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## Main Question or Discussion Point

I seek to construct an apparatus capable of moving a steel plate against gravity in 200 milliseconds.

The plate is roughly the same size and shape as the hatch on a submarine:

mass = 40 kg;

dimension: 0.3 meter diameter--> = radius in calculations below;

angle of rotation: 90 degrees--horizontal to vertical;

time available for actuator to work against gravity: 200 milliseconds;

distance traveled: 1/4 * Pi * Diameter = 1/4 * pi * 0.6m = approximately 0.5m;

actuator return time constraint: within 0.6 seconds;

life cycle: ideally: suitable for 100 million repetitions without fatigue.

maximum DC power source available: 48 volts (four automotive batteries in series).

So, to restate the problem in general: How to rotate 90 degrees, in 200 milliseconds, an object of mass 40 kg, a distance of 0.5m, against the force of gravity, relying upon not more than 4 auto batteries in series?

Torque = r * F * sin theta, where F is approximately 400 Newtons (40 * 9.8), and r, radius is 0.3 meter, (not 0.15m), and theta is 90 degrees, hence sin(90) = 1.

Thus the torque is 120 Nm.

Torque is also defined as rate of change of angular mommentum, i.e. dL/dt, where L = r * p* sin theta, where p is momentum, i.e. mass * velocity

So, p = 40kg * 0.5m/0.2 sec, which is about 100kg m/sec

Therefore, L should be approximately equal to 0.3m * 100kgm/sec : 30 kg m^2/sec

Using this value, then, one can estimate omega from the equation:

L = I omega, where I is the moment of inertia, and omega the angular velocity,

first simplifying by assuming, perhaps incorrectly, that I = mr^2, i.e. 40 * 0.3 ^2, or approximately 3.6 kg m^2

This would yield a value for omega of 30/3.6, or about 8.3 radians/sec

How to find, or construct, an actuator capable of meeting these requirements?

(If the calculations are correct!!)

Any ideas, suggestions, or improvements in the calculations would be welcomed.

With that amount of weight to move, i.e. 400 N, there will also be non-negligible frictional forces opposing rotation, and also bearing constraints, which have thus far been neglected....

Thanks for your advice, opinions, or comments

CAI ENG

The plate is roughly the same size and shape as the hatch on a submarine:

mass = 40 kg;

dimension: 0.3 meter diameter--> = radius in calculations below;

angle of rotation: 90 degrees--horizontal to vertical;

time available for actuator to work against gravity: 200 milliseconds;

distance traveled: 1/4 * Pi * Diameter = 1/4 * pi * 0.6m = approximately 0.5m;

actuator return time constraint: within 0.6 seconds;

life cycle: ideally: suitable for 100 million repetitions without fatigue.

maximum DC power source available: 48 volts (four automotive batteries in series).

So, to restate the problem in general: How to rotate 90 degrees, in 200 milliseconds, an object of mass 40 kg, a distance of 0.5m, against the force of gravity, relying upon not more than 4 auto batteries in series?

Torque = r * F * sin theta, where F is approximately 400 Newtons (40 * 9.8), and r, radius is 0.3 meter, (not 0.15m), and theta is 90 degrees, hence sin(90) = 1.

Thus the torque is 120 Nm.

Torque is also defined as rate of change of angular mommentum, i.e. dL/dt, where L = r * p* sin theta, where p is momentum, i.e. mass * velocity

So, p = 40kg * 0.5m/0.2 sec, which is about 100kg m/sec

Therefore, L should be approximately equal to 0.3m * 100kgm/sec : 30 kg m^2/sec

Using this value, then, one can estimate omega from the equation:

L = I omega, where I is the moment of inertia, and omega the angular velocity,

first simplifying by assuming, perhaps incorrectly, that I = mr^2, i.e. 40 * 0.3 ^2, or approximately 3.6 kg m^2

This would yield a value for omega of 30/3.6, or about 8.3 radians/sec

How to find, or construct, an actuator capable of meeting these requirements?

(If the calculations are correct!!)

Any ideas, suggestions, or improvements in the calculations would be welcomed.

With that amount of weight to move, i.e. 400 N, there will also be non-negligible frictional forces opposing rotation, and also bearing constraints, which have thus far been neglected....

Thanks for your advice, opinions, or comments

CAI ENG