تجزیه و تحلیل عملکرد از چرخ دنده قوسی تولید شده بر اساس اندازه گیری داده های فرم سمت دندان

A method for predicting and analyzing the tooth contact pattern, vibration, and strength of a generated hypoid gear is needed to achieve a low-noise design and adequate quality control. However, it is not easy to analyze the performance of a generated hypoid gear because the tooth flank form is complicated and has a significant influence on the overall performance. In order to solve this problem, in this research, a method for analyzing one of the gear dynamics excitations and contact condition of a generated hypoid gear that considers the measured tooth flank form is proposed. The contact pattern and transmission error are measured experimentally and are compared with the analysis results. It is confirmed that the result from the proposed analysis method agrees with the experimental result.

Hypoid gears have advantages over spiral bevel gears due to their strength and smooth rotation, and thus, they are widely used in rear-wheel drive and four-wheel drive vehicles. Recently, engine and road noise in vehicles has been improved, and therefore, better noise and vibration quality are demanded for hypoid gears. Moreover, the load carrying capability must be increased in order to transmit higher torques. To meet these requirements, performance analysis technology is necessary. For hypoid gears, a lot of research has been conducted on theoretical tooth geometry [1], [2], [3], [4] and [5]. Since CNC-controlled bevel and hypoid gear cutting machines and grinding machines were developed, much research related to CNC control has been conducted [6], [7], [8] and [9]. As for the analysis of real tooth flank form, Kin [10] studied spur gear adding the measured data to theoretical involute surface and interpolating them. And Zhang et al. [11] made unloaded tooth contact analysis of non-generated hypoid gear based on the measured tooth flank form data by CMM using similar approach with Kin. Most of it deals with the final drives of non-generated face mill hypoid gears for automobiles, of which the manufacturing method is rather simple. On the other hand, recently, cases that require a generated hypoid gear wheel instead of a non-generated one have increased. For example, these days, multipurpose four-wheel drive vehicles are very popular. In the case of a four-wheel drive system based on a front-wheel drive vehicle, a hypoid gear with a low ratio is used in the transfer gearbox. And in many applications the gear ratio becomes less than 2.5, and in that case, it is difficult to use non-generated cutting such as Formate® or Helixform® on such wheels. In that case, a generated hypoid gear must be used. In generated hypoid gears, the wheel tooth flank form becomes very complicated, and not much research has been reported on them. There is a report [12], in which the influence of misalignment to path of contact, minimal separation along the potential contact line and tooth contact pressure distribution are studied on generated spiral bevel gear with mismatched surface. But these studies are for the theoretical pinion surface and not using the actual tooth flank form. And tooth contact pattern and transmission error are not studied. Therefore, in this research, a method for analyzing the gear dynamics excitation and contacting condition of a generated face mill hypoid gear is developed. During manufacturing of a generated hypoid gear, a lapping process is used after gear tooth cutting and heat treatment. If gear tooth grinding is used, lapping is typically performed afterward. The gear dynamics excitation of a hypoid gear is largely affected by any small waviness of the tooth surface. For that reason, to accurately analyze the dynamic performance of a hypoid gear, detailed information on the tooth flank form must be considered. In the case where lapping is used, the tooth flank form of the hypoid gear after lapping becomes different from that after gear tooth cutting based on gear tooth cutting theory. Therefore, it is difficult to accurately analyze an actual gear set using tooth cutting theory. Also, analysis of the tooth flank form after heat treatment and lapping is required. There are few studies of analysis of hypoid gear using measured tooth flank form [11] and [13]. In the study [11], pinion tooth form measurement is made on machine setting base, but it is not suitable to analyze the tooth flank form after heat treatment or lapping accurately. And those studies use tooth flank form measurement data of 5 × 9 grid points, but they are not sufficient to get detailed information of the tooth flank form after heat treatment or lapping. The authors have presented an analysis method for the generated face mill hypoid gear tooth geometry based on conjugate tooth flank theory and developed a tooth flank scanning measurement method in the previous report [14]. This was then used to obtain detailed information on the tooth flank form of a generated face mill hypoid gear. In this research, a performance analysis method for a generated face mill hypoid gear that utilizes tooth flank form data obtained from the scanning measurement and takes the small waviness of the tooth flank form into account is developed. By comparing the result of the analysis with that of the experiment, the effectiveness of the proposed method is confirmed.

For generated hypoid gears, improvements in noise and vibration quality and strength are required. To achieve this, a method of performance analysis that considers the tooth contact condition under load is necessary, especially for generated hypoid gears, where small waviness affects their performance and must be considered in the analysis. In this research, a performance analysis program for generated hypoid gears that is capable of utilizing the measured tooth flank form data was developed. The analysis method for the generated tooth flank form of the generated hypoid gear and the calculation method for its deformation under load were presented, and a tooth contact simulation program was created. The actual tooth contact patterns were measured by experiment and were compared with the simulated results; it was confirmed that they had good agreement with each other. It was also confirmed that the measured and simulated tooth contact patterns agree with each other even with alignment error in the offset and pinion axis directions. The transmission error of the generated hypoid gear was also measured by experiment and was compared with the simulated results, and it was confirmed that they had good agreement with each other for the 1st and 2nd order transmission errors of the tooth mesh frequency. From these results, it was confirmed that the developed performance analysis method for a generated hypoid gear is capable of accurate analysis.