Is Lapping an Attempt to Make Hypoid Gears Conjugate?

<p style="text-align: center;"><span style="font-size: 14px;"><img src="/ueditor/php/upload/image/20260609/1781019376457384.png" title="1781019376457384.png" alt="1.png"/></span></p><p><span style="font-size: 14px;">Lapping, like grinding, is a hard finishing process. In grinding the same profile and length crowning applied in the soft cutting process is created. Grinding re-establishes the original surface function after the heat treatment. In lapping material is only removed in the tooth contact area. This not only establishes a good rolling condition, but it also makes the flank surfaces more conjugate in the area where the tooth contact patterns are located. Lapping and grinding are hard-finishing operations. The soft-manufactured bevel and hypoid gearsets must be heat-treated, which in the most common case begins with a case carburizing of standard gear steels such as AISI 8620 or 16MnCr5. To give the low-carbon steel a surface hardness in the 60 HRc range, a layer of carbon enrichment below the surface of 0.8 to 1.5 mm depth is placed by a diffusion process. After the carburizing and quenching in oil, an additional tempering takes place. The result is a surface hardness that is commonly close to 60HRc and a core hardness in the 30HRC range. Case hardening provides an ideal transition between surface and core hardness that makes gears on the surface hard and wear resistant, and in the core ductile. This makes shock loads and certain small plastic deformations tolerable without failure of the gearset. One major side effect of the heat treatment process is the distortion of the gears that is caused by carburizing, the recrystallization of the steel, and the quenching. To make a gearset after heat treatment suitable for power transmissions, for example, in cars and trucks, a hard-finishing operation is required. The hard-finishing operating eliminates the heat treatment distortions hereby providing the flank surfaces with the correct geometry from before the heat treatment. In addition, hard finishing improves the surface finish to a low roughness and waviness, which enhances the hydrodynamic lubrication and reduces noise. Grinding and skiving are the preferred hard-finishing methods, creating a defined surface form that duplicates the original designed surfaces in the single micron range. In case of face hobbed bevel and hypoid gearsets, grinding is not possible, because of the epicyclical flank lead function. Skiving can generate epicyclical lead functions but is not yet accepted for the high production volumes in the automotive and truck industry. This leaves only the lapping process for the hard-finishing of face-hobbed angular gearsets. However, the face hobbed surface texture and the relative sliding between the flanks of hypoid gears make lapping an ideal alternative. Lapping can remove the surface scale left from heat-treatment, and it re-matches two mating members by removing some runout and flank form distortions. Lapping can reduce the transmission error in many cases due to the fact that the major material removal is in the center region of the teeth, where the tooth contact under light load is expected. In order for the lapping to work well, more crowning than required in the hard-finished gearset is used in the gearset design for the soft cutting. Lapping removes about 30 percent of this crowning, such that the length and profile crowning are just right after the lapping. Soft cutting of parts that are lapped after heat treatment considers a stock allowance of .03 mm in the pinion and 0.01 mm in the gear. If grinding is the hard finishing process (for face-milled gearsets) then the design crowning is identical to the desired crowning after hard finishing. Between soft cutting and grinding, a uniform stock allowance of 0.10 mm to 0.15 mm is applied to the pinion and gear flanks. Summary Conjugacy between the members of straight bevel, spiral bevel, and hypoid gears was only the first step and goes back more than 100 years. Quickly, the early scientists and engineers found out that conjugacy only gives us an important basis, but not a solution for power transmissions. Angular gearsets under load experience deflections that move them away from their theoretical position by half a millimeter or more. Well-designed and manufactured bevel and hypoid gearsets today can live up to those requirements and still maintain a power density that is four times higher than it was 50 years ago. Transmission errors of 50 to 150 microradian that were normal in the 1970s are in today’s high-power-density gearsets only between 5 and 15 microradian. All this was achieved by converting a global length and profile crowning (Figure 18, left) first back to conjugacy (Figure 18, center) and then into a UMC-optimized selective crowning, which is limited to particular regions of the teeth, as shown in the right graphic in Figure 18. Notably, the flank center of the UMC-optimized Ease-Off is conjugate, and the transmission error is next to zero. In lapping, similar effects as in grinding are achieved by utilizing low-inertia spindles with rotational compliance and high-speed torque control (SmartLap).</span></p><p><span style="font-size: 14px;">The dream of conjugate angular gearsets turned out to be a false objective. Gear scientists, gear engineers, and gear manufacturers worked very successfully for many decades on finding the optimal flank forms and the optimal non-conjugate flank surface interaction. The conjugate tooth design today is considered simple compared to sophisticated higher-order surface modulation. There is still room for improvement, but this cannot be achieved by going back to antiquated conjugate designs.</span></p>