Friction and Lubrication in Mechanical Design Episode 2 Part 2 docx

The formula for determination off at heavy contact loads from more than 10,000 experiments is found to be: uo = kinematic viscosity of the lubricant cst at the mean surface V, = sum rol

Rolling/ Sliding Contacts 255

which suggests that the elasticity of the rollers causes the minimum film thickness to increase by approximately 100 times

Dowson and coworkers [4, 61 approached the problem from first prin- ciples and simultaneously solved the elasticity and the Reynolds equations Their formula for the minimum film thickness is given in a dimensionless form as:

Using the same dimensionless groups suggested by Dowson and Higginson

[4], the Grubin solution can be given as:

H = 1.95 7 ( Gu)0.73

(7.6)

What is particularly significant in the EHD theory is the very low depen- dency of the minimum film thickness on load The important parameters influencing the generation of the fdm are the rolling speed, the effective radius of curvature and the oil viscosity Consequently, Dowson and Higginson suggested the following simplified formula for practical use:

where

ho = minimum film thickness (in.)

qo = inlet oil viscosity (poise)

Re = effective radius (in.)

U = rolling speed (in./sec)

7.4 FRICTION IN THE ELASTOHYDRODYNAMIC REGIME

The EHD lubrication theory developed over the last 50 years has been remarkably successful in explaining the many features of the behavior of heavily loaded lubricated contacts However, the prediction of the coeffi- cient of friction is still one of the most difficult problems in this field Much experimental work has been done [7-211, and many empirical formulas have also been proposed based on the conducted experimental results

Plint investigated the traction in EHD contacts by using three two-roller machines and a hydrocarbon-based lubricant [14] He found that roller sur- face temperature has a considerable effect on the coefficient of friction in the

high-slip region (thermal regime) As the roller temperature increases the

coefficient of friction falls linearly until a knee is reached With further increase in temperature the coefficient of friction rises abruptly and errati- cally and scuffing of the roller surface occurs He also gave the following equation to correlate all the experimental results, which was obtained from

28 distinct series of tests:

21 300

f = 0.0335 log -

(0, + 40) - 44sb3 (7.8)

where 0, is the temperature on the central plane of the contact zone ("C) and

h is the radius of the contact zone (inches)

Dyson [15] considered a Newtonian liquid and derived the expression for maximum coefficient of friction as:

Rolling/ Sliding Contacts 257

Sasaki et al [16] conducted an experimental study with a roller test apparatus The empirical formula of the friction coefficientf in the region

of semifluid lubrication as derived from the tests is given as:

(7.10)

where

rj = lubricant dynamic viscosity

U = rolling velocity

U' = load per unit width

k = function of the slide/roll ratio

When slidelroll ratio = 0.3 1, k = 0.037; when slidelroll ratio = 1.22,

k = 0.026

Drozdov and Gavrikov [ 171 investigated friction and scoring under

conditions of simultaneous rolling and sliding with a roller test machine The formula for determination off at heavy contact loads from more than 10,000 experiments is found to be:

uo = kinematic viscosity of the lubricant (cst) at the mean surface

V, = sum rolling velocity (sum of the two contact surface velocities,

temperature (To) and atmospheric pressure

m/sec)

P,,, = maximum contact pressure (kg/cm2)

O'Donoghue and Cameron [ 181 studied the friction in rolling sliding con- tacts with an Amsler machine and found that the empirical relation relating friction coefficient with speed, load, viscosity, and surface roughness could

be expressed as:

(7.12)

where

S = total initial disk surface roughness (pin CLA)

V, = sliding velocity (difference of the two contact surface velocities) (in./sec)

Vr = sum rolling velocity (in./sec)

q = dynamic viscosity (centipoises)

R = effective radius (in.)

Benedict and Kelley [ 191 conducted experiments to investigate the friction in rolling/sliding contacts The coefficient of friction has been found to increase with increasing load and to decrease with increasing sum velocity, sliding velocity, and oil viscosity when these quantities are varied individu- ally The viscosity was determined at the temperature of the oil entering the contact zone The results are combined in a formula, which closely repre- sents the data as below:

where

(7.13)

R = effective radius (in.)

