In considering friction of a V-thread, the virtual coefficient of friction (μ1) is given by
A. μ1 = μsinβ
B. μ1 = μcosβ
C. $${\mu _1} = \frac{\mu }{{\sin \beta }}$$
D. $${\mu _1} = \frac{\mu }{{\cos \beta }}$$
Answer: Option D
Solution (By Examveda Team)
The virtual coefficient of friction in a V-thread is derived from the normal reaction forces and frictional forces acting on the inclined plane of the thread.In a V-thread, the friction force is influenced by the helix angle and the thread angle (\(\beta\)). The relationship between the actual coefficient of friction (\(\mu\)) and the virtual coefficient of friction (\(\mu_1\)) is determined by resolving forces along and perpendicular to the inclined thread surface.
For a V-thread, the normal force component acts at an angle, leading to the effective coefficient of friction being altered by a factor of \( \cos \beta \).
Thus, the virtual coefficient of friction is given by:
\[ \mu_1 = \frac{\mu}{\cos \beta} \]
This indicates that the effective friction increases as the thread angle (\(\beta\)) increases because the normal force component decreases, requiring a larger effective friction to compensate.
This Question Belongs to Mechanical Engineering >> Theory Of Machine
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Solution
Ans is:- option(C) if the angle is 2×B of thread angle
In V threads, the normal reaction acts at an angle beta which is the semi groove angle. This normal reaction is increased as its axial component must be equal to the load W acting in the horizontal direction.
W = R cos beta
or R = W/ cos beta.
Friction F = nu R
or F = (nu W) / cos beta
or F = (nu / cos beta) W
or F = nu' W
where nu' is the virtual coefficient of friction.
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