Question

how to calculate forces on cam and follower at various cam speed and angle.Cam and follower with SHM motion.What are the formula available

Answer 1

The force law equation for cam and follower with SHM is

Force, F= - kx;

The negative sign indicates that restoring force of spring and displacement are in opposite direction.

k is force constant = mw²

Where

m is moving mass

w is angular velocity

and

x is lift or displacement of follower

I will now tell a easy technique to calculate force on cam and follower in MS excel or spreadsheet. This method is suitable for any profile and all you need is Angle Vs lift/displacement data for 360° cam profile

I now assume that you have follower lift (possibly a knife edge follower) for each angle in steps of 1°. Note for roller follower there will be 2 lift profiles (cam lift and roller lift)

a) Enter Angle 0° to 359° in First column of excel spreadsheet. You will have 360 points if you are entering them in steps in 1°

b) Enter lift or displacement data of the follower against each angle in second column.

c) We know that rate of change of displacement is velocity. You will get 359 points in column c if you differentiate points in column b. Add 0 to first row of column c to get 360 points again.

d) Similar to step c, we know that rate of change of velocity is acceleration. You will get 359points in column d if you differentiate points in column c. Add 0 to first row of column d.

Now you have acceleration of cam profile at each angle.

Next evaluate the total moving mass of parts on cam like follower mass, spring mass (effectively 2/3rd), a piston sometimes, etc.

We know F = ma (Newton law)

Get the inertial force by mutiplying the acceleration in column d with constant moving mass and you can put these values in column e for good understanding of force on roller and follower at each cam profile point.

Note this acceleration in column d will be with unit metre/degree². You need to convert this unit into metre/second²(m/s²). It's easy. Get the speed of cam in revolution per second² (rev/s²) and multiply it with m/deg² to get m/s²

Note: revolution is just a count and 1 rev =360°

So 1° =1/360 rev. Ensure you are squaring this value when substituting this in place of deg²

We have got only inertial force. One can add spring force and hyfraulic force (if any) to get the total force on cam and follower