In a typical application, ball splines help make adjustments on sprocket spacing for industrial packaging machines by Salwasser Mfg. Co., Reedley, Calif.

The ball spline allows nearly friction-free linear motion while transmitting torque, whereas a conventional spline must resort to flat metal surfaces sliding on each other. The ball spline is to splines what the ball screw is to machine screws.

Figure 1, next page, shows an example of a ball spline. Here, it consists of the spline, or inner race, and a mating linear bearing, or outer race. The inner race is typically an alloy steel, induction heat treated to 56 to 60 Rc (Rockwell C hardness). Some splines have gothic-arch type ballgroove cross-sections for long life, low rotating lash, and smooth operation.

The outer race is typically of bearing quality steel hardened to 58 to 60 Rc. Recirculating bearing balls in circuits, Figure 1, reduce wear due to friction and allow for unlimited travel. The outer race typically has several active circuits, three or six being typical. Manufacturers offer standard versions and “high-performance” versions for higher-speed, heavyduty applications.

Where you’ll find them

Common ball spline applications include:
• Honing machines.
• Robotics.
• Oil, gas, and water exploration.
• Automation and packaging equipment.
• Medical.

Applications calling for linear movement while restraining the torque resulting from a cantilever load, Figure 2, are excellent uses for ball splines, and many serve in such cases. The maximum force in bending that an assembly can take depends on the diameter of the inner race and the position of the outer race on the inner race when the load is applied. If the load is applied in a cantilever application as in Figure 2, the distance from where the load is applied to the outer race is a factor that must be considered. A unique example of an application of the ball spline is the rotor driveshaft of a helicopter, Figure 3. The ball spline allows free-floating movement of the driveshaft while transmitting driving torque.

The inner and outer races can be modified per customer request. Keyways or setscrew holes for outer races, and journals or threaded ends on inner races, can be machined if needed. If you need extrasmooth motion, close tolerances, and longer life, you can get precision-ground ball splines. Hollow shafts can reduce system weight with little loss in stiffness, a technique also used on some ball screws.

How to select

Selection of the suitable inner and outer race for a specific application involves two interrelated considerations. A change in one can affect the other. The considerations are life expectancy and critical speed. Before selecting a ball spline, the designer must determine the maximum load (lb), desired life (linear travel, in.), speed (rpm), and length between the bearings on the spline (in.). Those conventional units of length and force serve most manufacturers’ calculation procedures.

Life expectancy. The right-size spline will give the life required at the average torque. The chart of Figure 4 relates life (in millions of inches of travel) to operating torque for one manufacturer’s line of standard ball splines. Use the highest torque expected over the length of travel to select the ball spline, ensuring some extra life. The point at which torque load and life requirements intersect is then established. Select the line, representing the specified spline, to the right or above the intersection point.

Critical speed. Your final step is to verify the critical speed of the spline shaft. Critical speed is the maximum speed at which the ball spline can rotate without setting up a spontaneous natural vibration or harmonic. Critical speed varies with diameter, distance between supports, load, rotary speed, and type of bearing supports (end fixity). The four common types of support (much like the possible supports for beam or column calculations) are:
• One end fixed and one end free.
• Both ends simply supported.
• One end fixed and the other simply supported.
• Both ends fixed.

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