# Conservation of Energy - Gear Box vs. CVT

• KingBongo
In summary, the conversation discusses the process of modeling a mechanical system with a snowmobile, specifically in relation to the use of a CVT (Continuous Variable Transmission) instead of a gear box. The differential equations for this system are described, taking into account the moment of inertia, torque, and gear ratio. The approach may change when using a CVT, and conservation of energy must be considered. The impact of changing gears instantly and potential transients are also discussed. The conversation ends with a request for recommendations on books about modeling gear boxes and CVTs.
KingBongo
I am working on a mechanical model for a Snowmobile and trying to figure out what the differential equations becomes when you have a CVT (Continuous Variable Transmission) instead of a Gear Box.

Assume that you have two shafts connected with each another through a (lossless) and stiff gear box, consisting of two gears only. If I understand it correctly, the differential equations describing this system are

J1*d2(Theta1)/dt2= M1 + g*M
J2*d2(Theta2)/dt2= M2 - 1/g*M

where Ji, i ={1,2}, are the Moment of Inertia's of the shafts (including gears) respectively and Mi, i={1,2}, are torques acting on the corresponding shafts (friction, external torques, a.s.o.). M is an auxiliary Torque describing the coupling between the two axes, and of course g is the gear ratio. Thetai, i={1,2} of course are the corresponding angles. We also assume that dg/dt is constant (except when changing gear instantly and re-initialize the system).

By using the fact that Theta2 = g*Theta1 (+ Constant), M can be eliminated and the equations above be reduced to a single equation, not shown here.

Questions:
1. Is everything above correct?

2. How will the approach change when the shafts are connected through a CVT and therefore dg/dt is NOT equal to zero? I understand conservation of energy must be used, but how?

3. If you have a fixed gear box and change the gear (instantly), will there be any transient effects, like Dirac pulses? This is mostly neglected in the literature, so I do not know if there will be any transients or not.

4. How do you extend the models for fixed gear box and CVT in order to include losses inside the gear box?

5. Are there any good books for modeling gear boxes and CVTs?

Last edited:
This can't be happening. Doesn't anyone have the slightest clue? I thought this would be an easy problem, :)

## 1. What is the conservation of energy?

The conservation of energy is a fundamental law of physics that states that energy cannot be created or destroyed, only transformed from one form to another.

## 2. What is a gear box and how does it conserve energy?

A gear box is a mechanical device that uses gears to change the speed or torque of a rotating shaft. In terms of energy conservation, a gear box is able to transfer energy from a high-speed, low-torque input to a low-speed, high-torque output, which can be more efficient for certain applications.

## 3. What is a CVT and how does it conserve energy?

A CVT (continuously variable transmission) is a type of transmission that can change seamlessly through a continuous range of gear ratios. This allows the engine to operate at its most efficient speed, resulting in better fuel economy and less energy waste.

## 4. Which is more efficient for energy conservation - a gear box or a CVT?

It depends on the specific application. In general, a CVT is more efficient for vehicles that require frequent changes in speed, such as city driving, while a gear box may be more efficient for constant speed applications, such as highway driving.

## 5. How does the conservation of energy relate to the use of gear boxes and CVTs in vehicles?

The conservation of energy is important in vehicle design and operation because it helps to minimize energy waste and maximize efficiency. Gear boxes and CVTs are both utilized in vehicles to help conserve energy by optimizing the speed and torque of the engine, depending on the driving conditions.

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