Gearing 101: A primer on internal ring gears

Internal gears are used with pinions to create mechanical systems that reduce speed and increase torque in inline shaft applications.

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What is an internal gear? An internal ring gear is a type of cylindrical-shaped gear that has teeth inside a circular ring. The gear teeth of the internal gears mesh with the teeth space of a spur gear. Spur gears have a convex-shaped tooth profile and internal gears have reentrant shaped tooth profile. They are a complex type of element commonly found in planetary gear systems and are always paired with a pinion.

Internal gears are used with pinions to create mechanical systems that reduce speed and increase torque in inline shaft applications. For straight tooth internal gears, the mating pinion(s) must be the same pitch, and the same pressure angle. In addition, the pinion must pass a check for involute interference, trochoid interference, and trimming interference. When the internal gear teeth are helical, the pitch, the pressure angle, the helix angle of both the pinion and the internal gear must be the same; however, the direction of the helix angle of each component must be opposite. In addition, the pinion must pass a check for involute interference, trochoid interference, and trimming interference.

The teeth of an internal gear are cut using a pinion cutter on a gear shaping machine. The shaping tool machines a section of the internal gear and then indexes similar to a hob producing a spur gear. The number of teeth produced by each cutter is limited as the cutter radius needs to account for the number of teeth on the internal ring gear. Internal ring gears can be produced from various materials, including steel, brass, bronze, or plastic, and depending on the application, they can be hardened based on the requirements for strength and durability.

Internal gears are used with pinions to create mechanical systems that reduce speed and increase torque in inline shaft applications.

The geometry of an internal gear is defined by several parameters. The primary considerations of the internal gear are the outer diameter and the thickness. If the outer diameter is not significantly large, then the ring will not have sufficient structural integrity. If the internal gear is not significantly thick, then the stresses introduced during machining will cause significant twist. In a theoretical sense, the outer diameter of the ring should be greater than the sum of the pitch diameter plus eight times the tooth height. The theoretical minimum thickness is four times the tooth height. Table 1 details the calculations for an internal gear and a pinon. In this case, the internal gear is produced with a profile shift. This gear tooth modification factor is not typically applied but is sometimes used to manipulate the center distance of an internal gear and pinon.

Table 1: The calculations of a profile-shifted internal gear and external gear.

The first value needed to produce an internal 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 helical 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, helical gears typically have values for pressure angle of 20 degrees or 14 degrees 30 minutes. For metric helical gears, the pressure angle is typically 20 degrees.

The number of teeth for the pinion is chosen by the end-user based on the speed ratio that is desired for the application. The ratio of a singular pinion engaged with an internal gear is simply the number of teeth on the internal gear divided by the number of teeth on the pinion. However, when constructed as a planetary system, the speed ratio will vary depending on which element is held fixed while the other two elements rotate.   

The addendum of an internal gear rack tooth is the linear distance between the pitch radius and the tooth tip. Correspondingly, the dedendum is the linear distance between the pitch radius and the tooth root. The sum of the addendum and the dedendum determines the total tooth height.

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

The design of an internal gear involves determining the pitch, module, pressure angle, addendum, dedendum, and backlash. These factors are dependent on the desired speed ratio, power transmission requirements, and the design of the mechanical system. Internal gears will only transmit power between parallel axes. As the pinion rotates, the teeth engage and transmit torque from the pinion to the internal gear. In order for this motion to occur, they must overcome involute interference, trochoid interference, and trimming interference.

Involute interference occurs between the dedendum of the external gear and the addendum of the internal gear. It is prevalent when the number of teeth of the external gear is small. Involute interference can be avoided by the conditions cited below:

Where αa2 is the pressure angle at a tip of the internal gear tooth.

Trochoid interference refers to an interference occurring at the addendum of the external gear and the dedendum of the internal gear during recess tooth action. It tends to happen when the difference between the numbers of teeth of the two gears is small. The equation presents the condition for avoiding trochoidal interference.

Where:

Trimming interference occurs in the radial direction in that it prevents pulling the gears apart. Thus, the mesh must be assembled by sliding the gears together with an axial motion. It tends to happen when the numbers of teeth of the two gears are very close. This equation indicates how to prevent this type of interference:

When:

Internal gears are a commonly used element in mechanical systems, particularly planetary systems, because they are simple in design, efficient in operation, and cost-effective. Understanding the technical definitions and design principles of internal gears 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.