Shaker Rigs revisited

Transcription

1 Shaker Rigs revisited One o the irst articles I ever wrote or Racecar Engineering was on 4 post and 7 post shaker rigs. That article was over 5 years a go and a lot o water has lowed under the bridge and the ChassisSim 7 post rig/shaker rig toolbox has been employed in racing categories as diverse as F3, V8 Supercars, IndyCar and GT categories. The purpose o this article is to bring you the lessons learnt in using this toolbox, because it s proven to be a very useul tool to tune or mechanical grip. Beore I go into the meat o this article I want to point out that I have not been in the vanguard o using this toolbox. The people who have made best use o this toolbox have been the members o the ChassisSim community who have told me what they have done. Usually these conversations have been, hey I did this what do you think? Typically I reply did it work and they said yes, and I just said carry on. You can thank the ChassisSim community or the insights I m about to present to you. To kick things o, what the shaker rig brings to the party is that it shows you what is going on with the car in the requency domain as opposed to the time domain. What this means in plain English is we subject the car to a requency input and we compare the ratios o inputs and outputs o the amplitudes and how ar the requencies lag behind. To quantiy this lets consider a typical cyclical road input as illustrated in Fig 1. Fig-1: Cyclical road input.

2 The car will respond with the same requency to this input but typically with dierent amplitude and a dierent phase angle that will lag behind the input signal. This lag is caused by the car catching up to the input signal that is applied to it. This is illustrated in Fig-2, Fig-2: Cyclical input versus cyclical output. The shaker rig measures this data or a wide spread o these signals. To appropriately measure this we need to be looking at this data in the requency domain as opposed to the time domain. In this domain we measure by requency as opposed to time. So how do we quantiy this? Fortunately a French physicist by the name o Joseph Fourier came to our rescue. He postulate that or any group o signals that repeat (which is what we get all the time in race data) they could be represented by the ollowing, y = = 0 A sin ( 2 π t + φ ) Where, y is what we are looking at on the graph, t is time; is the requency o each component and A and φ is the requency amplitude and phase lag respectively o each o the sine signals or requency components. The symbol means where summing all this together or all the measured requencies. When we are measuring this response in the requency domain we are plotting A and φ or each o the requencies we have measured on

3 the shaker rig. To come up with A and φ we use a tool called the direct Fourier transorm, but I will leave that to the interested readers to investigate in their own time. In terms o the testing regime that is applied to the car is we put the car on a set o pads and subject it to a swept sine test where we hold the peak velocity o the input constant. What this means is that the test will start at a large amplitude and will go down to a small amplitude at higher requencies. This amplitude can actually be quantiied by taking the derivative o the input signal. This input signal can be quantiied by the ollowing, y = A ( 2 π t) sin (2) Here y is the actual road input. To prove this all you need to do is take the derivative o equation (2) (Hint University Students/junior Race and data engineers reading this that means you). What we are doing here is we are logging suspension displacements and accelerations. Typically you ll wind up with a response that looks like this, Fig-3 Typical shaker rig response. There are a number o measures that are used to classiy a cost unction or a shaker rig test. One way is the contact path load variation given by Kowalczyk (1). This is deined below, ΔLoad CPL = (3) Δacc input The deltas represent the maximum rom the equilibrium condition or a given requency. At the end o the run these are added up and averaged. The CPL is deined as is load variation divided by input acceleration. Another ormulation o a cost unction is shown below,

4 c = c 1 Δz z o 2 Δθ θ 0 3 Δz z 0 In this equation the terms are, c = cost unction values c 1 -c 4 = user deined constants Δz = change in z (heave) rom rest condition. z 0 = heave at equilibrium condition Δθ = change in (pitch) rom rest condition. θ 0 = pitch angle at equilibrium condition. Δz = change in ront damper position rom equilibrium condition z 0 = ront damper position at equilibrium condition. Δz r = change in rear damper position rom equilibrium condition z r0 = rear damper position at equilibrium condition. ΔL = change in total ront load rom equilibrium condition L = total ront load rom equilibrium condition. ΔL r = change in total rear load rom equilibrium condition = total rear load rom equilibrium condition. L r 4 Δz z r r0 Equation (3) is computed or each requency. These are then added up and averaged or all o the measured requencies to return the inal cost unctions. Each o these measures are very much user dependent there will be some who will swear by either method. The advantage o the CPL is that it does give you a very good measure o mechanical grip. The lower the CPL numbers the better the grip. The advantage o the cost unction route is it can be customised very readily to what you want to get out o it. There s also no reason you can t use both. For example i you are running a car that has a lot o downorce you can increase the cost unction or the pitch and heave terms. Consequently you ll get penalized or changes that result in large pitch and heave variations which is an absolute premium or car s that are pitch sensitive and run a lot o downorce. But the question is can we simulate this beore we get to the rig so we can make our rig time more valuable? The answer is a resounding yes and in that regard I d like you to walk you through the ChassisSim 7 post/shaker rig toolbox. The irst part o the toolbox is setting up the requency test. This is illustrated in Fig-4, 5 ΔL L F F 0 6 ΔL L R R0 (4)

