# Life Expectancy: Precision Ball Splines

The selection of the correct inner and outer race involves two interrelated factors. A change in one may affect the other. Before attempting to choose the size of a ball spline, the designer must know the equivalent torque measured in pound-inches, the required life measured in linear inches of travel, speed measured in revolutions per minute and length between bearing supports measured in inches.

Use the chart to determine the correct size spline which will give the life required at the equivalent torque. The chart relates life to torque.

When the torque is relatively constant over the entire stroke, use the highest torque value to select an outer race. For applications where the torques vary significantly, an equivalent torque can be calculated using the following formula:

 Tm = ∛ %1 (T1)3 + %2(T2)3 + %3(T3)3 +...+ %n (Tn)3 100

### Where

Tn = each increment of load
%n = percent of stroke at load nT

### For Example

T1 = 150 pound-inch
T2 = 225 pound-inch
T3 = 725 pound-inch
 Tm = ∛ 30(150)3 + 45(225)3 + 25(725)3 100
T = 466 pound-inch

The life required is determined by multiplying the total stroke in inches by the total number of strokes required for the designed life of the equipment.

### To Use This Chart

1. Determine required life (in million inches of travel).
2. Find point at which torque and life requirement intersect.
3. Select spline to the right or above the intersect point.
Figure 1