Suspension Geometry Analysis

[koushik123]

Hello Everyone

I am currently learning vehicle dynamics and in this regard I started doing calculations for geometry analysis of an open wheeler with Push rod mechanism and a mono shock arrangement with belleville stacks.

The method I used to determine the movable points in the mechanism (during wheel travel ) was three point analysis (Ref : The Multibody systems approach to Vehicle dynamics,Damian Harty & Mike Blundell)

You can find the attached sketches that I made prior to the calculation.

511512

I would like to know if this calculation sequence is correct ?

Representative input : Damper length shortened by 50 mm i.e, JI is shortened to JI'
Motion : Pitch

As we need three known points to commence the calculation, here we shall take points J,Q and P to determine the new position I'

Once the point I' is determined then the remaining sequence is as follows

Using I',Q,P new position of point M i.e, M' can be determined

then

A,C,M' -----> N'
A,C,N' -----> B'
F,D,B' -----> E'
E',B',H -----> G'
E',B',G' -----> K'

I welcome all comments and suggestions

Thank you
Koushik

[Claude Rouelle]

And you are Koushik?

If you would want to feel welcome in a group you can't jump in without telling a bit about yourself, which school and where you are from if you (nhave already some experience in FS / FSAE

I think you have more chance to get answers or more chance to get more complete answers if you would introduce your self.

Simple common sense of being courteous....

[koushik123]

Hello Everyone

I am Koushik Sivasubramaniam, a recent automotive engineering graduate from India with keen interest in motorsport engineering.I graduated from Anna University,India in 2014.

Experience :
2015 - Freelance Vehicle Performance Engineer, Formula Renault 2.0 Northern European Cup
2014 - Intern,Spitfire Performance, India
2013 - Virtual Supra SAE INDIA ( Indian FS Pre qualifier round )
2013 - Mahindra Baja SAEINDIA
2012 - National Go Kart Championship,India

And thank you Mr.Claude for pointing out my lack of common sense.

Regards
Koushik

[Claude Rouelle]

Koushik,

Welcome to the forum.

What is the point of your calculations? What are you looking for? What is the ultimate goal?

[koushik123]

Thank you Mr.Claude.

Ultimately I would like to make a plot of Camber Vs Wheel Travel. Of course this can be done using any available suspension softwares. But I am trying to create my own kinematic solver in MATLAB so that it will help me in understanding the computations involved.

Koushik

[BillCobb]

I suggest you jump to SimMechanics if you will be using Matlab. You can still see the solution process, no suspension mechanism is just a bunch of rigid links, and your employer will be hugely disappointed with an overly simplified analysis that does not accurately (enough) provide the right answers (and direction).

You're not in school now, the real racing world demands sophisticated models that include elastic, nonlinear and deformable elements (plus the kitchen sink).

That's my opinion and I'm unanimous with it!

[Claude Rouelle]

If you are a FS student I can only applaud you to create your own kinematics software but it could take so much time that it could delay your car design and manufacturing

If you are a professional why do you want to reinvent the wheel when you can get it cheaper and quicker somewhere else? Buy a kinematics software then use you energy using the software to get the most or to improve of a given car suspension design.

[koushik123]

Hello Mr.Bill

Thank you for your response.I will have a look at SimMechanics too and I understand your point.

Regards
Koushik

[koushik123]

Mr.Claude

I am just curious enough to understand how a kinematics software solves the above problem.

I do not wish to re invent a wheel rather I wish to understand the wheel first before using it. Obviously while at work where quick and smart work is required I will not be using a paper and pen and a bunch of simultaneous equations doing algebra to get my results, I will ofcourse use a kinematics solver to get the work done.

Regards
Koushik

[Kevin Hayward]

Koushik,

I think you are on the right track, and I mildly disagree with both Bill and Claude.

I would advocate the use of both SimMechanics and OptimumK (or equivalent kinematics software). However complicated models have simple beginnings, and this world needs people who can build these models from scratch. Keep doing what you are doing.

If you haven't already try and solve this as a 2d problem. While 2d is not a good representation of what is happening it will help you sort out the general calculation flow as well as helping you get your head around how you will setup inputs and outputs.

Another point you may want to consider is that you have some great advantages over SimMechanics and OptimumK. First is that your solution method does not have to be computationally efficient. Second is that computation is cheap. Finally you do not have to account for a massive range of error checking. This allows you to keep your program lean and simple.

When I was doing the 3d kinematics as a student my program moved a suspension system through its expected motion by moving the lower a-arm through its expected angle of motion. Everything solved as a four bar linkage. All solutions to the mechanism were stored in a matrix. This was also swept with steering for the front as well. Done fine enough any point inbetween your calculations can be interpolated with minimal error. Once you have this data you can select the state using whatever measure you wish. Simple calculations from here can convert these motions to body based movements. A few functions for drawing (i.e. cylinders) and you had some cool graphical output. Please note this method works well for pure kinematics but cannot cover what Bill is leading to.

