Machinery's Handbook, 31st Edition
Ball Screw Selection and Design 2643 Design Overview: To design a ball screw assembly many interrelated factors such as load, bearing length, life, and speed must be considered. Changing one parameter will influence others and generally an iterative approach to balancing these requirements is re - quired. An example is the choice of a fine lead versus coarse lead. A fine line lead provides better positioning sensitivity and lower drive torque, but also requires a higher rotary speed to achieve the same linear rate of speed. A coarse lead results in lower rotary speed, but requires a higher drive torque that may require a larger motor and related drive compo nents. Table 1 identifies some of these design interrelationships. Table 1. Ball Screw Design Factor Interrelationships Increase In Affects How Increase In Affects How Screw Length Critical speed Decreases End Mounting Rigidity Critical speed Increases Compression load Decreases Compression load Increases
Critical speed
Increases
System stiffness
Increases Decreases Increases Increases Decreases Increases Increases Increases Increases
Inertia
Increases Load
Life
Compression load Increases
Positioning accuracy Increases
Screw Diameter
Stiffness Spring Rate Load capacity Drive torque Angular velocity Load capacity
Increases Increases
Preload
System stiffness Drag torque Critical speed Load capacity
Increases Angular Velocity Increases Nut length
Decreases Increases
Stiffness
Lead
Life
Positioning accuracy Decreases
Ball diameter
Stiffness
Ball diameter Increases Screws, Power Transmission.— The square form of thread has a somewhat higher effi ciency than threads with sloping sides, although when the angle of the thread form is comparatively small, as in the case of an Acme thread, there is little increase in frictional losses. The Acme thread has superseded the square form on many classes of equipment requiring lead screws or other power transmitting screws, because the former has practi- cal advantages in regard to cutting and also in compensating for wear between the screw and nut. Multiple thread screws are much more efficient than single-thread screws, as the efficiency is affected by the helix angle of the thread. Increases Load capacity Force Required to Turn Screw: In determining the force which must be applied at the end of a given lever-arm in order to turn a screw (or nut surrounding it), there are two con ditions to be considered: 1) When rotation is such that the load resists the movement of the screw, as in raising a load with a screw jack, F L r l l r R r 2 2 # # π µ πµ = − + . 2) When rotation is such that the load assists the movement of the screw, as in lowering a load, F L r l r l R r 2 2 # # π µ πµ = + − . In these formulas, F = force applied at end of lever-arm; L = load moved by screw; R = length of lever-arm; l = lead of screw thread; r = mean or pitch radius of screw; μ = coeffi cient of friction. If lead l is large in proportion to the diameter so that the helix angle is large, F will have a negative value, indicating that the screw will turn due to the load alone. The efficiency between a screw and nut increases quite rapidly for helix angles up to 10 or 15 degrees (measured from a plane perpendicular to the screw axis). The efficiency remains nearly constant for angles between about 25 and 65 degrees, and the angle of maximum efficiency is between 40 and 50 degrees. A screw will not be self-locking if the efficiency exceeds 50 percent.
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