Force and Torque Calculation and Observation

[DPress]

Something does not make sense. I have built a large bookcase on rolling wheels (on a concrete floor). I have connected it to wire rope and pulleys as shown in "Pulley Question.jpg". I always keep a 10 lb weight on each side so the lines do not go slack and fall off the pulleys.

I need to add an additional 42lbs to one side or another to get it to move.

Alternatively if I push the bookcase with a scale, the scale reads about 20lbs. (now with 10 lb weights on both upper wire ropes).

The only explanation I can think of is that the difference is caused by the delta between rolling and static friction that I am simply not seeing on the scale as I push it? But I thought there was none with the wheels under the bookcase? Could I have that much static friction in my pulley system?

Assuming I have not made some gross error in my thinking, does this imply that I would need a motor capable of suppying 672 oz-in of torque (42 * 16) of torque, as shown in "Pulley Question2.jpg"? Note I will be using a 1" radius chain sprocket on the motor.

Finally, I would like to do this with a stepper motor so I can accelerate and decellerate smoothly. I think I will need a geared motor to get the Torque I need at the fairly low top speed required of 30 inches per second**

Thank you for your time in looking at this.** I want the bookcase to move 45 inches in 3 seconds for an average speed of 15 inches per second. So assuming constant acceleration and deceleration I would need a top speed of 30 inches per second - right?

 

[jrmichler]

How heavy is your bookcase fully loaded with books? What type of wheels? Do the pulleys have plain or ball bearings? What are the pulley diameters? The wheel diameters? All pulleys add friction, and so do wheels. The top cable and pulleys are not needed to move the bookcase, but add friction. Can you put the motor down low so that the system only has two pulleys? Larger diameter wheels and pulleys have less friction. Harder wheels have less friction.

Your calculation for constant acceleration is correct. At your low speed, you may be better off to use a trapezoidal velocity profile, where you accelerate to a speed, run at constant speed, then decelerate to a stop. That gives you a lower top speed, which allows a larger gear reduction. Gear the motor so that it runs at or near its top speed. Size the motor / reducer to meet your worst case torque (starting plus acceleration) with about a 2:1 safety factor.

 

[JBA]

In addition to the above what is the type and diameter of the wire rope?
Edit: Also what is the style of grooves in or pulleys i.e. "V' or "U"?

 

[Tom.G]

Sounds like much of the force from the motor is used to bend the wire ropes around the pulleys.