Memory storage is not ideal. Calculation time is long for the difficulty of the problem. However in 2004 on a fairly normal pc solutions were calculated almost instantaneously.

One advantage over OptimumK is that each of the solved points is a geometrical solution. OptimumK uses a Newton-Raphson solver which is much better for more general purpose solving. But it is good to keep in mind you don't have to solve a general purpose mechanism, all you need are calcs on one type of kinematic linkage. Harty and Blundell's book is dealing with a similar problem.

I also noticed with the geometrical solution method that when you make a programming error you see it clearly in the output, as in it is almost always a big error. With the numerical solvers you can persist with something that looks right for a while without noticing the errors.

All that aside I use a different approach to solving pure kinematics problems these days for a simpler design process. 3d sketches in solidworks (or other CAD) can be very powerful. The temptation is to define sketches on link lengths and positions. However For each position you draw you can leave an unknown undefined. For example instead of defining your swing arm length draw the suspension in two positions, one static, one compressed. Make sure there are restraints to make the links of each sketch equal to each other. You have to define a lot of things but make sure one of your measurements is on the camber angle. The SAL will then be defined by everything else. 3 positions allows you 2 unknowns, and so on. The basic idea is to start with the values you want and then force the mechanism to comply. There will be plenty of times you cant get a solution, or the potential solution makes the mechanism invalid. What is great about this is that it is kinematics at the design level. Programs like OptimumK are great for analysing what you have, but they are slow when it comes to design. Design is inherently about iteration and exploration within a given solution space.

The ECU guys used this method to solve for the funky steering mechanism they used, which I will note cannot be modelled in any of the purpose made suspension kinematics software. Although SimMechanics and ADAMS are no problem, just a lot slower. Likewise the rear beam arrangement could also not be modelled. OptimumK's engine could easily handle it. All that would need to happen is the creation of appropriate input sheets, and a couple of changes to the calculation modules to build it in. One of the ways to make software accessible is to control and limit the input and output options. You will not need to do that with your own method. Just be careful that your method does not limit your design.

Hope something in all of that is useful.

Kev

[ChristianChalliner]

I second what Kevin said, simple sketches in a CAD program is a great way to go although specific programs do give a wealth of very useful data and some very cool visualisations they tend to be limited in their applications, for example, neither susprog or OptimumK can simulate a front beamarrangement which uses a peg and slot although I will admit this is a very specific case.

[koushik123]

Mr.Kevin

Thank you very much for sharing your detailed insight into the problem. I found it useful.

Regards
Koushik

[koushik123]

Christian

Thank you too for stopping by the thread and seconding Kev's post.

Regards
Koushik

[i6overboard]

To add to Kevin's post about the power of 3D CAD,

I've used Solidworks Motion Analysis add-in to generate all of my kinematic data. You simply cycle the linkage in the motion study with the equivalence of a linear actuator in SW and use trace paths, angle projections, and other data recording add-ins. These can be exported directly to Excel to further interpret the data with graphs and any other mathematic operations needed.

JR

[Claude Rouelle]

Koushik and all,

Here is a bit of food for thoughts about how kinematics software is or could be working.

At least a beginning of food for thoughts.

Let’s take the generic case of a one 5 links suspension.

You have 5 links. Each of them having an outboard pick up point O1, O2, O3, O4 and O5 and an inboard pickup point I1, I2, I3, I4 and I5 and a given length L1, L2, L3, L4 and L5

Also there is a wheel center C and a tire contact patch T. In this example the wheel has an infinitely small thickness so the contact patch is only one point

In this simplified example there is no compliance and there is no tire deflection.

If the outboard point O1 moves it will be moving on a sphere which has I1 as a center and L1 as a radius. Similarly for all other 4 points.

However there are constraints. Many of them. As we assume there is no compliance the distance O1 to O2, O2 to O3, well all the distance between all the outboard points … and also the distance between each outboard point On and C …. and also the distance between each outboard point On and T … cannot change.

Therefore when the wheel center C goes up (vertically) by let’s say z mm there will be an imposed trajectory of all the O points as well as the point T. There will be one and only one track variation, wheelbase variation, camber, toe, caster, KPI variation…

(Ouch… How do we measure the Caster and KPI angle on one 5 links suspension geometry? Let’s leave that for later and let’s simply say that there will be a rotation of the upright around the x axis and that will be the KPI and Camber variation and a rotation of the upright around the y axis and that will be the caster variation)

Now take 2 points of the wheel / upright assembly as far away as possible from each other. Let’s take T and another point. Let’s say that this other point is O1 and that O1 is the highest outboard point.

For z mm of the wheel center C vertical movement there will be a given movement in the x, y and z direction of point T and O1.

Let’s call Ti the initial point of T and Tf the final point of T after the wheel center z vertical movement and similarly O1i the initial point of O and O1f the final point of O after the wheel center z vertical movement.

