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13.2 KINEMATICS
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The primary function or design requirement of a power screw is to move an axial load F through a specified linear distance, called the travel. As a single-degree-offreedom mechanism, screw travel is constrained between the fully extended position xmax and the closed or retracted position xmin. The output range of motion, therefore, is xmax xmin. As the input torque T is applied through an angle of rotation , the screw travels x in proportion to the screw lead L or total number of screw turns Nt as follows: x = L = LNt 2 (13.1)
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In addition to range of motion specifications, other kinematic requirements may be prescribed, such as velocity or acceleration. The linear screw speed V, in/min, is obtained for a constant angular speed of n, r/min, as V = nL (13.2)
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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POWER SCREWS 13.4
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FIGURE 13.2 Basic thread forms. (a) Square; (b) general-purpose Acme; (c) buttress. The stub Acme thread height is 0.3p.
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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TABLE 13.1 Standard Thread Sizes for Acme Thread Form Size D, in 4 16 3 8 7 16 1 2 5 8 3 4 7 8 1 11 8 11 4 13 8 11 2 13 4 2 21 4 21 2 23 4 3 31 2 4 41 2 5
Threads per inch n 16 16, 14 16, 14, 12, 10 16, 14, 12, 10 16, 14, 12, 10, 8 16, 14, 12, 10, 8 16, 14, 12, 10, 8, 6 14, 12, 10, 8, 6, 5 14, 12, 10, 8, 6, 5 12, 10, 8, 6, 5, 4 12, 10, 8, 6, 5, 4 10, 8, 6, 5, 4 10, 8, 6, 5, 4, 3 10, 8, 6, 4, 4, 3, 21 2 8, 6, 5, 4, 3, 21 2, 2 6, 5, 4, 3, 21 2, 2 5, 4, 3, 21 2, 2 4, 3, 21 2, 2 4, 3, 21 2, 2, 11 2, 11 3 4, 3, 21 2, 2, 11 2, 11 3, 1 4, 3, 21 2, 2, 11 2, 11 3, 1 3, 21 2, 2, 11 2, 11 3, 1 3, 21 2, 2, 11 2, 11 3, 1
The preferred size is shown in boldface.
FIGURE 13.3 Ball screw assembly. (Saginaw Steering Gear Division, General Motors Corporation.)
The input speed may vary with respect to time t, resulting in a proportional change in output speed according to V(t) = x(t) = L (t) 2 L (t) 2 (13.3)
Similarly, the linear and angular accelerations of the load screw are related as follows: A(t) = x(t) = (13.4)
Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
POWER SCREWS 13.6
GEARING
Inertia forces and torques are often neglected for screw systems which have small accelerations or masses. If the screw accelerates a large mass, however, or if a nominal mass is accelerated quickly, then inertia forces and torques should be analyzed. The total required input torque is obtained by superposing the static equilibrium torque, the torque required to accelerate the load, and the inertia torque of the screw rod itself. The inertia torque of the screw is sometimes significant for highspeed linear actuators. And lastly, impacts resulting from jerks can be analyzed using strain-energy methods or finite-element methods.
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