Automotive Calculation of the reduced stiffness of a simple suspension

AI Thread Summary
The discussion centers on calculating the reduced stiffness of a front suspension, specifically addressing the relationship between vertical and inclined strokes. The key formula mentioned is k_f = k/cos²E, which raises questions about the origin of the squared cosine term. Participants clarify that the vertical spring force must be less than N_f*cos(ε), indicating that vertical stroke is proportionally smaller than the inclined stroke, which is factored in twice. The conversation emphasizes the need to understand how these relationships affect the stiffness calculations. Overall, the thread seeks clarity on the mathematical derivation of reduced stiffness in suspension systems.
Semat10
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Hello,

I have a problem with reducing a stiffness of a front suspension. Unfortunately I don't understand how to get the reduced stiffness on the right side in the picture. (k_f=k/cos^2E)

front_suspension.jpg


Thanks in advance for your help.

Many greetings,
Semat10
 
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The vertical stroke equals the inclined stroke times the cosine of angle ε.
 
Hello,

I was thinking the same thing but I don't know where the square came from?

Many greetings
 
The force of the vertical spring must be less than ##N_f*cos (ε)## ; therefore, the vertical stroke must be proportionally smaller ##(cos (ε))## than the inclined one (accounted for twice).

##k_{vertical} = N_f / {Vertical~stroke} = N_f / {Inclined~stroke}*cos (ε)##

##k_{vertical}/k_{inclined}=?##
 
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