Look at the segment Ti-Tf. Find the middle of this segment Ti-Tf (i for initial, f for final) Draw in your mind an imaginary 3 D plane perpendicular to the segment Ti-Tf in the middle of segment Ti-Tf. Let’s call this plane A.

Similarly, look at the segment O1i-O1f. Find the middle of this segment O1i-O1f. Draw in your mind an imaginary 3 D plane perpendicular to the segment O1i-O1f in the middle of segment O1i-O1f. Let’s call this plane B.

The intersection of planes A and B is your instant axis of the wheel about the chassis.

Obviously you will have different instant axis position for different x axis movement so ideally you want a lot of small iterations of the wheel center z movement.

If you want to know more have a look at http://papers.sae.org/2008-01-2949 New Method to Evaluate Bump Steer and Steering Influence on Kinematic Roll and Pitch Axes for All Independent Suspension Types

I hope this helps.

It took us several months to first create OptimumKinematics several years ago (and in fact Kevin Hayward was part of this effort when he was an intern with us) and a few other months a few years later to improve it. In fact we never stop improving it and there will be another version with forces and optimization probably next year (it could come in 2 months if we did not have any other consulting work to do…).

As a design judge I would give you a lot of credit if you would be a FSAE / FS participant and you would come with your own kinematics software…..providing the time you dedicate to this software did not hamper a good job on the design and manufacturing of all other suspension parts and the car development / tuning. Your personal goal may not be your team goal.

A few years ago I visited a FS team in Germany who wanted to design their own accelerometers. Good challenge but I asked them if they wanted to compete in Formula Student competition or in a Formula Accelerometer competition.

The question is: why do you want to reinvent the wheel if you can buy it cheaper an quicker somewhere else? Only you can answer this question.

If you want to do it, you now have one beginning of the answer at the beginning of this thread (I say one beginning because there could be other methods)

[Kevin Hayward]

Koushik and all,

Now that I have suggested that you continue developing your program I want to make the point that you should also use OpimumK (or an equivalent). The ECU team still uses OptimumK as part of its analysis procedure.

Up front I will say that I was involved with the development of the first version of OptimumK. It was an amazing team of people to work with and I am very proud of what we achieved. I am probably a little biased when I say that I think it is the best suspension kinematics analysis software out there. What it does it does very well, and is very easy to use. I will also add that when I went to work at OptimumG I had already created a geometry analysis program over a period of 2-3 years. It used a different calculation method and none of it was useful for the creation of OptimumK, which was built for entirely different reasons. I found the two tools (my own and OptimumK) to be complementary rather than any one being a replacement for the other. You should think about what your approach can add to your workflow. Reinventing the wheel is not necessary, but there are lots of different types of wheels out there that are operated under different conditions.

I have mentioned previously that OptimumK is not an ideal creation or iteration tool. It is difficult to force a wide user base into a particular method of geometry creation, and very likely to create more frustration than a better workflow. To that end everything is entered as x-y-z coordinates. You are probably already aware that is not the best way to approach suspension design. To alleviate this OptimumK can take a spreadsheet input so that geometry creation can be handled by something else. Excel is easily good enough for this.

It is also not an optimisation tool. The main issue here is that suspension geometry by its nature is a multi-objective problem, which optimisation routines do not play well with. Furthermore optimisation of a purely kinematics problem is prone to lead to bad car design as the problem is much more complex. The only real way to build a decent optimisation tool for racing is to use lap-time as an objective function, and it takes one heck of a program to include a full kinematics solution inside of a decent lap time simulation.

What it primarily serves as is an analysis tool. The main inspiration for the first OptimumK came from the easy to learn Solidworks UI and the Motec i2 software. The complete output data of a kinematics solve is to be able to be analysed and graphed as the user wants. Any input (with the assumption of a flat road) can be investigated. Comparisons between suspension systems is very easy.

What is not apparent to the user is how adaptable the underlying code is. The heart of the software is a general purpose kinematics solver. This means that updates for OptimumG are quite straight-forward. If the company wanted to it could make the same software analyse just about any kinematic linkage (not just suspensions). The layer that sits on top of that that deals with different types of suspensions makes the whole thing easy to use. Are you aware that some commonly used suspension systems are either always over constrained, or in certain positions over-constrained? A good example is the old v8 supercar rear suspension with a watts linkage. There is a layer of code on top of the general purpose solver that deals with these issues, while keeping it easy to use. In practice I would say nearly all relevant suspension systems are covered by the software.

I support the creation of your own software because I think one of the most important words for students in FSAE should be "and". Use your own software and SimMechanics and OptimumG. Build a good car and develop your program. FSAE students already stand out against other engineering students. But how do you stand out against all of the of the other FSAE students?

Additionally whatever program you create will not be as polished and user friendly as OptimumK. This means it will likely be much less useful to others on your team. For the price of OptimumK I would imagine that every FSAE team should have it, and then develop their own tools to complement it.

Kev

[Claude Rouelle]

Kevin,

Thank you for your good words and the positive criticisms (with which I mostly) agree of OptimumKinematics. Also good memories from about.... gee.... 9, 10 years ago?

