Motion System Design

Torque time

Torque, not horsepower, makes the world go around.

If you're just getting into motors and drives, here's some advice that will help you get off to a fast start.

Horsepower is useful in determining the total amount of work that must be accomplished in a given span of time. But torque is what brings machinery to life, turning feed screws, cutting tools, and countless other motion axes.

By understanding torque, and its relationship to speed and horsepower, you'll be less likely to make those beginners' mistakes when making decisions on motors and drives.

In a pickle

If you've ever had a tough time opening a pickle jar, then you're probably familiar with torque. Simply put, the reason you're on the outside staring at the pickles inside is that you can't apply enough torque to the lid to break it loose.

So what do you do? You can always get a better grip and try harder. You can use a rubber pad, or washcloth, to help you transmit more torque to the lid without slipping. Or you can use a mechanical device, like a pipe wrench, to multiply your torque-producing capability.

Torque is the product of force and its radial offset from the turning axis. If you care to know exactly how much torque you need to open the jar, for example, you can measure the jar lid and then find a way to gauge the force needed to break the lid free. The equation for torque T is:

T = F x r

where F = force (oz or lb) and r = radius (in. or ft).

Some people, when they can't open jars, tap on the lid with a butter knife. This technique is often successful and it illustrates another important point about torque. In realworld applications, it usually takes more torque to start a machine than to keep it running once it's going. The higher torque is required to overcome "stiction" and break the load loose from its resting position. Tapping the jar lid lowers this breakaway torque.

Stiction associated with a jar may be due to a combination of things, including vacuum pressure, sealing pressure, and friction between the lid and glass. In a machine, stiction depends on the geometry of the moving components as well as the type of bearings that support them. Once stiction has been overcome, a smaller "running" torque must be maintained to keep the system in motion. The proportion between starting and running torque varies with each load type.

Machine loads generally fall into one of three categories; constant torque, constant horsepower, and variable torque. In most applications, torque is independent of the speed at which the machine is driven. Thus, as the machine accelerates, the horsepower required to drive the load increases while torque remains essentially constant.

The basic considerations when sizing a drive for a constant-torque load are breakaway torque, running torque, and operating speed. Only after these have been determined is it possible to calculate the required horsepower. Beyond that, there are no other considerations because most variable-speed drives are inherently constant-torque devices.

Another load type – common in metal-working (as in drilling, boring, tapping, turning, milling, and grinding) – is constant-horsepower. Here, torque is inversely proportional to speed.

Consider a drill press. Large holes are typically drilled slowly at high torque, while small holes are drilled quickly at low torque. In either case, horsepower remains constant regardless of speed. Besides metal-working, constant-horsepower may also be required for center-driven winding and some mixing applications.

One way to identify a constanthorsepower load is to examine the machine output. If a machine is designed to produce a fixed number of pounds per hour – whether it's small parts at high speed or large parts at low speed – the drive requirement is apt to be constant-horsepower.

When selecting a drive for these applications, one approach is to match the drive's output with the machine's torque requirement at low speeds. The catch, however, is that the drive is likely to be grossly oversized for the rest of the speed range.

A more practical approach involves the use of variable-torque transmissions such as stepped pulleys, gearshifts, and adjustable-pitch belt drives. A dc (SCR) drive employing armature control at low speeds and field-weakening at high speeds may also work. In addition, some variablefrequency drives can approximate constant-horsepower (above 60 Hz) when operated at constant voltage.

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The third common load type, variable-torque, is often encountered in pumps, fans, and blowers. In such applications, both torque and horsepower are proportional to speed, with torque increasing as the square of speed and horsepower as the cube.

The key to sizing a drive for a variable- torque load is to make sure it can deliver adequate torque and horsepower at the maximum speed. Be generous when estimating speed, however, because an increase of just 9% over the "maximum" can require up to 30% more horsepower. Most variable-speed drives, if they can deliver the horsepower at maximum speed, are inherently capable of handling variable-torque loads.

Not all machines fit perfectly in one load class or another. Punch presses, spring coilers, and four-slide mechanisms, for example, frequently fall somewhere between constanthorsepower and constant-torque. Here, the drive needs to be sized for the most stringent requirements.

Effect of inertia

Inertia – the tendency of an object (if it's at rest) to remain at rest or (if it's moving) to keep moving – is another important factor when considering drive requirements and torque.

In the case of rotating bodies, inertia is defined as "WR2" or "WK2," where W = weight (lb) and R or K = radius of gyration (ft). The radius of gyration for various loads and shapes can be found in any standard mechanical handbook.

Flywheels, obviously, have high inertia as do large fans, centrifuges, hammer mills, and certain types of machine tools. In general, inertia is considered high any time the reflected load inertia at the motor shaft is greater than five times that of the motor's rotor.

The effect of inertia is of greatest concern during acceleration and deceleration. If a standard motor is applied to a large blower, for example, it's quite possible that the motor – even if it has enough torque and horsepower to drive the load at speed – can burn out on its first start.

During acceleration a motor typically draws many times its rated line current. If the acceleration interval lasts too long, the subsequent heat build up could reach a point where it damages the motor windings and insulation. Calculating the acceleration time ta for a direct-coupled load is fairly straightforward:

ta = WR2n/308Ta

where Ta = average accelerating torque (lb-ft), n = required change in speed (rpm), and WR2 = inertia (lb-ft2). The same equation can be rearranged to determine the average accelerating torque required to produce full speed in a given period of time:

Ta = WR2n/ta

In most cases, for standard motors through 100 hp, the average accelerating torque available is 150% or more of the full-load running torque. Unless the motor starts and stops frequently, accelerating times of up to 10 sec are generally going to be safe.

Reflecting back

The effective value of inertia, as seen by the motor, is altered dramatically with the addition of a speed-changing mechanism, such as a gear reducer or belt drive, between the motor and load. In these cases, the motor doesn't experience the actual inertia of the rotating load, but an equivalent or "reflected" inertia that's greater or less according to the speed ratio.

For belted or geared loads, the equivalent inertia WR2 eq is:

WR2eq = 1.1 WR2l (Nl/Nm)2

where WR2l = load inertia, Nl = load speed, and Nm = motor speed. The multiplier, 1.1, is a safety factor that accounts for the inertia and efficiency of the pulleys (sheaves) or gears themselves.

Once the equivalent inertia has been calculated, accelerating time and starting torque are found by substituting WR2eq into the standard equation.

If inertia and overheating are still a concern, there are a couple of ways to beat the heat including, oversizing the motor or frame, reducedvoltage starting, and using special motor windings or slip couplings between the motor and load.

The invention of the steam engine made it necessary to establish a unit of measurement that could be used to compare work done by competing engines. Not surprisingly, the unit chosen was related to the standard power source of the time – "horse power."

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