Re: Modelling an open differential

I'm kind of stuck on a similar issue. I have tried implementing a basic locked differential but my car barely moves! My problem is that I am trying to put in a clutch and differential at the same time, as the two kind of go naturally as it is all to do with rod torques, inertias and accelerations The procedure of my solution is thus: 1. Get engine torque due to the current RPM possibly using a look up table, (if launching, the current RPM will be the idle RPM) and relate it to the throttle. 2. Apply this engine torque as an output to the flywheel to get a flywheel acceleration. Now this is where things start getting tricky for me! 3. Get the speed of the rod going IN to the differential from the engine by multiplying the flywheel speed by the clutch amount (if engaged, 1.0f, if not 0.0, and anything else in between) and dividing by the currently selected gear ratio. 4. For now, for simplicitys sake, apply the same amount of torque to both wheels. This next bit gets even more confusing for me!... 5. Get the road reaction torque from the wheels, and use it as a resistive torque against the clutch. Multiply (?) by the torque ratio. 6. Put this resistive torque back in to the clutch, which will in effect fight against the engine flywheel. 7. Apply this resistive torque at the flywheel to the engine speed, which will reduce it. Doing this will mean that for example if you pull a wheel spin, the resistive torque will fight against the engine and bring the rpm back down. My main problem in this is getting the different accelerations of the rods, as they are based on torque/inertia of the drive train. If you have read Ruud Van Gaals page (racer.nl) there are documents about the squared inertia equation for two gears. Then the most difficult part for me is getting the resistive torque and putting it back into the engine. This is where my implementation is currently failing as my wheels spin, and the car starts moving, but the rpm does not reduce so as the rpm redlines there is no torque left to power the wheels and things start going wrong as I am at 1mph in 6000 revs :( To do it properly, you cannot make a direct link between the wheels and the rpm (clutch effects and inertias) , but it can be used as a guide so that you know what the rpm *should* be. Let me know if you get a solution! Regards, Alex

I need to use a more realistic approach in applying a torque on the wheels of my car sim, so I started reading up on engine RPM's, gear ratios, differentials, etc. Just to check that I have things right : 1. The engine works at some RPM (controlled by the throtle) 2. From that RPM we get an engine torque 3. This gets multiplied by a gear factor... 4. ... and a differential factor 5. The resulting torque is applied on the wheels Now a few questions : 1. Assuming that I'm modelling an open differential, how do I know how much of the engine torque it transmits to each wheel? I've read that the portion of the engine torque that a wheel gets is inversely proportional to the 'resistance' on the wheel. i.e. if one wheel is on top of ice and the other on tarmac, the first wheel will get most (all?) of the engine torque. So how do I determine the wheel's 'resistance'? I guess if the wheels are sitting/moving on different types of ground (ice, tarmac, etc) then I could use the friction coefficient. I'm more interested however on a car turning on tarmac. Since the outer wheel need to run faster, it needs to spin faster, i.e. it needs more torque. Is there a way to model this so that the required portion of the engine torque comes out of the math? 2. How is the engine RPM affected when you press the throtle? Obviously it increases, but by how much? Would the following procedure be correct? At every integration step : 1. Adjust engine RPM depending on throtle position 2. Follow the above procedure to work out torque on each wheel 3. Integrate quantities (e.g. using Euler) 4. Determine wheel RPM and make the engine RPM equal to it The last step troubles me the most. If both wheels rotate at the same speed, then it might be right, in the sense that the wheels will slow down (due to rolling friction), making the engine RPM drop (which is what I'd expect). To keep the car running at constant speed, you'd need to press the throtle just enough to produce the torque to overcome rolling (+ internal) friction. great! But what happens if the wheels are rotating at a different speed (e.g. when going around a corner)? Do I use some proportionality factors as in the differential? Anyway, sorry for the long post and I'll be grateful for any replies. The questions might be a bit basic, suggesting that the person asking them doesn't really know much about how cars work....which is true! ;) -- Morfeas

