How to Calculate Shaft Deflection
- 1). Measure the distance from the bearing center to the hub center of the pulley mechanism (a), and the distance between the two bearing centers (L). For the example, the measurements of (a) will be 7 inches and (L) will be 20 inches.
- 2). Measure the diameter of the shaft. Calculate the moment of inertia variable by multiplying the shaft diameter by 4 and dividing it by 64. (I = D * 4 / 64) Weigh the total weight of the load on the pulley on the scale (W). For example, if the diameter was 32 inches, then 32 x 4/64 = moment of inertia of 2. For the example, the weight is 150 lbs.
- 3). Multiply the distance from the bearing center to the hub center by 2. Subtract the resulting number from the distance between the bearing centers. (L-2a) = 20 - 2 (7) = 6.
- 4). Multiply the resulting number by the distance from the bearing center to the hub center, the total weight and then 180.
- 5). Multiply the moment of inertia by the modulus of elasticity. In most cases, this will be 29 x 106 psi since the majority of machinery is made of steel. Multiply the resulting number by 4 and then pi (approximately 22/7).
(4 x pi x E x I) = (4 x pi) x 29 x 106 x 2 = 77,289.143 - 6). Divide the first number obtained above by the number calculated in Step 5. The resulting number will be the degree of shaft deflection.
7560 / 77,289.143 = .097 degrees of shaft deflection.
The shaft deflection number should not be greater than .13 degrees. If it is, the shaft might be too small.
The final formula should be: angle of deflection= 180 x W x a (L-2a) / 4 x pi x E x I.