Cam design please help 1

[Jamaz17]

Hey all,

Is anyone good with cam calculations that might be able to give me a hand. I'm trying to find the force generated by a cam at different points on the cam. I've bin unsuccessful so far, I have a good idea where to start but I haven't done anything with cams before. Any help is greatly appreciated. (or any ideas as to where I might better find help)
Thanks,

 

[ivymike]

there's a problem - force isn't generated by the cam, displacement is.

There are a few approaches you can take:
- kinematic: force depends only on the displacement, the geometry of the system, and whatever you're using to hold the system against the cam. You didn't mention whether you're dealing with an automotive valvetrain or something else.
- pseudo-dynamic: force depends on the above, plus instantaneous acceleration of the system (cam profile and rotational speed will influence this)
- dynamic: every component has inertia and stiffness, and will vibrate, so force at any interface will depend on a whole lot - usually this force is measured or derived by simulation rather than calculated by hand.

 

[Jamaz17]

Thanks for the info, it it not being used on a vavletrain. I have a cam pushing a piston which in turns pushs on a hydraulic fluid. Any further information would be great

Thanks again

 

[zekeman]

Get the force to push the piston. Then determine the the ratio of the incremental distance the piston moves to the angular rotation the cam makes (in radans).
Then apply the energy conservaton equation, namely
F*dx=T*dtheta or T=F*dx/dtheta
where
F= piston force
dx/dtheta= ratio of piston to cam angle motions
T = torque on cam
Next draw the normal force vector actng on the cam at the surface. Finally,drop perpendicular from the center of rotation to the vector and call that distnce r.The torque can be written as
Fc*r where Fc is the normal force on the cam you seek.
Substituting into the eq above we get:
Fc*r=F*dx/dtheta and Fc=F*dx/dtheta/r

 

[Jamaz17]

Thanks for that info; I was with you right up until you got into dropping that perpendicular line? I'm not sure i follow this part because my normal force is acting thru the centre of rotation so there is no other line. Also I'm not sure what the force Fc is that you are refering to. If you could clarify that would be great.

 

[zekeman]

Be careful.The piston force F may be acting thru the centre of rotation. That isn't Fc. Fc is the normal(perpendicular) force to the cam surface and in general does not go through the centre, except during dwell periods at which time the two forces, F and Fc forces are equal and the energy eq degenerates.Fc is the force you are seeking.
Repeating,torque on the cam is the normal force, Fc acting on the cam surface multiplied by the distance r from the centre of rotation to the line of action of that force( the fundamental definition of torque).You get the distance,r by first drawing a line perpendicular to the cam surface at the point of contact with the follower and then dropping another line from the center of rotation to that line; the distance from the Centre of rotation to the line is r.
You must do this for the entire motion in order to find the maximum value of Fc.
I might further add that for very high speeds you may have to add the effects of inertial forces including the potential separation problem if the piston force is insufficient to decelerate the piston on the downstroke of the motion.

 

[Jamaz17]

Thanks Zekeman you've bin a huge help! I'm curious to know, in my situation my Cam is doing the driving (ie spining at a givin RPM) and my piston is in effect trying to stop the cam via hydraulic pressure on the opposing side of the piston. Will the formula's discribe still work for me in this situation. Also the cam I am using is not a true cam, but a circle with an ecentric centre which accounts for the stroke on the piston.

once again great post! I love cams and have to spend more time learning about them.

 

[israelkk]

CAM DESIGN HANDBOOK, Harold A. Rothbart, 2004 by The McGraw-HIll Companies, Inc.

CAMS Design ,Dynamic and Accuracy, Harold A. Rothbart 1956

 

[ivymike]

a star for you, zeke.

 

[Jamaz17]

I have another question Zeke, what is the difference between the F for and the Fc force you described. As well the torque value T you talked about what is that torque value describing?
Could you not just take the piston force x the length of the lever arm "r" to get the torque?

I just don't quite understand the value of the Fc ? Maybe I'm just not quite understanding right.

Thanks again

 

[Allen]

I'm not sure, but I guess "israelkk"'s books beside this software will help :

http://www.designofmachinery.com/Cam/index.html

Also if you are not sure about equations, do a FEM or kinematic modeling by "working Model".

 

[zekeman]

The torque T is the torque experienced by the cam during its rotation.And by the way your eccentric cam qualifies as a cam and is probably the most used cam in machinery owing to its simplicity of fabrication.
The piston force in the direction of the piston motion is due to the fluid preessure in your case and as I have previously noted, the force normal to the cam surface is Fc.
There is an easier way of determining Fc for your special case of a translating follower obtained by a force analysis at the follower.F is the vertical component of the Fc force vector; i.e., if the angle between the F and Fc vectors is alpha, then:
Fc*cos(alpha)=F and therefore Fc=F/cos(alpha) which for your case is simpler than using the energy conservation equation I earlier proposed.Alpha is called the pressure angle and its maximum design value could be as low as 45 degrees if there is enough friction in the slide of the pistion.
For a clear discussion of these principles inluding the effect of friction, you should look into an elementary cam book. Rothbart's Cam book "Cams, design, accuracy", Wiley, 1956 is one, but is out of print.

 

[CSLufkin]

Do you use Solid Works? It has a Cam Calculating function that is often forgotte about. Very handy though.