# Friction hinge design problem

1. Feb 11, 2016

### CarlLyon09

Hi,

I'm looking at a friction hinge design problem. See the image below for details. Looking through a machinist's handbook (pg. 1495), I get a few equations for fastener preload and wrench torque.

T = k * Fi * d, where T is wrench torque, Fi is preload, and d is the nominal bolt diameter, and k is a friction constant

Fi = 0.75 * At * Sp, where At is the bolt tensile area, and Sp is the proof strength of the bolt

By definition, Sp = 0.85*Sy, where Sy is the yield strength of the bolt.

To calculate preload, I used Sy = 340 MPa for Class 4.8 low/medium carbon steel bolts.

For At, I wasn't so sure what to use in this case. I assumed it was the area of the yellow looking washer.

Calculating preload, I ended up getting Fi = 14,300 N, which seems like a lot...

Fi = 0.75 * pi/4 * (0.01 m - .004 m)^2 * 0.85 * 340 x 10^6 Pa

Using that value, I calculated the nominal bolt diameter, d, using the first equation and got d = 0.06mm which doesn't seem to be right...

d = 300 N*mm / (0.35 * Fi)

I feel like the solution should be pretty simple... am I overcomplicating things???

Last edited: Feb 11, 2016
2. Feb 11, 2016

### CarlLyon09

Oh the wrench torque is given by the way.. T = 300 N*mm

3. Feb 12, 2016

### JBA

Since you are only showing a limited section of the problem it is hard to judge the correct problem process. I have found that too often these partial views are missing critical information in the problem description.

With regard to the bolt tensile area used for the formula, the standard area for this calculation is based upon the minor diameter of the bolt thread; but, that does not appear to be a part of the problem description. To check your max torque calculation for the bolt google "standard bolt torques"; but, remember your calculated torques are going to be a bit higher than those given in the tables you will find because those tables are based on the bolt thread minor diameter area.