Friction and Lubrication in Mechanical Design Episode 1 Part 8 pdf

Figure 5.27 represents the case of a metallic solid with an insulative surface layer in contact with another layered solid having an opposite combination of ther- mal properties.. It ca

Thermal Considerations in Tribology 155

siderable difference between the film and solid temperatures Figure 5.27

represents the case of a metallic solid with an insulative surface layer in contact with another layered solid having an opposite combination of ther- mal properties It can be seen from the figure that the heat partition is highly

near the surface, which mainly incorporates the layer thickness Figure 5.27

also demonstrates the possibilities for equalizing the heat partition between

surface layers Negligible sliding is assumed in this case

Figure 5.28 shows the variation in the maximum temperature rise in the

contact zone and the solid surfaces with respect to Hd/Haw The contact

Slower Surface Fader Surface

Thermal Considerations in Tribology IS 7 0.0080

K I = KO2, Kol = K2 Tmax/q, versus = I K 1 , Ha,, = Hd/Hm(rolling speed 104 in.) = 2000 in./sec, 1 = .02 in.,

zone temperature is almost identical to the solid surface temperature, which carries the conductive surface layer

The generalized equation for heat partition in lubricated line contact problems, which has been derived for steady-state conditions, is applicable

to all metallic solids It can be deduced from this equation that the deviation

by the conductivity and thickness of the lubricant film The existence of the lubricant film tends to equalize heat partition between the rolling/sliding solids independent of their thermal properties and surface speeds It is inter- esting to note that the maximum temperature rise for each moving solid is

the total heat flux, q , / l

The difference between the maximum film and surface temperatures is also controlled by the lubricant film thickness and its conductivity This can

be attributed to the fact that convection is not important in this case Although the problem of layered surfaces is appropriately modeled in the developed finite difference program, an evaluation of the effect of the different system parameters on the temperature distribution would be extre- mely difficult It was, therefore, imperative to limit the parametric analysis

to single layered solids for two specific regimens of thermal properties, layer thicknesses, width of contact and operating speeds

The following can be concluded from the dimensionless equations developed for the considered cases:

ductivity of the layers and their thickness due to the convection influence under such conditions

For conductive surface layers, the slide/roll ratio has little influence

on the maximum solid surface temperatures, while for insulative surface layers, the slide/roll ratio has a significant influence on the maximum temperature

For conductive surface layers with equal thicknesses, increasing the thickness decreases the maximum surface tempratures for both the solid and the surface layers

For insulative surface layers with equal thicknesses, increasing the thickness slightly decreases the maximum solid surface tempera- tures and increases the maximum surface layer temperatures

of the partition from the unlayered case, as shown in Fig 5.27 It can also be seen that with the above combination of properties it is possible to attain equal heat partition by proper selection of the

For the above case, the maximum contact temperature is approximately equal to the maximum temperature in the insulative solid with conductive

conductive solid with insulative layer is significantly lower than the interface temperature

Blok, H., “The Postulate About the Constancy of Scoring Temperature,” Interdisciplinary Approach to the Lubrication of Concentrated Contacts, P

3 Sakurai, T., “Role of Chemistry in the Lubrication of Concentrated

2

M Ku, Ed., NASA SP-237, 1970, p 153

Contacts,” ASME J Lubr Technol., 1981, Vol 103, p 473

Thermal Considerations in Tribology 159

Alsaad, M., Blair, S., Sanborn, D M., and Winer, W O., “Glass Transitions

in Lubricants: Its Relation to EHD Lubrication,” ASME J Lubr Technol.,

1978, Vol 100, p 404

Blok, H., “Theoretical Study of Temperature Rise at Surfaces of Actual Contact Under Oiliness Lubricating Conditions,” Proc Gen Disc Lubrication, Institute of Mechanical Engineers, Pt 2, 1937, p 222

Jaeger, J c., “Moving Sources of Heat and the Temperature at Sliding con- tacts,” Proc Roy Soc., N.S.W., 1942, Vol 56, p 203

Cheng, H S., and Sternlicht, B., “A Numerical Solution for the Pressure, Temperature, and Film Thickness Between Two Infinitely Long, Lubricated Rolling and Sliding Cylinders under Heavy Loads,” ASME J Basic Eng., Vol

87, Series D, 1965, p 695

Dowson, D., and Whitaker, A V., “A Numerical Procedure for the Solution

of the Elastohydrodynamic Problem of Rolling and Sliding Contacts Lubricated by a Newtonian Fluid,” Proc Inst Mech Engrs, Vol 180, Pt

3, Ser B, 1965, p 57

Manton, S M., O’Donoghue, J P., and Cameron, A., “Temperatures at Lubricated Rolling/sliding Contacts,” Proc Inst Mech Engrs, 1967-1 968, Vol 1982, Pt 1, No 41, p 813

Conry, T F., “Thermal Effects on Traction in EHD Lubrication,” ASME J Lubr Technol., 1981, Vol 103, p 533

