What is a gear rack?

Gearing 101: A primer on gear racks, what they are and how they’re used.

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A gear rack is a type of gear on which gear teeth are cut on one face of a bar. The bar can be square, round or rectangular in cross section and the teeth can be either parallel to the base or set at an angle. They are a simple and common type of element in mechanical drive systems and are always paired with a pinion.

Gear racks convert power and motion from rotary motion into linear motion. For straight tooth gear racks, the mating pinion must be the same pitch, and the same pressure angle. When the gear rack teeth are helical, the pitch, the pressure angle, and the helix angle of both the pinion and the gear rack must be the same; however, the direction of the helix angle of each component must be opposite.

The teeth of a gear rack are cut using a rack milling machine. The milling head machines a section of rack and then indexes to the adjacent section until the rack is completed. The maximum length of a rack is only limited by the length of the milling machine. Gear racks 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.

The geometry of a gear rack is defined by several parameters. In a theoretical sense, a gear rack is just a spur gear with an infinite pitch diameter. The calculations vary depending on whether the teeth are produced in the normal system or the transverse system. Table 1 details the calculations for a gear rack and a profile shifted pinion. This gear tooth modification factor is not typically applied but is sometimes used to manipulate the center distance of a gear rack and pinion. In most applications, this value is set to zero for the pinion.

A gear rack is a type of gear on which gear teeth are cut on one face of a bar.
Table 1: The calculations of dimensions of a profile shifted spur gear and a rack.

The first value needed to produce a gear rack 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. Each rotation of the pinion will travel a specific linear distance along the gear rack. A pinion with a smaller number of teeth will need to rotate faster than a larger pinion in order to travel the same distance. 

The addendum of a gear rack tooth is the linear distance between the pitch height and the tooth tip. Correspondingly, the dedendum is the linear distance between the pitch height 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 rack 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 rack and pinion at their point of contact. As rack and pinion systems are typically used for positioning applications, the accumulation of backlash errors can have a significant impact on position accuracy. Additional mechanisms such as optical encoders are incorporated into rack and pinion systems in order to maintain positional accuracy.    

The design of gear rack involves determining the pitch height, 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. Gear racks will only transmit power between perpendicular axes. As the pinion rotates, the teeth engage and transmit torque from the pinion to the gear rack. If the rack is fixed and the pinion is rotated clockwise, then the pinion will translate to the right. If the pinion is fixed and rotates clockwise, then the rack will translate to the left. The distance of translation along the rack is equal to the pitch circumference of the pinion. When using a normal module, this distance is fractional. When using a circular pitch instead of module, you can achieve a fixed translation. For example, a module 3 pinion with 30 teeth will translate 282.74 millimeters per rotation, whereas a CP10 pinion with 30 teeth will translate exactly 300 millimeters per rotation. Another way to achieve a fixed rotational value is to use a helical rack and pinion with a helix angle of 19° 31’ 41” as this value converts module to circular pitch as well.

Gear racks are a commonly used element in mechanical systems because they are simple in design, efficient in operation, and cost-effective. Understanding the technical definitions and design principles of gear racks 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.