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# How does this formula comes?(about shock absorber)2

## How does this formula comes?(about shock absorber)

(OP)
I read the stand test method of automotive telescopic shock absorber
,but i dont understand how the following formula comes:

v=(π*S*n/6)*e-4  m/s
where
s is the the stroke(travel) of the test shock absorber piston (mm)
n is the frequency of test shock absorber
π is circumference ratio
v is the piston movement speed in telescopic shock absorber

The key point for me is why the circumference ratio is added into the calculation formula. why can explain how to derive it.
Thanks a lot, first.

### RE: How does this formula comes?(about shock absorber)

(OP)
Sorry fot not giving the unit of n which is c、p、m（count per minute)

### RE: How does this formula comes?(about shock absorber)

Arishoda,
One of the "n"s is Pi. ( I guess you could call that the circumference ratio, being it is the ratio of circumfernce to diameter ).  V= omega r = 2 Pi f r = 2Pi (n/60)r = 2Pi(n/60)(s/2*1000) = Pi n s *10-4

### RE: How does this formula comes?(about shock absorber)

(OP)
But i can't still understand "V= omega r",you know, the "V" represent the piston straightlinear speed ,because it move up and down.and "V= omega r" means something is in circular motion,coudl you plz tell how this relationship forms.

### RE: How does this formula comes?(about shock absorber)

Arishoda,
Peak Linear Velocity is equal to the Angular Velocity ( Omega, in radians/sec ) times the Radius (R).  Note that we are talking Peak velocity - if you want instantaneous velocity then you need to multiply by the Cosine of the angle.

(OP)
gt6racer2

### RE: How does this formula comes?(about shock absorber)

Arishoda,
Now maybe I understand the confusion. Being so close to the subject has me making assumptions that everyone knows the basics.  Yes, typical test is a sine wave. This traditionally came about as the early test rigs used a spinning "cam" that was used to drive a linear motion into the shock. More recently with hydraulic testers we can use other wave forms such as constant velocity form, but the old measuring approach has stuck with the industry. ( Some OE's even still prefer the old machanical dynos )This is probably the most logical stroke pattern to use anyway, since it most resembles real life input. The output of this test is a "football" curve in the displacement domain, and an approximate line on the in the velocity domain.

### RE: How does this formula comes?(about shock absorber)

(OP)
gt6racer2
I have uploaded a test chart of some kind of shock absorber,see the attachment.In my view,  it is "a "constant velocity form" as you said.I marked the compression curve with corresponding velocity.Is the diagram the "football" curve you mentioned in your reply?

### RE: How does this formula comes?(about shock absorber)

Arishoda,
Your plot is a "football" curve and has been created using a sine wave as the input - not constant velocity. This trace only hits the velocity you indicate on the plot at the Peak - at any other point on the cycle the velocity is less than peak. What is commonly done is to pick of the force from the peak of each loop and then make a load Vs (peak) velocity plot, Sometimes the tester software will do it for you.

### RE: How does this formula comes?(about shock absorber)

gt6racer2 is right, I may add that a crankshaft-rod device to tranform motor rotational speed into linear wont give you a sine, but an aproximation. To have a sinusoidal movement, shock dyno manufacturers use a "scotch yoke", think of it as something similar to a cam, can be designed for a specific type of movement.

You need great passion, because everything you do with great pleasure, you do well.

### RE: How does this formula comes?(about shock absorber)

(OP)
ibelatti,That is what i have been confused about recently.But,a new question is confusing me.Why we set the test movement as a sine wave,does it realy reflect real-life operating condition? Anad,is the reason is that the shock absorber is usually assembled near the spring,and the moment of spring is a sine wave? If yes, i would think the test is just a approximate method,we know the vibrating system（absorber and spring togethe,not spring it self) does up-and-down movement with more vibration energy absorbed by the shock absorber,so under this condition ,the movement of the vibrating system wont be a sine one,but resemble a wave as possible.

### RE: How does this formula comes?(about shock absorber)

If you ever look at the motion of a wheel on a road you'll see that a sine wave is a pretty useless representation. If you run that waveform into your shock tester the curve of force vs velocity will bear only the slightest resemblance to the one you get from a sine test.

Cheers

Greg Locock

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### RE: How does this formula comes?(about shock absorber)

Arishoda,
There are two key components of shock absorber motion - that from the bottom - the wheel/suspension unspring mass ( road input-largely random, and unspring mass vibration-about 12 Hz ) and the top - vehicle body/sprung mass ( body bounce about 1.5 Hz). Of course the road input is not typically a sine, but the others are close enough for the very simplified discussion we've been having here.
As Greg aludes, the real world isn't so simple - either in terms of motion input, or in shock response. Real dampers are not purely velocity proportional - they will have elements of dependence on frequency, temperature, stroke and other factors. A sine wave test is a very rudimentary measure, and does not capture the true character of the damper, which is why, to get the right results,  we have to tune vehicle dampers by driving, rather than "valving by numbers".

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