Handbook of Lubrication Part 17 pdf

SYSTEMS ANALYSISHorst Czichos INTRODUCTION The foregoing chapters of the handbook have amply illustrated that there is a great range of technical systems to be lubricated as well as a gr

SYSTEMS ANALYSIS

Horst Czichos

INTRODUCTION The foregoing chapters of the handbook have amply illustrated that there is a great range

of technical systems to be lubricated as well as a great variety of tribological processes, i.e., contact, friction, lubrication, and wear processes, that occur in lubricated systems Whereas complex problems of this type have been solved in the past by isolating single events and treating these in terms of simplified cause-effect relationships, today a “multi-disciplinary” or “systems” approach is needed.1,2

The purpose of this chapter is to present an overall systems view which may help to systematize approaches to the solution of lubrication problems, taking into account the various influencing factors, processes, and parameters For more details the reader is referred to Reference 3, and References 4 to 7 provide examples of the general development and application of systems theory in contemporary science and technology

THE SYSTEM CONCEPT AND ITS APPLICATION TO TRIBOLOGY

General Considerations

As a starting point for an engineering systems approach to the analysis of tribological systems, consider a typical lubricated mechanical system, namely a gearbox The technical purpose of this system is to transform certain “inputs”, i.e., torque and angular velocity, into “outputs” The transformation occurs through the contact of gears, and as a consequence

of interactions of the gear teeth, friction and wear processes occur

Lubrication represents a deliberate attempt to avoid or reduce the effect of friction and wear upon a mechanical system A lubricant can also act, as it flows away, as a cooling agent removing heat from the location of the friction process If the sliding or rolling surfaces are completely separated by the action of a lubricant at all times, there may be no wear process In this event, the analysis is simplified (“no-wear model”) However, if in a lubricated slate there is some contact between surfaces or between boundary lubricants on the surfaces, the interfacial tribological processes are of paramount concern In such cases, the presence of a lubricant may complicate the analysis, partly because the reaction products present may be complex and difficult to characterize, and partly because transient conditions may be the major concern

The first step in a systems analysis is proper identification and isolation of the problem

As shown in Figure 1 for the example of a gearbox, the two partners (or the two “systems elements”) which form the tribologically interacting surfaces, i.e., gear 1 and gear 2, can

be hypothetically separated from their environment by the proper choice of a “system envelope” All components of the system are then by definition within this envelope and are part of the so-called internal “structure” of the system The structure consists of the elements (A) of the system, their relevant properties (P), and their interrelations (R), described formally by the set S = {A, P, R}

The “external” quantities which cross this system envelope from the outer world are the

“inputs” of operating variables, and the quantities which cross the system envelope from the inside are the “outputs” In other words, the inputs of the operating variables are transformed through the structure of the system into outputs which are used, the use-outputs Simultaneously, as a consequence of interactions between the elements, loss-outputs occur, denoted in summary by the terms friction and wear losses The way in which the inputs are transformed into outputs determines the technical function of the system

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FIGURE 2 Types of tribological systems.

Table 1 CLASSIFICATION OF TECHNICAL FUNCTIONS OF

TRIBOLOGICAL SYSTEMS

information by utilizing the motion of macroscopic bodies are steadily being replaced by devices in which there is little or no mechanical motion, for example the replacement of the mechanical clock by digital electronic clocks In other instances materials are not merely moved but also changed in state or form

In applying the system concept to other technical systems, e.g., electrical or electronic systems, the functional behavior of the system is often described in terms of mathematical input-output relations However, in attempting to apply the system concept to the subject

of tribology, a fundamental difference must be emphasized between the behavior and the functional description of electrical systems and mechanical systems in which friction and wear processes occur

Compare, for example, the behavior of an electrical transformer and a mechanical gearbox

