i c t i o n a l heating produce temperatures at

which oxidation is s u f f i c i e n t to change heat t r a n s f e r properties of

grease lubricated bearing performance data does not appear to follow

bearing accelerates surface chemical reactions with the l u b r i c a n t

providing a beneficial boundary f i l m

The above considerations have lead to the following suggested

PV modes of wear Under "dry wear" P~V = K may define the

transition to accelerated wear by flash temperature mechanisms

This condition provides the least margin for safe P-V operation

levels The next mode would be PV = K and may relate to the wear of

plastics or materials with low thermal conductivity and tendency to

soften when heated The t h i r d mode would be PV ~ = K and relates to

successful boundary lubrication and provides the largest margin for

safe P-V operation

REFERENCES

Glaeser, W.A., and Dufrane, K.F., Operating Limits of Heavily Loaded

Grease-Lubricated Cast Bronze Bearings, Lubrication Engineering, 31,

1975, pp 614-618

Glaeser, W.A., Wear Properties of Copper-Base Bearing Alloys,

Journal of Metals, Oct 1983, pp i-6

Kuhlmann-Wilsdorf, D., Demystifying Flash Temperatures, Materials

Science and Engineering, 93, 1978, pp 119-133

Glaeser, W.A., and Dufrane, K.F., The Design of Boundary Lubricated

Cast Bronze Bearings, Cast Bronze Bearing I n s t i t u t e and

International Copper Research Association, Inc., 1978

Crease, A.B., Heat Dissipation from Bearing Assemblies, Tribology

Handbook, edited by Neale, John Wiley Ltd., 1973

Copper Development Association Computer Aided Bearing Design

Program, Copper Development Association, Box 1840, Greenwich, CT,

Trang 37

(Mostly for Wear)

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THE STRUCTURE OF EROSIVE WEAR MODELS

Models," Tribological Modeling for Mechanical Designers,

ASTM STP 1105, K C Ludema and R G Bayer, Eds., American

Society for Testing and Materials, Philadelphia, 1991

complexity, the multiplicity of factors that affect the

erosion process are described and the effect of these

parameters in the context of erosion modeling is considered

The mechanisms of erosion that have led to the development

are based on the empirical approach while others are based

on the concepts such as cutting, low-cycle fatigue,

models is examined and the difficulty and limitations in

their application to practical erosive situations are

d i s c u s s e d The d i r e c t i o n s f o r f u t u r e work i n t h e c o n t e x t o f

modeling a r e p r o v i d e d S o m e s u g g e s t i o n s a r e made to a s s i s t

t h e d e s i g n e r s i n d e s i g n i n g a g a i n s t e r o s i o n ,

erosion variables, design for erosion

The mechanical removal of material as a result of the impact of

many engineering applications, erosion results in heavy expense by

limiting the efficiency of turbomachinery and the life of equipment

used in catalytic cracking of oil, coal transport lines, mining and

its economic significance, erosion has been studied extensively in

the past decade in the phenomenological sense but the efforts at

successful modeling of the process have been disappointing

The mechanisms of erosion caused by the impact of single particles

such as small spherical particles of a hard material are different for

impact damage causes radial and lateral cracks and the extent of

Dr Bahadur is Professor of Mechanical Engineering at Iowa State

University, Ames, Iowa 50011

33

C o p y r i g h t 9 1991 b y A S T M I n t e r n a t i o n a l w w w a s t m o r g

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radial fracture depends upon the toughness of target material and the velocity and size of ball [I I During indentation on soda-lime glass, Lawn and Swain [2] observed that the radial cracks were formed during loading of the indenter while unloading produced lateral cracks that

mechanisms identified during the impact of small spheres on ductile material are plastic deformation, work-hardening, flake formation and lip fragmentation [3,4] Single particle impact studies have helped considerably in understanding the mechanisms applied to multiple

similar mechanisms are applicable to erosion by both single particle

significant so that the interaction between oxidation and erosion

modeling is limited to ductile erosion under ambient conditions only

interaction between a sliding asperity and the crack present in the substrate for sliding wear or between the indentation of a particle

with the sequence of events producing an outcome and are based on evidence gathered by direct observation of the affected areas

Analytical models combine variables in the form of a mathematical expression and thus provide the basis for quantitative prediction

models that are useful for quantitative design

PHENOMENOLOGICAL MODEL FOR DUCTILE EROSION

The removal os material in the form of chips has commonly been

an irregularly-shaped impacting particle acts like a miniature

single-point tool and produces a deep scar in the surface, Finnie [5]

removal here occurs due to the displacement of a cutting particle and fracture is preceded by a large plastic strain [6] Narayan and Washburn [7] and Narayan [8] studied dislocations in single crystals

observed that the plastic damage was stored in the form of dislocation dipoles (two closely spaced dislocations of opposite sign) and was caused by shear cutting

It was later indicated [9-ii] that cutting was by no means the

in erosion revealed that material was extruded in the impact direction

as well as towards the sides forming fragile ridges which were damaged

impacts caused 'cutting r erosion while 'plowing' or deformation

the topographic features of craters and subsurface damage produced in

concluded that the impact craters were formed by~pIastic flow and displacement of material that produced an upward extrusion of the surface around the craters

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Kosel et al [14] examined the mechanisms of erosive wear in pure nickel and copper using scanning and transmission electron microscopy With angular AITO~ particles impacted under vacuum in a slinger type erosion test faEiIity, they noted the development of a cellular

and cutting types were found

Edington and Wright ]15] studied solid particle erosion of a

commercial alloy composed of brittle carbide phases in a ductile

erosion of the surface and (b) adhesion of the alumina particles to

rebounding from the surface was ruled out since the indented surface

evidence of plowing, lip removal by extrusion nor of particle

material loss in the ductile matrix with the possibility of very

indentations was held responsible for the removal of brittle carbide

rapid build-up of high dislocation density and deformation twins was observed in the surface layers but there was no evidence of local

heating at the point of impact in either the ductile matrix or the

brittle carbides

Smeltzer et al [6] studied the eroded surfaces of a number of

materials by scanning electron microscopy and concluded that melting

mate, the kinetic energy available per impacting particle was enough

to melt the volume of target material removed by it Two mechanisms

of material removal were proposed: melting of the surface in contact with an impacting particle followed by splattering of the molten

material; and bonding of solidified material to embedded particles

which in turn were removed by subsequent impacting particles

Winter and Hutchings [16] studied erosion mechanisms by impacting

certain orientations the particle penetrated deeply into the specimen displacing the material at the exit end of craters in the form of a

localized shear deformation in narrow bands in the crater lip which

the bands indicated that the deformation was large enough to produce

by Zener and Hollomon [17] Many other workers [18-20] have taken

scanning electron micrographs showing severe deformation and used it

as indirect evidence of target melting

From the above discussion, it will be noted that there are three

cutting, deformation, and localized melting and thus each can serve as

best controversial because the contradictions outnumber the evidence

because any surface eroded by fine particles shows evidence of both

Tiêu đề	Tribological Modeling for Mechanical Designers
Tác giả	Kenneth C Ludema, Raymond G Bayer
Trường học	University of Washington
Chuyên ngành	Mechanical Engineering
Thể loại	Special Technical Publication
Năm xuất bản	1991
Thành phố	Philadelphia

Định dạng
Số trang	188
Dung lượng	3,51 MB