7.6 Journal Bearings

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Theodora Fisher
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1 7.6 Journal Bearings

2 7.6 Journal Bearings Procedures and Strategies, page 1 of 2 Procedures and Strategies for Solving Problems Involving Frictional Forces on Journal Bearings For problems involving a loosely fitting pulley (or wheel or collar or similar device) on a fixed shaft, follow these steps. Fixed shaft F Pulley Belt forces acting on pulley are equal. 1. Calculate the angle of friction and radius r f of the circle of friction from the equations tan -1 where is the coefficient of friction r f = r sin where r is the radius of the shaft (which, because the pulley fits "loosely", is approximately equal to the inner radius of the pulley) Contact point P 1 F For clarity, the difference in size between the radius of the shaft and the inner radius of the pulley has been exaggerated in the diagram. 2. Draw circles showing the positions and contact point of the shaft and the central hole in the pulley, when no rotation has occurred. 3. Draw circles showing the positions and contact point of the shaft and the pulley hole, after rotation has occurred. F Fixed shaft Pulley Belt forces acting on pulley are not equal. Unbalanced forces cause pulley to rotate to new contact point. P 2 F + F

3 7.6 Journal Bearings Procedures and Strategies, page 2 of 2 4. Draw a sketch of the pulley, with the circle of friction inside. On this sketch, show the friction force from the shaft opposing the rotation. Furthermore, show the line of action of the resultant of the normal and friction force, say R, passing through the contact point and lying tangent to a circle of radius rf (the circle of friction). 5. Draw a free-body diagram of the pulley, expressing R in terms of x and y components, Rx and R y. 6. Write equilibrium equations: Sum forces in the x and y directions and sum moments about the center of the pulley. Note that the moment of R is R r f, because R is tangent to the circle of friction, which has radius r f. Also, R = Rx 2 + R y 2 7. Solve the equations. Note: The above discussion applies when the pulley fits loosely on a fixed shaft. If instead the pulley is rigidly fixed to the shaft, but the shaft fits loosely on a supporting bearing, then the steps above can be followed, except that a) the shaft rotates to a new contact point relative to the fixed bearing, and b) a free-body diagram of the shaft rather than the pulley is used. Circle of friction (not the shaft) Frictional force opposes rotation F Sense of rotation of pulley Rx f R Pulley r f N Pulley P 2 r f Line of action of resultant, R, is tangent to circle of friction. P 2 R = Rx 2 + R y 2 R y F + F

4 7.6 Journal Bearings Problem Statement for Example 1 1. The pulley has a radius of 80 mm and has negligible weight. If the pulley fits loosely on a 12-mm-diameter fixed shaft, and the coefficient of static friction is s = 0.2, determine the minimum force F required to start the pulley rotating clockwise. F 80 mm 140 N

5 7.6 Journal Bearings Problem Statement for Example 2 2. The pulley has a radius of 80 mm and has negligible weight. If the pulley fits loosely on a 12-mm-diameter fixed shaft, and the pulley rotates with constant angular velocity counterclockwise, determine the coefficient of kinetic friction, µ k. 135 N 80 mm 140 N

6 7.6 Journal Bearings Problem Statement for Example 3 3. The force from the belt causes the 130-mm-radius pulley to rotate counterclockwise with constant angular velocity. The pulley fits loosely on a fixed shaft of 24-mm diameter. Determine the value of the belt force F if the coefficient of kinetic friction is µ k = 0.3. Assume that no slipping occurs between the belt and pulley. 100 N 130 mm F

7 7.6 Journal Bearings Problem Statement for Example 4 4. The stepped pulley has radii of 4 in. and 8 in. and fits loosely on a 0.5-in.-diameter fixed shaft. If the given loads cause the pulley to rotate clockwise with a constant angular velocity, determine the normal and frictional forces from the shaft acting on the pulley. Also find the coefficient of kinetic friction, µ k. 8 in. 4 in. 20 lb 40.5 lb

8 7.6 Journal Bearings Problem Statement for Example 5 5. The couple forces P are intended to rotate the shaft and wind the cable around the drum, thus raising the 5-kg mass. The shaft has a diameter of 30 mm and fits loosely in the journal bearing B. If the combined mass of the shaft handle A and drum C is 15 kg, and the coefficient of static friction is µs = 0.2, determine the minimum value of P required to initiate upward motion of the 5-kg mass. Assume the drum C is attached rigidly to the shaft. Diameter of drum = 200 mm C 5 kg P A B 150 mm 150 mm P

9 7.6 Journal Bearings Problem Statement for Example 6 6. Pulleys A and B are identical. Each has a radius of 10 in., weighs 10 lb and fits loosely on a 0.5-in.-diameter fixed shaft. Determine the maximum value of the weight W that may be supported without causing the pulleys to rotate. Also calculate the value of the tension in the cord between the pulleys. The coefficient of static friction is µs = in. 10 in. A B 100 lb W

10 7.6 Journal Bearings Problem Statement for Example 7 7. The 100-kg cart has four 200-mm-diameter wheels, 25-mm-diameter axles, and center of mass G. Each wheel has a mass of 10 kg. The coefficient of kinetic friction is Determine the horizontal force P required to move the cart at constant speed. Assume that the axles do not rotate, the wheels fit loosely on the axles, and rolling resistance between the wheels and the plane is negligible. 100 kg G P 100 mm 400 mm 400 mm

11 7.6 Journal Bearings Problem Statement for Example 8 8. The 100-kg cart has four 300-mm-diameter wheels, 30-mm-diameter axles, and center of mass G. Determine the angle for which the cart will roll down the incline at constant speed. Also determine the reactions from the incline acting on each wheel. The coefficient of kinetic friction is 0.2. Assume that rolling resistance and the weight of the wheels are negligible, the wheels fit loosely on the axles, and the axles do not rotate. 200 mm G 500 mm 500 mm

Plane Motion of Rigid Bodies: Forces and Accelerations

Plane Motion of Rigid Bodies: Forces and Accelerations Reference: Beer, Ferdinand P. et al, Vector Mechanics for Engineers : Dynamics, 8 th Edition, Mc GrawHill Hibbeler R.C., Engineering Mechanics: Dynamics,