# Determining gearbox moment of inertia

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As far as I get it, the inertia of transmission at the clutch side depends:

• if it's not connected to the rest part(neutral gear) and if clutch is not locked, than it's only the inertia of the bar
• if it's not connected to the rest part, but clutch is locked, than the inertia at that point is bar + engine inertia
• if it's connected to rest part(any gear except neutral), but clutch is not locked, than it's transmission bar + gears + differential inertia + drive wheel inertia
• if it's connected to the rest part and clutch is locked, than it's transmission bar + gears + differential inertia + drive wheel inertia

I've got several problems:

1. How to determine the affect of inertia from each of gear ratios? Also, does inertia differ, for example, between gear 1 and gear 2?
2. Where could I find some example values for those moments of inertia?

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As far as I get it, the inertia of transmission at the clutch side depends:

• if it's not connected to the rest part(neutral gear) and if clutch is not locked, than it's only the inertia of the bar
• if it's not connected to the rest part, but clutch is locked, than the inertia at that point is bar + engine inertia
• if it's connected to rest part(any gear except neutral), but clutch is not locked, than it's transmission bar + gears + differential inertia + drive wheel inertia
• if it's connected to the rest part and clutch is locked, than it's transmission bar + gears + differential inertia + drive wheel inertia

I've got several problems:

1. How to determine the affect of inertia from each of gear ratios? Also, does inertia differ, for example, between gear 1 and gear 2?
2. Where could I find some example values for those moments of inertia?

I'm not sure if you can find some good examples of those values but I've seen in couple of places that generally you would ignore moment of inertia of shafts, as their MOI is insignificant when compared to inertia of wheels and flywheel of the engine. With manual transmission, layshaft of the gearbox will have all gear attached to it and this can add MOI to the system, but again, it will be much smaller than that of wheels and flywheel.

Gears modify moment of inertia in a quadratic way. For example, effective moment of inertia on the layshaft of gear-box would be:

EffectiveLayShaftMOI  = LayshaftMOI + (1/GearRatio)^2 * TotalDriveShaftMOI

where TotalDriveShaftMOI is a moment of inertia of all parts connected to it. Which means that if you have a differential with a gear, between gear-box and wheels, you have to calculate effective moment of inertia for differential too.

At the same time effective MOI on the drive shaft of the gear box is calculated like this:

EffectiveDriveShaftMOI  = DriveShaftMOI + (GearRatio)^2 * TotalLayShaftMOI

So the rule is pretty simple, the higher the gear ratio the less of the moment of inertia your clutch or engine will experience and from the wheel side it would be reverse.

You can calculate moment of inertia for simple shapes using this:
https://en.wikipedia.org/wiki/List_of_moments_of_inertia

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Thanks for info, this must help!:)

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I agree with @BoredEngineer. My simulation considers the MOI at wheels and engine only. All other parts are considered to have negligible inertia so these don't take part in the calculations.

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Hm... I assumed those equations and guessed that lay shaft might have 0.025 kg.m2 inertia and the drive shaft might have around 0.1 kg.m2 inertia. Assuming this, a car in air resulted in noticeable difference between 1st and 6th gear. The rev was falling slower at 6th gear, although the engine friction torque was the same. It doesn't seem so negligible. But it may again be matter of how high accuracy each of us needs.

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