**Carl Becker**

**Vice President of Engineering**

**Nuttall Gear, LLC**

**Delroyd Worm Gear Products**

**Niagara Falls, N.Y.**

Worm gears reduce speed by meshing an involute helicoid gear with a worm. This arrangement provides high ratio reductions in a small package. In most systems input is from the worm while output comes from the gear. Because worm gears work like screws, friction is inherent in their operation. Nonetheless, worm gears transmit high loads and are capable of high reduction ratios.

Worm gears have at least two teeth in contact at all times. When the teeth mesh they tend to crush together rather than bend as with spur gears. These qualities offer several advantages. First, vibration, chatter, and other gear noises are virtually nonexistent, producing continuous, quiet and shockless power transmission. The gears also have a high shock-load capacity. The few moving parts are completely enclosed in an oiltight gearbox, which eliminates the possibility of foreign objects falling into the teeth.

Before designing a wormgear unit there are a few important concepts to understand. For instance, backlash is the difference between tooth space and tooth thickness along the pitch circle of mating gears. Backlash is necessary to permit gear lubrication and to allow thermal expansion. However, backlash also produces noise and inefficient power transmission. While all gears require some backlash, it is usually not critical for worm gears, except when index accuracy or timing is important.

Lubrication is also critical in all gearboxes. Oil in the worm-gear housing is directed by splash to the worm bearings and the tooth-contact zone. Once the reservoir is filled, oil levels should be checked and maintained regularly with a complete oil change recommended every six months of normal service.

While some geartrains are not reversible, all worm gears are. However, although the worm can turn in either direction and move the gear correspondingly, turning the gear will not always turn the worm. This irreversibility, or selflocking characteristic, is unique to worm gears but not always desirable. Irreversibility results from high, inefficient ratios and from worms with large diameters or with lead angles of 5° or less. Gear-reducer designs usually aim for highest efficiency, which means avoiding irreversibility. It is also important to note that worm gears that self lock when subjected to a light load may creep if the load increases. The same problem can result when a steady load begins to vibrate. Rather than designing for irreversibility, most reducers lock with a brake that releases electrically when the motor starts. The best location for such a brake is on the motor input shaft or the reducer input shaft.

Manufacturers typically provide performance tables essential when selecting a gear package. These list values, such as mechanical ratings, thermal ratings, and overhung load capacity, and depend on the nature of the application. Mechanical ratings reflect gear wearing capacity while thermal ratings give a measure of the unit’s maximum acceptable operating temperature. Thermal ratings can be ignored in occasional or intermittent service since the reducer will cool between runs.

Overhung load capacity provides the maximum radial load that the gear shafts can withstand. No overhung load exists for vertical shafts, which means overhung load capacity is not a concern in applications such as a vertically mounted agitator.

Another consideration is the peak starting load, since it will exceed the normal operating load. If the peak starting load is below 300% of the normal operating load and has a starting period of 2 sec or less, select a reducer based on the catalog rating with a 1.0 service factor. If the starting load exceeds 300% of the listed rating, divide the peak load by three before selecting a reducer. If the starting load is exactly 300% of the catalog rating and exceeds two seconds, choose a larger reducer.

To demonstrate the selection procedure for a worm gear, consider a typical application where a horizontal worm gear reducer drives a medium- duty hoisting drum. In this case a sprocket with a 5-in. pitch diameter mounts on the output shaft. The sprocket drives a chain that provides a 3:1 reduction between reducer shaft and drum shaft. The drum has an 8-in. radius and turns at 10 rpm while lifting a load of 1,700 lb. The service is intermittent with moderate shock loads. The drum runs five or six times a day for no more than 1 min during a 1-hr period. The requirement is to determine the horsepower necessary from the motor, which runs at 575 rpm.

The first step is to determine the output speed of the reducer by multiplying drum speed by chain reduction ratio as follows:

*O = D × R _{c}*

* 30 = 3 × 10*

where *O* = reducer output speed, rpm; *D* = drum speed, rpm; and *R _{c}* = chain reduction ratio. Substituting values produces a reducer output speed of 30 rpm. Calculate the reduction ratio of the worm gear as:

where *R _{g}* = worm gear reduction ratio; and

*I*= input speed, rpm. The ratio is rounded to a more standard value of 20:1.

The next step is to determine torque at the reducer output shaft. First torque at the drum:

*T _{d} = r_{d} × L_{d}*

* 13,600 = 8 × 1,700*

where *T _{d}* = torque at the drum, lb-in.;

*r*= drum radius, in.; and

_{d}*L*= drum load, lb. Then calculate torque at the reducer output shaft:

_{d}where *T _{r}* = torque at the reducer output shaft, lb-in. Use this torque to determine the horsepower input to the reducer as follows:

where *H* = motor horsepower, hp; and *E* = motor efficiency, obtained from the manufacturer.

Next determine the service classification and corresponding service factor from manufacturer’s data. A service factor of 1.0 corresponds to occasional, moderate shock, total operating time not exceeding 1⁄2 hr/day, electric motor driven.

Manufacturer’s tables for the 20:1 ratio show that a 4-in. reducer running at 575 rpm has a mechanical rating of 3.11 hp. The reducer rating for this service is calculated as:

where *R _{r}* = reducer rating,

*M*= mechanical rating, and

*S*= service factor. Since the 3.11 reducer rating exceeds the required load to be transmitted, the next smaller unit, a 31⁄2-in. reducer, can be used. Thermal rating limitations are not required since the load is applied intermittently.

The final check is for the overhung load. This is found as follows:

where *L _{o}* = overhung load, lb; and

*r*= pitch radius, in. Manufacturer’s data shows the overhung load capacity of the 31⁄2-in. unit low speed shaft to be 2,850 lb at speeds under 50 rpm. The overhung load in this case is 1,810 lb, which makes this unit acceptable.

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