Equation of motion spring with dampers

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Rustem 1988
Rustem 1988
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Equation of motion spring with dampers

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Hello. I try do equation of suspension. How make equation of motion spring with damper x=x(t) where x-displacement of spring?

Greg Locock
Greg Locock
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Re: Equation of motion spring with dampers

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F=k*x+dx/dt*c

Where k is the spring stiffness and c is the damping coefficient.

That assumes c is constant, normally it is not.

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Mudflap
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Re: Equation of motion spring with dampers

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Dang you forgot m*a.
Unforgiveable
How much TQ does it make though?

Greg Locock
Greg Locock
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Re: Equation of motion spring with dampers

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Did op mention mass? No. Silly sausage.

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Mudflap
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Re: Equation of motion spring with dampers

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Where have you ever seen an equation for a massless spring?

What's the acceleration of such a thing? What is its natural frequency?

If it has no mass then it has no degrees of freedom therefore it cannot have equations of motion.

Maybe open up a book before ruining someone else's homework.
How much TQ does it make though?

Greg Locock
Greg Locock
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Re: Equation of motion spring with dampers

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Clue. When you are in a hole, stop digging. In the world of vehicle dynamics it is very common to assume that springs and shocks are massless. For example a linear spring in ADAMS is represented by an equation that boils down to f=k.x its mass is lumped into the sprung and unsprung mass. I answered the OP's question exactly. If he asked the wrong question he can ask another. So, what's your answer ?

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Mudflap
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Re: Equation of motion spring with dampers

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He asked for the equation of motion. Please describe what the acceleration is in your equation.

You can't.

There is only one equation and thats
F=ma+cv+kx.

Yes you do assume springs are massless but they are always connected to a lumped mass-that's what gives the system its degrees of freedom. You can only describe the motion of the mass points.

You should spend less time writing 'smart' condescending replies and more time studying engineering texts.
How much TQ does it make though?

Greg Locock
Greg Locock
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Re: Equation of motion spring with dampers

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It would be interesting to know which answer is most useful to the OP.

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PlatinumZealot
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Re: Equation of motion spring with dampers

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Greg Locock wrote:
Fri Sep 08, 2017 9:54 am
It would be interesting to know which answer is most useful to the OP.
If he is designing parts he needs to know the dynamics of it (with mass). If he only wants say a simple motion sort of thing, he can work with the kinematics alone.
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LH44

Greg Locock
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Re: Equation of motion spring with dampers

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I can model various proprietary metrics of primary ride on measured road surfaces with an R^2 of 0.8 using my approach. However I'm sure the textbooks will help improve that.

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Mudflap
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Re: Equation of motion spring with dampers

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What exactly is your approach ? The one where there is no mass ?
How much TQ does it make though?

Greg Locock
Greg Locock
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Re: Equation of motion spring with dampers

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Yup, the one where the spring is k.x and the damper is c(v).v

Works up to 8Hz for full vehicle ride models.

How good are your textbook models, oh, let me guess, you don't know.

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Mudflap
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Re: Equation of motion spring with dampers

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These textbook models are used everywhere from driveline torsional vibration to high speed rotordynamics, valvetrain and geartrain models. Even models with very high non linearity can correlate to within measurement error for up to several kHz.

Your model that only works for a very narrow frequency range and even then does not account for 20% of variability is poor by any standard. And if you try to argue that whatever it is you are predicting is independent of wheel mass I'm not buying it.

The reason your model seems to work is because your suspension excitation frequency is much higher then its natural frequency (I suspect about 2 Hz ? I'm not a suspension guy) and hence the transmissibility is very low. This however constitutes a very particular case - it simply won't work at resonance.

Probably just about adequate for designing a wheelie bin.
How much TQ does it make though?

Greg Locock
Greg Locock
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Re: Equation of motion spring with dampers

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I didn't say it didn't use mass i said the spring and damper were modelled using the equations given. You are out of your depth. Its a full vehicle adams model, used to predict both steady state handling and limit handling and rollover and now primary ride, all correlated with real vehicle tests. I'll take your advice on accuracy and stick it where it belongs. Let me guess, you've never measured ride on a real car, so you have no idea about test to test variability.

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Mudflap
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Re: Equation of motion spring with dampers

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Im not quite sure if you are being deliberately obtuse - if your system has mass ,springs and dampers then the system equation (Newton) is the one I have mentioned. It is valid for any number of degrees of freedom and any form of excitation in either time or frequency domain.

Regardless of the software you are using it will either solve Newton's equations (which obviously involve mass) or the Lagrange method (where kinetic energy is mv^2/2, again dependent on mass).

I'm sure you can use software too bad you can't understant how it works.
How much TQ does it make though?