Formula for calculating thrust and torque of ball screw

When analyzing the performance of screw products, we often need to calculate torque, and the formula for calculating thrust and torque of ball screw is one of the important basic principles in the mechanical design of ball screw. Through this formula, the situation of ball screw can be simplified and understood.
The calculation formula for thrust and torque of ball screw is thrust T=PD/2 π L; torque M=PD ^ 2/4 π L ^ 2, where P is the transmission force of the ball screw, D is the diameter of the ball screw, L is the length of the ball screw, T is the thrust of the ball screw, and M is the torque of the ball screw. Due to the transmission characteristics of the ball screw, the thrust T and torque M are proportional to the diameter D and length L of the ball screw, and proportional to the square ratio of the transmission force P.
Formula for calculating the thrust of ball screw:
T=FL/{2 * PAI (3.14) * n (transmission efficiency)}
T=motor input torque
F=screw thrust
If there is a gearbox, output torque=input torque * speed ratio
For example:
The lead screw rotates one circle, and the turning force x1 has a circumference equal to the thrust Fx and lead P. The turning force f=T/r, fx2 ∏ r=FxP, that is, 2 ∏ T=FxP
Assuming the efficiency of the reducer is η 1=0.75; The efficiency of ball screw is calculated according to η 2=0.95:
The output torque of the reducer is M=3 × 40 × 0.75=90 (N.m).
Lead h=0.01 meters, axial thrust T, T × h=M × 2 × π× η 2
Additional Information:
The torque output of the motor is related to the speed and power of the motor.
P=T * ω (power=torque * angular velocity)
T=9550P/n This formula is commonly used in engineering: torque; Power; The calculation formula for the relationship between rotational speed and three factors.
In the formula: T - torque (unit: N.M) 9550- treat it as a constant (without investigating its source) P - power of the motor (unit: kW)
N - Output speed (unit: revolutions per minute)
The origin of constant 9550: The work completed by T is the work output by the electric motor.
Reference source: Baidu Baike - Motor Torque
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