A. I do agree with you about students making their own software: it helps them to better understand what they are dealing with... but making the software USEFUL with good graphical interface and user friendly features is another story: do they have the time? I have seen so many students Matlab simulation where you need to go in the codes to change the spring, you cannot overlay, you cannot zoom etc..

B. Lap time.... Ah Lap time.....

"The only real way to build a decent optimization tool for racing is to use lap-time as an objective function,"

Lap time, yes but also
- tire use (in % of use of each traction ellipse if possible at each meter of the track, traction ellipses shapes and size which never stop changing either)
- balance (which in simple terms means do you have the yaw moment you want when you want)
- consistency (which in simple terms means tire grip consistency with tire wear and temperature, track conditions and fuel load - that one not important on a FSAE car)
- off and on center control (yaw moment generates by degree of steering (delta) for a given chassis slip angle (beta), this chassis slip angle being zero at the corner entry and "something else" at the apex
- off and on center stability (yaw moment generates by degree of chassis slip angle (beta) for a given degree of steering (delta), this steering angle being zero at the corner entry and "something else" at the apex

Control and Stability can be translated in an other words: drive-ability. We have found that lap time is actually a smaller factor than balance (which is yaw moment) control and stability. The reason is that these last 3 factors link the car with the driver with some quantification of the human-machine interface.

In professional driver debriefing we discover that after a while there is clear link between o
Om one hand
- driver subjective data (Grip, control and stability are quoted from 0 to 10, 0 is bad 10 is excellent- but good drivers are never happy so I rarely see a 10 in their debriefing sheet - and balance quoted for - 10 being bad understeer and + 10 being bad oversteer and 0 being neutral)
Amd on the other hand
- and the control (Nm/ deg of delta for a given beta)
- and the stability (Nm/ deg of beta for a given delta)

When you have played with these other factors you will see that lap time is not as useful as a quantification of the car performance, Useful but not the # 1 parameters to consider. the best prove is setup a will suit driver 1 and setup B will suit driver 2 with equal lap time....

The whole yaw moment Vs lateral acceleration graph is well explained in the Milliken book.

C Kinematics Optimization; we are working on that (as well as suspension elements forces for given tire force sand moments input) be patient. That being said you can still use the automated batch run. Many students are not even aware of this function. That is because t do not read the help file but there little we can do for them; it is not a not an OptimumKinematics specific issue....

D. Finally let's not forget that any pure kinematics software has its limitation because it doesn't take into account tire deflection and compliance. It is just a tool to compare camber, track, toe, caster, caster trail, scrub radius, etc... variations, roll and pitch axis position and movement (here we go again) for different kinematics solutions and different heave, roll pitch and steering movement (and/or combination of those).

A DTM race car manufacturer bought 8 OptimumKinematics professional licenses. They just want to know, for example, if and how much bump steer there is when the chassis goes down 50 mm. Without tire deflection and/or compliance. THEN they use Adams. And they save a lot of time by doing so instead of inputting all kinematics and compliance.

A passenger car manufacturer (you know the car with bushing at each suspension element end) does the same and also saves a lot of time.

[dynatune]

Koushik,

if you are interested in doing your own kinematics solver have a look on this website to get some idea's www.dynatune-xl.com. The tool is completely vector algebraic
and can therefor calculate all types of independent (multi-link) suspension, do compliance analysis and predict accurately link loads, all in one go and in excel.

Cheers,
dynatune

[Kevin Hayward]

Claude (and others),

Coming up on 10 years soon. A lot has happened in that time, but working with the group of people at OptimumG will always be a fond memory. Despite the stressful deadlines :) The big bonus was I learnt a lot of dirty French words, while I am still waiting for the opportunity to use this in life I am sure it will come in use one day.

I definitely agree with the points you made about the usefulness of software. It is important to be very clear about what you want the software to do, and who it is for.

The point I was making about lap-time is that just about any approach to optimisation I have seen requires single objective functions. Most multi-objective ones end up essentially as weightings on the various objectives to make one objective. Otherwise the outputs can be represented as points against different objective scales such as pareto sets. Lap time is not the only useful metric, but probably the one that is best suited to optimisation.

It might be good to include things like driver/tyre condition as a set of random variables. This will help move the global optimisation towards solutions that are not overly sensitive. It is worth noting that while the performance of a car is not 1-1 with most variables the solution space is reasonably clean (i.e. not a lot of local minima). A decent heuristic optimisation routine should be able to deal with the random inputs and the solution space quite readily.

