Motors are sized for torque and speed in units of horsepower or watts (usually kilowatts). James Watt invented the unit of horsepower to describe the work over time of ponies lifting coal. From a rough estimate, he decided a good rough estimate was a single horse could haul 33,000 pounds of coal up one foot in one minute. This estimate continues in use today in any motor’s HP rating. To find power in the metric units of watts or kW, simply divide the work (N-m) by the time to get it done in seconds (1 W = 1 N-m/s).
To calculate your power needs, there are two approaches.
- Use force and velocity (in feet/min or m/s)HP = (Tw)(V)/(33000) or Power, P in watts = (T in N/m)(w in m)(V in m/s)
T = Tension in lbs/in or N/m
w = Width in inches or meters
V = Velocity in feet/minute or m/s
- Use torque and speed (in rpms or rad/s)HP = (M)(n)/5250 or Power, P in watts = (M in N-m)( w in rad/s)
M = Torque in ft-lbs or N-m
n = Speed in revolutions per minute (RPMs)
w = Speed in radians per second
I recommend using the second approach since tension isn’t the only need for torque in web handling. The torque of a web handling drive point is the tension differential x radius + inertia x acceleration + torque losses in transmission or from rolling resistance.
For a winder or unwinder, the tension differential is the full web tension, a negative value for unwinding.
In an intermediate drive roller (what I usually call a pull roller), the tension differential is the difference between the upstream and downstream tension setpoints. This can be a negative or positive value. If the upstream tension is higher, the pull roller is in power mode, assisting the downstream tension to oppose the higher upstream tension. If the downstream tension is higher, the pull roller is in regeneration mode, assisting the upstream tension to oppose the higher downstream tension. If the upstream and downstream tension are equal, the motor has little work to do except overcoming rolling resistance.
Motor size can also be viewed in terms of actual physical size. One of my expert controls resources once told me that motor physical size (and cost) is more a function of torque than power. This is one reason many web processes use a speed reducer; to increase motor efficiency and reduce costs. However, there may be unintended consequences of limiting your control options (forcing the use of speed control over-torque control), increased torque losses, increase mechanical complexity, and less responsive performance. He argued that yes, this will increase motor cost, but also improve performance. (More on this later.)