Wang, K L., and Cheng, H S., “A Numerical Solution to the Dynamic Load, Film Thickness, and Surface Temperatures in Spur Gears; Part 1 Analysis,” ASME J Mech Des., 1981, Vol 103, p 177

Knotek, O., “Wear Prevention,” International Conf on the Fundamentals of Tribology, Suh, N., and Saka, N., Eds., MIT Press, Cambridge, MA, 1978, p

927

Torti, M L., Hannoosh, J G., Harline, S D., and Arvidson, D B., “High

Performance Ceramics for Heat Engine Applications,” AMSE Preprint No Georges, J M., Tonck, A., Meille, G., and Belin, M., “Chemical Films and Mixed Lubrication,” Trans ASLE, 1983, Vol 26(3), p 293

Poon, S Y., “Role of Surface Degradation Film on the Tractive Behavior in

Elastohydrodynamic Lubrication Contact,” J Mech Eng Sci., 1969, Vol I1(6), p 605

Berry, G A., and Barber, J R., “The Division of Frictional Heat - A guide to the Nature of Sliding Contact,” ASME J Tribol., 1984, Vol 106, p 405 Shaw, M C., “Wear Mechanisms in Metal Processing,” Int Conf on the Fundamentals of Tribology, Suh, N., and Saka, N., Eds., MIT Press, Cambridge, MA., 1978, p 643

Burton, R A., “Thermomechanical Effects on Sliding Wear,” Int Conf on the Fundamentals of Tribology, Suh, N., and Saka, N., Eds., MIT Press, Cambridge, MA., 1978, p 619

Ling, F F., Surface Mechanics, J Wiley, New York, NY, 1973

84-GT-92, 1984

Conf., IIT Res Inst., June, 1978

Winer, W O., “A Review of Temperature Measurements in EHD Contacts,”

5th Leeds-Lyon Symposium, 1978, p 125

Townsend, D P., and Akin, L S., “Analytical and Experimental Spur Gear

Tooth Temperature as Affected by Operating Variables,” ASME J Lubr

Technol., 1981, Vol 103, p 219

Rashid, M., and Seireg, A., “Heat Partition and Transient Temperature

Distribution in Layered Concentrated Contacts Part I : Theoretical Model, Part 2: Dimensionless Relationships, ASME J Tribol., July 1987, Vol 109, p

496

Taylor, E S., Dimensional Analysis for Engineers, Oxford University Press,

London, England, 1974

David, F W., and Nolle, H., Experimental Modeling in Engineering,

Butterworths, London, England, 1974

Arpaci, V S., Conduction Heat Transfir, Addison-Wesley, Reading, MA,

1966, p 474

Hamrock, B J., and Jacobson, B O., “Elastohydrodynamic Lubrication of

Line Contacts,” ASLE Trans., 1984, Vol 27, p 275

Wilson, W R D., and Sheu, S., “Effect on Inlet Shear Heating Due to Sliding

on Elastohydrodynamic Film Thickness,” ASME J Lubr Technol., 1983, Vol 105, p 187

Suzuki, A., and Seireg, A., “An Experimental Investigation of Cylindrical

Roller Bearings Having Annular Rollers,” ASME J Lubr Technol., 1976, Vol 98, p 538

6

Fluid film bearings are a common means of supporting rotating shafts in rotating machinery In such bearings a pressurized fluid film is formed with adequate thickness to prevent rubbing of the mating surfaces There are two main types of fluid film bearings: hydrostatic and hydrodynamic The first type relies on an external source of energy to supply the lubricant with the necessary pressure In the second type, pressure is developed within the

6.1.1 Hydrodynamic Equations

The basic equation governing the behavior of the fluid film in the hydro-

velocity gradient relationship, the equilibrium of the fluid element (Fig 6.2)

161

p = oil viscosity (assumed constant throughout the film)

U = tangential velocity in the journal

The solution of this equation for any eccentricity, e, would result in expres- sions for the quantity of flow required, the frictional power loss and the pressure distribution in the oil film The latter determines the load-carrying

capacity of the bearing A closed-form solution of Reynolds’ equation can

be obtained with either of the following assumptions:

generally known as the Sommerfeld bearing In this case the change in pressure in the axial direction can be neglected com-

Accordingly:

Design of Fluid Film Bearings

Figure 6.2 Equilibrium of fluid element in the x-direction

and Eq (6.1) reduces to:

Referring to Fig 6.1 with the condition:

163

dy dr

p = p m a x at h = hl

Design of Fluid Film Bearings 165

lysis of this case is called the short bearing approximation The

greater than that in the circumferential direction Accordingly, Reynolds' equation reduces to

6.1.2 Numerical Solution

The development of high-speed computers made it possible to obtain

behavior can be calculated for any given geometry and boundary condi-

most widely known Their data are presented in the form of design charts with Sommerfeld number as the main parameter The numerical solutions are based on the assumption of an isoviscous film independent of pressure and temperature variations The film viscosity is calculated at the mean temperature in the bearing The bearing performance charts of Raimondi and Boyd are given in Figs 6.3-6.7

6.1.3 Equations for Predicting Bearing Performance

A system of equations, based on these charts, is developed by approximate

curve fitting The equations are utilized in the automated design system described later in this chapter These equations are:

Sommerfeld Number, S

Figure 6.6 Peak pressure

J = Joule'r equivalent of heat

Design of Fluid Film Bearings

1.2

2.0

2.1

169

The following notation is used in the analysis:

C = radial clearance (in.)

