Vibration generated from a specially design cam

[HanYeoh]

Hi all,

I have a question, I am trying to do to measure the stress on human feet while standing on a vibrating platform. The platform was placed on top of a cam and the cam was driven by a motor. I know most of the parameter, i.e. frequency, speed, acceleration but how can i calculate the force/stress?

Pls help.

 

[minger]

As a quick hand-esque calculation you could...

Assume a sinusodial cam profile. Take two derivatives to get acceleration. Should be negative displacement times frequency squared. Multiply that by the mass of the person and assume that is the force applied to the feet.

Divide by area of contact of the feet for some sort of normal stress.

 

[HanYeoh]

As a quick hand-esque calculation you could...

Assume a sinusodial cam profile. Take two derivatives to get acceleration. Should be negative displacement times frequency squared. Multiply that by the mass of the person and assume that is the force applied to the feet.

Divide by area of contact of the feet for some sort of normal stress.

What is the displacement you mention? the distance the cam lifting the plate? Thank you for the reply.

 

[minger]

Yes. Using that assumption, your cam will be sinusodial with a certain maximum amplitude described by
$$x = A\sin(\omega t)$$
Where A is some maximum amplitude (think of maximum runout of the cam). The acceleration is then:
$$\ddot{x} = -\omega^2 A \sin(\omega t)$$

 

[HanYeoh]

Yes. Using that assumption, your cam will be sinusodial with a certain maximum amplitude described by
$$x = A\sin(\omega t)$$
Where A is some maximum amplitude (think of maximum runout of the cam). The acceleration is then:
$$\ddot{x} = -\omega^2 A \sin(\omega t)$$

Hi Minger,

Thanks a lot for the reply. One more question, if the platform is placed on top of 4 identical cam, then the total stress on the feet will still the same, right?

that mean the force generated by each of the cam will need to divided by 4?

 

[minger]

Yes yes, In this assumption we're guessing that both the cams and floor are completely rigid, and the motor powering it is infinitely strong. Thus, the force on the feet is due to acceleration. So, it does not matter if there are one or 100 cams driving it.

Now something to think about. The inherent "softness" of the feet will cause a type of structural damping in your problem. This will then cause a phase shift in the displacement of the feet to the displacement of the cam. As such, there will be an impact at bottom dead center when the cam starts to move up but the feet are still moving down. Quantifying this would be quite difficult at best.

If you are assuming low frequencies then you can assume that the feet and cams stay relatively well in phase though.

 

[HanYeoh]

Yes yes, In this assumption we're guessing that both the cams and floor are completely rigid, and the motor powering it is infinitely strong. Thus, the force on the feet is due to acceleration. So, it does not matter if there are one or 100 cams driving it.

Now something to think about. The inherent "softness" of the feet will cause a type of structural damping in your problem. This will then cause a phase shift in the displacement of the feet to the displacement of the cam. As such, there will be an impact at bottom dead center when the cam starts to move up but the feet are still moving down. Quantifying this would be quite difficult at best.

If you are assuming low frequencies then you can assume that the feet and cams stay relatively well in phase though.

Well, Thank you for the suggestion. Actually, I am looking at the skeletal system (metatarsal). not the soft tissure (muscle). it is very good to have you answer my question.

Han

 

[minger]

Right, but the skin and muscle will act as a spring/damper system. Just take your results with quite a grain of salt and do plenty of research.