Friction and Lubrication in Mechanical Design Episode 2 Part 6 pot

Case Illustrations of Surface Damage 355 force effects of solid rollers cause an additional loading at the outer race contact and a second-order, not significant unloading at the inner

Case Illustrations of Surface Damage 355

force effects of solid rollers cause an additional loading at the outer race contact (and a second-order, not significant unloading at the inner race con tact)

Harris and Aaronson [40] made analytical studies of bearings with annual rollers to investigate the load distribution, fatigue life, and the skid- ding of rollers Their work shows that hollow rollers increase the fatigue life

of the bearing and decrease the skidding between the cage and roller set They suggested that attention should be paid, however, to the bending stress

of the rollers and to the bearing clearance

This section describes an experimental study undertaken by Suzuki and Seireg [41] to compare the performance of bearings with uncrowned solid and annular rollers under identical laboratory conditions Bearing temperature rise and roller wear are investigated in order to demonstrate the advantages

of using annual rollers in applications where skidding can be a problem

Test Bearings

The two bearings used in the study have the same dimensions and configura- tions with the exception that one bearing has annular rollers and the other bearing has solid rollers The details of the bearings are given in Table 9.1 Brass is selected as the roller material in order to rapidly demonstrate the effect of annular rollers on temperature rise, and roller wear

The ratio of the inside to the outside diameter of the hollow roller is taken as 0.3 Three sets of inner rings with different outside diameters are

used for each bearing in order to produce the different clearances

Special efforts were undertaken in machining the rollers and rings to approach the dimensional accuracy and surface finish of conventional har- dened bearing steels

Test Fixture

The experimental arrangement is diagrammatically represented in Fig.9.12 the two test bearings (a) and (b) (one with hollow rollers and another with solid rollers) were placed symmetrically near the middle plane of a shaft (c) The shaft is supported by two self-lubricated ball bearings (d) on both sides

A variable speed drive is used to rotate the shaft through a V-belt (e) and

and a pulley (f) at one end of the shaft

The load is applied radially on the outer rings (g) inside which the bearing is placed by changing the weight (j) suspended at one end of a bar (k) The latter loads a fulcrumed beam-type load divider, which is

especially designed to provide identical loads on both bearings A strain

gage ring-type load transducer (i) monitors the load applied on the test bearings to confirm the equality of the load on them at all times Separate

Table Q.1 Test Bearing Specifications

Bearing outside diameter

Bearing inside diameter

Bearing width

Outer race inside diameter

Inner race outside diameter

Outer and inner race material

Surface finish for rollers and races

0.0038 in

Brass Mild steel

8-10 pin.-rms

(10.99947 cm) (4.999228 cm) (2.6924 cm) (9.4462 cm) (6.517132 cm) (6.51 1798 cm) (6.50478 cm) (1.464564 cm) (1.67386 cm) (0.436626 cm) (0.005334 cm) (0.009653 cm)

Load

Figure 9.1 2 Diagrammatic representation of experimental setup for dynamic test

Case Illustrations of Surface Damage 35 7

oil pans (1) are placed below each of the test bearings Oil is filled to the level

of the centerline of the lowest roller Copper+onstantan thermocouples are used to measure the bearing temperatures as well as the oil sump tempera- ture The bearing thermocouples are embedded 30" apart at 0.01 in (0.25mm) below the surface of the outer rings where rolling takes place The thermocouples are connected to a recorder (s) through a rotary selec- tion switch (q), and a cold box (r)

Results

Figure 9.13a shows the time history of the outer race temperature rise for the bearing with annular rollers Steady-state temperature conditions are reached after approximately two hours Figure 9.13b shows the bearing temperature rise as well as oil temperature rise at steady state conditions for a shaft speed of 1000 rpm The temperature rise for both solid rollers and annular rollers are essentially the same at this speed At speeds of 2000 rpm and 3000 rpm, on the other hand, the temperature with solid rollers is higher than that with annular rollers The temperature rise differences are most pronounced at 2000 rpm

Wear Measurement

The radioactive tracing technique used in the test is similar to that used by

L Polyakovsky at the Bauman Institute, Moscow for wear measurement in the piston rings of internal combustion engines

The test specimens (hollow or solid rollers) are bombarded by a high- energy electron beam emitting gamma rays The strength of the bombard- ment is governed by the energy of the electron beam, the exposure time, and the material of the specimen The radioactivity, which naturally decays with time, is also reduced with wear of the bombarded surface The rate of reduction of the radioactivity is approximately proportional to the depth

of wear The amount of wear can therefore be detected by monitoring the radioactivity of the specimen and using a calibration chart prepared in advance of the test The main advantage of this method is the ability to detect roller wear without disassembling the bearing The disassembling process is not only time consuming, but it may also alter the wear pattern

of the test specimens

In this study, one roller in each bearing is bombarded and assembled with the rest of the rollers A scintillation detector (w) is placed on the outer surface of the outer ring of the bearing (Fig 9.12) and a counter is used to monitor the change in radioactivity of the bombarded rollers The diameter

of rollers is periodically measured using an electric height gage to check the accuracy of the radioactive tracing technique

