Friction and Lubrication in Mechanical Design Episode 2 Part 3 docx

280 Chapter 7

7.7.4 Effective Viscosity

Using the notation:

Th = absolute bulk disk temperature (e.g., Tb = 273.16 + "C)

A Ts = temperature rise for steel-steel contact

ATc = temperature rise from Eq. (7.27) using the material properties of

A T = A Tc - A Ts = temperature rise difference between the steel-coating

AT, = effective temperature rise difference between the steel-coating con￾the contacting surfaces for steel-coating contact

contact and the steel-steel contact

tact and the steel-steel contact

Then:

AT'> = ATP (7.31)

where B is the coating thickness factor from the previous section.

Then T', = Tb + AT, is used to calculate the viscosity for that coating

conditions, and the viscosity is then substituted into Eq. (7.24) to calculate

the corresponding coefficient of friction. The viscosity of 10W30 oil is

calculated by the ASTM equation [27]:

lOg(cS + 0.6) = a - b log T, (7.32a)

therefore

(7.32 b)

(7.32~)

where T, is the absolute temperature (K or R), cS is the kinematic viscosity

(centistokes). a = 7.827. b = 3.045 for 10W30 oil. For some commonly used

oil, a and 6 values are given in Table 7.3.

7.7.5

For the reasons mentioned before, the effective modulus of elasticity, Et,,

for coated surface is desirable. Using the well-known Hertz equation, one

calculates the Hertz contact width for two cylinder contact as [27]:

Coating Thickness Effects on Modulus of Elasticity

(7.33)

RollinglSliding Contacts 281

Table 7.3 Values of a and b for Some Commonly Used

Lubricant Oils

Oil a b

SAE 10

SAE 20

SAE 30

SAE 40

SAE 50

SAE 60

SAE 70

~~ ~

11.768

11.583

11.355

I 1.398

10.43 1

10.303

10.293

4.64 18

4.5495

4.4367

4.4385

4.03 19

3.9705

3.9567

E' and U are the modulus of elasticity and Poisson's ratio.

Coating material properties are used for E2 and u2 because coating

thickness is an order greater than the deformation depth (this can be seen

later). Therefore, the deformation depth is calculated by (Fig. 7.18):

hd = RsinOtanO

8 is very small, therefore:

(7.34)

The variation of the deformation depth with load is shown in Fig. 7.19.

Then the effective modulus of elasticity of the coated surface is proposed as:

(7.35a)

where

Eh = modulus of elasticity of base material

E,. = modulus of elasticity of coating material

E, = modulus of elasticity of coated surface

h,. = coating film thickness

hd = elastic deformation depth

r = constant (it is found that r = 13 best fits the test data)