Physics Calculations on the winch

[Sunny]

So, I took the physics of a winch system, and I put it down on paper and into things we can understands. I'm not going to explain the concepts behind my calculations, they are very basic, but I will put my math, and you can feel free to ask me about a certain step later.

Givens:
The stall torque on a motor is 2.2 Nm.
The RPM of a motor is 5500 RPM.

Assumed:
2" winch radius which is .05 meters.
Fg = Force of Gravity
Height to be pulled up is 6 feet.
Weight of robot = 145 Pounds

Formulas:
Torque = Distance * Force
Fg = Mass * Gravity
Linear Velocity = (Radius * 2 * pi) * number of rotations/time

Winch with no gear reductions:
2.2 = .05 * Fg
Fg = 44 Newtons

44 = 9.8 * Mass
Mass = 4.49 Kilograms or 9.89 pounds

Lifting Time = 0 Seconds

Winch with standard toughbox reduction(12.75: 1):
2.2 * 12.5 = 27.5 Nm
27.5 = .05 * Fg
Fg = 550 N

550 = 9.8 * Mass
Mass = 56.12 Kg or 123.72 pounds(which is a little bit less than the robot with the battery, bumpers, etc.)

5500/12.5 = 440 RPM
Linear Velocity = (1/6 * pi * 2 *440 )/60 = 7.67 ft/second

Lifting Time: .782 seconds

Winch with toughbox reduction * 2:1 reduction in chaining(25.5:1)
2.2 * 25.5 = 51.1
51.1/.05 = 1020 N

1020/9.8 = 107.37 Kg or 236.71 pounds

5500/25.5 = 215.686 RPM
Linear Speed: (1/6 * pi * 2 * 215.686)/60 = 3.76 ft/second

Lifting Time: 1.595 seconds

Motor running at stall torque of 1.1 Nm with reduction of 25.5:1
It said on the forums that it is best if the motor runs on 1/2 its stall torque. It prevents too much battery usage and it protects the motor. So the below calculations are using a 25.5:1 reduction and assuming a 1.1 Nm of stall torque.

1.1 * 25.5 = 28.05 Nm
28.05/.05 = 561 Fg
561/9.8 = 57.244 Kg
Weight = 126.201 Pounds (This weight is still a bit too low.)

5500/25.5 = 215.68RPM
Linear Speed: (1/6 * pi * 2 * 215.686)/60 = 3.76 ft/second

Lift Speed: 1.59 Seconds

Motor running at stall torque with GEM500 Gearbox(49.4:1)
1.1 * 49.4 = 54.34 Nm
54.34/.05 = 1086.8 N
1086.8/9.8 = 110.89 Kg = 244.47 Pounds(This is more like it)

5500/49.4 = 111.33 RPM
Linear Speed: (1/6 * pi * 2 * 111.33)/60 = 1.94 ft/second

Lift Time = 3.09 Seconds

[Tanner]

I see you've been busy, so have I.

It seems like the choice is clear what we need to do. It's nice to see all the options up and with full source of equations.

-Tanner

[Sunny]

It seems like the choice is clear what we need to do. It's nice to see all the options up and with full source of equations.

I had to show my work for full credit, but also I wanted people to be able to follow along just so they don't feel like I'm pulling numbers out of thin air.

[Tanner]

It seems like the choice is clear what we need to do. It's nice to see all the options up and with full source of equations.

I had to show my work for full credit, but also I wanted people to be able to follow along just so they don't feel like I'm pulling numbers out of thin air.

Hehe. That's pretty good though - 244.47 lbs. That's enough for two robots.

-Tanner

[Michael Kapp]

It should be noted that your calculations for the GEM500 at 49.4:1 are at half stall torque
In the meetings, several people brought up that we should be able to hold two robots in addition to ours, so I took the liberty of calculating the gear reduction necessary for this.

3 robots = 3 * 120 pounds + extra = 375 Pounds
375= 170.1 kg
170.1 * 9.8 = 1667 N
1667 * .05 = 83.35 Nm
83.35/1.1 = 75.77 (75.77:1 gear reduction)

The resultant lift speed is:
5500/75.77 = 72.58 rpm
1/6 * pi * 2 * 72.58/60 = 1.267 ft/s
6 ft / 1.267 = 4.74 seconds

Now, I'm not sure that an extra 1.65 seconds is worth being able to hold 3 robots (unlikely situation) and besides, sunny's calculation at 49.4:1 were done at half torque, meaning that at full torque, it could theoretically lift a maximum of 244.5 * 2 = 490 pounds. I think that this is fine, and there is no real need to gear it up more than that.
That being said, I believe that there is an error in sunny's calculations. He used 2 inches (1/6 foot or .05m), but with a winch, as you wind it up, the cord wraps around itself, effectively creating a greater radius. I shall here use 3 inches (1/4 foot or .075m) as the radius to simulate this effect on the GEM500 at 49.4:1.

1.1 * 49.4 = 54.34 Nm
54.34/.075 = 724.53 N
724.53/9.8 = 73.93 Kg = 163 Pounds

at full stall torque, this is 163 * 2 = 326 pounds. This will not lift 3 robots, but it will work for 2.

To calculate lift speed, I shall find use lift speed with both radii and assume a constant acceleration, so I can find the average velocity. (and thus the theoretical time)
final velocity =
5500/49.4 = 111.33 RPM
1/4 * pi * 2 * 111.33/60 = 2.91 ft/second

initial velocity (same as sunny's calculations) = 1.94ft/s

acceleration = 1/2 * ((final velocity)^2 - (initial velocity)^2)/(change in distance)
1/2 * ((2.91)^2 - (1.94)^2)/6 = .394 ft/s^2 acceleration

interestingly, it will be ascending faster the higher it goes.
time to ascend = ((final velocity) - (initial velocity))/acceleration = (2.91 - 1.94)/.394 = 2.46 seconds

[Sunny]

Now, I'm not sure that an extra 1.65 seconds is worth being able to hold 3 robots (unlikely situation) and besides, sunny's calculation at 49.4:1 were done at half torque, meaning that at full torque, it could theoretically lift a maximum of 244.5 * 2 = 490 pounds. I think that this is fine, and there is no real need to gear it up more than that.
That being said, I believe that there is an error in sunny's calculations. He used 2 inches (1/6 foot or .05m), but with a winch, as you wind it up, the cord wraps around itself, effectively creating a greater radius. I shall here use 3 inches (1/4 foot or .075m) as the radius to simulate this effect on the GEM500 at 49.4:1.

a) Back in '07, the robot's arm extended 10 feet in the air, and the winch had more than 20" of rope on there. And even then, the radius did not increase by 1". I believe the rope would wrap itself right next to itself before it started to wrap over itself. With this being said, I made the assumption that the winch would be wide enough so that the radius of the system never went above 2".

b) If you are assuming that the motor is running just below stall torque when it starts to pick up the robots or at 2", then if the cord begins to wrap over itself, the motor will most definitely stall due to the increased radius.

Sunny

[Logan]

Just a heads up, CIMs have a stall torque of 2.42 Nm, not the 2.2 used in your calculations.

[Sunny]

Just a heads up, CIMs have a stall torque of 2.42 Nm, not the 2.2 used in your calculations.

The world on CD seems to be consistent on 2.2, but it's ok if we under calculate the max weight a little bit.