At a first glance, the functional purpose of both systems appears to be analogous, i.e., to transform certain inputs — voltage and current in the electrical system, and angular velocity and torque in the mechanical system, respectively — into outputs used for technical purposes The function of both systems may be described formally as a transformation of the inputs into the outputs via a certain transfer function However, the dynamic performance of both systems is accompanied by perturbations In both systems, energy losses occur due to electromagnetic or frictional resistances The fundamental difference between the behavior

of the electrical and mechanical systems originates from their different “structure” The structure of the electrical system generally remains constant with time In this case, the transfer function can be worked out mathematically This has led to various applications of (he powerful systems engineering method of network theory and related methods charac-terizing functional behavior.8-10In the mechanical case, however, the structure of the system generally changes with time, through friction and wear This aspect, which is of great importance for the reliability of the system under question, is described in more detail later

Operating Variables

The most characteristic operating variable of a tribological system is the type of relative motion between tribo-element (1) and tribo-element (2) The basic types of motion are sliding, rolling, spin, and impact Every type of relative motion between system components can be expressed as a superposition of these four basic types of motion In addition to characterization of the type of motion, its dependence on time should be specified, being for example: continuous, oscillating, reciprocating, or intermittent

The other basic operating variables are the following quantities:

1 Load, FN

2 Velocity, v

3 Temperature, T

4 Distance of motion, s

5 Operating duration, t

For some tribological systems, these physical operating variables are accompanied by material inputs, e.g., flow rate of the lubricant Some disturbing inputs may also be present, e.g., vibration and radiation It may also be necessary to specify derived quantities, e.g., contact pressures, temperature gradients, etc

Structure of Tribological Systems

As described above, the structure of a tribological system is given by the system elements (the material components of the system), their relevant properties, and their interrelations described formally by the set S = {A, P, R}

648 CRC Handbook of Lubrication

FIGURE 3 Analysis of the structure of tribological systems.

Elements of the System, A = {a i}

If the system envelope is located as closely as possible around the “interacting surfaces

in relative motion”, four different basic elements are involved in the friction and wear processes in most tribological systems As illustrated in Figure 3 for a simple sliding system, the pair of interacting surfaces involving moving element (1) and stationary element (2) The other two basic elements are the lubricant (3) (if any) and the atmosphere (4) These main elements are linked to others or may be composed of subconstituents For example, element (3), the lubricant, may consist of a base oil and additives In Table 2 elementary elements or components (1), (2), (3), and (4) are listed as examples from every group of the basic tribological systems compiled in Table 1

Properties of the Elements, P = {P(a i )}

Behavior of any tribological system is influenced by many properties of the basic elements (1), (2), (3), and (4) Although the great variety of tribo-mechanical systems and tribological processes makes it difficult to provide a comprehensive general compilation, the following properties of the elements are of primary concern:

1 Properties of tribo-elements (1) and (2): these can be subdivided into “volume” and

“surface” properties Volume properties: geometry, chemical composition and me-tallurgical structure, elastic modulus, hardness, density, thermal conductivity Surface properties: surface roughness and surface composition

2 Properties of the lubricant (3): these may be classified into system-independent and system-dependent properties

3 Properties of the environmental atmosphere (4): primarily chemical composition and the amount and pressure of its components, especially water vapor

Interactions Between the System Elements, R = {R(a i ,a j )}

Tribological interactions between the elements of a mechanical system, i.e., the contact, friction, lubrication, and wear processes, are of paramount interest Figure 4 provides

sim-plified schematic diagrams for systems of increasing complexity, i.e., increasing number of interacting elements

In an ultrahigh vacuum, the simplest tribological system consists only of interacting partners (1) and (2) The main interactions are then covered by the terms contact deformation, surface fatigue, abrasion, and adhesion In air, these processes are supplemented by inter-actions with the atmosphere (4) Finally in a lubricated system, direct (contact) interinter-actions between moving and stationary elements are prevented or influenced through the different mechanisms of lubrication

Also, interactions between (4) and (3) with (1) and (2) should be taken into account For instance, the diffusion of atmospheric oxygen into the lubricant (4) → (3), followed by oxidation processes between the lubrication and the moving and stationary partners (3) → (1), (2), can distinctly influence the mechanisms of mixed and boundary lubrication

Tribological Characteristics

Characteristics that describe the dynamic changes of a lubricated mechanical system as a consequence of friction and wear processes may be divided into the following three groups: tribo-induced changes in the system structure, tribo-induced energy losses, and tribo-induced material losses

