POWER TRANSMISSION REFERENCE
GUIDE
All about rigidity in
linear actuation THE
default method for increasing ballscrew rigidity is to increase the preload of the ball nut. However,
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the ball nut is one of the most rigid components in the ballscrew assembly … so increasing ball nut rigidity has little effect on the overall system rigidity (except when upgrading from a ball nut with no preload to one that is preloaded). Also, higher preload causes higher frictional torque, which means more heat is generated and more torque is required to drive the screw. A double ball nut is somewhat more rigid than a single nut but again, the effect is minimal due to the nut’s already high rigidity relative to the other components. Ballscrew rigidity is calculated:
A double ball nut has higher rigidity than a single nut, but the overall effect on the ballscrew system’s rigidity is relatively small.
Where: Rtot = Rigidity of the screw system (N/μm) RS = Rigidity of the screw shaft (N/μm) RN = Rigidity of the ball nut (N/μm) RB = Rigidity of the support bearings (N/μm) RH = Rigidity of the ball nut and bearing housings (N/μm) The limiting factor for rigidity in a ballscrew assembly is typically the screw shaft. The rigidity of the screw shaft depends on its modulus of elasticity, diameter (which determines its crosssectional area), and unsupported length. The screw’s modulus of elasticity is dependent on the material (typically steel) and its diameter is primarily determined by the required thrust force and speed. The unsupported length of the screw shaft is determined by the stroke and the end bearing arrangement. While the screw’s material and diameter are generally set by the application, the end bearing arrangement (and hence, its influence on unsupported length) is chosen based on factors such as speed, buckling load, and rigidity. There are four common end bearing combinations for
8
DESIGN WORLD — MOTION
Nuts can help boost rigidity.
5 • 2020
ballscrew assemblies. From most to least rigid, they are fixed-fixed, fixed-floating, floating-floating, and fixed-free. A fixed end uses an angular contact thrust bearing, for support against both radial and axial loads, while a floating end uses a simple radial bearing, with no support for axial loads. A free end has no bearing support. Using the stiffest bearing arrangement – fixed-fixed – increases the rigidity of the screw shaft by four times compared to the least rigid arrangement of fixed-free. This is due to two design advantages. First, using angular thrust bearings on both ends allows forces to be transmitted through the screw on both sides of the ball nut. In addition, with thrust bearings on both ends, the maximum distance between the ball nut and either one of the fixed bearings occurs when the nut is at the middle of the stroke, which means the unsupported length is one-half the length of the screw. Another effective method to increase ballscrew rigidity is to change the way the assembly operates: hold the screw stationary and rotate the ball nut. In a rotating nut design, because the screw itself does not rotate, there is no need for support bearings on the motioncontroltips.com
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