A prominent member of the power-transmission linear-actuator family is the ball screw assembly, a device that converts torque to thrust, in which rolling motion of the balls provides energy transmission efficiency over 90%. That’s twice the efficiency of sliding-type lead screws. Nearly all the power (torque times angular velocity) can be used as linear power (force times linear velocity), moving the ball nut and any attached member. The advantages: lower energy consumption, less wear, long-lasting preload and precision, and predictable life. But those advantages can be lost because of poor choice of end-fixity conditions.

You can draw free-body diagrams for the screw, nut, and bearing end-mounts, Figure 1. Every action is opposed by an equal and opposite reaction. If the screw rotates, then the nut must translate for power transmission to occur. To react the force, one component must be fixed with respect to linear motion.

Because most screws are electric-motor- driven, the screw is usually constrained with respect to linear motion. Typically, it is installed on bearings that are mounted on the same base as the motor. The forces of load and acceleration created on the ball nut are thereby reacted by an axial thrust at the bearing end (or ends) of the screw. This is why the method used to mount the screw has a major impact on the system’s load capacity, stiffness, responsiveness, and speed.

The methods of fixing ball-screw ends and their effects on performance are many.

Supported vs. fixed

Mounting of ball-screw ends is described as either supported or fixed. A supported end offers one focal point of the ball screw and does not react bending moments; instead, the angle between the axis of the screw and the rotary bearing increases, Figure 2. A fixed end can react moment loads because it is based on two rotary bearings sufficiently spaced apart so the ball screw remains perpendicular to the planes of the rotary bearings. Effective centers 1.5 times nominal screw diameter are usually enough. Figure 3 shows details of the fixed end of a screw, including hardware.

Two advantages of a screw with a fixed end are greater column strength and higher critical speed. More about these later. The advantages of a supported end are compactness and lower cost. A fixed end is generally harder to align and install than a supported end, so installation cost is a factor.

It is the function of linear motion bearings, which are typically an integral part of a linear motion system, to support side loads (radial loads). Apart from considerations of end fixity, side-loading could introduce misalignments and strains in the ball nut and reduce its expected travel life. Therefore, you might ask, “Why must end fixity counteract bending forces?” The answer has to do with column strength and critical speed.

From simplest to more difficult mounting arrangements, a ball screw can be:
• Fixed at one end and free at the other. With one end free, the ball screw is easily bent because the free end can move like a cantilever beam.
• Supported at both ends.
• Fixed at one end and supported at the other.
• Fixed at both ends.

Figure 4 shows these cases. The relative lengths correspond to lengths that would result in the same critical speed for equal-diameter ball screws.

Column strength

The ability of a ball screw to avoid buckling under a compressive load is called its column strength. The screw must carry an axial load that is equal and opposite the load generated on the ball nut by the motor’s torque. In general, column strength is the controlling design parameter because, for long columns, it is much lower than the material’s strength in compression.

Because the length-to-diameter ratio is important in column buckling, it is no surprise that the compressive load strength of ball screws is a function of length. A length-to-diameter ratio (L/D) exceeding 100:1 requires special design consideration; consult the manufacturer regardless of anticipated loads or fixity.

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