Journal Bearing

Tutorial 7 - Design of a Journal Bearing

Goals: • Design a journal bearing. • Calculate important operating parameters of hydrodynamic bearings.

©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Problem Statement Given: A heated roll is used to evaporate water from pulp in the production of paper. This roll is mounted onto a two inch diameter shaft for which a journal bearing needs to be designed. The roller sees a total load of 1500 pounds, which is distributed evenly between two identical bearings. The roll speed is 2000 rev/min and SAE 10 oil is readily available (it is used throughout the paper mill and is in abundant supply). The oil inlet temperature is thought to be around 110°F. Because of clearance issues, the bearing width must be one inch or less. Find: 1.) The radial clearance of the bearing for optimum load carrying capacity. 2.) The surface finish required on the bearing. 3.) The temperature rise, friction coefficient, flow rate and side flow rate of oil through the bearing. (These are needed to prescribe heat exchangers for the oil reservoir.) 4.)Comment on the importance of the inlet temperature, that is, what effect on the bearing performance would occur if the inlet temperature were 130° F?

©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Solution Outline • Preliminary Calculations • Determination of Bearing Characteristic Number • Determination of required clearance • Determination of bearing parameters and surface roughness • Effect of inlet oil temperatures • Concluding Remarks Note: The approach presented is only one of many approaches which can be pursued. Although the indicated steps are in a logical order, they are not to be considered the essential order.

©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Preliminary Calculations Since the bearing width is restricted to one inch or less, it will be taken as one inch. The reason for this is that there is no advantage from an operating standpoint to have a smaller width, and if the bearing will be manufactured through a grinding operation, the cost of finishing a one inch wide surface on a large roller is insignificantly larger than a 0.75 inch bearing, for example. Therefore, the diameter to width ratio for the bearing is 2in λ = =2 1in j

©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Determine the bearing characteristic number and the dimensionless film thickness

©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Determination of Bearing Characteristic Number

The bearing characteristic number is Bj=0.35. The dimensionless film thickness parameter is hmin /c=0.42.

See the Next Slide for details of the analysis! ©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Analysis Details These values can be directly read from Figure 2.28, since it is known that the diameter to width ratio is 2 and the bearing is to be designed for maximum load carrying capability:

From the chart, the bearing number Bj is approximately 0.35 and the dimensionless film thickness variable is hmin /c is 0.42. The bearing number will be used to obtain the clearance once the average viscosity is calculated. ©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Determine the dimensionless coefficient of friction variable for the bearing.

©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Dimensionless Coefficient of Friction Variable

The dimensionless coefficient of friction variable is rbµ /c=9.5.

See the Next Slide for details of the analysis! ©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Analysis Details The coefficient of friction can be read from Figure 12.30, since the bearing number is known to be 0.35:

The dimensionless coefficient of friction variable can be seen to be around 9.5. ©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Determine the dimensionless volume flow rate for the bearing.

©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Dimensionless Volume Flow Rate

The dimensionless volume flow rate is Q=5.1.

See the Next Slide for details of the analysis! ©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Analysis Details The dimensionless volume flow rate is obtained from Figure 12.31:

The dimensionless volumetric flow is 5.1.

©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Determine the side-leakage flow ratio.

©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Side Leakage Flow Variable

The side leakage flow variable is qs/q=0.73.

See the Next Slide for details of the analysis! ©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Analysis Details The side leakage flow variable can be obtained from Figure 12.32:

The value is qs/q=0.73. ©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Calculate the temperature rise in the lubricant in the bearing and the average lubricant viscosity.

©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Temperature Rise and Lubricant Viscosity

The temperature rise is 113°F. The average lubricant viscosity in the bearing is µ=1.16 x 10-6 lbf-s/in2.

See the Next Slide for details of the analysis! ©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Analysis Details The dimensionless load on the bearing is Wr* =

Wr 750lbs = = 375psi 2rbwt 2 1in 1in

( )( )

Therefore the temperature rise can be calculated from Equation (12.91b):  rµ  0.103 Wr*   0.103375 9.5  c ∆tm =  = = 113°F qs  5.1 1− 0.5 0.73 Q 1− 0.5  q 

( )( ) ( )( ( ))

The average lubricant temperature is then 110°F + 113°F/2=166°F = 74°C. The oil viscosity is from Figure 8.13, µ0=0.008Ns/m2, or using the conversion from Table 8.2, µ0=1.16 x 10-6 lbf-s/in2. ©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Calculate the required radial clearance, the minimum film thickness and the required shaft surface roughness.

©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Journal Information

The required radial clearance is 540 µin. The minimum film thickness is 230 µin. The maximum surface roughness is 23 µin.

See the Next Slide for details of the analysis! ©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Analysis Details The required radial clearance, now that the viscosity is known, is obtained from the Bearing number (Equation 12.85): η ω r w  r 2 B j = 0.35=  0 b b t   b ;c = 0.00054 in= 540µ in  πWr   c 

The minimum film thickness is obtained from the dimensionless film thickness parameter previously determined: hmin = 0.42;hmin=0.420.00054 in)=230µin ( c

To maintain full film lubrication, the surface finish should be at most onetenth the film thickness, or 23µin. Fortunately, this is obtainable through standard grinding operations (see Table 8.1). ©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Calculate the friction coefficient of the journal bearing.

©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Friction Coefficient

The friction coefficient is 0.005.

See the Next Slide for details of the analysis! ©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Analysis Details

The dimensionless friction coefficient has been previously obtained as rbµ/c=9.5. Since the bearing radius is 1 in and the clearance is 540 µin, the coefficient of friction is simply 0.005.

©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Comment on the importance of the inlet oil temperature. Specifically, what effect would an inlet temperature of 130°F have on the bearing performance?

©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Inlet Temperature Importance As can be seen from Figure 8.13, the effect of increasing the oil temperature would be minimal for such a small temperature rise. However, if the viscosity were to fall significantly, then the film thickness would be small enough to allow the film to break down and have surface-to-surface contact. This would lead to quick failure of the bearing.

Also, care must be taken so that the lubricant does not become excessively heated and degrade chemically.

©1998 McGraw-Hill

Hamrock, Jacobson and Schmid

Concluding Remarks

The design of the bearing was relatively easy, using the figures from the textbook. Fortunately, this problem did not require consideration of a number of different bearing widths, which is normally the case in design. Also, this problem resulted in clearances, surface finishes and bearing dimensions which were reasonable and easily obtained, so the bearing design did not require successive iterations.

©1998 McGraw-Hill

Hamrock, Jacobson and Schmid