Why is Conjugacy not Desirable for Real World Applications?

<p style="text-align: center;"><img src="/ueditor/php/upload/image/20260609/1781019585636999.png" title="1781019585636999.png" alt="1.png"/></p><p><span style="font-size: 14px;">In 1926, Ernest Wildhaber (Refs. 3, 8) was the first to propose applying surface crowning on hypoid gears. Wildhaber acknowledged that the slightest deviations in the gear housing and in the building position, as well as deflections affected by load and heat, will cause edge contact with peak stress levels of a multiple of the allowable values the gearset had been designed for. The conjugate gearset used for the TCA in Figure 11 was repeated with realistic displacement values of 50 ?m offset, 50 ?m pinion cone, and 30’ of shaft angle change. The results in Figure 14 show warped and tilted Ease-Offs and severe edge contact on the heel and top. This edge contact will cause noisy operation, followed by pitting and tooth fracture.</span></p><p><span style="font-size: 14px;">The theoretically conjugate hypoid set will depart from fulfilling any of the fundamental gearing laws in case of the smallest gearbox inaccuracies or deflections. As mentioned above, already small deflections at moderate loads lead to load concentrations on the edges of conjugate flank pairs and can cause material damage and considerable noise emission. As such, the conjugate gear pair is not suitable for any task in power transmissions. The introduction of 80 ?m length crowning and 15 ?m profile crowning to the conjugate hypoid design delivers the analysis results shown in Figure 15. The crowning makes the gearset insensitive to expected inaccuracies in the gear housing and load, and heat-affected deflections. Applying the same amounts of shaft displacements as those used for the TCA of the conjugate hypoid set in Figure 14 moves the mean point slightly out of the initial position (see Figure 16), but a large contact area within the tooth boundaries is still maintained.</span></p><p><span style="font-size: 14px;">It was demonstrated that the hypoid gearset with length and profile crowning in Figure 15 was developed based on a conjugate design. The first and third fundamental gearing laws, mentioned in this chapter, apply to the hypoid set in Figure 15 at the mean point roll position, if the load is zero. The first and third fundamental gearing laws will apply in the area of contact as the load increases and the Hertzian contact spreads in the contact line direction as well as in the path of contact direction. This ideal condition can only be achieved with correct amounts of crowning, adjusted to the operating displacements. It is interesting to mention that a hypoid gearset with crowning will fulfill the first and third fundamental gearing law even in the case of gearbox inaccuracies. Transmission Orientations Hypoid gearsets are used as final drive gears in cars and trucks. Hypoid gears are not used as simple reducers, but their purpose is to redirect rotation and torque by a certain angle, commonly 90°. In case of hypoids, the second purpose of lowering the center of gravity of a vehicle body has become very important in the automotive and truck industry. The redirection of rotation and torque has to be done at the driving axle of a vehicle. The engine orientation of vehicles with a rear wheel drive is longitudinal. Because engines of cars and trucks are commonly in the front, a longitudinally oriented propeller shaft transmits the engine rotation to the rear drive axle, as shown in Figure 17. The transmission, which is located between the engine and the propeller shaft, needs to have a gear shaft orientation identical to the direction of the engine crankshaft. The hypoid gearset redirects rotation and torque and provides the final reduction at the drive axle. The advantage of this concept is the lower torque in the complex shift or automatic transmission, and the high torque only at the ring gear at the drive axle.</span></p><p><br/></p>