【正文】 . The mean gaping obtained from both flanks is, to a large extent, independent of the helix angle and the distribution of the cone angle to both gears.　　The selection of the helical and cone angles only determines the distribution of the mean gaping to the left and right flanks. A skewed axis arrangement results in additional influence on the contact gaping. There is a significant reduction in the effective helix crowning on one flank. If the axis perpendicular is identical to the total of the base radii and the difference in the base helix angle is equivalent to the (projected) crossed axes angle, then the gaping decreases to zero and line contact appears. However, significant gaping remains on the opposite flank. If the axis perpendicular is further enlarged up to the point at which a cylindrical crossed helical gear pair is obtained, this results in equivalent minor helix crowning in the easeoff on both flanks. In addition to helix crowning, a notable profile twist (see Fig. 8) is also characteristic of the easeoff of helical beveloids. This profile twist grows significantly as the helix angle increases. shows how the profile twist on the example gear set from is ch。 the root contact path at the driver should be smaller than the tip contact path. Fig. 6 shows the distribution of the sliding velocity on the driver of a beveloid gear pair.4　CONTACT ANALYSIS AND MODIFYCATIONS　POINT CONTACT AND EASEOFFAt the uncorrected gearing, there is only one point in contact due to the tilting of the axes. The gaping that results along the potential contact line can be approximately described by helix crowning and flank line angle deviation. Crossed axes result in no difference between the gaps on the left and right flanks on spur gears. With helical gearing, the resulting gaping is almost equivalent when both beveloid gears show approximately the same cone angle. The difference between the gap values on the left and right flanks increases as the difference between the cone angles increases and as the helix angle increases. This process results in larger gap values on the flank with the smaller working pressure angle. shows the resulting gaping (easeoff) for a beveloid gear pair with crossed axes and beveloid gears with an identical cone angle. shows the differences in the gaping that results for the left and right flanks for the same crossed axes angle of 10176。.　MICRO GEOMETRYThe pairing of two conical gears generally leads to a pointshaped tooth contact. Outside this contact, there is gaping between the tooth flanks , Fig. 7. The goal of the gearing correction design is to reduce this gaping in order to create a flat and uniform contact. An exact calculation of the tooth flank is possible with the stepbystep application of the gearing law /5/, Fig. 4. To that end , a point (P) with the radiusrP1and normal vectorn1is generated on the original flank. This generates the speed vector V with (4)For the point created on the mating flank, the radial vector rp: (5)and the speed vector apply (6)The angular velocities are generated from the gear ratio: (7)The angle γ is iterated until the gearing law in the form (8)is fulfilled. The meshing point Pa found is then rotated through the angle (9)around the gear axis, and this results in the conjugate flank point P.3　GEARING DESIGN　UNDERCUT AND TIP FORMATIONThe usable face width on the beveloid gearing is limited by tip formation on the heel and undercut on the toe as shown in Fig. 3. The greater the selected tooth height (in order to obtain a larger addendum modification), the smaller the theoretically useable face width is. Undercut on the toe and tip formation on the heel result from changing the addendum modification along the face width. The maximum usable face width is achieved when the cone angle on both gears of the pairing is selected to be approximately the same size. With pairs having a significantly smaller pinion, a smaller cone angle must be used on this pinion. Tip formation on the heel is less critical if the tip cone angle is smaller than the root cone angle, which often provides good use of the available involute on the toe and for sufficient tip clearance in the heel.　FIELD OF ACTION AND SLIDING VELOCITYThe field of action for the beveloid gearing is distorted by the radial conicity with a tendency towards the shape of a parallelogram. In addition, the field of action is twisted due to the working pressure angle change across the face width. Fig. 5 shows an example of this. There is a roll axis on the beveloid gearing with crossed axes。 Automatic car transmissions for AWD /4/, Fig. 22　GEAR GEOMETRY　MACRO GEOMETRYTo put it simply, a beveloid is a spur gear with continuously changing addendum modification across the face width, as shown in Fig. 3. To acplish this, the tool is tilted towards the gear axis by the root cone angle ? /1/. This results in the basic gear dimensions:Helix angle, right/lefttanβ=tanβ) for robots /2/ 174。 Steering transmissions /1/174。Table 1.Conical gears are spur or helical gears with variable addendum correction (tooth thickness)across the face width. They can mesh with all gears made with a tool with the same basic rack. The geometry of beveloids is generally known, but they have so far rarely been used in power transmissions. Neither the load capacity nor the noise behavior of beveloids has been examined to any great extent in the past. Standards (such as ISO 6336 for cylindrical gears ), calculation methods, and strength values are not available. Therefore, it was necessary to develop the calculation method, obtain the load capacity values, and calculate specifications for production and quality assurance. In the last 15 years, ZF has developed various applications with conical gears: 174。. These boundary conditions require a deep understanding of the design, manuf