Tom Bishop, P.E.
EASA Technical Support Specialist 

Have you ever had to deal with chronic drive end ball bearing failures with a v-belt application? This article will take some of the mystery out of how to determine the load on a bearing, and how to increase the bearing capacity when necessary. The focus will be on bearing loading due to belt pull with v-belt drives. How to modify a motor to accept a cylindrical roller in place of a lower ca­pacity ball bearing will also be detailed. 

Calculating bearing load and life 
The calculation of bearing loading may at first appear to be a daunting task due to the many vari­ables involved. However, taken a piece at a time, the calculations are rather straightforward. An ex­ample will be used to illustrate this point. 

Our example application is a 15 horsepower, 1150 rpm, 284T frame motor driving a belted load with a 6.75" (171mm) outside diameter pul­ley (sheave). The motor has a 6310 ball bearing on the drive end and a 6210 bearing on the oppo­site drive end. The pulley is located near the end of the motor shaft. 

The first step is to determine the forces acting on the bearings. The precise method would require measuring the center distance between drive end and opposite drive end bearings, and the distance from the center of the drive end bearing to the cen­ter of the belt pull. Rather than dismantle the motor, it is suitable to measure the distance between bear­ings by inspecting the motor and estimating the bearing to bearing center distance. The graphic be­low illustrates the measurement points. 

The measurements in this case are: X = 21.5”(546mm), Y = 17”(432mm), and Z = 4.5”(114mm). From a sheave manufacturerís catalog we find that the pitch diameter of the pulley is 6.0”(152mm). The next step is to deter­mine the belt driving force, using the following formula: 
P = f_p x Q/R 
The P is the belt force in pounds, f_p is the belt tension factor, Q is the motor torque in pound-inches, and R is the pitch radius of the pulley. The belt tension factor typically varies from 1.5 to 3.0 and we will use 2.5 for conservative results. The pitch radius is one half of the pitch diameter, that is, 6.0/2, or 3.0”(76mm).

The motor torque is: 
Q = 63000 x (hp/N), where hp is rated horse­power and N is rated speed in rpm. 
Thus we have: 
Q = 63000 x (15/1150) = 822 pound-inches
 (94.7 kilogram-meters), and 
P = 2.5 x (822/3) = 685 pounds (311 kilograms). 

The total load on the bearings will be a combi­nation of radial and axial load. The distances X, Y and Z in Figure 1 affect the radial load Rr on each bearing. The radial loads for each bearing are: 
Drive End Rr = P x (X/Y) = 685 x (21.5/17) 
= 866 pounds (393 kilograms) 
Opposite Drive End Rr = P x (Z/Y)
 = 685 x (4.5/17) = 181 pounds 
(82.1 kilograms) 

Because the radial load on the opposite drive end bearing is low, it will be disregarded here. The belt drive application should not impose any sig­nificant axial load, however, to be conservative we will assume an axial load that is 10% of the radial load. As the following calculations illustrate, the axial load is not a factor unless it is very large, e.g., vertical motor applications. 

The total load on the drive end bearing is the combination of radial and axial loads. The radial load Rr is 866 pounds (393 kilograms), and the assumed axial load Ra will be 87 pounds (39.5 kilograms). The sum of these forces RE is calcu­lated by the formula: 

pounds (395 kilograms). That is, the total load is the square root of the sum of the squares of the ra­dial and axial forces. 

Note that the 10% axial load increased the total load by less than 0.5%. That is the reason we stated above that the axial load really isnít needed for the belt load calculations. 

Calculating Expected Life Of Bearing 
The remaining calculation is the expected life of the bearing with the dynamic load applied to it. Bearings have static and dynamic load capacity, however, only the dynamic load is a concern with belt loads. Bearing load ratings vary from one manufacturer to another; how­ever, the variation is not very great. The catalog of the bear­ing manufacturer we chose states that the dynamic load rating C of the 6310 bearing used on the motor drive end is 14000 pounds (6350 kilo­grams). Bearing life is based on a factor that assumes a certain percentage of bearings in a large population failing within that time. The standard life equation usually assumes a 10% failure rate, de­noted as the L10 life based on the total number of bearing revolutions. The expression for bearing L10 life in hours is L10h. The lifetime varies by such factors as user preference and the type of applica­tion. The high end of user expectations for electric motor bearings is typically 100,000 hours.

Since we want to remain conservative in our approach we choose 100,000 hours as the desired L10h life. 

The formula for ball bearing life is: 
L_10h = (16700/N) x (C/R_E)³ 
The value 16700 is a constant. 

Inserting the values from our example, the equation becomes: 
L_10h = (16700/1150) x (14000/870)³ 
= 60512 hours. 
The desired life is at least 100,000 hours; therefore the 6310 bearing with an L10h life of 60512 hours is not adequate. The two most com­mon options are to use a maximum capacity ball bearing or a cylindrical roller bearing. The conser­vative approach is to use an NU310 cylindrical roller bearing because of its high radial load ca­pacity. To confirm that the NU310 bearing meets the desired life requirement, its L10 life is calcu­lated by the following formula: 

L₁₀ = (12100/N) x (C/R_E)^3.33. Note that the con­stant has changed from 16700 to 12100, and the exponent has increased from the power of 3 to 3.33. 

