Mathematical Modeling of an Elevator System

[hornet09]

Hi, I'm a physics major working an internship for an engineering company at present. I have been trying to model the energy consumption and/or power for an elevator system. The goal is to be able to input different variables (cab weight, capacity, counterweight percentages, motor types, gearing systems, etc) and be able to get a peak power and RMS power. I have been using Mathcad and Maple to analyze the speed profile of the elevator, and have created a program that allows me to view the jerk, acceleration, velocity, and distance traveled of the elevator as a function of time. My question is: how do I analyze the energy of the system.

Known values are:
Cab weight, capacity, counterweight percentage, rope weights, hoistway efficiency, motor efficiency, gearing efficiency, elevator profile speeds (jerks given, acceleration given, holding velocity given), pulley radius, building height.

We can assume that the elevator gets fully loaded on the ground floor, travels to the top floor, everyone exits, and travels empty back to the ground floor.

 

[SteamKing]

Figure the change in potential energy due to the change in elevation and the change in kinetic energy to get the cab from rest to its travel velocity and back to rest. You will probably need to define a cycle history, which can be analyzed to determine the changes in energy required to move the elevator.