Machine Design

# The problems of Horsepower Ratings

Blind calculation of horsepower for positioning motors can yield values that seem nonsensical to the uninitiated.

It's common to see manufacturers of ac motors publish horsepower ratings for their products. It is equally common for designers to use these ratings as a means of comparing one motor to another.

In contrast, manufacturers of servo and stepping motors almost never rate their products in units of horsepower. The reason is readily understood. These motors deliver levels of torque and power that differ dramatically at different speeds. This makes horsepower potentially useless as a unit of measure for steppers and servos.

For example, an engineer calculating horsepower for two different positioning motors might find that one producing 0.5 hp at a given speed is physically much larger than another putting out 1.5 hp. Vendor specmanship with thermal ratings may account for some of the disparity, but not all of it. What really gives here?

Designers can make sense of such apparent anomalies by comparing motor outputs in terms of the work done, rather than by straight power. The differences between the two viewpoints can be subtle but important. Insights into work and power can allow designers to see previously unrecognized trade-offs available for meeting size or cost goals.

Work and power
Perhaps the best way to explain the concept is to refer back to the original definition of work. When a body undergoes a displacement under the influence of a force, work is the term used to describe this circumstance. It is defined as just the force times the displacement. (In the general case, of course, it is the dot product of force and displacement.)

Power is the time rate at which a machine can do work. Work output is not a measure of this capacity because even a small motor can deliver a large amount of work if given enough time. Power is force multiplied by the displacement, divided by the elapsed time. For example, one horsepower is defined as the power needed to move a 550-lb weight 1 ft in 1 sec. (The convention arose as an easy way of explaining to waterwheel operators how many horses they could replace with a steam engine of a given size, or horsepower rating.)

Work and power relationships change slightly for motors. A motor does an amount of work equal to the torque it delivers times the angle through which it turns. Motor power, then, is the torque times the angular speed.

P = T V/5,250

where P is output power, hp; T is torque, lb-ft.; and V is rotational speed, rpm; and 5,250 is a conversion factor when working in lb-ft. (It becomes 63,000 for lb-in.)

This relationship shows that 3 lb-ft roughly corresponds to 1 hp in typical ac-motor systems running at 1,800 rpm. Since most ordinary ac motors operate at 1,800 rpm, it is easy to talk about mechanical power as horsepower in such instances. In fact, it has become common practice to do so in the motor industry even for the fractional-horsepower ac motors in appliances and instrumentation. With most plant machinery, specifying applications for ac motors in terms of their horsepower requirements works reasonably well and causes no confusion.

Trouble comes when comparing a variablefrequency ac motor drive to alternatives built with different base speeds, specifically servos, dc drives, and steppers. Their speed ratings can range from 500 rpm for direct-drive systems to 10,000 rpm for universal motors found in sewing machines. It becomes useless to talk about their horsepower output without going into some detail about the operating conditions. All in all, a horsepower rating does not tell much about how servos or steppers stack up against an ac drive.

Clearly, selecting the right motor for an application requires a level means of comparison. Ironically, horsepower as a unit of work does indeed hold the key to resolving the problem. The formula can provide valid comparisons as long as the engineer applies it consistently to account for motors operating at different speeds.

For example, suppose the application of interest requires a specific amount of horsepower applied to a load. Finding an ac motor of the right output is merely a matter of cross referencing a horsepower rating to a specific model. To find a candidate servo or stepper, the engineer figures the amount of work (torque) required, then works the horsepower equation to figure motor speed. When comparing servomotors, use the supplier's rated torque and speed values to calculate the effective horsepower for a better comparison.

Usually, the servo or stepper able to provide the needed torque won't do so at anywhere near the 1,800 rpm that is the base speed for an ac-motor system. Steppers produce peak torque at low rpm; today's servos produce full-rated torque at any speed. So a servo may need to be combined with a speed reducer when powering loads specifically designed to run at 1,800 rpm.

Interestingly, it is often true that a high-speed servo combined with an appropriate speed reducer will cost less than a comparable ac-drive system. Understanding this trade-off often leads to equipment designs that are small, lightweight, and more economical than some direct-drive alternatives.

In particular, winders and feed-to-length applications that require frequent and accurate starting and stopping are candidates for servo technology. These systems are powered by ac motor drives through clutches. This approach now costs more and is less precise than a servo-based solution.

Recent trends
As an aside, seasoned practitioners will note that gearboxes and speed reducers designed to work at the higher speeds of servos are a relatively recent phenomenon. Most horsepower-rated drive equipment of a decade ago was designed for 1,800 rpm. Thus designers of high-speed servo equipment were forced to use special planetary gearboxes and other mechanical transmission gear that was costly. Fortunately, the situation has changed. Lessexpensive transmission equipment has emerged to work at the higher speeds that are typical of servos.

Designers should also be aware of how thermal ratings can affect horsepower calculations. Simply put, there is no standard for thermal testing of servomotors (despite years of trying). Every major supplier has a slightly different methodology of rating its motors. This means an apples-to-apples comparison between brands is not possible using only catalog data. (For more elaboration on this, see Time, Torque, and Inertia, MACHINE DESIGN, 3/1/01, pg. 104.)

When evaluating servomotors from different vendors, designers should look for differences in rating temperatures to see if catalog torque data is based on cold-start or full-on running conditions. It is also advisable to notice differences in the size of heat sinks that different vendors use in establishing their motor ratings. Lastly, the duty cycle of peak performance is important. Some vendors specify a 5-sec limit of peak performance, others specify as much as 10% of total on-time.

Watt's that you say? How many horses does it take to screw in a lightbulb?
Everyone knows that James Watt invented the steam engine, right? WRONG!

Thomas Newcomen actually invented the steam engine as a solution for pumping water and forcing air into the coal mines of England. Unfortunately, his version of the steam engine was not particularly efficient because the boiler and the cylinder were combined. James Watt improved the steam engine by separating the boiler and condenser system from the reciprocating piston, making it one of the most-efficient machines of all time. Watt was granted a patent on the improved system and several others including one for the sun-and-planet gear arrangement, which motion-control users will recognize as the planetary-gear reducer.

James Watt should be remembered for inventing the horsepower as a unit of steam-engine output. Later, designation of the Watt as a unit of electrical energy recognized Watt's many contributions in engineering.

Something as basic as the need to measure work performed, which seems obvious now, simply did not exist at the time. Watt recognized that he would have to find a simple way of explaining to potential customers how efficiently steam could be turned into mechanical work. Put another way, he would have to show people how they would save money by buying a steam engine. Thus the necessity of selling steam engines led to the invention of horsepower to permit a comparison between engines and horses.

The definition Watt devised is that one horsepower is the work done lifting a 500-lb load 1 ft/sec. (In more recent times the definition has been amended to 550 lb, presumably as an average value.) Besides being a handy way of selling steam engines, the horsepower became a tool for defining work performed. It is now customary to use horsepower ratings for comparing gas and diesel engines, or hydraulic and electric motors.

Units of horsepower work out well for measuring power in numerous situations. It is also helpful in finding annual operating costs for energy consumption. For example, in the case where electrical power costs \$0.08/kW-hr, multiplying horsepower load by 0.746 kW/hp 8,760 hr/yr \$0.08/kW-hr reveals that electricity costs for a 1-hp electric motor will be \$523 if operated full time for a year.