What is a helical gear?

Gearing 101: A primer on the function and design of helical gears.


What is a helical gear? A helical gear is a type of cylindrical gear on which the teeth are helicoid, that has teeth that are cut at an angle to the axis of rotation. They are similar to spur gears but offer advantages both in torque capacity and smoothness of operations.                      

Helical gears transmit power and motion between two parallel shafts. In order to do so, the pitch, the pressure angle, and the helix angle of both gears must be the same — however, the direction of the helix angle must be opposite. Helical gears can increase or decrease the speed and torque of the rotating shaft depending on the sizing and arrangement of the gears.

The teeth of a helical gear are cut using a gear hobbing machine or a gear shaping machine. Helical 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.

The geometry of a helical gear is defined by several parameters. The calculations vary depending on whether the teeth are produced in the normal system or the transverse system.

Figure 1 shows the relationship between the tooth pitch in the normal system and the tooth pitch in the transverse system.

Figure 1: Fundamental relationship of a helical gear (right-hand helix).

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

Table 1 details the calculations for a pair of helical gears in the normal system with a profile shift coefficient. Table 2 details the calculations for a helical gear designed in the transverse system.

Table 1: The calculations of a profile shifted helical gear in the normal system.
Table 2: The calculations for a profile shifted helical gear in the transverse system.

The first value needed to produce a helical 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 each gear is chosen by the end-user based on the speed ratio that is desired for the application. In this example, the desired speed ratio is 1:5.

This gear tooth modification factor is not typically applied but is sometimes used to manipulate the center distance of a helical gear pair. When the value is set to zero for both gears, they are considered to be standard helical gears.

When the profile shift coefficients are set to zero, the working pressure angle and the reference pressure angle are equal. If there is a profile shift coefficient on one or both of the gears, a detailed calculation needs to be performed to determine the working pressure angle.

If there is a profile shift coefficient being used on either gear, then a center distance modification factor needs to be calculated. However, if the profile shift coefficients are both zero, then the center distance of a pair of helical gears is equal to one half of the sum of each gear’s reference diameter. The reference diameter of a helical gear is also known as the pitch diameter. 

The addendum of a helical gear tooth is the radial distance between the pitch circle and the tooth tip. 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 helical gear is also known as the outer diameter or the outside diameter. For standard helical gears, the tip diameter is equal to the reference diameter plus two addendums.

Although not shown in Table 1, the value for backlash is important for helical gears. 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 helical gears involves determining the pitch diameter, module, pressure angle, helix angle, addendum, dedendum, and backlash. These factors are dependent on the desired gear ratio, power transmission requirements, and the design of the mechanical system. Helical gears will only transmit power between parallel shafts. As the gears rotate, the teeth engage and transmit torque from the driving gear to the driven gear. The direction of rotation of the driven gear is always opposite to that of the driving gear, and the speed of the driven gear is determined by the gear ratio. With the introduction of a helix angle, these gears will also produce a radial force. The strength of this force is proportional to the helix angle. 

Helical gears are most commonly used in high-speed and high-torque mechanical systems because they permit the transfer of higher torque values and quieter operation due to their effective tooth width. They are also are simple in design, efficient in operation, and cost-effective. Understanding the technical definitions and design principles of helical 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.