There are ways to build good driver models into lap time sims, but the computation time starts increasing to a point where wrapping an optimisation routine around it starts taking a lot of computation time. This starts to get outside of the realms of usefulness for the race engineer at the average computer and into the more professional teams. In other words difficult to make money on. You only have to look at the large number of variables to get a concept of how much computation could be needed. It is a similar problem in other simulation fields. Shape optimisation is a good example. A single FEA run might take a few seconds. Multiply it by 10000 and you have a big portion of the day gone. 10000 sounds like a lot, but what if you had 10 variables each with 10 options only (i.e quite coarse). Your 10000 runs only cover 0.0001% of the solution space. Project this into multi-objective optimisation and the limiting factor quickly becomes the running time of your simulation. The main solution is to get it to run quicker, but that usually comes at a loss of fidelity. In the end you are searching through an abstracted solution space anyway so great care needs to be taken.

I normally tell my students that this is a good thing otherwise all of us engineers would be out of a job pretty quickly if problems weren't this hard.

For kinematics sims I think the batch runs are good enough. Optimisation brings its own problems, that can work against the user. What function do you optimise for? What variables are kept free? All of this working in such a neat user interface would be a big challenge. I am personally more excited about seeing the springs etc. going into the software. Also maybe starting to address the movement of the contact patch centre. I have this already in my own code, but the ease of use in a developed package will make for a lot less headaches. As always I bet the challenge for OptimumG is not in doing the math, but putting it into something foolproof with a decent UI. Once it is in the product easily goes into its own unique space. Somewhere smack between full VD capable software and the purely kinematics software, while still maintaining the ability to do pure kinematics. At a decent price point it would make the latter almost completely without a market.

However my main preferences are for well designed tools that do specific jobs well, rather than all purpose tools that need a lot of fiddling around to get results. I am not surprised by the DTM manufacturer example. That would come pretty close to how I would work on the problem. Kinematics only for the simple things, iterate until you get something that looks reasonable and then go to more depth if necessary.

Ultimately finding good solutions means exploring as much of the solution space as possible. Doing some initial searching with coarse tools allows you to narrow down to areas of interest, which you can then analyse in more depth. This would be akin to using a telescope before the microscope. If you only have a microscope you get a really good view of your immediate surroundings, but no clue as to what is only a small distance away.

Kev

[Tim.Wright]

I also made an excel based kinematic solver which also calculated link forces and I learnt a great deal. I was without adams for a few weeks and needed to get started on a 5 link suspension design. As a learning tool I can highly recommend it.

The kinematics were an open form and iterative.

The basic equations came from a vector analysis of the system where a vertical velocity vector of unit length is applied to the contact patch and the remaining 5 degrees of freedom are solved based on the kinematic constraints:
1. The velocity vector of each point on the upright is a function of the 5 "response" degrees of freedom (dTrack, dWheelbase, dToe, dSpin, dCamber)
2. The dot product of the axes of each link and the velocity vector of its outboard point = 0 (since they must be perpendicular)

This gives you 5 equations and 5 unknowns which is easy to solve in excel in matrix form.

Then you can do cool stuff like this:
Roll centre height = Track x (dTrack / dZ) / 2
Anti-dive/raise angle (braking) = dWheelbase/dZ
Anti-lift/squat angle (acceleration) = some function of dWheelbase, dSpin & dZ but I don't remember now.
Camber gain = dCamber
Bumpsteer = dToe

But the even cooler stuff is when you realise you can rewrite the equations so you input design parameters (roll centre height, anti angles, bumpsteer, and camber gain) and the equations calculate the pickup points.

Its the duck's nuts.

I use this method in parallel with my adams work as it allows you to change (for example) the roll centre height without touching the bumpsteer, even with a complicated 5 link setup. Otherwise you find yourself manually iterating forever in adams or optimumk to arrive at a set of pickup points that satisfy all of your design targets. In fact I'd even go as far as saying if you don't have SOME sort of (possibly simplified) support calculations going on beside your adams/optimum K model you aren't really engineering, you are just playing.

[Claude Rouelle]

Kevin,

I agree with you about the importance of the usefulness character of any simulation


"I am personally more excited about seeing the springs etc. going into the software"

That is what OptimumDynamics is for. Imagine OptimumKinematics + Spring and ARB + Tire vertical deflection + Aeromaps and you have OptimumDynamics with all "magic numbers"(or TLTD) etc... Not perfect No simulation is) . But useful.

We have another OptimumDynamics version with tire model, yaw moment, grip, stability, control and influence of each design and setup parameters on those performances indexes.

We only use this version for our consulting customers but we could put it on the market next year. By the end of this year we will be looking for beta tester for that new version.

[koushik123]

Mr.Claude

Thank you for the comprehensive reply. Although one point that is a little confusing



Obviously you will have different instant axis position for different x axis movement so ideally you want a lot of small iterations of the wheel center z movement.


" for different x axis movement " ??? Isn't that the movement in z- axis ?? Clear me if I am wrong here.

And as well the "why" question about re inventing ?

