Basic tooth profile size parameters of bevel gears
The basic bevel gear tooth profile refers to the standard tooth shape found on the developed surface of the back cone at the large end of a bevel gear. It serves as the foundation for bevel gear design and manufacturing. my country’s national standard GB/T 12369-1990 specifies the basic tooth profile parameters for spur bevel gears, including module, pressure angle, addendum coefficient, top clearance coefficient, and tooth thickness. These parameters directly impact the meshing performance, load capacity, and interchangeability of bevel gears. The tooth profile parameters of bevel gears are both related to and distinct from those of cylindrical gears. Because the tooth height gradually decreases from the large end to the small end, the small end dimensions must be converted from the large end dimensions. Understanding the definitions and calculation methods of these parameters is crucial to ensuring bevel gear transmission accuracy.
The module (m) is a core parameter of the basic bevel gear tooth profile. It is defined as the ratio of the large-end pitch diameter to the number of teeth (m = d/z), expressed in millimeters (mm). It serves as the benchmark for determining the dimensions of various tooth profile components. The module of bevel gears is selected according to the national standard GB/T 1357-2008, with the first series (1, 1.25, 1.5, 2, 2.5, 3, 4, 5, etc.) being preferred. Power transmission bevel gears typically have a module between 2 and 20 mm. A larger module increases the tooth profile and the load capacity. For example, for a bevel gear with a module of m = 5 mm, its large-end pitch diameter d = m × z (z is the number of teeth). If the number of teeth z = 20, then d = 100 mm. The choice of module depends on the transmitted power, speed, and operating conditions. The higher the power and the lower the speed, the larger the module. For example, the module of bevel gears for mining machinery is generally 10-20 mm, while that of bevel gears for precision instruments is generally 2-5 mm.
The pressure angle (α) refers to the angle between the normal pressure direction of the tooth profile and the tangent direction on the pitch circle. The standard pressure angle for bevel gears is 20° (GB/T 12369-1990), although angles of 14.5°, 25°, and other pressure angles may be used in certain special applications. The pressure angle directly affects the tooth profile shape and tooth contact strength. A larger pressure angle increases the tooth root thickness and increases tooth contact strength, but transmission efficiency is slightly reduced. A smaller pressure angle results in a more “sharp” tooth profile and smoother transmission, but with lower tooth root strength. The pressure angle of bevel gears is measured on the developed surface of the large end back cone. The pressure angles at the tooth tip and tooth root must be consistent with the pitch circle pressure angle, with a deviation of ≤±30°. In meshing transmissions, the pressure angles of a pair of bevel gears must be equal; otherwise, meshing interference will occur, affecting transmission smoothness.
The addendum coefficient (ha*) and the top clearance coefficient (c*) are used to determine the addendum and top clearance dimensions. For standard teeth, the addendum coefficient ha* is 1, for stub teeth, it is 0.8, and for top clearance coefficient c*, it is 0.2 (standard teeth) or 0.3 (stub teeth). Addendum (ha) = ha × m, root height ( hf) = (ha + c*) × m, and total tooth height (h) = ha + hf = (2ha* + c*) × m. For example, for a standard bevel gear with a module m = 5mm, ha = 1 × 5 = 5mm, hf = (1 + 0.2) × 5 = 6mm, and h = 11mm; for a stub bevel gear, ha = 0.8 × 5 = 4mm, hf = (0.8 + 0.3) × 5 = 5.5mm, and h = 9.5mm. Top clearance (c) = c* × m, refers to the gap between the tooth top of a pair of meshing bevel gears and the tooth root of the other gear. It is used to store lubricating oil and avoid interference. The standard top clearance c = 0.2m, which can ensure good lubrication effect.
Tooth thickness (s) and tooth space width (e) are important parameters on the pitch circle. For a standard tooth profile, the tooth thickness on the pitch circle is equal to the tooth space width (s = e = mπ/2), ensuring uniform backlash during gear meshing. A negative upper deviation in tooth thickness, and an even more negative lower deviation, creates a certain amount of backlash to prevent seizure caused by temperature fluctuations or manufacturing errors. Backlash is determined based on operating conditions, with a larger backlash (e.g., 0.05m-0.1m) for high-speed transmissions and a smaller backlash (e.g., 0.02m-0.05m) for precision transmissions. The root fillet radius (ρf) is the radius of the tooth root transition curve. The standard value is ρf = 0.38m. This reduces stress concentration at the tooth root and improves the tooth root bending strength. For example, when m = 5mm, ρf = 1.9mm. Too small a root fillet radius can lead to excessive stress at the tooth root, which can easily cause fatigue fracture.
The dimensional parameters of the basic tooth profile of bevel gears must be selected according to a standard series to ensure interchangeability. Common parameter combinations include: m = 2-20 mm, α = 20°, ha* = 1, and c* = 0.2. These parameters must be clearly marked on the gear working drawing, using the notation “m = 5 mm, α = 20°, ha* = 1, c* = 0.2 GB/T 12369-1990.” For non-standard bevel gears, the specific values of each parameter must be individually indicated, along with the tolerance range. During machining and inspection, templates must be made based on the basic tooth profile parameters, or a gear measuring instrument must be used to ensure that the tooth profile conforms to design requirements. Deviations in tooth addendum and tooth root height must be ≤ ±0.05 mm, pressure angle deviations must be ≤ ±1°, and tooth thickness deviations must be within the designed backlash range. Standardizing basic tooth profile parameters ensures interchangeability and meshing performance of bevel gears, reducing design and manufacturing costs.
