# Total torque of a multi motor system

• Pinon1977
Pinon1977
TL;DR Summary
Trying to estimate the total torque of a multimotor system. This is a theoretical system, but one which I would like to make reality.
So I have four motors, each capable of producing 1 newton meters of torque. They are all running into a singular drive axle at 90degree offsets. There's no gearbox exchange or power transfer medium. It's axle to axle engagement with a pinon gear. Disregarding any sort of losses that may be encountered from the gear mesh, how can I estimate the total torque being witnessed at the primary drive axle? My initial guess would be 4 Nm.

Pinon1977 said:
My initial guess would be 4 Nm.
That assumes mitre gears with a 1:1 ratio.

Pinon1977 said:
TL;DR Summary: Trying to estimate the total torque of a multimotor system. This is a theoretical system, but one which I would like to make reality.

So I have four motors, each capable of producing 1 newton meters of torque. They are all running into a singular drive axle at 90degree offsets. There's no gearbox exchange or power transfer medium. It's axle to axle engagement with a pinon gear. Disregarding any sort of losses that may be encountered from the gear mesh, how can I estimate the total torque being witnessed at the primary drive axle? My initial guess would be 4 Nm.

Pinon1977 said:
...
So I have four motors, each capable of producing 1 newton meters of torque. Disregarding any sort of losses that may be encountered from the gear mesh, how can I estimate the total torque being witnessed at the primary drive axle? My initial guess would be 4 Nm.
I believe that your ideal guess is correct.

Because of that arrangement, all the motors and pinions and central shaft will be forced to turn at the same rotational speed as of any one of the single motors.

Each motor will be consuming the same amount of electricity than when working alone; therefore, the input work will be four times greater than if using a single motor.

The output work will need to be similar to that of a single motor times four.
The only way to have that for the same rotational speed is by having increased the output torque four times.

Energy = work = force x distance = torque x rotated angle

Power = work/time = force x velocity = torque x rotational velocity

https://en.wikipedia.org/wiki/Work_(physics)#Units

Pinon1977
Pinon1977 said:
This is a theoretical system, but one which I would like to make reality.
Stall torques (or torques for a forced stable speed) might be additive, but in a real system you'll meet with complicated speed-torque-load (-power) dependencies

You would fare lot better without complications like multiple motors.

Pinon1977
For any arrangement of motors and transmissions you can think of, this will be true about power ##P##:
$$P_{out} = P_{in}$$
Having 4 motors as inputs and a single drive axle, you get:
$$P_{out} = P_{in\ 1} + P_{in\ 2} + P_{in\ 3} + P_{in\ 4}$$
$$T_{out}\omega_{out} = T_{in\ 1}\omega_{in\ 1} + T_{in\ 2}\omega_{in\ 2} + T_{in\ 3}\omega_{in\ 3} + T_{in\ 4}\omega_{in\ 4}$$
$$T_{out} = T_{in\ 1}\frac{\omega_{in\ 1}}{\omega_{out}} + T_{in\ 2}\frac{\omega_{in\ 2}}{\omega_{out}} + T_{in\ 3}\frac{\omega_{in\ 3}}{\omega_{out}} + T_{in\ 4}\frac{\omega_{in\ 4}}{\omega_{out}}$$
Where ##T## is the torque and ##\omega## is the angular velocity (or RPM).

Instead of the mechanical power (##T\omega##), you could even use the sum of electrical power going in (voltage X current of an electric motor for example) or the "combustion" power (mass flow rate X heat of combustion for a specific fuel) as the input power - or even a mix of all of those. Of course, the power losses (usually through heat) have to be included in the equation; and the closer you are to the "true" input (e.g. the quantity of fuel or electricity going into a motor), the more losses you may have.

It's the principle of conservation of energy.

Lnewqban
jack action said:
For any arrangement of motors and transmissions you can think of, this will be true about power ##P##:
$$P_{out} = P_{in}$$
Having 4 motors as inputs and a single drive axle, you get:
$$P_{out} = P_{in\ 1} + P_{in\ 2} + P_{in\ 3} + P_{in\ 4}$$
$$T_{out}\omega_{out} = T_{in\ 1}\omega_{in\ 1} + T_{in\ 2}\omega_{in\ 2} + T_{in\ 3}\omega_{in\ 3} + T_{in\ 4}\omega_{in\ 4}$$
$$T_{out} = T_{in\ 1}\frac{\omega_{in\ 1}}{\omega_{out}} + T_{in\ 2}\frac{\omega_{in\ 2}}{\omega_{out}} + T_{in\ 3}\frac{\omega_{in\ 3}}{\omega_{out}} + T_{in\ 4}\frac{\omega_{in\ 4}}{\omega_{out}}$$
Where ##T## is the torque and ##\omega## is the angular velocity (or RPM).

Instead of the mechanical power (##T\omega##), you could even use the sum of electrical power going in (voltage X current of an electric motor for example) or the "combustion" power (mass flow rate X heat of combustion for a specific fuel) as the input power - or even a mix of all of those. Of course, the power losses (usually through heat) have to be included in the equation; and the closer you are to the "true" input (e.g. the quantity of fuel or electricity going into a motor), the more losses you may have.