When I was a FS and Baja participant I never really knew that there is this much of kinematics and calculations going behind suspension and as well the whole FSAE design process.I was just playing with a pickup point table in Adams idiotically with out any clear goal.Lack of knowledge and guidance was the biggest issue.I took the initiative to start the first FS and BAJA team in my college. The sad truth is even few of my faculty wondered what is SAE when I told about them (It is a harsh and sad truth that 90% of Indian engineering colleges were founded just as money making mills and there were no quality in the education provided and as well we never really had faculty who taught us what engineering really is, I do not want to start blaming anyone then I have to blame from the fundamental state board high school syllabus here,rather I blame myself for my late self discovery of this forum,there were times during my initial days to this forum when I didn't even understand most of the simple conversations,it was then I started thinking "Where am I standing as an engineering grad in the world?").Most of the time during the FS project flew by in just making my team and my college management understand about SAE, the event and its benefit.A team can't succeed unless everyone in the team works for it.I was working day and night on the entire design of the vehicle when my fellow team mates blinked when I asked them what exactly is the function of a spring and damper.Enough of blaming,since you were a design judge here in the first edition of FS India I guess you must have seen a lot of poor designs.Well, Let me get to the point.

So after my graduation I decided to start co-relating my self paced 4 years of engineering study with the reality,it doesn't really mattered even if I am unemployed for an year I just had a strong intention that I must not become a terrible engineer.I have a strong emotion towards motorsport engineering and a belief that I will become a race engineer one day.Right now I am doing this project for a team who gave me an opportunity to learn and hone my vehicle dynamics skills though this work is not of much use to the team as they already use a good kinematics software for their work.I hope this helps the "Why" question.

Mr.Tim nailed it very nicely in his post

" In fact I'd even go as far as saying if you don't have SOME sort of (possibly simplified) support calculations going on beside your adams/optimum K model you aren't really engineering, you are just playing "

This is what I am looking for, I want to understand,implement and enjoy what I am doing and what is the point in doing something when I don't really know what exactly I am doing?

I don't fear failures and I don't care what others tell or think about me as I can see very clearly where I will be in ten years.

I never really wanted to write an essay or put a specific nation's situation in this thread,since the question was raised I did it.I apologize to everyone If I had bored you somewhere while reading this as it is off from the thread topic.

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I appreciate Mr.Kevin,Mr.Claude and Mr.Tim for their valuable and in depth contributions to this thread.I also thank dynatune and i6overboard.

Regards
Koushik

[dynatune]

Koushik,

if you really want to understand what happens in a suspension I can only recommend to you the book from Wolfgang Matschinsky: http://books.google.it/books/about/Road_vehicle_suspensions.html?id=BHRTAAAAMAAJ&redir_esc=y
It is amongst experts considered the Bible of Suspension Design and besides being quite expensive it is quite tough to read which combined did make it not so popular. If you have understood
that book you are as much of an expert as one can get. I did start reading the book in 1989 and find myself re-reading it again and again and still finding text that impresses me again and again.

Cheers,
dynatune

[DougMilliken]

This is what I am looking for, I want to understand, implement and enjoy what I am doing...
In case you haven't seen it, Olley works through a simplified set of suspension kinematics in some detail. He was forced to simplify since he only had a slide rule for calculation! It's in our book, "Chassis Design", http://books.sae.org/r-206/ His approximate approach might give you a different perspective on the trade-offs involved and also give a better physical feel than can be had from complex software.

[Tim.Wright]

Koushik,

if you really want to understand what happens in a suspension I can only recommend to you the book from Wolfgang Matschinsky: http://books.google.it/books/about/Road_vehicle_suspensions.html?id=BHRTAAAAMAAJ&redir_esc=y
It is amongst experts considered the Bible of Suspension Design and besides being quite expensive it is quite tough to read which combined did make it not so popular. If you have understood
that book you are as much of an expert as one can get. I did start reading the book in 1989 and find myself re-reading it again and again and still finding text that impresses me again and again.

Cheers,
dynatune

Buggar me, now available in englische sprache. Perhaps I might be able to read it now at a rate faster than 1 page per hour...

[Claude Rouelle]

Koushik,

I meant "for different z axis movement". Sorry for the typo.

More comments to come later.

Claude

[dynatune]

Buggar me, now available in englische sprache. Perhaps I might be able to read it now at a rate faster than 1 page per hour...

There were pages that took definitely more time than that ......:o

[Z]

Koushik and all,

Here is a bit of food for thoughts about how kinematics software is or could be working.
...
Let’s take the generic case of a one 5 links suspension.
...
In this simplified example there is no compliance and there is no tire deflection.
...
Now take 2 points of the wheel / upright assembly as far away as possible from each other. Let’s take T [= "contact patch"] and another point. Let’s say that this other point is O1 and that O1 is the highest outboard point.
...
Look at the segment Ti-Tf. Find the middle of this segment Ti-Tf (i for initial, f for final) Draw in your mind an imaginary 3 D plane perpendicular to the segment Ti-Tf in the middle of segment Ti-Tf. Let’s call this plane A.

Similarly, look at the segment O1i-O1f. Find the middle of this segment O1i-O1f. Draw in your mind an imaginary 3 D plane perpendicular to the segment O1i-O1f in the middle of segment O1i-O1f. Let’s call this plane B.

