Involute cylindrical gear
Involute cylindrical gears are the most widely used type of gear in mechanical transmission. Their tooth profile is an involute curve, offering advantages such as smooth transmission, high load-bearing capacity, and easy processing. They are widely used in the automotive, machine tool, engineering machinery, aerospace, and other fields. The basic parameters of involute cylindrical gears include module, number of teeth, pressure angle, tooth height coefficient, and top clearance coefficient; these parameters determine the gear’s size and transmission performance. Depending on the direction of the tooth profile, involute cylindrical gears can be divided into spur gears and helical gears. Spur gears have a tooth contact line parallel to the axis, resulting in less smooth transmission and suitable for low-speed transmission. Helical gears have a tooth contact line inclined to the axis, resulting in a high degree of overlap and smooth transmission, making them suitable for high-speed, heavy-load transmission. Understanding the characteristics, parameters, processing methods, and precision requirements of involute cylindrical gears is crucial for the proper design and use of gears.
The formation principles and characteristics of the involute are fundamental to understanding the transmission characteristics of involute cylindrical gears. An involute is the path of any point on a straight line when it rolls purely along a circle. This circle is called the base circle, and the straight line is called the generating line. Involutes possess the following key properties: the normal at any point on the involute must be tangent to the base circle; the shape of the involute depends on the size of the base circle; the larger the base circle, the flatter the involute; involutes on the same base circle are symmetrical; the pressure angle of the involute on the base circle is 0°, increasing with distance from the base circle. These characteristics give involute gears the following advantages in transmission: a constant transmission ratio, as the transmission ratio of the two gears is equal to the inverse ratio of their base circle diameters, which are fixed; divisibility of the center distance, meaning that the transmission ratio remains unchanged even if the actual center distance of the two gears deviates slightly from the designed center distance; and a fixed line of engagement, with a constant force direction and smooth transmission. These advantages have made involute cylindrical gears the most predominant gear type in mechanical transmission.
The calculation of the basic parameters and geometric dimensions of involute cylindrical gears is a core element of gear design. These basic parameters include: module m (in mm), which determines gear size. A larger module increases the gear’s pitch and load capacity. National standards specify a standard module series (e.g., 1, 1.25, 1.5, 2, etc.); the number of teeth z, which refers to the total number of teeth on a gear; a larger number of teeth increases the gear’s size and reduces the transmission ratio; the pressure angle α, which refers to the pressure angle of the involute on the pitch circle; the national standard specifies a standard pressure angle of 20°; the tooth height coefficient ha*, with a standard value of 1 (normal gear) or 0.8 (short gear); and the top clearance coefficient c*, with a standard value of 0.25 (normal gear) or 0.3 (short gear). Based on these basic parameters, the main geometric dimensions of the gear can be calculated: pitch diameter d = mz; addendum diameter da = d + 2ham = m(z + 2ha); root diameter df = d – 2 (ha* + c*) m = m (z – 2ha* – 2c*); pitch p = πm; tooth thickness s = p/2 = πm/2; and space width e = p/2 = πm/2. For example, for a spur gear with a module m = 2mm, number of teeth z = 20, pressure angle α = 20°, ha* = 1, and c* = 0.25, its pitch diameter d = 2 × 20 = 40mm, addendum diameter da = 40 + 2 × 1 × 2 = 44mm, and root diameter df = 40 – 2 × (1 + 0.25) × 2 = 35mm.
The machining methods for involute cylindrical gears can be categorized into forming and generating. The forming method directly produces the tooth profile using a forming tool with the same shape as the gear tooth groove. Common forming tools include disc gear milling cutters and finger gear milling cutters. The advantages of the forming method are simple equipment (can be processed on a standard milling machine or planer) and low cost. However, its disadvantages are low machining accuracy (generally 9-12 grades) and low efficiency. It is suitable for single-piece, small-batch production, and gears with low precision requirements. The generating method uses the generating motion (conjugate motion) of the gear tool and the workpiece to produce the tooth profile. Common generating tools include hobs, gear shaping cutters, gear shaving cutters, and gear grinding cutters. Hobbing is the most common generating method. It utilizes the helical tooth profile of the hob and the rotational motion of the workpiece to create the generating motion. It can produce spur and helical cylindrical gears with machining accuracies reaching 6-9 grades, high efficiency, and suitable for mass production. Gear shaping utilizes the reciprocating and generating motion of the gear shaping cutter and the workpiece to produce tooth profiles. It is suitable for machining internal gears, multi-gear gears, and racks, and offers comparable precision to hobbing. Gear shaving utilizes the free engagement of the shaving cutter with the machined gear, removing a small amount of metal through relative sliding between the tooth surfaces. This improves gear precision (reaching Grades 5-7) and surface quality (Ra ≤ 0.8μm). It is commonly used for finishing after hobbing or shaping. Gear grinding, the primary method for gear finishing, utilizes the generating motion of the grinding wheel and workpiece to produce tooth profiles. It achieves precision grades 3-6 and a surface roughness of Ra ≤ 0.4μm. It is suitable for machining high-precision gears (such as machine tool spindle gears and automotive transmission gears), but it is costly and inefficient.
The accuracy grade and tolerances of involute cylindrical gears are crucial indicators for ensuring gear transmission performance. According to the national standard GB/T 10095.1-2008, involute cylindrical gears are classified from Grade 0 (highest) to Grade 12 (lowest), with grades 5-9 being the most commonly used. Gears of different accuracy grades are suitable for different transmission applications: Grade 5 gears are used for high-speed, high-precision transmissions (such as precision machine tool spindle drives); Grades 6-7 gears are used for medium-speed, medium-precision transmissions (such as automotive transmissions and machine tool feed drives); and Grades 8-9 gears are used for low-speed, low-precision transmissions (such as agricultural machinery and lifting machinery). Gear tolerances include: pitch deviation (fpt, Fp), which controls pitch uniformity; total profile deviation (Fα), which controls tooth profile shape accuracy; total helix deviation (Fβ), which controls tooth profile accuracy; tooth thickness deviation ( Esn), which controls tooth backlash; and radial runout (Fr), which controls the radial position error of the ring gear relative to the reference axis. For example, the cumulative total pitch deviation Fp of a grade 7 precision gear is ≤0.063mm (module m=2mm, number of teeth z=20), the total tooth profile deviation Fα ≤0.016mm, and the total helix deviation Fβ ≤0.018mm. To ensure gear accuracy, in addition to employing high-precision machining methods, it is also necessary to control the gear material and heat treatment quality. For example, alloy structural steels such as 40Cr or 20CrMnTi should be used, and after quenching and tempering or carburizing and quenching, the hardness should be controlled within 220-250HB (quenching and tempering) or 58-62HRC (carburizing and quenching) to ensure gear strength and wear resistance.