Depending on the processes within a lubricated mechanical system, the tribo-induced changes of a system structure (a) may concern:

1 Destruction or creation of elements, e.g., the degradation of a lubricant or, on the contrary, the creation of “frictional polymers”

2 Changes in properties of elements, for instance, changes in contact topography and surface composition

3 Changes in interrelations between elements, for instance, changes of wear mechanisms under the action of the operating variables, or changes in the lubrication mode

Friction-induced energy losses (b) and wear-induced materials losses (c) may be expressed formally as:

Friction losses = f (operating variables; system structure)

Wear losses = f (operating variables; system structure)

Consequently, friction coefficient, f, and wear rate, w, may be expressed formally as:

f = f (X;S) w = f (X;S) Although parameter groups X and S are not independent variables since they are connected with each other through the tribological interrelations R, the above symbolic representation

of friction and wear characteristics can be conveniently used as a starting point for application

of the system methodology From the above symbolic equations it follows that any systematic approach to the solution of a lubrication problem in a mechanical system must be based on the detailed knowledge of both the operating variables and the structure of the system

Influence of Tribological Processes on Structure, Function, and Reliability of Mechanical Systems

In the upper part of Figure 5, a typical tribological system, namely a gear box, is shown schematically As already described in Figure 1, the technical function of the system is to transform certain inputs, namely angular velocity and torque, into useful outputs via a certain transfer function

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In some cases, the failure rate λ(t) of a component in a system can be estimated from the point of view of the physical behavior of the material used.l3 Empirically, and sometimes theoretically, the following probabilities have been proposed:

Exponential Distribution

λ(t) = constant = C f(t) = C · exp (–Ct) R(t) = exp (–Ct)

In this case, the failure rate is constant It means physically that any failure occurs accidentally without any accumulation of fatigue-like effects during its service time Many kinds of electronic components follow this type of failure Components in a machine break down in this mode when the failure is brittle fracture

Rayleigh Distribution

λ(t) = Ct f(t) = Ct · exp (–Ct 2 /2)

In this case, the failure rate increases with time The constant C, indicates the rate of deterioration of the component which depends upon the stress level applied to it

Normal Distribution (Truncated)

f(t) = l/s(2π) 1/2 exp {– 1/2 (t –μ/s) 2 }

Many components of machines obey this distribution, especially if the failure occurs due

to wear processes The failure rate of this distribution cannot be expressed in a simple form

Weibull Distribution

This is a distribution with two parameters, to, the nominal life, and the constant C The distribution is found to represent failure of many kinds of mechanical systems, such as fatigue in ball bearings

Gamma Distribution

where Γ(x) is a gamma function This is also a distribution with two parameters Theoret-ically, the importance of this distribution is attributed to the equation being an x-fold

Table 3 PHENOMENA OF DETERIORATION AND MODE OF FAILURE

654 CRC Handbook of Lubrication

convolution of the exponential function It means physically that a component fails at the x-th shock which occurs as a Poisson statistical process

These are representative distributions which appear in the failure process of various components and systems As a general overview, Table 3 provides a compilation of the phenomena of deterioration and the mode of failure in connection with underlying physical processes.14

From the experimental determination of failure distribution curves conclusions may be drawn on the type of failure mechanism For most tribological systems failing as a conse-quence of wear processes, the failure behavior is characterized by the normal distribution

or the Weibull distribution Knowledge of the failure mode and the type of failure distribution can often be used to improve the reliability of the system For instance, this approach can

be used to select the type of ball or roller bearing system to operate under a given set of operating conditions with high operation safety.15,16 In this connection, the importance of lubrication technology on system reliability has been emphasized.17,18

To conclude the discussion on failure and reliability, the dependence of the failure rate

on the operating duration of a system should be considered If the failure rate is plotted as function of time, a unique “bathtub-curve” is often found, as shown in Figure 6 None of the distributions discussed above have this shape, but an approximation may be obtained

by selecting an appropriate probability density function for each of the three regimes.19 Regime (a) describes the region of the “infant death” of the system This regime is char-acterized by a decrease of the failure rate with time, for example with effective running-in Regime (b) of constant failure rate is the region of normal running Here, failure occurs as

a consequence of statistically independent factors Regime (c) is characterized by a rising failure rate which is the normal mode of wear-induced failure of mechanical systems Here, failure may be due to aging effects