5 Fig-4 Setting up a requency run The comments and ilenames are pretty sel explanatory. Just put in something relevant to the setup and store the log ile or test where you are going to remember it. However the controls you need to pay attention are the speed o the test and the peak input velocity o the road input. You choose the speed o the test to choose the corners you want to simulate. I you want to simulate a low speed corner choose say 100 km/h, or i you are looking at a high speed corner you choose say km/h. You ll also notice you have an option to set the downorce at a ixed value. This is ok or validation work, but personally I preer to leave this o. The reason is the ride height map will impact on the requency response o the car and in high speed corners this will make its presence elt. In terms o the peak input velocity you choose a value that represents the peak input velocity that is representative o the road input. There are a number o ways you can do this. For a rough rule o thumb, 50 mm/s approximates a relatively smooth surace, 100mm/s is middle o the road, and 150mm/s represents a pretty bumpy circuit. Another way you can do it is look at the data. Look at the peak damper velocity and divide the results by say about 3. It s a rough measure but it will get you by. I in doubt start the test at 100mm/s. In terms o what this toolbox is it will return a plot o Output Amplitude on input Amplitude. The output o the toolbox is shown in Fig-5,

6 Fig-5 Output o the shaker rig toolbox. You ll see that the Contact Patch Load variation (CPL) is shown in the top o the graph. This is averaged over the whole requency run and the units are kg. This is the delta load variation rom the static load or the conditions speciied or the test. The plots below are the ratio o output vs input amplitudes. Here we have shown heave and pitch or a heave input to the car. The irst thing you will get out o this is it will tell you the requencies you need to be looking or in the data. The requencies we need to be watching or are the requencies at which you see the peak responses. This is called resonance and you ignore this at your peril. The way you translate this to looking at data is i you have a particular handling problem, the irst thing you do is look at the data in the time domain and you are looking or damper requencies that correspond to the resonant requency. I you see this that is your queue you need to do something in the setup. An example o what to look or is this situation illustrated in Fig-6

7 Fig 6 Resonant behaviour or an F3 car. Note here how the dampers are oscillating like mad and the steering response is responding in sympathy. I you have a car handling like this, typically the driver will be reerring to you in negative terms (i.e. the 4 letter variety) However the real power o this toolbox is tying the CPL igures with the requency response. This technique was actually pioneered by a colleague o mine Pat Cahill when he was engineering a GT car at Bathurst in The technique is actually breathtakingly simple. The irst part o the process is that you play with springs and large damper adjustments to minimize CPL. What will happen is when you get into the zone the CPL will hit a minimum and actually won t vary too much. Once you hit this you start playing with minor spring and damper changes to get the shape o the requency response that you want. It s actually that simple. This technique has been used very successully in cars with C L A numbers rom The result o this has been a marked improvement in mechanical grip without compromising driver eel. When you make these changes it s critical you don t go silly with the magnitude o the changes. Remember when you go to a shaker rig, whether it s virtual or actual don t orget what makes the car work. Remember the results you get are a tuning tool, not a magic wand that will make you 20s a lap quicker. So keep the spring changes in the range that will still

8 keep the temperature in the tyres, and don t think you can make outrageous changes to bump and rebound just because it makes the pitch response look impressive. The technique we discussed here have been discussed have been applied to cars with low to medium downorce, but what do we do about high downorce cars. For cars in the C L A o say 3.5 and above, the heave and pitch response start to outweigh the mechanical grip. The technique here was very well explained by Kowalczyk (1). In this technique you actually tune the pitch cross response almost to the expense o the initial heave response. The thinking here is that i you get into trouble you can just raise the ride heights. However I would reer you to the paper by Kowalczyk (1) because he articulates this very well. In conclusion the shaker rig toolbox when used properly is a very powerul tool. What it does is it gives you a window into the world o the requency response o the car that yields valuable inormation into what to look or in the data. However the key to getting the most out o it is to make sure you set the correct speed to represent the downorce levels and represent the peak input velocity o the road inputs. When using the ChassisSim shaker rig toolbox, tune or CPL and then tune the requency output to get the responses you are ater. However also be mindul when running high downorce levels this might need to change. Used in this ashion you should see a measurable improvement o the mechanical grip o the car. 1) H. Kowalczyk Damper Tuning with the use o a 7 post shaker rig - SAE Technical Paper Series, SAE , 2002