## Example: Driving a chain conveyor with a gear motor and VFD

Input data: A chain conveyor is to transport wooden boxes up a slope of α = 5° at a speed of 0.5 m/s. There is a maximum of four boxes each weighing 500 kg on the conveyor. The chain itself has a weight of 300 kg. The friction factor between chain and base is specified at μ = 0.2. A mechanical stop is mounted at the end of the chain conveyor which aligns the boxes before they are pushed onto a second conveyor belt. During this process, the box slides on the chain with a friction factor of μ = 0.7.

The application calls for a helical-worm gear unit that is frequency-controlled up to approximately 50 Hz.

Velocity: v = 0.5 m/s

Incline: α = 5°

Weight of transported material: m_{L} = 2,000 kg

Weight of chain: m_{D} = 300 kg

Friction factor between chain and base: μ_{1} = 0.2

Friction factor between box and chain: μ_{2} = 0.7

Desired acceleration: a = 0.25 m/s^{2}

Sprocket diameter: D = 250 mm

Starting frequency: 10 cycles/hour and 16 hours/day

Calculating the optimum motor size depends on considering all the variables and following the right equations. For example, simply calculating the total resistance that the motor has to overcome involves the weight and friction of the conveyor itself carrying the load, additional friction when a box hits the stop, plus the efficiency of the gear unit itself attached to the motor.

Here is the calculation for determining the resistance force of the conveyor, half the weight of the chain, and the maximum load of boxes:

Here is the calculation for the additional resistance when a box hits the stop:

This is just the beginning since making a complete analysis of the application includes a number of additional factors:

- Efficiency of the worm-gear unit
- External moment of inertia
- Load torque on the motor
- Acceleration torque on the motor
- Conveyor speed relative to motor RPM
- Gear unit ratio
- Service factor, and
- Static power

Ultimately, once the conveyor is built and operating in real-world conditions, it will be a simple task to measure the performance of the motor and verify the accuracy of your starting assumptions.

The full set of calculations for this example can be found here.