D =journal diameter (in.)

e =journal eccentricity (in.)

f = coefficient of friction

ho = minimum film thickness (in.)

L = bearing length (in.)

N =journal rotational speed (rps)

P = bearing average pressure (lb/in.2)

P,,, = maximum oil film pressure (lb/in.2)

Q = quantity of oil fed to bearing ( i ~ ~ ~ / s e c )

R =journal radius (in.)

At = oil temperature rise ( O F )

W = bearing load (Ib)

p = lubricant average viscosity (reyn)

oil flow variable

length to diameter ratio

P

Sommerfeld no =

6.1.4 Whirl and Stability Considerations

The whirl of rotors supported on fluid films is of considerable practical importance and it is no surprise that it has been the subject of numerous investigations The designer is generally interested in predicting beforehand not only the stability of the rotor operation but the expected peak amplitude

of unbalance The safety during the transient start-up phase has to be also

Design of Fluid Film Bearings I71

and related bibliographies can be found in Refs 5-12

A simplified stability criterion, based on an analysis by Lund and Saibel

[Ill, is also given in Fig 6.8 A modified Sommerfeld number,

condition for the onset of bearing instability according to the relationship plotted in the figure, where

M = rotor mass per bearing

C = radial clearance

w =journal rotational speed (rad/sec)

W = bearing load

6.1.5 The Effect of Rotor Unbalance on Whirl Amplitude and Stability

It is well known that rotor unbalance can have significant effect on whirl

and stability A study by Seireg and Dandage [13] utilized the phase-plane

isoviscous film Response spectra were obtained to illustrate the trend of the

influence of the magnitude of unbalance, speed, average film viscosity, load, clearance, and rotor start-up, acceleration on the whirl amplitudes

0

I

0 I I .o 10 100 MODIFIED SOMMERFELO N O 0

The equations of motion for the rotor under consideration from the steady-state position can be written as:

which represents a system of coupled nonlinear second-order equations in which:

er = force due to the unbalance in the x-direction = rnrw’ cos(wt + 4)

do

dt

- mr - sin(wt + 4) in the transient phase

F, = mrw2 cos(ot + 4) during the constant speed operation

dw

dt F,, = rnrw2 sin(wt + 4) during the constant speed operation

= mrw2 sin(ot + 4 + rnr - cos(ot + 4) in the transient phase

where

rn = rotor mas per bearing

mr = amount of unbalance

w = rotating speed

4 = phase angle between the unbalance force and the movement of the center

of mass of the rotor in the x-direction

k.vy, C,,., k,, CYy, k,,, and C,, are given in the following They are derived

evaluated at any instant from the instantaneous eccentricity ratio

Stiffness Coefficients

- I.0181 K.r.r = 0.5979 (g) ~-0.8863+0.1927(L/D)

-0.2 I27

K.ry = 2.501 (g) s-0.37 I 3 + 0 1 4 7 6 ( ~ / ~ )

K,,r = -0.4816 + 1.7006 - 0.9335s + 1 1.6940S2 - 16.3368s

+ 2.2198S(L’D’

Design of Fluid Film Bearings I 73

Design of Fluid Film Bearings I75

+ 5.6523 - 7.791S2 + 61.060s 0.134s- 0.8367S2 + 6.204s

- 0.105S2 + 5.534s

In order to analyze the motion from the start of the rotation until the final uniform speed is reached, the start-up velocity pattern can be incorpo- rated in the integration

Two sets of coordinates are used in the analysis The first set is a Newtonian frame for the dynamic analysis The second set is attached to the shaft and is used to define the film geometry and corresponding dynamic film characteristics at any instant The necessary transformations between the two frames are continuously performed throughout the simulation Unless otherwise specified, the following parameters for the bearing rotor system are used in the calculations:

I 131

D = bearing diameter = 2.5 in (6.35 cm)

c = radial clearance = 0.0063 in (0.0 16 cm)

W = Mg = rotor weight = 100 Ib (45.4 kg)

L = bearing length = 2.5 in (6.35cm) Unbalance mr = 0 to 0.0007 Ib-sec2 (0 to 0.00031 8 kg-sec2)

Examples of typical computer-plotted whirl orbits, and time history of

the eccentricity ratio are shown in figs 6.9-6.14 The results given in Figs 6.9-6.1 1 are for a perfectly balanced rotor and very high start-up accelera-

tion, (To = 0) It can be seen that at very low speeds, the balanced rotor

gradually reaches steady-state equilibrium at a fixed eccentricity (Fig 6.9) If