Figure 9.14a shows a comparison of the wear of the roIIers during the test As can be seen from the figure, the wear of the annular rollers is

Case Illustrations of Surface Damage

40 -

359

- -.- - Sdid Roller Bearing

-A- Annular Roiler Bearing

Flgure 9.14

oil (a) Roller wear (b) Temperature difference between bearings and

considerably lower than that of the solid rollers It should be noted that after an initial running period of 30 hours, the oil was changed and a con- siderably lower rate of wear resulted The wear rate during this phase of the test is shown as 5.7 x 10-7 in./h (14.5 x 10-6 mm/h) for the hollow roller as

compared to 8 x 10-7 in./h (20.4 x 10-6 mm/h) for the solid roller

It was observed throughout the test that the wear detected using radio- active tracing technique is slightly higher than that measured directly using the electric height gage The reason may lie in the fact that the wear detected

by the radioactive tracing technique is an average wear, which includes the

indentations due to local pittings or flakings Consequently, if the interest is

to study the effect of wear on the change of bearing clearance, it would be more appropriate to use the height gage for measuring the dimensional change On the other hand, if the interest is to investigate the surface damage, the radioactive tracing technique would be a good tool for this purpose Better accuracy can be expected with this technique when steel rollers are used Gamma-ray emission is stronger with steel and conse- quently the influence of the radioactivity existing in the natural sp: :e on the results is reduced

The temperature rise in the bearings and oil during the wear est is shown in Fig 9.14b The temperature of the outer race of the solid roller bearing is shown to be consistently higher than that of the annular roller bearing at all times

It is interesting to note that the annular roller exhibited a small number

of local pits scattered on the rolling surface In the solid roller, however, a large number of pits were observed in the rolling direction only at the central region of the rolling surface This may also be due to the cooling effect at the ends of the rollers

9.3 SURFACE TEMPERATURE, THERMAL STRESS, A N D WEAR

IN BRAKES

The high thermal loads, which are generally induced in friction brakes, can produce surface damage and catastrophic rotor failure due to excessive sur- face temperatures and thermal fatigue The temperature gradients and the corresponding stresses are functions of many parameters such as rotor geo- metry, rotor material, and loading history

Due to the wide use of frictional brakes, an extensive amount of work has been undertaken to improve the performance and extend the life of their rotors Some research has been aimed towards studying the effects of rotor geometry on the temperature and stress distribution using classical analyti- cal [42-45] or numerical [46-521 methods Other studies have concentrated

on investigating the effects of rotor materials on the performance of the

brake [53-551

The efforts to improve the automobile braking system performance and meet the ever increasing speed and power requirements had resulted in the introduction of the disk braking system which is considered to be better than the commonly used drum system A newer system which is claimed to be superior to both of its predecessors is now being introduced The crown system [56] which can be viewed as a cross brake, with a drum rotor and a

Case Il[ustrations of Surface Damage 361

disk caliper, combines the advantages of both drum and disk systems It has the loading symmetry of the disk caliper which results in less mechanical deformation It also has the larger friction surface areas and heat exchange areas of the drum which result in better thermal performance and lower

temperatures A study by Monza [56], in which the disk and crown are com- pared, indicated that more weight and cost reduction are attainable by using the crown system Moreoever, under similar testing conditions, the crown rotor showed 10-20% lower operating tempratures than its counterpart This section is aimed at investigating the thermal and thermoelastice performance of rotors subjected to different types of thermal loading Although there are many procedures in the literature for the analysis of temperature and stress in brake rotors based on the finite element method [ l , 3, 8, 91, these procedures would require considerable computing effort

Efficient design algorithms can be developed by placing primary emphasis

on the interaction between the design parameters with sufficient or reason- able accuracy Sophisticated analysis can then be implemented to check the obtained solution and insure that the analytical simplifications are acceptable

For the thermoelastic analysis in this section, a simplified one-dimen- sional procedure is used The rotor is modeled as a series of concentric circular rings of variable axial thickness Furthermore, it is assumed that the rotor is made of a homogeneous isotropic material and that the axial temperature and stress variations are negligible The procedure first treats the thermal problem to predict the temperature distribution which is then used to compute the stress distributions

9.3.1

This algorithm used to calculate the temperature rise is a simplified one- dimensional finite difference analysis The analysis consideres the transient radial temperature variations and neglects both axial and circumferential variations The rotor, which is subjected to a uniform heat rate, Qr at its external, internal or both cylindrical surfaces dissipates heat through its exposed surfaces by convention only The film coefficient depends only on the geometrical parameters

The proposed analysis is based on the conservation of energy principles for a control volume This can be stated as:

