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Background

Static analysis of Clutches and Brakes can be used to calculate the effectiveness of static brakes, which helps in deciding which materials and design should be used
This method should be able to predict the effectiveness of a doorstop
Proving this theory shows that this method can be relied on when designing a braking system

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Theory

If doorstop dimensions, center of pressure location on the brake pad, and coefficient of static friction are found, it can be predicted if the brake will work using:

c is horizontal distance from the hinge to the back of the brake pad
a is vertical distance from the hinge to the ground
ubar is the distance from the back of the break to the center of pressure,
f is the critical friction coefficient.

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Theory

If ubar from the prior equation is unable to be accurately assumed, it can be found using:

After solving for f_cr, if the actual friction coefficient is smaller than f_cr, the brake will fail
Assumptions: the door stop is not off centered, and that the actual friction coefficient is known

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Predictions

Values used from doorstop specs:

Height to hinge (a) = 4in
Length from hinge to start of brake (c) = 1.6in
Length of brake pad (w₁) = 1in
Thickness of brake pad (w₂) = 0.75in
Actual friction coefficient (f) = 0.4
Force pushing up on the pad (F) = 10lbs

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Predictions

Calculating for the ubar value using the equation:

Which goes to

Which makes ubar = 0.3597

From this we can find:

Since the f = 0.4 < 0.535, which means this break would fail to stop the door.

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Method/Design - Required Materials

Doorstop
Scale that can measure continuously
Pull scale
Piece of wood that the doorstop can attach to
ruler or calipers
Multiple materials with varying coefficients of static friction

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Method - Part 1

Finding the true coefficient of static friction

Place doorstop on the scale to measure the normal force
Hook pull scale to doorstop
While recording weight on both scales, pull doorstop with the pull scale
Calculate coefficient of static friction by dividing the measured pull string force by the normal force

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Method - Part 2

Attach the doorstop to a piece wood, and attach that do a door
Place the scale on the ground with one of the materials being tested attached on top
Place the doorstop setup on the material being tested against
Have cameras on the weights of the scale, along with the doorstop itself to record all data
Push the door to test if it is a self-acting brake

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Results of Experiments

Materials	Avg Normal Force (lbs)	Avg Pull Force (lbs)	Length A (in)	Length B (in)	Length ubar (in)
Rubber on Steel	13.5	7	4.78	0.136	0.75
Rubber on Aluminum	12	3.7	4.75	0.5	0.6
Rubber on Plastic	13	6	4.75	0.5	0.7
Cloth on Plastic	12	2	4.75	0.5	0.7

Experiments done in the Maker Lab on 3/19/22

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Analysis

Every time the real coefficient of friction was higher than the critical, it stopped the door.

Hence, all predicted values were correct.

No error was found in our experiment, although there is uncertainty from the small number of data points.

Materials	f-critical	Greater or Less	f-real	Stops door?
Rubber on Steel	0.19	<	0.52	Yes
Rubber on Aluminum	0.25	<	0.30	Yes
Rubber on Plastic	0.25	<	0.46	Yes
Cloth on Plastic	0.23	>	0.17	No

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Conclusion

The results of our experiment support that the theory is correct
Since the experiment had binary results, no error was found. This could be improved in future experiments
While methods were valid, some points to consider in order to improve accuracy are

Have more accurate measurements of the geometry and angles
Obtain a much higher number of data points when testing both real and critical friction coefficients

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Sources

Equations and images from:

Shigley’s Mechanical Engineering Design, Eleventh Edition, section 16-1

Table of coefficients of friction:

https://www.engineersedge.com/coeffients_of_friction.htm

Photo from title page:

amazon.com