YES AND NO.

No. If you assume the conveyor belt is a rigid body and does not stretch, then time is not relevant. Only differential force and elasticity are relevant to tell you the take-up travel distance. Time to accelerate or decelerate can tell you the force.

Yes. If you assume the belt is elastic and locally stretches or contracts with transient forces along the belt loop, then time is relevant. Now both time and force are needed to tell you the travel. We call this dynamic analysis. Depending on which school of dynamic analysis you prescribe to, the problem can be simple or hard.

If you solve the time transient behavior using linear ordinary differential equations. There is a "not simple" result which can be written and solved in a straight forward action. This is the model of Dr. Alex Harrison and others. With this method you can pick any point in time, such that all conditions around the elastic belt can be instantly deterimined, including take-up travel.

If you solve the transient behavior using non-linear differential equations, the solution for any point in time is derived by integrating all previous points in time in your solution set. We call this a time integration method. It is the of choice to solve many ODE's that have to be solved using a forward integration method such as Runga Kutta. This is the method we practice. This model is needed to solve: a) moving mass, b) rolling resistance that varies with belt tension and load, c) belt sag displacement in the vertical plane between idlers, d) non linear elasticity, and other conditions.

There are other methods but I think you get the idea. There is no simple method to solve the time, displacement, non-linear mechanics,and force conditions.

Good Luck

Lawrence Nordell

Conveyor Dynamics, Inc.

website: www.conveyor-dynamics.com

email: nordell@conveyor-dynamics.com ■