On Fri, 24 Jan 2003 21:41:00 +0000, Morfeas <[email hidden]> wrote: >1. The engine works at some RPM (controlled by the throtle) Only indirectly; especially when you add a diff, first get the engine right. At a certain RPM the engine has a POTENTIAL torque that it can output. The throttle then roughly interpolates between no usage of that torque and max usage. As you also have engine slowdown due to friction and cylinders pumping (etc) you can do something like: - Get a torque curve; at RPM x you have y torque available. - Get a slowdown curve; as this is mostly linear you can use a formula instead: T_min=coeff*rpm Then the engine must become its own rotating entity; engRotVel, engInertia. Throttle gets used like this: - T_min=coeff*rpm - T_max=torqueCurveValue[rpm] - throttle=getInput() (assume 0..1) - T_engine=throttle*(T_max-T_min)+T_min (the engine torque output) Then you use the T_engine to accelerate the drivetrain. That's where things get tougher, but in the end it's a whole system with an effective inertia (indeed note the squared inertia effects that Alex noted on my site). >1. Assuming that I'm modelling an open differential, how do I know how much >of the engine torque it transmits to each wheel? Going out towards the wheels, the torque will be T_input/2 at both wheels (that's open diff specific). See RCVD; it has a chapter on the open and locked diffs. > I've read that the portion >of the engine torque that a wheel gets is inversely proportional to the >'resistance' on the wheel. Not the torque that goes there; actually the reaction torque (which is ~0 for ice) doesn't fight the input torque as much as the tarmac side, so the wheel on ice accelerates much faster. >So how do I determine the wheel's 'resistance'? That's the road reaction force; the track surface pushing back, as a result of the tire spinning at a different speed from the surface moving underneath it (called 'slip ratio'; 'slip velocity' is actually less important). Use Pacejka or just F_road_reaction=slipRatio*anotherCoeff for a quick starter. >Is there a way to model this so that the >required portion of the engine torque comes out of the math? Multiple ways, and some may be more elegant or understandable. Some use a balanced and off-balanced way (like Gregor Veble and Todd Wasson; try googling for those names and 'Car physics' in RAS). Try getting your hands on a Lego differential (Tecnic) and things may get clearer. Important is to check the end results; (vel_out_1+vel_out_2)/2=vel_input (not taking into account the gearing ratio) I still at one point want to do a full Lego-diff simulation, to check what the diff is doing visually. Would be fun. :) Ruud van Gaal Free car sim: http://www.racer.nl/ Pencil art : http://www.marketgraph.nl/gallery/

On Fri, 24 Jan 2003 20:13:42 +0000 (UTC), "Alex Smith" <[email hidden]> wrote: > My problem is that I am trying to put in a clutch and >differential at the same time, as >the two kind of go naturally as it is all to do with rod torques, inertias >and accelerations You can ignore the clutch as long as it's locked; in that case you have a big pre-diff rotating assembly. Note that then includes the engine's inertia, as the clutch looks as if it's rigid. Once the clutch torque is overcome (T_engine>T_clutch for example), the clutch starts slipping (note that T_clutch can be made dynamic depending on the clutch pedal input). Then you have 2 assemblies; 1 is the engine, the other is from the clutch onwards. I think in my Racer I'm making a mistake somewhere: once the clutch starts slipping, what is the effective inertia of the entire drivetrain? Does it include the full engine's inertia, or just a proportional part of it? (there's a bug in Racer where pressing the clutch fully and braking does not do the same thing as putting the gearbox in neutral and braking). >2. Apply this engine torque as an output to the flywheel to get a flywheel >acceleration. You might see this as the engine as a whole. One big assembly for a complete 'engine inertia'. In Racer the clutch/diff setup is a bit too non-generic still; that's why no 3-diffs setup has been done yet. But see the drivetrain as a bunch of independently rotating objects, each with their own ratio and inertia. That's what I do. The problem is when things start locking on to eachother; you might do some approximation for locking torques to avoid the harder LaGrange approach that Racer has (thanks to Gregor Veble), since that's more flexible (but may hide some tricky vibrational issues). Also note that due to rounding errors, at some point you need to check whether the parts of the assembly are still rotating correctly; at times, my engine and rest of the drivetrain start floating off a bit. I then unlock the clutch and let it lock back up again. Before starting to implement things, also take a look at the brakes; these don't just generates torque but only up to a point, until they lock. Interesting stuff I haven't thought of a really graceful method for yet. Ruud van Gaal Free car sim: http://www.racer.nl/ Pencil art : http://www.marketgraph.nl/gallery/

