How Do You Calculate Component Forces in an Automotive Drum Brake?

[AutoEngineers]

TL;DR

Working with Vectors

I'll try and keep this as easy as I can. The Right Triangle above represents the forces acting through the trailing shoe of a automotive drum brake.
Point A is the central position of the brake expander. When the foot brake is depressed, a force is created that pushes the brake expander piston towards the point B. The force applied from A to B is 102.32 N. When the force applied presses the brake shoe against the drum surface, the frictional force created is 32 N.

This is were I'm having doubts what to do next! The force applied is 102.32 N, the frictional force created from the applied force is 32 N.

I now want to calculate the component force acting within the brake shoe! Initially I was thinking; 102.32 x cos 37.59 = 81.1 N, but do I need to recognise the 32 N in my calculations?

If I also calculate the force acting along CA, then 102.32 x cos 52.41 = 62.4 N.

If I were to use pythagorus then those forces would work out 102.32 N correctly.

Conclusions...

I'm not sure if the frictional force acting should be taken into consideration?

I',m not 100% confident that the component forces calculated are correct?

Please advise if possible.

 

[jack action]

Drum brakes are complicated to evaluate and design details are important. The following videos explain how to do it for simple drum brakes:

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For other drum brake designs, refer to Brake Design and Safety by Rudolf Limpert, p.76-93.

 

[AutoEngineers]

Thank you for the information. Any chance you could advise the author name and ISBN of the book please!

 

[Baluncore]

Brake Design and Safety.
By Rudolf Limpert.
Third Edition. 2011 SAE International
eISBN: 978-0-7680-5789-8

Shigley’s Mechanical Engineering Design.
Richard G. Budynas; J. Keith Nisbett;
Eleventh Edition. ISBN 978-0-07-339821-1
Copyright © 2020 by McGraw-Hill Education.
Chapter 16. Clutches, Brakes, Couplings, and Flywheels. Page 829.