Stopping forces in an emergency stop

[simonwait]

Hi

I'm trying to calculate the forces applied when suddenly stopping an object. I have a pair of winches which lowering an object at 400mm/s and would normally decelerate to a stop at 150mm/s^2. If the Estop for this winch is hit then we decelerate at 2000mm/s^2. However, if the power is pulled then the brakes are applied instantly and stop at whatever time it takes the brakes to arrest the load. There are 2 brakes both at 75Nm of torque on each winch one after the other on the output shaft so four brakes in total (not sure if having double brakes makes a difference).

What I am trying to figure out is what the force is during this uncontrolled stop and how far the load would travel in that time.

 

[FactChecker]

I think the information is incomplete. For the brakes that you know the deceleration rate, you need to know how much mass is being decelerated before you can calculate the brake force. For the 2 brakes where you know the torque, you need to know the lever arm length (or the gear radius). Also, it's not clear which information is relevant to the "uncontrolled stop" that you are trying to figure out.

 

[simonwait]

Oh sorry - I put that in and then seemly deleted it. The load is 1600kgs, The output shaft radius is 12mm. The 150mm/s^2 and 2000mm/s^2 show normal conditions and controlled stops, I am trying to find an uncontrolled stop - ie like pulling the power so the motor locks up and the brakes instantly apply. I assume there will be a short amount of time where the inertia will drag the brake through the load.

 

[sophiecentaur]

I am sure the 'spring constant' or resilience of the rope is very relevant here. The can make a massive difference to the peak force involved. If the rope temporarily stretches by double the distance when the brake is applied then the extra force could be halved.

 

[CWatters]

You know the torque the brakes can apply so if you know the drum diameter you can calculate the stopping force and deceleration.

I agree the elasticity of the rope will be a factor.

 

[JRMichler]

You need the spring constant of the entire system to solve this problem. Imagine the load hanging freely at zero speed. You pull the load downward with a force, and measure the resulting movement. Divide the applied force by the amount of movement, and you get the spring constant. You can also calculate the spring constant from the sum of winch rope stiffness and length, shaft diameter and length, and gear train stiffness.

Then calculate the kinetic energy of the moving load just before the brake is applied. Equate that to the equation for spring potential energy: KE = 1/2 * K * x^2, where:
KE = kinetic energy
K = spring constant
x = peak displacement of the spring (how far the load moves after the brake is applied)

Peak force is then K * x.