8.11 : Screw: Problem Solving

In mechanical engineering, the interaction between a threaded screw shaft and a plate gear involves analyzing the resisting torque on the plate gear that can be overpowered when a specific torsional moment is applied to the shaft. To better comprehend this concept, consider a generic situation with a threaded screw shaft with a given mean radius and lead and a plate gear with a specified mean radius. The coefficient of static friction between the screw and gear is also provided.

To evaluate the resisting torque on the plate gear that can be overpowered when a certain torsional moment is applied to the shaft, the first step is to calculate the static friction angle using the coefficient of static friction. The static friction angle, denoted as φ, is the angle whose tangent is equal to the coefficient of static friction.

Next, the lead angle is determined by substituting the values of the lead and mean radius. It is equal to the ratio of the lead to the circumference of the shaft.

The axial force, denoted as F, is the force acting along the axis of the shaft that causes the plate gear to rotate. For an impending motion in a specific direction, the axial force developed in the shaft can be determined by using a formula involving the torsional moment, static friction angle, lead angle, and mean radius.

The resisting torque on the plate gear equals the product of the shaft's axial force and the mean radius of the gear. By substituting the values, the resisting torque that can overpower the applied torsional moment can be determined.

Also, if the static friction angle is greater than the lead angle, the shaft is self-locking even if the moment is removed.

Finally, one can determine whether the shaft is self-locking through a series of calculations involving the static friction angle, lead angle, axial force, and resisting torque. This analysis is crucial in understanding the mechanical behavior of shafts and gears in various engineering applications.