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

AI Thread Summary
The discussion focuses on calculating component forces in automotive drum brakes, specifically through the trailing shoe. A force of 102.32 N is applied from the brake expander to the shoe, resulting in a frictional force of 32 N when the shoe contacts the drum. The user is uncertain whether to include the frictional force in their calculations and is attempting to determine the correct component forces using trigonometric functions and Pythagorean theorem. They express doubts about the accuracy of their calculations and seek clarification on the role of friction in this context. Resources for further understanding, including a book by Rudolf Limpert, are also provided.
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Brake force diagram.png

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