Name: screw torque and self-locking
Uploaded: 2023-09-22T11:49:29.000Z
Duration: 1 min 21 s
Channel: JoVE

Consider a shaft of square-threaded screw with a mean radius of 20 millimeters and a lead of 10 millimeters in contact with a plate gear of mean radius of 35 millimeters. The coefficient of static friction between the screw and gear is 0.3.
Evaluate the resisting torque on the plate gear that can be overpowered when a torsional moment of eight newton-meter is applied to the shaft.
Initially, calculate the static friction angle using the coefficient of static friction and determine the lead angle by substituting the values of lead and mean radius.
For an upward impending motion, the axial force developed in the shaft can be determined by substituting the corresponding values.
The resisting torque on the plate gear equals the product of the shaft&#39;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.
Here, the static friction angle is greater than the lead angle. So the shaft is self-locking even if the moment is removed.

screw: problem solving

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.
<img alt="Static equilibrium equation; balance analysis with force and torque variables." src="/files/ftp_upload/14321/14321_PT_Equation_1v2.svg" style="text-align: center; height: 30px;" data-altupdatedat="1761830439000" data-alt="Equation 1">
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.

In mechanical engineering, the interaction between a threaded screw shaft and a plate gear involves analyzing the resisting torque on the plate gear that ...

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screw torque and self-locking

Screw torque and self-locking are analyzed by looking at a threaded screw shaft and a plate gear. The shaft has a mean radius and a lead. The plate gear also has a mean radius. The coefficient of static friction between the screw and the gear is part of the setup.

The first step is to find the static friction angle, φ. This angle is defined by the coefficient of static friction. Next, the lead angle is calculated from the lead and the mean radius of the shaft. It gives the screw geometry needed for the torque analysis.

The axial force, F, acts along the axis of the shaft and drives the plate gear to rotate. For impending motion in a chosen direction, this force is found from a formula that uses the torsional moment, static friction angle, lead angle, and mean radius. The resisting torque on the plate gear is then the axial force multiplied by the gear’s mean radius.

By substituting the given values, the resisting torque can be determined and compared with the applied torsional moment. The same calculations also show whether the shaft is self-locking. If the static friction angle is greater than the lead angle, the shaft stays locked even after the moment is removed.

Screw Torque and Self-Locking

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key terms and concepts

Learn how to calculate axial force, resisting torque, and self-locking for a threaded screw shaft and plate gear using friction and lead angle.

Screw Torque and Self-Locking | JoVE K12

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Screw Torque and Self-Locking

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