Why Are T1 and TL Negative in Gear Train Dynamics?

[xzibition8612]

Homework Statement

See attachment.

Homework Equations

The Attempt at a Solution

Equations (1) and (2) describe this gear train system. I'm confused about them.

For (1):
If I rewrite it (∑F=0 format) I get:
T-T1-Jθ''-Bθ' = 0
The figure clearly shows θ1 positive spinning towards the bottom. Why then is T1 negative if it is spinning in the same direction as θ1? I understand the inertia and damping is always opposite to the defined positive direction.

For (2):
T2-TL-Jθ''-Bθ' = 0
Since the figure doesn't show the direction TL is going, why is it negative?

Also why is there a T1 and T2 if I only apply a load T? Shouldn't it just be T-Jθ''-Bθ' = 0 ? Where did T1 and T2 come from if I only applied T? And what exactly is a load torque?

Now I'm thinking isn't it physically impossible for a single shaft to have two torques going in opposite directions?

I'm obviously very confused on this. Any help would be appreciated.

 

[KataKoniK]

I completely understand your confusion with the equations and the direction of the torques. Let me try to explain it to you.

Firstly, in equation (1), T1 is negative because it is acting in the opposite direction of θ1. This means that T1 is trying to resist the rotation of the gear in the positive direction (towards the bottom). Similarly, in equation (2), TL is negative because it is acting in the opposite direction of the gear's rotation.

Now, for your question about why there are two torques (T1 and T2) when you only applied one load torque (T), the answer lies in the gear train system itself. The gear train is a system of gears connected by shafts, and each gear has its own torque. In this system, the load torque (T) is being transmitted through the gears and is divided among them. This is why there are two torques (T1 and T2) in the equations.

As for your last question, it is not physically impossible for a single shaft to have two torques acting on it in opposite directions. This is a common occurrence in gear train systems, where the gears are connected to the shaft and are rotating in different directions.

I hope this clears up your confusion. If you have any further questions, please don't hesitate to ask. Good luck with your studies!