It's the principle of conservation of energy.
Thanks, jack action. You have been most helpful and thorough in your explanation. Gold star !!!!

Last edited by a moderator:
berkeman
Lnewqban said:
I believe that your ideal guess is correct.

Because of that arrangement, all the motors and pinions and central shaft will be forced to turn at the same rotational speed as of any one of the single motors.

Each motor will be consuming the same amount of electricity than when working alone; therefore, the input work will be four times greater than if using a single motor.

The output work will need to be similar to that of a single motor times four.
The only way to have that for the same rotational speed is by having increased the output torque four times.

Energy = work = force x distance = torque x rotated angle

Power = work/time = force x velocity = torque x rotational velocity

https://en.wikipedia.org/wiki/Work_(physics)#Units
Thank you sir! Your input is greatly appreciated.

Lnewqban
berkeman said:
No offense, berkman, but I can always count on you to be the Negative Nancy when I ask any sort of question. That being said, there are several differences; consequently, the most notable of which is this particular question dealt with overall power, not efficiency. It also did not utilize any sort of gearbox or power transfer medium other than the bevel gears. This is also a theoretical system not a real live system. Need I continue?

weirdoguy and russ_watters
berkeman said:
Sir, I realize my questions may seem rather remedial to you guys, but there is a reason why I am asking them. More often than not, the question is a rhetorical question and I just need validation of my presumption.

I value y'all's opinion tremendously. That's why I continue to post questions to this site. Even amidst all the sarcasm and shots being fired, I have thick enough skin to understand that a lot of this seems elementary to you guys, and you really mean no harm in your comments.

Thanks and keep up the good work.

weirdoguy
Pinon1977 said:
Sir, I realize my questions may seem rather remedial to you guys, but there is a reason why I am asking them. More often than not, the question is a rhetorical question and I just need validation of my presumption.

I value y'all's opinion tremendously. That's why I continue to post questions to this site. Even amidst all the sarcasm and shots being fired, I have thick enough skin to understand that a lot of this seems elementary to you guys, and you really mean no harm in your comments.

Thanks and keep up the good work.
Just keep in mind that we don't allow multiple thread starts on the same question. I'll look again at your past thread(s) to see if they should be merged with this new thread start...

Pinon1977 said:
Sir, I realize my questions may seem rather remedial to you guys, but there is a reason why I am asking them. More often than not, the question is a rhetorical question and I just need validation of my presumption.

I value y'all's opinion tremendously. That's why I continue to post questions to this site. Even amidst all the sarcasm and shots being fired, I have thick enough skin to understand that a lot of this seems elementary to you guys, and you really mean no harm in your comments.

Thanks and keep up the good work.
This concerns me. You clearly are not giving us the full story while are asking questions which at face value have trivially obvious answers. To me this makes the questions pointless and possibly feeding some sort of false premise (which, again, you aren't telling us). This makes us uncomfortable and probably doesn't actually help you - you just think it does.

Your prior thread was just plain bad/wrong. This one is trivially obvious/pointless. Thinking they are guiding you in a positive direction is worrisome.

weirdoguy, jrmichler, berkeman and 2 others
Pinon1977 said:
TL;DR Summary: Trying to estimate the total torque of a multimotor system. This is a theoretical system, but one which I would like to make reality.

So I have four motors, each capable of producing 1 newton meters of torque. T
You seem to be suggesting an ideal model here. It's a bit like discussing four batteries, connected in series; mostly, you will get V1+V2+V3+V4 on the terminals but that will only work for identical batteries in identical states of charge (they are no longer Ideal Voltage Sources). Even worse, connecting batteries in parallel can cause three to discharge into the one with slightly low volts.

Point is that unless you only want an ideal (trivial) answer, you have to talk about detailed spec and consider the effect of even slight imbalance.

## What is total torque in a multi-motor system?

Total torque in a multi-motor system is the combined rotational force generated by all the motors in the system. It is the sum of the individual torques produced by each motor, which can be used to drive a common load or perform a specific mechanical task.

## How do you calculate the total torque of a multi-motor system?

To calculate the total torque of a multi-motor system, you simply add the torques produced by each motor. If the motors are connected in parallel and contribute to the same axis or load, the total torque (T_total) is given by the sum of the individual torques (T1, T2, T3, etc.): T_total = T1 + T2 + T3 + ... + Tn.

## What factors affect the total torque produced by a multi-motor system?

The total torque produced by a multi-motor system can be affected by several factors, including the power ratings of the individual motors, the efficiency of each motor, the load distribution among the motors, and any mechanical losses in the system such as friction or gear inefficiencies.

## Can different types of motors be used together in a multi-motor system?

Yes, different types of motors can be used together in a multi-motor system, but it requires careful consideration of their characteristics such as torque-speed curves, control methods, and power requirements. Compatibility and synchronization of the motors are crucial to ensure efficient and stable operation of the system.

## How do you synchronize multiple motors in a multi-motor system to achieve desired torque?

Synchronizing multiple motors in a multi-motor system typically involves using advanced control strategies such as master-slave control, field-oriented control (FOC), or vector control. Feedback mechanisms like encoders or resolvers can be used to monitor the position and speed of each motor, allowing for precise adjustments to ensure all motors work in harmony to achieve the desired torque output.

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