## How are speed or length measured?

Most web speed and length measurements are based on measuring the RPMs of a non-slipping roller of a known circumference.

V = 2pnr (V = speed in fpm, p = 3.1415, n = RPMs, r = radius in feet)

V = wr (V = speed in inches/s, w = radians per sec, r = radius in inches)

To calculate length, simply multiply speed times time.

L = 2pnrt (L = length in feet, p = 3.1415, n = RPMs, r = radius in feet, t = time in minutes)

L = wrt (L = length in inches, w = radians per sec, r = radius in inches, t = time in seconds)

These calculations assume the web speed and the roller surface speed are 1:1, no slip, no strain.

Besides slip on the monitoring rollers, there are two other sources of error in speed and length measurement – strain from tension and strain from curvature. (I’ve told you before that strain is the key to web handling.)

The difference between a tensioned and untensioned webs is strain. Any speed or length measurement made while the web is tensioned will overestimate the untensioned length of material by the percent strain of the web. If you measure PET at 0.2% and compare it to a sample unrolled on the warehouse floor, you will see you have lost 0.2% from your measured length. For a 5000 ft roll, you will lose 10 feet. If you are running PE or PP at 1% strain, you will lose 50 feet out of 5000.

I usually recommend using an existing roller to monitor web speed, often a driven roller that already has an encoder or tachometer. However, measuring speed on a wrapped roller will have a small error due to the through-thickness or Z-direction strain variation of a curved web. When a web conforms around a roller the outer surface of the web elongates and the inner layer contracts. The difference in strain from the outer to inner surface is equal to the web thickness over the roller radius.

De = t/r (De = change in strain, t = web thickness, r = roller radius)

The center of the web will be at average strain, but the inner surface where you are measuring speed will be at a lower strain equal to half this value shown above. For thicker webs on smaller rollers, this is a significant error. If you measure a 10 mil web using a 4-inch diameter roller, the t/2r is 0.010/4 or 0.025 or 2.5%. Over 5000 ft, this would be a 125 foot error! For thinner webs and larger roller, this is a big deal. For a 1-mil web on a 10-inch diameter roller, t/2r = 0.001 / (2)(5) = 0.0001 or 1/100 of 1%. Over 5000 feet, this would be only a 6-inch error.

To avoid the curved web measurement error, use a tally wheel style roller that rides on the flat web between rollers.

## How are speed controlled?

Electric motors can operate in speed or torque control mode. For a DC motor, you control the input voltage and current. To run in torque control, set the voltage high and the motor torque will be proportional to the supplied current (amps). In torque mode, there is no speed control. The motor speed will be determined by the load on the system. Amps supplied to the DC motor is like gas flow supplied to your car’s engine. For a given accelerator position and gas flow, your car may go at a steady speed on a flat road (opposed by friction and wind resistance), accelerate down a hill (aided by gravity), or stall going up a hill (opposed by gravity).

To control the speed of your car, you can use a cruise control or close the loop manually yourself. In either speed control approach, the speed is monitored (either by you watching the speedometer or the cruise control sensing axle rotation) and gas flow is increased or decreased whenever the car drifts too far off the desired speed.

To run a DC motor in speed control, set the current high and the speed will be proportional to the supplied voltage as long as the load doesn’t exceed the motor’s torque and power limits. If you put too much load on the motor, the speed will drop (and you may damage the motor).

Most accurate motor speed controllers rely on speed feedback loop. An encoder or tachometer monitors the motors actual speed and trims the torque loop to correct deviations off of the desired speed. The accuracy and precision of the motor speed will depend on many things including: resolution of the speed measurement, load variations, motor and system inertia. If you want a constant speed, a high-inertia flywheel will discourage a system speed change, but you will sacrifice performance during acceleration and deceleration. If you oversize a motor, you may have plenty of torque to overcome inertia at speed changes, but you may sacrifice the ability to make subtle speed changes under light loads.

Here’s a nice online reference on electric motors.

(Caveat: As always, I’m a mechanical engineer, so always get a second opinion when you get controls or electronic advice from me. -tjw)

## How accurate is motor speed control?

First, refresh the definitions of accuracy and precision. Accuracy is averaging at the desired value. Precision is a close grouping of values, not necessarily at the desired value. Of course, most people want web speed to be both accurate and precise.

First, refresh yourself with my caveat above on getting electrical-related advice from a mechanical engineer.

One leading vector drive supplier will say “This enables the drive to regulate motor speed to an accuracy of 0.001 percent over a wide operating speed range.” I expect this applies to best-case scenarios, such as under consistent (non-changing) torque demands. It would be no surprise to find that if the load or applied torque on the motor changes, there will be a speed upset proportional to the torque upset, the inertia of the motor – roller – drive train, and the available motor power (torque and rpms).

## How are speed variations reduced?

Many speed variations aren’t due to a shortcoming in the motor or drive, but in the drive train that connects the motor to the roller. Gears, timing belts, speed reducers, couplings, shafts, bearings, and the roller itself…pretty much everything between the motor and the web have been known to create speed variations. The more you can eliminate these components with a simple drive train, eliminate backlash, and eliminate twisting and deflections, the more you are moving in the right direction to reduce speed variations.

Any move to simplify the drive train should help speed control. Where possible, eliminate speed reducers, place the motor close to the roller to reduce shaft lengths and couplings. In some ultra-speed-sensitive process, some specialty motor designs are built right onto the roller, combining the roller shaft and motor rotor on the same cylinder and bearings.

Inertia is another factor, but is a double-edged sword. High inertia can reduce speed variations, essentially creating a high mass flywheel that resists speed changes. High inertia is good if you like the speed you are at, but is bad when you want to change your speed, such as during acceleration, deceleration, or small speed changes used to trim a tension control loop.