Aiming at the situation where the conjugate relationship between spur gears and cylindrical gears is not satisfied, which limits their application in small transmission ratio scenarios, a small gear and its hobbing method conjugate with spur gears are proposed. Firstly, the tooth surface equations of the spur gear and its conjugate small gear were established, and the tooth surface deviation morphology of the conjugate small gear compared to the cylindrical gear was obtained; Subsequently, the tooth surface equation of Archimedes gear rolling cutter was derived, and a mathematical model of cylindrical gear was established based on the rolling motion coordinate system and meshing principle; On the basis of the motion of hobbing cylindrical gears, the cutting edge of the hob approaches the conjugate tooth surface by increasing the radial movement of the hob and the additional rotation of the workpiece. The additional motion is represented by a Taylor polynomial, and the additional numerical control motion polynomial coefficients are obtained by establishing a sensitivity matrix equation and iteratively solving the equation using singular value decomposition method. Finally, the numerical control machined tooth surface is obtained; To evaluate the transmission performance of spur gear pairs, a tooth surface bearing contact analysis was conducted and compared with traditional face gears – circular gears Comparison was made between column gear pairs. The research results indicate that under the same parameters, the load-bearing performance of the straight textured surface gear pair is basically the same as that of the traditional surface gear pair, and it can completely replace the transmission of the traditional surface gear pair; The verification of this method through numerical examples and simulation processing shows that the numerical example error does not exceed 1 μ m, and the simulation result error does not exceed 6 μ m, proving the feasibility and accuracy of this method.
Face gear transmission is a special form of bevel gear transmission, which relies on the meshing of cylindrical gears and face gears to transmit motion and power between two intersecting or staggered axes in a new type of gear mechanism. Due to its high degree of coincidence, compact structure, light weight, and free axial positioning, it has broad application prospects in aerospace, vehicles, ships, and other fields. Traditionally, the tooth surface of a face gear is regarded as a special spatially complex curved surface, and whether it is rough machining or precision machining, the process is mostly point contact. Grinding teeth for point contact machining limits the machining efficiency of face gears and is accompanied by disadvantages such as poor tool and machine tool versatility and high machining costs. A straight tooth surface for face gears was proposed, and the theoretical development process of the straight tooth surface of face gears and the machining method of straight edge cutting tools were studied. This method not only changes the machining of face gears from point contact to line contact, but also simplifies the tool structure, makes it easier to repair, and does not require a new machine tool structure, reducing manufacturing costs and making mass production of face gears possible. A study was conducted on the straight grain surface of the opposite gear, and a side milling method for the straight grain surface was proposed. The correctness of this machining method was proved through experiments. However, the above literature is all focused on the study of new tooth profiles for face gears and does not consider small gears that mesh with face gears. We studied the load-bearing contact performance of spur surface gears and spur cylindrical gears, and proved the feasibility of this combination. However, it is limited to applications under high transmission ratio conditions, such as helicopter gearboxes; In applications with small transmission ratios, such as fishing reels, instrument mechanisms, etc., the newly defined ruled surface has a larger tooth profile deviation than traditional face gears, which cannot meet the conjugate relationship with spur cylindrical gears. Therefore, the transmission of the two has many adverse effects on their meshing performance, transmission accuracy, and service life. In order to solve the problem of large tooth profile deviation caused by the straight tooth surface, this paper proposes a small gear conjugate with the straight tooth surface gear under small transmission ratio conditions and its processing method, replacing the traditional face gear cylindrical gear pair with a straight tooth surface gear pair.
The tooth surface deviation and CNC machining effect of cylindrical gears and conjugate small gears. The maximum tooth surface deviation between the cylindrical gear tooth surface and the conjugate tooth surface is 14.02 μ m, and the variation pattern of tooth surface deviation is basically the same as the analysis in the section; By applying additional motion, the maximum error between the CNC machined tooth surface and the conjugate theoretical tooth surface is only 0.65 μ m, and the polynomial coefficients of the motion axis are obtained. As shown in the table, even if the deviation of the conjugate tooth surface varies within a wide range, CNC machining of the tooth surface can still approximate the conjugate tooth surface well, and the theoretical error can be controlled within 1 μ m. This indicates the correctness of the hobbing method for conjugate tooth surface machining, and the use of singular value decomposition to solve the sensitivity matrix equation and obtain the increment of CNC polynomial coefficients is stable.
(1) On the basis of the aforementioned research, a small gear is conjugate from a spur gear, and its tooth surface is compared with that of a cylindrical gear. The deviation is mainly distributed at the tooth root, and the tooth surface deviation will increase with the increase of the transmission ratio Large and small.
(2) A corresponding rolling cutter model was established and a machining method for the conjugate small gear tooth surface was proposed. This method can better approximate the conjugate tooth surface by adjusting the additional movement of the rolling cutter and the additional rotation of the small gear.
(3) The contact analysis algorithm of tooth surface bearings has verified the feasibility of replacing traditional face gear pairs with straight tooth surface gear pairs under small transmission ratio conditions, further expanding the application scope of straight tooth surface gear pairs.