Friction of a v-thread

FRICTION OF A V-THREAD

In V-threads (or ACME or trapezoidal threads), the axial load W does not act perpendicular to the surface of the threads, as shown in Fig.6.14. Unlike threads, in V-threads the normal reaction RNI between the screw and nut is increased (because the axial component of RN is equal and opposite to the axial load W).

Let 2β be the angle included between two sides of the thread (ie., angle of the V-thread).

Frictional force tangential to the thread surface is given by

Note

1. When coefficient of friction, μ1 = μ / cos β is considered, then the V-thread is equivalent to a square thread.

2. All the equations of square threaded screw also hold good for V-threads. But in case of V-threads, μ1 may be substituted in place of u in all the equations. 

1. Square Threads Vs V-Threads

• V-threads are stronger and offer more frictional resistance to motion than square threads. 

• A given load may be lifted by applying lesser force by square threads as compared to V- threads.

• V-threads are capable of taking more loads as compared to square threads.

Example 6.12 

A bolt is having V-threads. The pitch of the threads is 5 mm and the V-angle is 55°. The mean diameter of the bolt is 20 mm. The bolt is tightened by screwing a nut. The mean radius of the bearing surface of the nut is 25 mm. The load on the bolt is 5000 N. The coefficient of friction for nut and bolt is 0.1 whereas for nut and bearing surface is 0.16. Determine the force required at the end of a spanner 0.6 m long.

Given data: 

p = 5 mm = 0.005 m; 2β = 55° or β = 27.5°; d = 20 mm = 0.02 m; H2

R = 30 mm = 0.03 m; W = 5000 N; μ = tan ϕ = 0.1; μ2 = 0.16; l = 0.6 m.

Solution:

We know that virtual coefficient of friction,

⸫ Force on the screw is given by

We know that the total torque transmitted,

Let P1 = Force required at the end of a spanner

We also know that the torque at the end of a spanner,

Example 6.13 

The lead screw of a lathe has ACME threads of 50 mm outside diameter and 10 mm pitch. The included angle of the thread is 29°. It drives a tool carriage and exerts an axial pressure of 2500 N. A collar bearing with outside diameter 100 mm and inside diameter 50 mm is provided to take up the thrust. If the lead screw rotates at 30 rpm, find the efficiency and the power required to drive the screw. The coefficient of friction for screw threads is 0.15 and for the collar is 0.12. Also state whether the screw is self-locking.

Given data: 

d0 = 50 mm = 50 × 10-3 m; p = 10 mm = 10 × 10-3 m; 2β = 29° or β = 14.5°; W = 2500 N; D0 = 100 mm or R0 = 50 mm = 50 × 10-3 m; Di = 50 mm or Ri = 25 mm = 25 × 10-3 m; N = 30 rpm; μ = 0.15; μ2 = 0.12.

Solution: 

Virtual coefficient of friction,

Force required at the circumference of the screw is given by

We know that mean radius of the collar,

We know that the power required to drive the screw

Efficiency of the screw drive is given by

Since the efficiency of the same screw is less than 50%, therefore the screw is self-locking screw. Ans.