Reverted Gear train

F.Turner
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I have a design problem that has two predictions that I must make. The constants that I am given is the amount of teeth each gear has, the diameter of the gears, the input torque, speed in rpm and voltage of the DC motors, and finally the time it takes the toy car to travel 10 feet when its in the slow speed high torque setting. I have to predict the time the car takes to travel 80 ft in the high speed setting and secondly the time it'll take the car to scale 5ft incline using the high torque setting.

I would appreciate any incite that can given to me to start the problem.

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If you are given the rpm of the motor as a constant then the car has constant velocity.
You can find the car velocity for the high torque setting from the time to cover 10ft. Then the high speed setting velocity can be found from the ratio of the gear ratios (for want of better terms).

That interpretation is rather trivial and I'm guessing that the intended question is to not assume constant velocity and to find accelerations from the motor power.
In that case you'll have to provide or find more data. The motor curves for your particular motor would help.
Or you could make some assumptions eg input torque is constant over the rpm range. the rpm given is max rpm etc etc

F.Turner
If you are given the rpm of the motor as a constant then the car has constant velocity.
You can find the car velocity for the high torque setting from the time to cover 10ft. Then the high speed setting velocity can be found from the ratio of the gear ratios (for want of better terms).

That interpretation is rather trivial and I'm guessing that the intended question is to not assume constant velocity and to find accelerations from the motor power.
In that case you'll have to provide or find more data. The motor curves for your particular motor would help.
Or you could make some assumptions eg input torque is constant over the rpm range. the rpm given is max rpm etc etc
Thanks for reply Billy, yes I plan on assuming the torque and speed values I'm given is constant. I've outlined the steps I'll take to solve this problem and my final step I expect to be able to know the angular velocity of gears A1 and B1 that will allow me to know the torque and velocity of the drive shaft depending on which gear setting. Does this seem like the right step to take?

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Thanks for reply Billy, yes I plan on assuming the torque and speed values I'm given is constant.
I've outlined the steps I'll take to solve this problem and my final step I expect to be able to know the angular velocity of gears A1 and B1 that will allow me to know the torque and velocity of the drive shaft depending on which gear setting. Does this seem like the right step to take?

Well there's no point calculating the output torque if you're assuming the motor runs at a constant RPM.

At constant RPM the output (& input) torque will depend on the load. That is, to maintain constant rpm when load increases, such as when going up a ramp, the torque output of the motor much increase. Of course, this is not what really happens, in reality your toy car will go slower up a ramp than on level ground.

In other words, you cannot make both of these assumptions:
yes I plan on assuming the torque and speed values I'm given is constant.

If you want to get any accurate outputs you'll need better inputs. That is, you need to consider acceleration with the motors power curve.
IME with this sort of thing is that the losses in poorly made plastic gear trains are large and unknown. No matter how accurately you model the motor power output during acceleration it won't give realistic performance predictions because gear train losses are significant and unknown.
I'd recommend building in enough adjustability so you can find peak performance via testing.

2021 Award
I have a design problem that has two predictions that I must make.
What academic course is this problem from?

F.Turner
What academic course is this problem from?
Project for mechanical design. I was stuck and not sure how I should take on the problem so was looking for some pointers.

2021 Award
The required concepts are;

Power is the rate of energy flow.
Power is the product of RPM and torque.
Energy is conserved in perfect gearboxes.
So power in = power out.

Gears are transformers of RPM and torque.
The transformation ratio is determined by the tooth count ratio.
The tooth count ratio must also be the gear radius ratio, since teeth must mesh.

Road speed is proportional to output shaft RPM.
Chemical energy from the battery is converted to potential energy of the vehicle mass.

Assuming the motor voltage is fixed.
A DC motor generates a torque that is proportional to current.
When motor is stalled current is limited by motor resistance.
At maximum RPM motor has zero available torque.
Torque from motor is linearly related to RPM, with a negative slope.

billy_joule