What is a worm gear?

Gearing 101: A primer on worm gearing and how they are used.

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What is a worm gear? A worm gear is a type of cylindrical gear on which the teeth are helicoid — it has teeth that are cut at an angle to the axis of rotation. They are similar to helical gears but offer advantages both in torque capacity and smoothness of operations. Worm gears are part of a set of gearing components and require a mating worm in order to function. The gear teeth of the worm gear mesh with the teeth of a mating worm. They are a complex type of element commonly found in applications that require a change in direction and a reduction in speed.                                                   

Worm gears are used with worms to create mechanical systems that reduce speed and increase torque in perpendicular shaft applications. In order to do so, the pitch, the pressure angle, and the lead (helix) angle of both the worm and the worm gear must be the same. Additionally, the lead angle for both components must be of the same hand. Worm gearing operates such that the speed is always decreasing, and the torque of the output is always increasing.

The teeth of a worm gear are cut using a gear hobbing machine and are typically cut with a recess for the worm to settle in. This recess is known as the throat of the worm gear. Worm gears can be produced from various materials, including steel, brass, bronze, or plastic, however, the material chosen for the worm gear should always be softer than the material chosen for the worm. The reason for this differential in material durability is the interaction of the mesh between the worm and the mating gear. The worm operates continuously in mesh, but the worm only engages one tooth per revolution.

The geometry of a worm gear is defined by several parameters. The calculations vary depending on whether the teeth are produced in the normal system or the transverse system. The parameters are designated as detailed in Figure 1.

Worm gears are part of a set of gearing components and require a mating worm in order to function. The gear teeth of the worm gear mesh with the teeth of a mating worm.
Figure 1: Dimensions of cylindrical worm gear pair.

The advantage of worm gearing produced in the normal system is that a hob of a specific module and pressure angle can cut a worm gear with any lead angle. For transverse system worm gearing, this is not the case. For transverse gearing, the hob must be modified for each lead angle.

Table 1 details the calculations for worm gearing designed in the axial system.

Table 2 details the calculations for worm gearing designed in the normal system.

Table 1: The calculations for an axial module system worm gear pair.
Table 2: The calculations for a normal module system worm gear pair.

The first value needed to produce a worm gear is the pitch. In the metric system, this is known as the module. As the value of the module increases, the size of the gear tooth increases. In the English standard system, the pitch of a worm gear is known as the diametral pitch (DP). It represents the number of teeth that are found on a gear with a one-inch reference diameter. The pressure angle is the angle between the line of action of the gears and the tangent to the pitch circle. It determines the contact between the teeth of the gears and affects the load-carrying capacity and efficiency of the gears. In the English system, worm gears typically have values for pressure angle of 20 degrees or 14 degrees 30 minutes. For metric worm gears, the pressure angle is typically 20 degrees or 14 degrees 30 minutes.

The number of starts for the worm is chosen by the end-user based on the speed ratio that is desired for the application. The ratio of a single start worm engaged with a worm gear is simply the number of teeth on the worm gear divided by the number of starts on the worm. In this example the reduction ratio is 30:2.   

The addendum of a worm gear tooth is the radial distance between the pitch circle and the throat circle. Correspondingly, the dedendum is the radial distance between the pitch circle and the tooth root. The sum of the addendum and the dedendum determines the total tooth height.

The tip diameter of a worm gear is also known as the outer diameter or the outside diameter. For standard worm gears, the tip diameter is equal to the reference diameter plus three addendums.

Although not shown in Table 1, the value for backlash is important for worm gearing. This value measures the distance between mating gear teeth when they are not in contact. It is necessary to have a minimum amount of backlash in order for the gear teeth to mesh properly and for lubricant to engage with the gears at their point of contact.   

The design of worm gears involves determining the pitch diameter, module, pressure angle, lead angle, addendum, dedendum, and backlash. These factors are dependent on the desired gear ratio, power transmission requirements, and the design of the mechanical system. Worm gearing will only transmit power between perpendicular shafts. As the worm rotates, the teeth engage and transmit torque from the worm to the worm gear. The direction of rotation of the worm gear is determined to be the direction of rotation of the worm and the direction of the hand of the lead angle. The speed of the worm gear is determined by the gear ratio. Since these gear sets incorporate a lead angle, the gears will also produce radial forces. The strength of this force is proportional to the lead angle. 

Worm gears are commonly used in applications that require a reduction in speed and an increase in torque. They are also simple in design, efficient in operation, and a cost-effective solution. Understanding the technical definitions and design principles of worm gearing is essential for anyone working with mechanical systems. 

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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.