The intersection of planes A and B is your instant axis of the wheel about the chassis.

If you want to know more have a look at http://papers.sae.org/2008-01-2949 New Method to Evaluate Bump Steer and Steering Influence on Kinematic Roll and Pitch Axes for All Independent Suspension Types

Claude,

The above emboldened quote is VERY WRONG, on many different levels (*).

This is very disappointing, given that I have been harping on about exactly this issue for at least three years here on this Forum. It is even more disappointing in your case, since I made efforts to explain all this to you, including giving you a list of good references, way back in 2002.

But most disappointing is that in the abstract to your SAE paper it says, "... A new method is proposed that addresses the limitations of the “classic” method.". This is either a GROSS INSULT to "Classical Kinematics", which was giving the exact answers (ie. completely correct!) hundreds of years ago, or it is giving unduly high status to the "cottage-industry 2 x 2-D methods" by calling them "classic".

Anyway, I really wish you would make the effort to learn a bit more about Classical Mechanics, rather than just making this stuff up as you go along and then passing it off as good Engineering.

(* I am NOT going to pay $25 to read above paper just so I can point out the many places where it is WRONG. But as a start, and based on your above post:
1. At any instant your two points T and O1 define a LINE. Significantly more work is required to describe the motions of BODIES.
2. The two points T and O1 are on two DIFFERENT bodies, namely the wheel and the upright. So common things like Inboard-Drive/Braking, or Outboard-Geared-Drive, etc., throw a big spanner in the works.
3. What has the VD (cottage-) industry got against the "Instantaneous SCREW Axis"? Have these people never seen a nut-and-bolt?
4. To stress above point, where is the "Instant Axis" for a nut moving on a bolt!!!???)
~~~o0o~~~

Tim and Koushik,


(Posted by Tim):
The basic equations came from a vector analysis of the system...
...
2. The dot product of the axes of each link and the velocity vector of its outboard point = 0 (since they must be perpendicular)

YES!!! (Kinematically speaking...)

The above is equivalently saying that the "axes of each link" are "n-lines", namely straight-lines in 3-D space that have NO motion along them. But whatever you call the various bits, the above method is essentially what Kinematic researchers were doing hundreds of years ago.

Koushik, I have not yet read the Matschinsky book linked to above, but I suspect that it gets this stuff RIGHT. A rare thing in the VD world.

As a detail point I note that Tim had to talk in terms of "velocity vectors" because displacement vectors for the ROTATIONS of 3-D Bodies DO NOT COMMUTE. That is, they are a PITA to deal with (you need Quaternions...). But very small rotation vectors do commute, and a "rotational velocity" is simply the necessarily small rotational displacement that happens over a very small period of time. So vector methods work fine with rotational velocities and accelerations, but NOT displacements.


Then you can do cool stuff like this:
Roll centre height = Track x (dTrack / dZ) / 2
Anti-dive/raise angle ([OUTBOARD!!!] braking) = dWheelbase/dZ
...

Why not "Anti-Roll angle = dTrack/dZ"?

This fits in much better with the longitudinal "Anti-dive angle", etc. That is, it just boils down to knowing the lateral and longitudinal n-line slopes through the wheelprint. (Note that the behaviour of Inertial forces acting on the wheel-assembly, such as GYROSCOPIC Couples, are understood by knowing the positions of other n-lines...)

Z

[Tim.Wright]

Why not "Anti-Roll angle = dTrack/dZ"?


Just convention. Same reason I calculate wheel frequencies instead of static deflections - it lets me compare the value to other car's simulation/k&c data which is all done in the same convention.

Regarding the screw theory vs instant axes my view is this. For kinematic calculations the instant axis method is not ok for the reasons you have stated. But, for force (jacking) analysis it is fine.

To elaborate: The instant axes construct is mainly (actually I'd say 95% of the time) used to calculate jacking effects in a simplified "back of a napkin" model, usually in support of a proper 3D model. For this job they are adequate. The main information that you lose is the effect that bumpsteer has on the anti-pitch angles but the error is quite small and inconsequential. Anyway, once you add in longitudinal wheel centre compliance the anti angles all turn to shit anyway - so the extra "precision" doesn't help. With this method you can calculate the jacking effects to a reasonably high degree of "accuracy" using a simple drawing board method implemented in excel.

The screw axis instead requires an extra parameter to define and then its a full blown 3D problem. Moreover, this extra complexity doesn't come with a useful increase in accuracy for jacking calculations (in my experience).

For kinematics on the other hand - a single instant axis is missing too much information to properly define the wheel path and, unlike the case of a jacking analysis, the information that's missing is critical (being toe angle change).

[dynatune]

I can only recommend very strongly to everyone to read the book from Matschinsky. It explains clearly what has been discussed in this forum many times with many different opinions
methods. Actually all in the book is explained on the method of "velocities" which are differential displacements.

Moreover the book explains in great detail how to relate from a 3D movement of the upright/knuckle to 2D interpretations and where there are the problems/inaccuracies. For instance
