I am sourcing a servo for a tiltrotor drone and need to calculate the required torque to rotate the propeller and the motor from facing the front to facing the top. I understand that the minimum required torque equals to the torque needed to hold the prop and motor up horizontally plus the torque required to swing up the prop and motor and stop the servo when the prop and motor are facing the top. However, when the propeller is turning, there would be changes to the propeller's angular momentum. But equations I found online only mentions cases that the axis of torque equal to the axis of angular velocity of whatever is turning, but this time, the axis of torque is perpendicular to the axis of angular velocity of the propeller. Could you tell me how to calculate the amount of torque required?
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$\begingroup$ That servo has a rough job and it's not like you're trying to optimize to tilt the rotor has quickly as possible. Combined with the fact you're limited to what you can buy, just go with the highest torque servo you can find. It will also be the slowest servo which will reduce the torque required. I would be considered about bearing support. (And in case you did not realize how much torque you need depends on how quickly you want to tilt the rotor. Just like how much force you need to move something depends on how quickly you want it to accelerate). $\endgroup$– DKNguyenJan 24, 2022 at 0:42
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$\begingroup$ But I have a weight and money budget, so I need a formula $\endgroup$– Faito DayoJan 24, 2022 at 1:28
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$\begingroup$ High torque RC servos in the same class don't weigh or cost any more than high speed servos. They are just geared differently. In any case, you still have not specified a desired tilt speed or acceleration. No matter what you calculate though, in practice you're still stuck with the servos you can buy and you're still best going with the highest torque servo in that class. $\endgroup$– DKNguyenJan 24, 2022 at 1:43
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$\begingroup$ "But equations I found online only mentions cases that the axis of torque equal to the axis of angular velocity of whatever is turning, but this time, the axis of torque is perpendicular to the axis of angular velocity of the propeller." makes it sound like you were just searching up moment of inertia. But you want the gyroscopic stabilizing torque. I found this very easily: veemmarine.com/wp-content/uploads/2015/11/… $\endgroup$– DKNguyenJan 24, 2022 at 1:43
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$\begingroup$ "However, when the propeller is turning, there would be changes to the propeller's angular momentum" What do you mean by turning? The propeller can spin or tilt and word turning can be used for both so it is a bit vague. Either way though. I am not sure what you mean by the angular momentum changing. My understanding is that doesn't happen. Do you mean the moment of inertia changes? Because that does happen on 2-blade propellers as you tilt the propeller disc. $\endgroup$– DKNguyenJan 24, 2022 at 1:48
2 Answers
If we ignore the effects of changing the angle of the rotor causing changes in lift and as a starter point to give us a basic idea of how to rotate the axis of the tilt-rotor.
Let's assume your rotor is initially spinning horizontally like a helicopter and you want to rotate it so that its disk is facing forward like an airplane propeller.
Let's call the angular momentum of the rotor L.
To rotate the rotor we need to apply a torque perpendicular to it meaning a couple of forces in the horizontal plane (right-hand rule).
$$L_{rotor}= I_{rotor}*\omega \quad \omega =rotor_{angulr-speed}$$ Let's say we apply a torque
$$\tau= f*r=\tau_{ srevo}$$
Angular speed of rotation of the axis of the rotor will be:
$$\omega_{axis-of-rotor}=\frac{\tau_{ srevo}}{L_{rotor}}$$
So we see we can use any servo power but the higher torque of the servo the faster the rotor axis will tilt.
But in practice, the servo has a power ramp-up and power ram down that has to be calibrated.
If I understood you correctly, you want to basically place the propeller at the end of a stick and tilt the propeller disc with a servo at the other end of the stick. But all the equations for the gyroscopic stabilizing torque you can find have the servo tilting the propeller disc at the propeller center, not some distance away from the center.
Good news. The gyroscopic stabilizing torque stays the same.
In the image above, the red moment is that of the gyroscopic stabilizing torque. Notice that it's a couple moment which means that it is purely rotational with no translational side effects. Instead of applying just one linear force and having something rotate about a point, two parallel, opposite, but off-center forces are applied to produce a pure rotation. That means you can move it anywhere along the beam and it doesn't change. It is experienced the same everywhere along the rigid body.
Since the servo is also applying a pure torque (a moment couple) that means that it is also exerted the same at any point along the beam.
The only thing that the changes due to having the propeller at the end of the stick is all the normal effects of moment of inertia that arise from rotating a mass away from the center of rotation.
So the stabilizing torque that the servo must overcome by the servo is still:
http://veemmarine.com/wp-content/uploads/2015/11/White_Paper_1403-How_Gyros_Create_Stabilizing-Torque.pdf
Though, like I mentioned in the comments, the propeller tilt servo has a rough job and doesn't need to be fast. A slower servo also reduces the torque required. So you're better off just picking the highest torque servo you can get since RC servos of the same class don't weigh more or are any more powerful. They are just geared differently. You should also try to built a motor-propeller mount that has the center of gravity as close to the servo point of rotation as possible since the servo already has a tough job. It doesn't need to be fighting an off-balance weight the entire time on on top of gyroscopic stabilizing torque and propeller/motor vibration.
And something you still have not done if want to actually calculate is SPECIFYING how long you're willing to wait for the propeller to tilt because torque, like forces, overcomes resistances and ACCELERATES things. Forces and torques do not move things because objects in motion remain in motion in the absence of any forces.
