Machine Design

# Ball Screw Speed Basics

A look at the three important speeds when it comes to these essential devices.

Speed is an important characteristic in ball screws, as it is for most motion control devices. But ball screws have three kinds of speed associated with them. Here’s a quick look at all three.

### Critical Speed

Critical speed is the lowest rotational speed at which the ball-screw shaft is in resonance. In applications with rotating shafts, it limits the screw’s rpm. Variables that influence critical speed are shaft diameter, unsupported length, and the configuration of support bearings.

Similar to buckling, critical speed depends on how the support bearings are laid out. Fixed support bearings are assumed to resist angular deflection of the shaft, while simple support bearings do not. A bearing assembly consisting of two simple bearings with a spacer would however qualify as “fixed” bearing for these purposes.

For long screws, Steinmeyer, a worldwide leader in ball screws, recommends using the following equation. Make sure to select the proper factor for the bearing configuration used in it:

where nk is the critical speed (rpm), dN is the nominal diameter (mm),  ls  is the screw’s unsupported length (mm), and k  is the support-bearing factor

### Maximum Speed

A second limitation, which determines the maximum speed, stems from inertial forces on the balls. It depends on the internal construction of the ball nut (in particular the ball return) and the ball size. In general, ball screws with small balls have somewhat lower speed limits than screws with larger balls. For Steinmeyer ball screws, speeds can range from 4,500 rpm for 3-mm balls) to about 1,050 rpm for 125-mm balls. (For a breakdown of speeds, see the table here.

### DN Value

The concept of DN is a simplified way of determining the maximum rotational speed of a ball screw. DN is simply the multiplication of nominal diameter of the ball screw (in mm) times the maximum allowable speed (in rpm). Keep in mind that for very small and very large screws this will not return valid numbers.

DN, the driving speed values allow easy comparison between different ball screw designs. More sophisticated ball return systems have higher DN values and, conversely, lower DN values are associated with less sophisticated ball return methods. DN values provide direct correlation to ball velocity. It is calculated by:

DN = nmax ∙ dN

Where nmax is the maximum speed (rpm), dN  is the nominal diameter (mm), DN  is the driving speed value.

Most ball screws available today have maximum DN values between 60,000 and 120,000, and in some cases even higher.

Bruce Gertz, Executive Vice President

Steinmeyer Inc.

Burlington, Mass.