in the book is clearly explained what kind of suspensions architectures can be defined according to instantaneous axis of rotation.

1) If the instantaneous axis is "free" floating in space AND does have a significant "thread" it is called the instantaneous "screw" axis and describes a full blown 3D Suspension - which
cannot accurately be analyzed on a 2D paper (complex 5 link or so called Integral link suspensions where 1 link is connected to another).

2) The next "lower" level of suspension architecture is defined by an instantaneous axis of rotation that ALWAYS goes through a fixed point, a so called Shperical Suspension. These
suspensions can be analyzed on a 2D paper with some geometrical tricks (typically a Toyota RAV 4, BMW E36, old Corvair).

3) Then the "lowest" complexity suspensions are the ones where the instantaneous axis of rotation is rather fixed in space with minimal Thread. These suspension can be analyzed without any problems on a 2D piece of papar and are therefor called "Planar" Suspensions
(McPherson or Double Wishbone).

After having read and if lucky understood all that is written in the book, one has transformed from thinking of drawing lines through pick up points and links to just looking at the movement
of the upright and start from there. The downside is however that you find out that there is no magic in kinematics and you realize that 35 years ago someone was a lot smarter than all
of us together. Besides that the book will make you understand why BMW became the "ultimate" driving machine over the last 3 decades :-) and where I took my inspiration from. :-)

Cheers,
dynatune www.dynatune-xl.com

[slicktop]

I believe that the method Claude is outlining here is the use of "natural coordinates". I would also like to add that it is easy
to use this at the front when you have a steered wheel. The inner toe link position can become an input to the model.
Then, it is also possible to add in the rack ratio, rack travel and handwheel angle to produce steer/steer graphs as well
as bump steer graphs. It is not really that difficult to throw together this type of kinematic analysis. Not really too terribly
difficult to make a nice little GUI in matlab either, that way you don't have to go into your code to make changes.
Beats the hell out of doing it in solidworks all day.
The real fun is adding masses, forces, springs and dampers then applying a touch of Lagrange.

BTW, when i was first trying to figure out how to do this I found the first couple of chapters of this book very helpful. And its free.
http://mat21.etsii.upm.es/mbs/bookPDFs/bookGjB.htm

[koushik123]

Thank you Mr.Doug,Dynatune, and slicktop for your reading recommendations.

-----------------------------------------------------------------------------------------------
Mr.Claude

Thank you for the typo confirmation.

Regards
Koushik

[stever95]

Great thread, all. Looking forward to getting into these references.

For FSAE, I maintain the OPINION that 2D napkin-sketches are good enough for a team looking to get in the top 10. There are so many other things to get right that are completely unrelated to suspension design, that I don't think it's worth it for a small group to try to tackle a 3D situation, when in reality it won't be gaining them any points - just losing them design, manufacturing, and testing time.

As I said though, this is just my OPINION, and I haven't been through both 2D and 3D design cases.

Perhaps someone else can comment on how many more points you expect to get by using a 3D suspension tool..?

[Tim.Wright]

A 3D tool is required unless you have time and the adjustability to manually tune out the bumpsteer after the car is built. Reason being that 2x2D and instant axes type calculations cut out this information. If you want a solid, predictable, unspectacular suspension to use as a base - the only thing you need to get right is the bumpsteer. Everything else is negotiable. If you wheels are all steering in the wrong direction, you will never be able to fix it.

The discussion here is whether there is any value in writing this tool yourself.

[Claude Rouelle]

Stever95,

Same opinion as Tim Wright but in different words…

How do you know if you still have the bumpsteer you want (top view) and the camber variation you want (front view) if you look at you “anti” (dive, lift, squat) in side view only.

Everything interact

You need 3 D kinematics analysis. The world is 3D (well at least...no quantum physics here :)), at least not yet)

Besides it is not about getting the most point in design: it is about getting the most comprehension of vehicle dynamics. That is what this competition is about.

Who are you by the way? No signature details, nothing in your profile…. Worth to introduce yourself. I think I invited you to do so about 1 year ago but I can’t see if you did

[OspreysGoSWOOP]

This thread is incredibly fascinating. I find using the intersection of engineering and technology to solve problems one of the most amazing aspects of our field.

It's always a good idea to avoid wasting time re-inventing the wheel if you just want to use the wheel, but re-inventing the wheel for the sake of understanding how the wheel works should never be viewed at a fruitless effort. It should be championed.

I don't really have anything useful to add to the discussion, but I wanted to thank everyone for such a good thread.

Kevin thanks for sharing your experience with the roots of OptK.

Claude thanks for being a strong supporter of the FSAE, starting OptimumG, giving the seminars, and consistently commenting on most of the threads regardless of the post quality. I just finished Matt Brown's FSAE book and you've been consistent with your support (and jokes!) for a long time. Thanks.