Hobbing large prime number gears
Large prime gears are gears with a prime number of teeth (no factors other than 1 and itself). Because their number of teeth is not divisible by the common pitch ratio, traditional hobbing methods struggle to ensure pitch accuracy. Therefore, hobbing large prime gears is a challenge in gear machining. Large prime gears have unique application value in mechanical transmissions. For example, they can avoid periodic meshing interference in speed-up or speed-down transmissions, improving transmission smoothness and lifespan. They are widely used in precision machine tools, aerospace, instrumentation, and other fields. Hobbing large prime gears requires special pitching methods and process measures to ensure pitch accuracy, tooth profile accuracy, and surface quality. Common methods include differential pitching, electronic gearboxes, and approximate pitching.
The differential gearing method is a traditional method for hobbing large prime number gears. It achieves precise gearing by incorporating a differential mechanism into the gearing transmission chain of the hobbing machine, using differential motion to compensate for approximate errors in the gearing ratio. The gearing transmission chain of a hobbing machine typically requires a gearing ratio of i = z1/z2 (z1 is the number of hob heads, z2 is the number of gear teeth). When z2 is a large prime number, finding a precise gearing ratio is difficult. In this case, an approximate value z’ close to z2 can be selected, and an additional motion is generated by the differential mechanism to compensate for the gearing error caused by the difference between z’ and z2. The key to the differential gearing method is calculating the differential gear parameters to ensure that the additional motion accurately compensates for the error. The resulting gearing accuracy can reach levels 7-8 as specified in GB/T 10095. This method is applicable to ordinary gear hobbing machines and does not require major modifications to the equipment. It is low-cost, but the adjustment is complicated and requires a high level of technical skills from the operator. The compensation accuracy is limited by the accuracy of the differential mechanism itself. It is suitable for small and medium-sized batch production and large prime number gears with low precision requirements.
The electronic gearbox method, an advanced method that emerged with the development of CNC gear hobbing machines, utilizes the electronic gearbox function within the CNC system to achieve precise generating motion between the hob and the workpiece, eliminating the need for a mechanical gear pulley. This method completely solves the challenge of tooth generation for large prime-number gears. The CNC gear hobbing machine’s electronic gearbox uses software to program parameters such as the number of hob heads, number of gear teeth, and helix angle. A servo motor drives the hob axis and workpiece axis, achieving synchronized motion. Gear generation accuracy depends solely on the accuracy of the servo system and the interpolation accuracy of the CNC system, reaching levels 5-6 according to GB/T 10095. The electronic gearbox method is easy to use; simply input the gear parameters to automatically generate the machining program. Changing gear types eliminates the need to change gear pulleys, significantly reducing auxiliary time. It is suitable for single-piece, small-batch production, and high-precision gear hobbing of large prime-number gears. Furthermore, the electronic gearbox method can also process special gears such as variable-thickness and non-circular gears. Its exceptional flexibility and versatility make it the current mainstream method for hobbing large prime-number gears.
The approximate tooth pitch method is a simple and easy method. By selecting an approximate tooth number z’ close to the prime number z, the gear ratio i = z1/z’ can be accurately achieved, thereby approximately producing a gear with the same number of teeth z. The gear pitch error in the approximate gear pitch method is Δz = zz’. To ensure pitch accuracy, Δz/z is typically required to be ≤ 0.001, meaning the difference between the approximate tooth number z’ and the actual tooth number z should be within 0.1%. For example, when machining a gear with a prime number z = 97 teeth, z’ = 97.097 can be selected. In this case, the gear ratio i = 1/97.097 ≈ 0.0103, which can be achieved through gear combination. The advantages of the approximate gear pitch method are its simplicity and the lack of a differential mechanism or CNC system. It is suitable for standard hobbing machines and applications with low precision requirements. However, the gear pitch error is unavoidable, so it can only be used for gears with low transmission smoothness requirements, such as low-speed transmission gears and manual mechanical gears. When using the approximate tooth separation method, the pitch error of the processed gear needs to be detected to ensure that the error is within the allowable range.
Tool selection and cutting parameter optimization for hobbing large prime number gears significantly impact machining quality and efficiency. High-precision hobs, such as AA or A-grade gear hobs, should be used. These hobs have a profile error of ≤0.01mm and high chip flute accuracy to ensure profile accuracy. High-speed steel or carbide are preferred hob materials. High-speed steel hobs are easy to sharpen and are suitable for small and medium-volume production and low-speed cutting. Carbide hobs offer excellent wear resistance and high-speed cutting, making them suitable for large-volume production and machining high-strength gears. As for cutting parameters, due to the long machining time of large prime number gears, it is important to rationally select cutting speed, feed rate, and depth of cut to balance machining efficiency and tool life. When processing carbon steel gears such as 45 steel, the cutting speed of high-speed steel hobs is generally 15-30m/min, and that of carbide hobs is 50-100m/min; the feed rate is determined according to the gear module. When the module m=2-5mm, the feed rate is 0.5-1.5mm/r; the cutting depth is carried out in multiple times, with the first cutting depth being 2/3 of the full tooth height, and subsequent cutting is gradually carried out to the full tooth height to reduce cutting force and tool wear.
Targeted measures are required for the hobbing process and quality control of large prime number gears. The process should be a “rough hobbing – semi-finishing hobbing – finishing hobbing” process. After rough hobbing, most of the stock is removed, leaving a 0.3-0.5mm stock for finishing. Semi-finishing hobbing corrects tooth profile errors, leaving a 0.1-0.2mm stock for finishing. Finishing hobbing ensures final accuracy. Rough and semi-finishing hobbing can be performed using approximate or differential toothing methods, while finishing hobbing requires an electronic gearbox to ensure ultimate accuracy. Quality control focuses on testing metrics such as cumulative pitch error, ring gear radial runout, and tooth profile error. Gear measuring instruments can be used for comprehensive testing. For gears with higher precision requirements, tooth surface roughness testing (generally requiring Ra ≤ 1.6μm) and hardness testing (the surface hardness of case-hardened gears is 58-62HRC) are also required. During machining, care should be taken to maintain the sharpness of the hob and regularly sharpen it to avoid increased tooth profile errors due to tool wear. Workpiece clamping accuracy must also be ensured, using a spindle or specialized fixture to position the gear blank so that the axis coincides with the worktable’s rotation center, with radial runout ≤0.01mm. Through rational process planning and strict quality control, the hobbing quality of large prime gears can be effectively guaranteed.
