Horizontal reaction force wrong?

When checking the block "translational detent" in the SimDriveline library, and trying to perform the calculations myself, I encountered the following problem.

It appears that SimScape calculates the horizontal force acting on the detent as:

Fh = x*k / tan(alpha) + F_preload / tan(alpha)

Where: x is the horizontal displacement, k the spring stiffness (which is mounted vertical), 2*alpha the detent angle (according to the description in the help), and F_preload the preload force on the spring.

However, this would mean that the spring force is directly related to the horizontal displacement, while the spring is mounted vertically. Actually, the vertical displacement of the ball is y = x/tan(alpha). Therefore, shouldn't the correct formula be:

Fh = y*k / tan(alpha) + F_preload / tan(alpha) = x*k / tan(alpha)^2 + F_preload / tan(alpha) ?

Is there anybody who can explain me where I'm wrong?

Answer 1

[Martin]

Your formulation for Fh is correct, and that is what is used in the Translational Detent.