Hey Ruud, and welcome back! :) > You can ignore the clutch as long as it's locked; in that case you > have a big pre-diff rotating assembly. Note that then includes the > engine's inertia, as the clutch looks as if it's rigid. okay

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> Then you have 2 assemblies; 1 is the engine, the other is from the > clutch onwards. I think in my Racer I'm making a mistake somewhere: > once the clutch starts slipping, what is the effective inertia of the > entire drivetrain? Does it include the full engine's inertia, or just > a proportional part of it? (there's a bug in Racer where pressing the > clutch fully and braking does not do the same thing as putting the > gearbox in neutral and braking).

Thats similar to what I'm having problems with. I get the engines angular acceleration due to throttle, but transferring it to the clutch is difficult as I'm not sure which inertias to use. Do I just use (don't take the +s literally, I'm using them to denote which inertias to use) I_effective = [clutch_inertia + final_drive_inertia + diff_inertia] and do I include the powered wheel inertias? If so, how? > > >2. Apply this engine torque as an output to the flywheel to get aflywheel > >acceleration. > > You might see this as the engine as a whole. One big assembly for a > complete 'engine inertia'. Yes, I do. > The problem is when things start locking on to eachother; you might do > some approximation for locking torques to avoid the harder LaGrange > approach that Racer has (thanks to Gregor Veble), since that's more > flexible (but may hide some tricky vibrational issues). Perhaps a problem I am experiencing above? Also, to get the resistive torque back into the engine from the wheels, do I calculate the I_effective in the reverse direction starting from the wheels to the clutch? Or do I use the same inertia as is calculated for accelerating the clutch? Thanks!

Did any of that take the transmisions ratio at specific engine RPM ? I suck at reading any of those formulas, so this question may have already been answered. "Ruud van Gaal" <[email hidden]> wrote in message news:[email hidden]...

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> On Fri, 24 Jan 2003 21:41:00 +0000, Morfeas <[email hidden]> > wrote: > > >1. The engine works at some RPM (controlled by the throtle) > > Only indirectly; especially when you add a diff, first get the engine > right. At a certain RPM the engine has a POTENTIAL torque that it can > output. The throttle then roughly interpolates between no usage of > that torque and max usage. > As you also have engine slowdown due to friction and cylinders pumping > (etc) you can do something like: > > - Get a torque curve; at RPM x you have y torque available. > - Get a slowdown curve; as this is mostly linear you can use a formula > instead: T_min=coeff*rpm > > Then the engine must become its own rotating entity; engRotVel, > engInertia. Throttle gets used like this: > > - T_min=coeff*rpm > - T_max=torqueCurveValue[rpm] > - throttle=getInput() (assume 0..1) > - T_engine=throttle*(T_max-T_min)+T_min > (the engine torque output) > > Then you use the T_engine to accelerate the drivetrain. That's where > things get tougher, but in the end it's a whole system with an > effective inertia (indeed note the squared inertia effects that Alex > noted on my site). > > >1. Assuming that I'm modelling an open differential, how do I know how

much

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> >of the engine torque it transmits to each wheel? > > Going out towards the wheels, the torque will be T_input/2 at both > wheels (that's open diff specific). See RCVD; it has a chapter on the > open and locked diffs. > > > I've read that the portion > >of the engine torque that a wheel gets is inversely proportional to the > >'resistance' on the wheel. > > Not the torque that goes there; actually the reaction torque (which is > ~0 for ice) doesn't fight the input torque as much as the tarmac side, > so the wheel on ice accelerates much faster. > > >So how do I determine the wheel's 'resistance'? > > That's the road reaction force; the track surface pushing back, as a > result of the tire spinning at a different speed from the surface > moving underneath it (called 'slip ratio'; 'slip velocity' is actually > less important). > Use Pacejka or just F_road_reaction=slipRatio*anotherCoeff for a quick > starter. > > >Is there a way to model this so that the > >required portion of the engine torque comes out of the math? > > Multiple ways, and some may be more elegant or understandable. Some > use a balanced and off-balanced way (like Gregor Veble and Todd > Wasson; try googling for those names and 'Car physics' in RAS). Try > getting your hands on a Lego differential (Tecnic) and things may get > clearer. > Important is to check the end results; > (vel_out_1+vel_out_2)/2=vel_input (not taking into account the gearing > ratio) > > I still at one point want to do a full Lego-diff simulation, to check > what the diff is doing visually. Would be fun. :) > > > Ruud van Gaal > Free car sim: http://www.racer.nl/ > Pencil art : http://www.marketgraph.nl/gallery/

