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Having troubles quantifying inertia

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LAN_403

Dr. Slack

Fri Apr 13 2007, 10:11AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

Here's an approximate electrical model of the engine. The most accurate is the engine inertia, modelled as a capacitor. The throttle is pretty approximate, the closer the pedal gets to the metal, generally the higher pressure on the hot side of the piston, but it's non-linear with throttle position, very engine speed dependant, but it will do for this simple model. The main features are it is limited, you adjust it to control the engine speed, when the load increases on the engine you have to give it more to maintain speed. The increasing engine torque losses with speed are just a simple way of getting a variable load into a simulator, a better way would be to write equations giving frictional torque as constant, windage going as the square etc.

Form this simple model, you can see that if you short circuit the output into a capacitor (statioanry wheels), a very large current will flow (torque will be delivered) unless limited by the clutch slipping.

Create similar models for the clutch, the wheels, the wheel/road interface, and for the inertia of the vehicle reflected into the transmission, wire them all up, and see what happens.

Steve Conner

Fri Apr 13 2007, 10:28AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Yes, it's this stored angular momentum in the engine that we're talking about. The engine has a heavy flywheel spinning fast, and all the other components like pistons, rods and crankshafts have momentum too. The equation for the stored kinetic energy, like a previous poster said, is

E=0.5*I*omega^2

where I is the effective moment of inertia of all the engine bits, and omega is the angular velocity (RPM multiplied by 120*Pi)

This stored energy is just like a charged capacitor as NeilThomas said, and dumping the clutch with the engine going at speed is like shorting the capacitor. It cannons your car forward the same way as a capacitor discharge fires a bullet from a railgun. You could theoretically have infinite torque for a very short time!

I'm not kidding about infinite torque BTW. The lab where I used to work had an engine test facility, where a car engine could be connected, by a short propshaft that you bolted to the flywheel, to a 150bhp water cooled eddy-current brake. One time the propshaft came loose from the brake while the engine (a 2 litre four cylinder unit from a Fiesta XR2) was doing about 5000rpm at full throttle. I wasn't there, but I heard that when the shaft came loose, it whipped round, struck the base of the test stand, and all that angular momentum we were talking about ripped the engine off its mountings (although these mountings could easily stand the torque of the engine at full throttle) and hurled it clean across the lab.

stop4stuff

Fri Apr 13 2007, 09:23PM

Registered Member #64 Joined: Thu Feb 09 2006, 06:25AM
Location: Southampton, UK
Posts: 68

more thinking...

forget about clutch heat loss...
because when the clutch is dis-engaged the engine still develops the torque, the clutch is not slipping & no torque is delivered to the drivetrain...
so...

its got to be 'time to apply the clutch' vs 'clutch friction'
something along the lines of...

engine_torque * (clutch_friction/time_taken_to_engage_clutch) = torque_available_to_drivetrain

paul

Dr. Slack

Sat Apr 14 2007, 06:18AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

Stop4, please don't do this, you're confusing people. The mechanics is very simple, break it down to its component parts and model it electrically in as much detail as you need.

Here is an indication of how far you can push the model. If you slip the clutch at high revs and high torque, eventually it will overheat and burn out. If you run the constant current biassed transistor equivalent of a clutch at high voltage and high current, eventually it will overheat and burn out. Both for the same reason, power is voltage x current and is revs x torque. As long as you measure everything in consistent SI units, so rotational speed in radians/second (roughly rpm/10 for back of envelope) and torque in Nm, the answer will actually come out in watts!

In fact, to answer the subject of the thread precisely, INERTIA is a thing that stores energy proportional to speed^2 (just as a capacitor stores energy proportional to V^2). The constant of proportionality is called mass for linear speed, moment of inertia for rotational speed, and capacitance for electricity.

As a more general observation, to model any energy storing/transmission system electrically, find a pair of parameters whose product is power, and relate them to voltage and current. Check that there are things that store energy proportional to the square of either, so inertia and spring constant for V^2 and torque^2 are equivalent to capacitance and inudctance for voltage and current. Check that there is a loss mechanism for their ratio, so viscocity is torque per speed, which is the equivalent of resistance. It works for hydraulics and pneumatics too, use pressure and flow rate, which is a nice reversal of the hydraulic analogy taught to everyone to explain electricity (use a bit of care with pneumatics because of the compressability).

Does anyone feel like working up mechanical modeling into a wiki article? Is there one there already?

Coronafix

Sat Apr 14 2007, 09:40AM

Registered Member #160 Joined: Mon Feb 13 2006, 02:07AM
Location: Melbourne, Australia
Posts: 938

The_Zander wrote ...

RE: Goldsphere

What your getting at it that the rotational inertia of the engine resists the change in velocity applied by the sudden application of the clutch and thus excerts more power @ the wheels. concrete, but i still don't know how to quantify that added energy.

Breaking it down further, Torque = Force x radius
The radius being the size of the flywheel, the size relating to how much the engine can turn.
I think this is what everyone is saying, that at low revolutions, there isn't enough stored inertia in the flywheel to spin the tyres.

Bjørn

Sat Apr 14 2007, 10:56AM

Registered Member #27 Joined: Fri Feb 03 2006, 02:20AM
Location: Hyperborea
Posts: 2058

now that's out of the way, i can pose the remainder of my question, how do i quantify the magnitude of the additional torque imposed by the inertia of the spinning engine components. the force that causes wheel spin when dropping the clutch but not when easing it out.

If you want an accurate answer you measure it. If you want an approximate answer you do a lot of calculations depending on how approximate is good enough.

All normal car engines have a flywheel, look up the size and weight, then look up the formula for the stored energy in wikipedia. For the engine itself it is more complicated since it is several parts of different shape.

Finding the resulting theoretical maximum torque is more difficult since there are many parts in the drive train that will absorb energy and release it at a different time. The drivetrain is designed that way to reduce stress on the components. In real life the tires will set the limit.

As Steve says the maximum torque can be very very high, but it will be different from car to car and also different on the same type of car depending on the wear on the components.

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