S = surface roughness (pin rms)

V, = sliding velocity (in./sec)

V, = sum rolling velocity (in./sec)

W = load per unit width (lb/in.)

qo = dynamic viscosity (cP)

The limiting value of S is 30pin

formula: Misharin [20] also studied the friction coefficient and derived the

where

(7.14)

V, = sliding velocity (m/sec)

Vr = sum rolling velocity (m/sec)

uo = kinematic viscosity (cSt)

Rolling/ Sliding Contacts 259

The limiting values are:

R: nonsignificant deviation from 1.8 cm slide/roll ratior 0.4-1.3

contact stress 2 2500 kg/cm2 0.08 sf 2 0.02

The accuracy of this empirical formula is reported to be within 15%

Ku et al [21] conducted sliding-rolling disk scuffing tests over a wide range of sliding and sum velocities, using a straight mineral oil and three aviation gas turbine synthetic oils in combination with two carburized steels and a nitrided steel It is shown that the disk friction coefficient is dependent not only on the oil-metal combination, but also on the disk surface treat- ment and topography as well as the operating conditions The quasisteady disk surface temperature and the mean conjection-inlet oil temperature are shown to be strongly influenced by the friction power loss at the contact, but not by the specific make-up of the frictional power loss They are also influenced by the heat transfer from the disk, mainly by convection to the

oil and conduction through the shafts, which are dependent on system design and oil flow rate

For AISI 93 10 steel:

+ - c.5 i- W c6 + 1965

where

(7.15)

(7.16)

V, = sum rolling velocity (m/sec)

V, = sliding velocity (m/sec)

W = load (kN)

S = surface roughness (pm CLA)

7.5 DOMAINS OF FRICTION IN EHD ROLLING/SLIDING

CONTACTS

The coefficient of friction for different slide-to-roll ratio z has three regions

of interest as interpreted by Dyson [15] As illustrated in Fig 7.2, the first region is the isothermal region in which the shear rate is small and the amount of heat generated is so small as to be negligible In this region,

the lubricant behavior is similar to a Newtonian fluid The second region

is called the nonlinear region where the lubricant is subjected to larger strain rates The coefficient of friction curve starts to deviate significantly from the Newtonian curve and a maximum coefficient of friction is obtained, after which the coefficient of friction decreases with sliding speed Thermal effects

do not provide an adequate explanation in this region because the observed frictional traction may be several orders of magnitude lower than the cal- culated values even when temperature effects are considered The third region is the thermal region The coefficient of friction decreases with increasing sliding speed and significant increase occurs in the temperature

of the lubricant and the surfaces at the exit of the contact

Almost all the empirical formulas discussed in the previous section are for the thermal regime Each formula shows good correlation with the test data from which it was derived, as illustrated in Fig 7.3, but generally none

of these formulas correlates well with the others, as shown in Fig 7.4 This suggests that these formulas are limited in their range of application and that a unified empirical formula remains to be developed

Slide / Roll Ratio - 2

Figure 7.2 Friction in rolling/sliding contacts

Cameron's formula with Cameron's experiments (c) Comparison of Kelley's formula with Kelley's experi-

ments (d) Comparison of Misharin's formula with Misharin's experiments

Drozdov’s formula with Misharin’s experiments (c) Comparison of Kelley’s formula with Cameron’s experi- ments (d) Comparison of Kelley’s formula with Misharin’s experiments

R ollingl Sliding Contacts 263

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

0.08 I

0.01 0.08 0.05 0.04

Misharin’s formula with Drozdov‘s experiments (8) Comparison of Cameron’s formula with Misharin’s

experiments (h) Comparison of Misharin’s formula with Cameron’s experiments

No formulas are available in the literature for determination of pure rolling friction in the EHD regime

7.6 EXPERIMENTAL EVALUATION OF THE FRICTIONAL

COEFFICIENT

An experimental study was undertaken by Li [22] to simulate typical engi- neering conditions, and explore and evaluate the effects of different para- meters such as loads, speeds, slide/roll ratios, materials, oil viscosi ties, and machining processes on the coefficient of friction The results were then used

to derive general empirical formulas for the coefficient of friction, which cover the different lubrication regimes These formulas will also be com- pared with other published experimental data to further evaluate their gen- eral applicability The formulas developed by Rashid and Seireg [23] are used to calculate the temperature rise in the film

The experimental setup used in this study is schematically shown in Fig

7.5 It is a modified version of that used by Hsue [24] The shaft remained

unchanged during the tests, whereas the disks were changed to provide different coated surfaces The shaft was ground 4350 steel, diameter

61 mm, and the disks were ground 1020 steel, diameter 203.2mm The coat- ing materials used for the disks were tin, chromium, and copper Uncoated steel disks were also used The coating was accomplished by electroplating with a layer of approximately 0.0127 mm for all the three coated disks, and the contact width was 3.175mm for all the disks The disk coated with tin and the one coated with chromium were machined before plating The measured surface roughness is shown in Table 7.1 and the material proper- ties are shown in Table 7.2 A total of 240 series of tests were run

The disk assembly was mounted on two 1 in ground steel shafts which could easily slide in four linear ball bearing pillow blocks The load was applied to the disk assembly by an air bag This limited the fluctuation of load caused by the vibration which may result from any unbalance in the disk The frictional signal obtained from the torquemeter was relatively constant in the performed tests

