Do opposites really attract?

When choosing a gear, it is important to understand which gear it mates with. 

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With Valentine’s Day this month, it is time to celebrate with your partner. Whether you are on your first date with a longtime crush, or on a casual date with someone you have been communicating with via the latest app, or you are just enjoying a date night with your longtime love, we all look forward to spending time with that unique individual who complements us and who we can refer to as our better half. Just like us, gears work best when they are properly matched.

Spur gears are the most common form of gearing. They match well with either other spur gears or with gear racks. In order for them to mesh properly, there are several criteria that need to be met. The most important is that the gears are the same pitch. Whether it be module, circular pitch or diametral pitch, both gears must be of the same type and value. In addition to having the same pitch, the gears must also have the same pressure angle. If the pressure angles are different but the pitch is the same, the gears will not mesh properly. A final consideration for good mesh is the face width. Although not a firm requirement, it is recommended that the face width of both gears be the same, as this will allow for the maximum contact ratio. If one of the gears has a face width larger than the other, the gear with the larger face width is likely to suffer from premature wear failure.

Helical racks and gears require additional considerations in order to mesh. Like spur gears, the pitch and the pressure angles must be the same, and ideally the face widths should be equal. However, the helix angles of the gears need to be considered. In order for a helical gear to mesh with a helical rack, they both must have the same helix angle but the direct of the helix must be opposite. A right-hand helix pinion will not mesh with a right-hand helix rack. It will only mate with a left-hand helix rack and vice-versa, as noted in Figure 1.

Figure 1.

Screw gears are a unique subset of helical gears. They have a helix angle of 45 degrees. For these gears, they need to have the same pitch and pressure angle, but the direction of helix angle is dependent on the application. If they are to be used in a parallel shaft application, then the helix direction needs to be opposite — for example, a left-hand driver and a right-hand driven. If they are used in a crossed axis application, then the direction of the helix needs to be the same — for example, a right-hand driver and a right-hand driven.

For intersecting axes, the most common style of gear is the bevel gear. The term bevel gear is used to describe both a specific type of gear and any of a variety of derivatives of this style.

Bevel gears are a very common form of intersecting axis gearing. When trying to mesh bevel gears, the pitch and pressure angle must be the same. The differentiators for whether bevel gears will mesh is the pitch cone angle and the shaft angle. When the ratio of a bevel gear set is 1:1, and the shaft is set to 90 degrees, then the pitch angle of each gear will be 45 degrees. If the same gear is produced for a different speed ratio then the pitch angle will vary. In Table 1, the values for cone angle, tip angle, and root angle are calculated for a Module 3, 20 tooth pinion that mates at 90 degrees with another 20 tooth pinion.

Table 1: Calculations for a pair of straight miter gears in the Gleason system.

In Table 2, the same dimensions, cone angle, tip angle, and root angle are calculated, except for a Module 3, 20 tooth pinion that mates at 90 degrees with a 40 tooth gear.

Table 2: Calculations for a pair of straight bevel gears in the Gleason system.

From these calculations, you can see that the tooth form of a 20 tooth miter gear differs greatly from the that of a 20 tooth bevel pinon and that the cone angle is extremely important when selecting bevel gears to mate.

Spiral bevel gears and spiral miter gears introduce additional criteria to consider in order to mesh properly. These gears not only need to have the same pitch, pressure and the proper cone angle, they also have
to have the same spiral angle and be opposite in hand. When selecting the proper direction of spiral, it is important to consider the direction of rotation of the input as this will change the direction of thrust loading on the bevel pair. If the system is bi-directional, then this consideration can be ignored.

Worm gear pairs are another style of intersecting axes gearing. They consist of
a worm wheel which resembles a helical gear and its mate, the worm, which resembles a screw. For these gear pairs, the pitch and the pressure angle must be the same. For a worm pair, the helix angle is called the lead angle and similar to helical gears, each part of a worm pair must have the same value. Similar to screw gears, worm pairs must have the same lead angle direction in order to operate as intersecting gears. The one additional factor that needs to match with worm gear pairs is the number of starts. This value is the number of unique threads that are produced on the worm. It is vital in determining the speed ratio of the pair.

For example, if  a 30 tooth worm wheel is designed to mate with a single start worm, the pair will have a speed ratio of 30:1. However, if the same gear pair is designed such that the 30 tooth worm wheel mates with a double start worm, then the speed ratio is 30:2 or 15:1. If all of the geometry of two worm gear pairs is identical, but the number of starts changes, the lead angle will also change. For this reason, you cannot simply replace a single start worm with a double start worm to change the speed ratio. If you try to do this, then the difference in lead angles will cause an offset to the shaft alignments.

For all gear styles, it is required that both gears have the same pitch and pressure angle. For some gear styles, they must be opposite in hand in order to mesh, yet other styles require that they be the same hand in order to mesh. Like each of us, gears have a suitable mate waiting for them, we just have to find it. 

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is general manager of KHK USA Inc, a subsidiary of Kohara Gear Industry with a 24-year history of working in the industrial automation industry. He is skilled in assisting engineers with the selection of power-transmission components for use in industrial equipment and automation. Dengel is a member of PTDA and designated as an intern engineer by the state of New York. He is a graduate of Hofstra University with a Bachelor’s of Science in Structural Engineering.