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# Specifying damping from models and data

## Specifying damping from models and data

(OP)
Given a simple 4th order quarter car model where you have the sprung and un-sprung mass and no tire damping I'm trying to develop a useful and robust way of specifying damping rates.

My present path is to use a bode plot of tire spring deflection (power output from tire spring might be useful as well) over road input and to ultimately reduce the area under the gain curve for the frequencies I care about (determined from a data file or a standard road spectrum) to reduce load fluctuation in those frequencies. Weight being given based upon the density of each frequency in the domain of concern and the change in gain vs zeta(damping ratio). So if there is a high density of a particular frequency then it may need to be tended to more than an infrequently seen frequency and so that if any frequency is highly sensitive to damping ratio compared to another that it is also given more importance since it will have a larger effect on the area under that curve. Ultimately I will wind up with a bode plot of minimum area under the curve that I can use the phase angle to calculate the damping ratio from.
This is assuming the damping is linear, however, and it very much is not. I have a sinusoidal shock dyno and matlab at my disposal and I am the one revalving the dampers. I realize that a true damper model is way more complex than a simple linear approximation, but this may sometimes work in order to get a ballpark curve that the customer can adjust to his liking.

The end game here is to produce a useful and robust way of setting a baseline quantifiable value for the damping on a series of adjustable dampers that isn't just "experience", hoccus pocus or old wives tales. By the way I am usually lean on information which is why Im sticking to a simpler quarter car model and not an axle, bicycle or full car model.

Does anyone have any suggestions or inputs to what I mentioned? Any insights that I may be missing? Any useful and interesting info about anything I just discussed?

Thank you!

### RE: Specifying damping from models and data

It sounds like you are doing something a lot more complex than the way I would go about it. A typical plot of "sprung mass response to road input" transmissibility indicates that a damping ratio of anywhere from 0.2 to 0.4 is a good compromise. For the 1958 Jaguar XK150S the front suspension (w/o ARB) critical damping calculates out to be 29.1 lb-sec/in, which means the damping coefficient should be around 8.73 lb-sec/in, and not the 5.6 lb-sec/in I was initially using. The 5.6 lb-sec/in gave me a high peak transmissibility value around 12 (!!), and now I know why. I'm going to have to re-run the transmissibility equations (from Gillespie's "Fundamentals of Vehicle Dynamics", page 150) again, but I think I will see a fundamental improvement. By the way, the "sprung mass response to sprung mass input" transmissibility equation (Eq. 5-17) has a typo in my 1992 edition of Gillespie's book; the odd symbol in the equation numeratior should be a Greek lower case "chi" for "unsprung mass to sprung mass ratio". Both that transmissibility equation, and the response to road input equation, work out very well for me, but the "sprung mass response to unsprung mass input" is completely wacko. You wouldn't know of any corrections to the equation, would you? I sent an inquiry to the great man himself, but who knows if I'll get a response. I tried checking with Dukkipati (et al) in his book "Road Vehicle Dynamics", but he only shows the two transmissibility functions that I already know to be correct. A literature search came up with more of the same, plus a transmissibility function for "unsprung mass response to road input", which is very good thing to use for road holding determinations, but still not what I need....BPW

### RE: Specifying damping from models and data

(OP)
Im not familiar with the Gillespie book to honest. Its neat that you tried to get a hold of him though. Thank you for presenting your method!

The reason Im not using just sprung output over road input is that it leaves out whats actually going on at the contact patch which for the moment is what I am after. Body control is important especially for aero setups critical to ground clearance as well as ride comfort, but thats not my main focus with this.

Im literally using load fluctuation at the road surface for a ton of different frequencies in the form of a body plot and defining the road based upon a power spectral density (there are a number that define varying road conditions). That allows me to weigh the importance of each frequency to the system as 20kHz is probably not pertinent nor is .01Hz (which wouldnt give much response anyways). The sensitivity of load fluctuation at that frequency to damping ratio will also be given weight.

At the end of the day damping needs to be different in both directions and at least modeled as varying with velocity (non-linear) so this is merely a ballpark like I said.

The problem im having is finding a way to find a particular curve of damping that varies with velocity bi-directionally and is solved for minimal load fluctuation (area under the gain curve). This ignores the concept of driver control through low speed damping and many others considering its only a quarter car, but that can be ironed out in later refinements.

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