Basic teeth and module of involute cylindrical gears
Involute cylindrical gears are the most widely used gear type in mechanical transmissions. Their involute tooth profiles offer advantages such as smooth transmission, strong load-bearing capacity, and mature processing technology. They are widely used in automotive, machine tool, and construction machinery applications. The basic tooth profile and module are the two core parameters of involute cylindrical gears. The basic tooth profile determines the gear’s tooth profile shape and dimensional proportions, while the module is the fundamental parameter measuring gear size. Together, they determine the gear’s transmission performance and geometric dimensions and are the foundation of gear design, manufacturing, and inspection.
The basic tooth profile parameters of involute cylindrical gears refer to standardized tooth profile parameters, including the addendum coefficient, top clearance coefficient, and pressure angle. The standardization of these parameters ensures the interchangeability and versatility of gears. China’s national standard (GB/T 1356-2001) stipulates that the addendum coefficient for a normal gear system is 1, and the top clearance coefficient is 0.25; the addendum coefficient for a short gear system is 0.8, and the top clearance coefficient is 0.3. The addendum coefficient determines the size of the tooth height, which is equal to the product of the addendum coefficient and the module. A normal gear system with a larger addendum provides higher gear contact and smoother transmission, but also results in thinner tooth tips and weaker impact resistance. A short gear system with a smaller addendum and thicker tooth tips provides greater impact resistance, but also has lower contact, making it suitable for applications with heavy shock loads. The pressure angle is another important parameter for basic teeth. National standards stipulate a standard pressure angle of 20°. The magnitude of the pressure angle affects the gear’s force transmission performance and tooth root strength. A larger pressure angle increases the tooth root thickness and load-bearing capacity, but also increases radial forces. A smaller pressure angle results in smoother transmission and reduced radial forces, but also lower tooth root strength. Basic teeth also include parameters such as the tooth root fillet radius and tooth width. These parameters together constitute the basic gear tooth profile and are the foundation of gear design.
The module is the most fundamental parameter of involute cylindrical gears and serves as the basis for calculating gear geometry. It is represented by the symbol “m” and is expressed in millimeters (mm). The module directly determines the size and load-bearing capacity of the gear. A larger module increases the gear’s tooth thickness, tooth height, pitch diameter, and other dimensions, and thus increases its load-bearing capacity. A smaller module reduces the gear’s size and load-bearing capacity, but also allows for a more compact transmission structure. my country’s national standard (GB/T 1357-2008) specifies standard module series, divided into the first and second series. The first series represents the preferred modules, such as 1, 1.25, 1.5, 2, 2.5, 3, and 4, while the second series is a supplementary series, such as 1.75, 2.25, and 3.5. In gear design, modules from the first series should be preferred to ensure interchangeability and processability. The choice of module needs to be determined based on factors such as the transmitted torque, speed, and working conditions. Gears that transmit large torque require a larger module, such as the gear module in heavy machinery can reach more than 20mm; gears that transmit small torque can use a smaller module, such as the gear module in instruments and meters can be as small as 0.1mm.
The basic tooth diameter and module together determine the geometric dimensions of involute cylindrical gears. All dimensional parameters can be calculated from the module and basic tooth parameters. The pitch circle diameter is the base diameter of the gear, equal to the module multiplied by the number of teeth (d = m × z), and serves as the basis for calculating other dimensions. The addendum diameter is equal to the pitch circle diameter plus twice the addendum height, i.e., da = d + 2ha = m × z + 2ha*m (ha is the addendum height coefficient). The addendum diameter for a normal tooth system is m × (z + 2), while that for a stub system is m × (z + 1.6). The root diameter is equal to the pitch circle diameter minus twice the addendum height, i.e., df = d – 2hf = m × z – 2 (ha + c)*m (c is the top clearance coefficient). The root diameter for a normal tooth system is m × (z – 2.5), while that for a stub system is m × (z – 2.2). The tooth pitch is the arc length of the tooth profiles on the same side of two adjacent teeth on the pitch circle, equal to π multiplied by the module (p = π × m). The tooth thickness is the arc length of a tooth on the pitch circle (s = p/2 = π × m/2). The tooth space width is equal to the tooth thickness (for standard gears). The standardization of these dimensional parameters ensures proper meshing and interchangeability of gears and is a crucial basis for gear manufacturing and inspection.
The proper selection of basic tooth size and module is crucial to the transmission performance of involute cylindrical gears, directly impacting their load-bearing capacity, transmission efficiency, and service life. During the design process, the module size must be determined based on factors such as transmission power, speed, and operating environment. Typically, a preliminary estimate of the module can be made based on the transmitted torque, which is then verified in conjunction with the gear’s structural dimensions and strength requirements. For example, for a gear transmission with a transmission power of 10 kW and a speed of 1000 rpm, a module of 3-4 mm can be initially selected, and its suitability can be determined through strength calculations. The selection of basic tooth size also needs to consider the operating conditions. For applications with high impact loads, a short tooth size is recommended to increase root strength; for high-speed transmissions, a normal tooth size is preferred to improve contact and ensure smooth transmission. Furthermore, processability must be considered. Standard modules and basic tooth parameters can be machined using standard tools, reducing manufacturing costs. With the advancement of gear technology, non-standard basic tooth sizes and modules are finding use in some specialized applications, but these require specialized tools and processing techniques, which can be costly. In short, the scientific selection of basic teeth and module is the basis for ensuring the transmission performance of involute cylindrical gears, and it is also the core content that needs to be focused on in gear design.