Do you mean having a different engine output at different rpm? like a torque curve? This is catered for in the following > > - T_min=coeff*rpm // HERE > > - T_max=torqueCurveValue[rpm] > > - throttle=getInput() (assume 0..1) > > - T_engine=throttle*(T_max-T_min)+T_min > > (the engine torque output) torqueCurveValue[rpm] would return the torque depending on the rpm given, and would be defined by you. It could be a look-up table, whereby you give it an rpm and it returns a torque for that rpm, but would require a huge array. A better way would be to approximate a curve by having a similar lookup table, but for, say every 1000rpm not every 1 rpm, then interpolate between the bounds the rpm lies between and returning that. Example: Torque[0] = 100; at 0 rpm, torque = 100 Torque[1] = 150; at 1000 rpm, torque = 150 Torque[2] = 180; at 2000, torque = 180 ... Torque[6] = 0; at 6000rpm, torque = 0; then if you want to find say the torque at 3500 rpm // obviously you would need to pre-determine which table entries the rpm you are looking for // lies between. For this example, between Torque[3] and Torque[4] torqueBoundarySize = 1000; // rpm step per entry in the rpm table, constant torqueChange = Torque[4] - Torque[3]; // since it lies between 4000 and 3000rpm, get the difference torqueAtRPM = Torque[3] +[ (3500 - 3000) / torqueBoundarySize] * torqueChange; return torqueAtRPM; this is just a suggestion, but I believe it is a simplified method of what Ruud's Racer uses but Racer can use any amounts of boundaries and variable steps in rpm, and the value retrieved is a normalised value (0....1) and the resultant is multiplied by the maximum torque the engine can procude, to give the final torque. Hope this helps!

Oh yeah melt my mind with your mathmatical prowness...yall need to apply at NASA they could use some help. "Alex Smith" <[email hidden]> wrote in message news:b1muig$4l0$[email hidden]... > Do you mean having a different engine output at different rpm? like atorque

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> curve? > > This is catered for in the following > > > > - T_min=coeff*rpm > > // HERE > > > - T_max=torqueCurveValue[rpm] > > > > - throttle=getInput() (assume 0..1) > > > - T_engine=throttle*(T_max-T_min)+T_min > > > (the engine torque output) > > torqueCurveValue[rpm] would return the torque depending on the rpm given, > and would be defined by you. > It could be a look-up table, whereby you give it an rpm and it returns a > torque for that rpm, but would require > a huge array. A better way would be to approximate a curve by having a > similar lookup table, but for, say every 1000rpm > not every 1 rpm, then interpolate between the bounds the rpm lies between > and returning that. > > Example: > > Torque[0] = 100; at 0 rpm, torque = 100 > Torque[1] = 150; at 1000 rpm, torque = 150 > Torque[2] = 180; at 2000, torque = 180 > ... > Torque[6] = 0; at 6000rpm, torque = 0; > > then if you want to find say the torque at 3500 rpm > > // obviously you would need to pre-determine which table entries the rpm

you

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> are looking for > // lies between. For this example, between Torque[3] and Torque[4] > > torqueBoundarySize = 1000; // rpm step per entry in the rpm > table, constant > torqueChange = Torque[4] - Torque[3]; // since it lies between 4000 > and 3000rpm, get the difference > torqueAtRPM = Torque[3] +[ (3500 - 3000) / torqueBoundarySize] * > torqueChange; > > return torqueAtRPM; > > this is just a suggestion, but I believe it is a simplified method of what > Ruud's Racer uses > but Racer can use any amounts of boundaries and variable steps in rpm, and > the value retrieved is a normalised > value (0....1) and the resultant is multiplied by the maximum torque the > engine can procude, > to give the final torque. > > Hope this helps! > > > > >