In considering friction of a V-thread, the virtual coefficient of friction (μ₁) is given by

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.