Temperature Rise Due to Frictional Heating

where Qin and Qour are the rate of energy entering and leaving the volume,

by heat conduction and convection respectively and Qslorcd is the rate of

energy stored in the volume For the shaded element of Fig 9.15, Eq (9.4) with appropriate substitution becomes:

where Qc,n and &+, are heat quantities entering and leaving the volume by

conduction, and Qv,n and Q d , n are geometry dependent convection heat

quantities entering and leaving the body depending on the surrounding

temperature, T,

With a current temperature rise above room temperature, T,,, at the

interface M , one can solve for the future temperature rise, at time t + 1, for

the same location [57]:

Case Illustrations of Surface Damage 363

Similar expressions can be obtained for the temperature at the inner and outer surfaces The temperature rise in the next time step at the outer radius is:

(9.7)

and the temperature rise in the next time step at the inner surface is

obtained by replacing all the 2,O and U subscripts in Eq (9.7) by m, i,

and I , respectively

In the above equations Ao, A,, and A, are the cylindrical areas of the outer, inner, and interface surfaces, respectively Au,, and are the ring side areas, upper, and lower halves Ad,, is the area generated by the thick- ness difference between two adjacent rings (refer to Fig 9.15) As can be seen, the above algorithm can easily be modified to allow for any variations

in heat input, convective film, and surrounding temperatures with location and time

9.3.2 The Stress Analysis Algorithm

The geometrical model of this algorithm is identical to that of the tempera- ture algorithm For this analysis, both equilibrium and compatibility con- ditions are satisfied at the rings interfaces Considering the inner and outer sides of the interface rn+l of Fig 9.16, the continuity condition (or strain

equality) can be expressed as a function of the corresponding stresses as follows [58, 591:

Representation of the disk geometry and the notations used in the

The radial stress

sures on both sides of the interface, can be derived as:

at the radius I-,,+~, which is the average of the pres-

The tangential component o , , ~ + ~ is calculated by averaging the stress on both sides of the interface as:

(9.1 I )

Case Illustrations of Surface Damage 365

where

where 0, is a geometry function given by 0, = (r,,/r,,+,)* Equations (9.9)

and (9.10) are used to determine the radial and tangential stress distribu- tions Substitution in Eq (9.1 1) for each node produces a set of simulta- neous equations to be solved for the known boundary pressures P2 and P,,

to give the radial distribution in the disk This set of simultaneous equations

is solved by assuming two arbitrary values for P3 and using linear interpola- tion or extrapolation to satisfy the pressure P,,, at the inner boundary [52] The temperature and stress algorithms are then coupled such that the

temperature distribution is automatically used in the stress algorithm This

approach makes it possible to incorporate material properties and heat

convectivity that are geometry and temperature dependent [SS, 591 Similar algorithms for disk brakes are given in Refs 60-62

9.3.3 Numerical Examples

The coupled temperature-stress algorithm is used, as a module, to predict the temperature and thermal stresses generated by a given conductive heat flux applied at a given surface or surfaces of a disk of any given material and geometry Several examples are considered to illustrate the capabilities of the developed algorithm

The following geometrical, loading and material parameters are used in the considered cases:

Geometry:

Disk outer radius, ro = 12.0in

Disk inner radius, ri = 6.0in

Disk thickness, fmax = 12.0 in

Material:

Density, p = 0.286 lb/in.3

Young's modulus, E = 30 x 106 psi

Coefficient of thermal expansion, a = 7.3 x 10-6 in./(in.OF)

Thermal conductivity, k = 26.0 BTU/(hr-ft-OF)

Specific heat, c = 0.1 1 BTU/(lb-OF)

Loading conditions:

Total conductive heat flow rate, QT (constant) = 500,000 BTU/hr

Heating time, t = 180sec

Average convective heat transfer coefficient at exposed surfaces,

The case of a disk with uniform thickness is considered to investigate the effect of the loading location on the thermal and thermoelastic behavior of the disk by applying the total heating load at the disk outer surface and the inner surfaces respectively The case where the load is shared equally between the two surfaces is also considered, as well as the case where the

thermal load sharing between the surfaces is optimized [59] The tempera-

tures and tangential stresses for the three loading cases are shown in Tables The results obtained from the report study illustrate the significant effects of the loading location and load sharing ratio on the thermal

and thermoelastic performance of brakes Tables 9.2-9.4 show that when

the thermal load is shared between the internal and external cylindrical surfaces, a considerable reduction can be expected in the temperature and stress magnitudes It also indicates that the maximum tensile tangential stress is shifted from the inner or outer surface towards the middle where the probability of failure is reduced The results also show that, for the given case, internal loading produces the highest temperature and stress

h = 5.0 BTU/(hr-ft2-"F)

9.2-9.4

Table 9.2 The Maximum Temperatures ( O F ) for the Investigated Cases

Load condition (:) = 0.25 (2) = 0.50 (:) = 0.75

1 Uniform thickness and external loading 448.9 465.2 0.75

2 Uniform thickness and internal loading 1345.8 787.9 469.8

3 Uniform thickness and equal load

4 Uniform thickness and optimal load