The dynamic load rating of an NU310 bearing, from the manufacturerís catalog we chose, is 25000 pounds (11340 kilograms). The life equa­tion becomes: 
L_10h = (12100/1150) x (25000/866)^3.33 = 767880 hours. Note that we have used 866 for R_E because the NU style cylindrical roller bearing has no axial load capability. 

The cylindrical roller bearing has more than 7 times the required expected life. That provides a high level of confidence that even if work begins. Namely, convert­ing the motor from ball bearing to roller bearing on the drive end. 

Ball to roller bearing conversion 
Motors equipped with ball bearings typically have the drive end bearing locked in place axially. The opposite drive end bearing must then be free to grow axially, i.e.,“float”, to al­low for thermal growth and contraction. A wavy washer may also be installed on the outboard side of the opposite drive end bearing, to preload the bearing assembly and to assist the bearing in moving inboard with contraction as it cools down. 

When equipped with a cylindrical roller bearing on the drive end, the opposite drive end bearing is locked in place axially. The cylindri­cal roller bearing is of the type that allows the rollers on the inner or outer race to move unrestricted in either axial direction. Therefore, the shaft on the drive end bearing is not fixed. 

The cylindrical roller bearing to be installed in the drive end should be equivalent in physical mounting dimensions to the ball bearing it re­places. Unless there is a reason to do otherwise, use an NU series cylindrical roller bearing, hav­ing a standalone inner race with the outer race retaining the rollers and cage. The drive end of the motor does not need to be modified to accept the cylindrical roller bearing. 

Measuring and recording endplay
The modification process begins before disassembling the motor to be converted from drive end ball to roller bearing. Attach a dial indicator to the end bracket on the drive side of the motor, with the dial against the end of the shaft. Measure and record the endplay. (For additional information about endplay measurement, see the article“Follow These Procedures When Checking Endplay In A Ball Bearing Machine “ in the May 2000 issue of Currents.) If the drive end bearing is correctly locked, there will only be the internal endplay of the ball bearing, which should be less than
.003”(.076mm). If the endplay exceeds this value the drive end bracket should be removed and temporary shimming placed between the inner bearing cap and the drive end bearing, to eliminate the endplay. The drive end bracket is then reinstalled, the bearing cap bolts retightened, and the endplay rechecked to confirm that it is less than .003”(.076mm). Leave the dial indicator on the end of the shaft.

Loosen the drive end bearing cap bolts, taking care not to disturb the shaft endplay setting. Push the shaft inboard, i.e., toward the opposite drive end and measure the endplay. Record this value as dimension “AA”. Retighten the bearing cap bolts on the drive end to bring the shaft back to its original position and then loosen the bearing cap bolts. Pull the shaft outboard, i.e., toward the drive end and measure the endplay in this direction. Record this value as dimension “BB”. Retighten the bearing cap bolts then loosen them. Push the rotor to the opposite drive end limit and ìzeroî the dial indicator. Then pull the shaft toward the drive end, to its limit, and measure the total endplay. Record this value as dimension “CC”. The sum of dimensions AA and BB should approximate dimension CC. There can be up to.003”(.076mm) difference due to axial endplay in the fixed bearing.

Use spacer rings to lock bearing
After disassembling the motor, determine the outer diameter of the opposite drive bearing from a bearing table. Two spacer rings will be needed to lock this bearing for use with the drive end roller bearing. Each ring should be about .010”(.25mm) smaller in outer diameter than the opposite drive end bearing, and the inner diameter about 3/8”(9.5mm) smaller than the ring outside diameter. The spacer ring on the outboard side of the opposite drive end bearing should have a thickness equal to dimensions AA, and thickness of the inboard spacer ring should be equal to dimension BB. If there is enough material in the bearing back cap, machine the dimension BB off of its face rather than making a spacer.

The machined back cap will be easier to assemble than a back cap and spacer combination.

The opposite drive end ball bearing now becomes the locking or fixed bearing, whereas it was previously free to move or“float”. Upon reassembly check the endplay to verify that it is less than .003”(.076mm). If the endplay exceeds the internal play of the ball bearing, but is less than .010”(.25mm), increase the thickness of the outboard spacer by the amount of endplay. If the endplay is greater than .010”(.25mm), check for assembly or prior measurement errors.

Run test the motor for about 5-10 minutes to verify proper operation. If the roller bearing becomes noisy, due to rollers “skating”, end the run test. Cylindrical roller bearings may become noisy without radial preload. In those cases, running the motor in the actual application will be required to confirm that the cylindrical bearing is in satisfactory condition.

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Categories: Bearings, Design/theory/application

Tags: Bearing load

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