Table 4 TRIBOLOGICAL SYSTEMS DATA SHEET APPLIED TO A JOURNAL BEARING

shortened, extended, or grouped in another order, in ail applications the total of the four groups of parameters compiled in Table 4 should be taken into account

Systematic Lubricant Selection Procedure

The system concept provides a guideline which may help to systematize the lubricant selection procedure Clearly, the systematic guideline can be only a rough skeleton which must be completed by using information from the preceding chapters From the system point

of view, in a lubricant selection procedure system-independent and system-dependent char-acteristics must be distinguished Typical charchar-acteristics falling in the system-independent

category are cost, availability, and physical and chemical properties such as chemical com-position, density, thermal conductivity, acidity, flash and fire point, pour point, etc

For the testing and specification of system-independent lubricant properties and charac-teristics, well-known tests have been worked out and standardized (This has been done, for instance, in the U.S by the American Society for Testing and Materials, (ASTM-D2),

in the U.K by the Institute of Petroleum, and in the Federal Republic of Germany by the Fachausschuβ Mineralöl und Brennstoffnormung in Deutschen Institut für Normung (FAM-DIN) The details of the various tests can be found in the official publications of these institutions and in other portions of this handbook

The system-dependent characteristics of lubricants depend essentially on the specifications

of the whole tribological system Thus, all of the systems characteristics described earlier must be taken into consideration, at least in principle, to make sure that no important operational aspect or influencing parameter has been overlooked

In contrast to the standardized tests for the system-independent physical and chemical properties of lubricants, the testing of system-dependent characteristics should be performed

in connection with the technical function of the actual tribo-engineering system in which the lubricant is used These tests assess predominantly the overall ability of a lubricant to permit rubbing surfaces to operate without scuffing, seizing, or other manifestation of material destruction This can be broadly classified in three groups.22

Simplified bench tests — These tests employ simplified test geometries leading to point,

line, or flat contact Most of these tests were devised to differentiate between EP and

non-EP oils, and their accuracy is sometimes not good enough to grade different levels of non-EP activity Erratic results can occur if operating variables (e.g., temperature of the lubricant) are not closely controlled Predicting the performance of lubricants on the basis of these tests alone is almost impossible On the other hand, they are convenient for acceptance testing, for production control, and as indicators of batch variations of lubricants

Testing with tribo-technical components — Because of the above shortcomings, a

different type of lubricant testing is required to permit control of as many variables as possible while simulating actual performance requirements A convenient way of doing this

is to test lubricants in the laboratory, where operating conditions can be controlled, with the parts under test being those used in the complete tribo-engineering unit

Full-scale tests — There is general agreement that the only satisfactory means of evaluating

the performance characteristics of lubricants is by full-scale tests of their actual use in tribo-engineering systems Since the cost of field or proving-ground tests is considerable, this type of testing is generally used only as final proof of the decisions made while developing the design of an actual tribo-engineering system

The systematic lubricant selection procedure may follow the “flow chart” as shown in

Table 5 From the technical function (A) of the mechanical system, it is often possible to make a preselection of the lubricant, i.e., to specify the “type” or “class” of the lubricant, e.g., gear oil or cutting fluid, etc

For the further specification of the lubricant, allowable ranges should be known for the operating variables (B), such as load FN (or pressure p), speed v, operating temperature T (including the friction-induced temperature rise ΔT), operating duration t, as well as the allowable limits of the tribological characteristic (C), such as friction coefficient, wear rate, and heat and vibration data

The structure of the system (D) determines the other system components which interact with the lubricant Material and surface properties of the other system components are to

be considered A crucial factor is an estimation of the tribological processes to be expected, i.e., contact conditions, interfacial friction and wear mechanisms, and the prevailing lubri-cation mode

In addition to the dependent parameters from the groups (A) to (D), the

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