A variable speed transmission was used to adjust the rolling speed to any desired value A toothed belt system guaranteed the accuracy of sliding-

rolling ratios This was particularly important for the rolling friction tests The lubricant used was 10W30 engine oil with a dynamic viscosity of 0.09Pa-s at 26°C; the loads were 94,703, 189,406,284,109, and 378,8 12 N/m;

the slide/roll ratios were 0,0.08,0.154,0.222,0.345; the rolling speeds varied from 0.3 to 2.76 m/s, and the sliding speeds were in the range 0 to 0.95m/s

6 Couplings 13 Oil Valve

7 Digital Oscilloscope

9 Torque Meter

11 Variable Speed Transmission

14 Oil Container

Figure 7.5 Experimental setup

Table 7.1 Surface Roughness Measurement

Disk coating material Surface roughness (pm AA)

The experimental results cover rolling friction, the isothermal regime, the nonlinear regime, and the thermal regime The variables in the tests include load, speed, slide/roll ratio, surface roughness, and the properties

of the coated layer The following conclusions can be drawn from the test results

7.6.1 Friction Regimes

Although many investigators have conducted experimental investigations

on the coefficient of friction, no experimental results have been reported

in the literature for the rolling friction with EHD lubrication This is prob-

ably due to the difficulties of measuring the very small rolling friction force

to be expected in pure rolling It is found in the performed tests that rolling friction is very small and increases gradually with load in all cases It decreases at a relatively rapid rate with rolling speed when the rolling speed is small (< 1.5 m/s), then decreases at a lower rate at higher rolling speeds The effects of the coated material properties and surface roughness

on rolling friction appear to be insignificant for all the performed tests Figure 7.6 shows the experimentally determined variations of rolling friction with load and rolling speed

In the isothermal regime, it is expected that the surface roughness, the modulus of elasticity of the coated and base materials, and the thickness of the coated layers play an important role On the other hand, the material thermal properties do not appear to have significant influence Coating layers

of soft materials are found to give a higher coefficient of friction The surface roughness also increases friction The coefficient of friction is also found to increase with load and decrease with rolling speed Figures 7.7-7.10 show the variation of coefficient of friction with slide/roll ratio It can be seen from these figures that the coefficient of friction for steel and copper coating reaches its maximum in the nonlinear regime For chromium and tin coat- ings, the coefficient of friction continues to increase, but at much slower rate than in the isothermal and the nonlinear regimes The magnitude and posi- tion of the maximum value of the coefficient of friction are influenced by the surface roughness, material physical properties, load, speed, and viscosity

In the thermal regime the coefficient of friction is found to decrease slightly with the slide/roll ratio The thermal properties of the coated and the base materials are found to have significant effect on the coefficient of

friction as would be expected The surface with a high diffusivity K / ( p C )

usually produces a lower coefficient of friction because the surface contact

temperature rise is lower, and consequently, the actual oil viscosity is higher,

which produces a better lubrication condition Rough surfaces give higher coefficient friction as in the isothermal and nonlinear regimes However, the

N/m, U = 0.303 m/sec

4

378,812

load appears to have no direct effect on the coefficient of friction in the thermal regime

Rolling speed is found to have a significant effect on the coefficient of friction in pure rolling conditions and in the isothermal, the nonlinear, and the thermal regimes The coefficient of friction always decreases with increasing rolling speed The rate of decrease is more significant for low rolling speeds, and is relatively lower for high rolling speeds

Both the physical and the thermal properties of the coated materials

influence the coefficient of friction The modulus of elasticity decreases the

coefficient of friction in the isothermal and nonlinear regimes The thermal properties of the surface influence the coefficient of friction in the thermal regime

There are many published empirical formulas for evaluating the coefficient

of friction They were developed by different investigators under different experimental conditions, and therefore, it it no surprise that they do not correlate with each other All of these formulas are developed from test data

in the thermal regime The generalized empirical formulas presented in this section cover all the three regimes, as well as rolling friction All the vari- ables in these formulas are dimensionless The formulas calculate the coeffi- cient of friction at three sliding/rolling conditions which can then be used to construct the entire curve, as illustrated in Fig 7.10 The first point is fr,

which gives the magnitude of the rolling coefficient of friction The second point isf,, which gives the coefficient of friction in the nonlinear region, and

z*, its location This point is assumed to approximately define the end of the isothermal region or the maximum value in the nonlinear regime The third one is the thermal coefficient of friction,f,, and the corresponding slidelroll

ratio location is chosen as 0.27, after which the coefficient of friction is

assumed to be almost independent of the slide/roll ratio The coefficient

of friction curve is then presented by curve fitting the three points by an appropriate curve

In the isothermal and the nonlinear regimes, four dimensionless parameters are used They are: 1

U2P 10'0 Rolling speed a = -