In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of s...In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of spiral bevel and hypoid gears were investigated analytically. Firstly, a mathematical model of spiral bevel and hypoid gears with circular blade profile was established according to the cutting characteristics of the duplex helical method. Based on a hypoid gear drive, the tooth bearings and the functions of transmission errors of four design cases were analyzed respectively by the use of the tooth contact analysis(TCA), and the contact stresses of the four design cases were analyzed and compared using simulation software. Finally, the curvature radius of the circular profile blade was optimized. The results show that the contact stresses are availably reduced, and the areas of edge contact and severe contact stresses can be avoided by selecting appropriate circular blade profile. In addition, the convex and concave sides are separately modified by the use of different curvature radii of inside and outside blades, which can increase the flexibility of the duplex helical method.展开更多
In this work,synchronous cutting of concave and convex surfaces was achieved using the duplex helical method for the hypoid gear,and the problem of tooth surface error correction was studied.First,the mathematical mod...In this work,synchronous cutting of concave and convex surfaces was achieved using the duplex helical method for the hypoid gear,and the problem of tooth surface error correction was studied.First,the mathematical model of the hypoid gears machined by the duplex helical method was established.Second,the coordinates of discrete points on the tooth surface were obtained by measurement center,and the normal errors of the discrete points were calculated.Third,a tooth surface error correction model is established,and the tooth surface error was corrected using the Levenberg-Marquard algorithm with trust region strategy and least square method.Finally,grinding experiments were carried out on the machining parameters obtained by Levenberg-Marquard algorithm with trust region strategy,which had a better effect on tooth surface error correction than the least square method.After the tooth surface error is corrected,the maximum absolute error is reduced from 30.9μm before correction to 6.8μm,the root mean square of the concave error is reduced from 15.1 to 2.1μm,the root mean square of the convex error is reduced from 10.8 to 1.8μm,and the sum of squared errors of the concave and convex surfaces was reduced from 15471 to 358μm^(2).It is verified that the Levenberg-Marquard algorithm with trust region strategy has a good accuracy for the tooth surface error correction of hypoid gear machined by duplex helical method.展开更多
It is known that manufacture of hypoid gears is difficult and complicated,the reason lies on the limitation of traditional mechanical machine tools. With the development ofNC machine tools, there should be new ways of...It is known that manufacture of hypoid gears is difficult and complicated,the reason lies on the limitation of traditional mechanical machine tools. With the development ofNC machine tools, there should be new ways of cutting this kind of gear. Therefore, an idea togenerate gears with conjugating tooth surfaces is proposed, based on the 'flexibility'characteristic of NC that means various motions, in a sense, can be performed, arbitrarily on NCmachine tools. Using this method, the direction of the contact path on tooth surfaces can becontrolled, and also, theoretically, the generated tooth surfaces can transmit motion at specifictransmission ratio curve.展开更多
A virtual computerized numerical control C CNC） processing system is built for spiral bevel and hypoid gears. The pre-designed process of the solution to locate the way of realization is investigated. A kind of combi...A virtual computerized numerical control C CNC） processing system is built for spiral bevel and hypoid gears. The pre-designed process of the solution to locate the way of realization is investigated. A kind of combined programming method and principle of solid modeling are chosen. Multienvironmental programming thought and the inter-connected mechanisms between different environments are applied in the proposed system. The problems of data exchange and compatibility of modules are settled. Environment of the system is founded with object oriented programming thought. AutoCAD is located as the graphic environment. Matlab is used for editing the computation module. Virtual C ＋＋6.0 is the realization environment of the main module. Windows is the platform for realizing the multi-environmental method. Through establishing the virtual system based windows message handling mechanism and the component object model, the application of multienvironmental programming is realized in the manufacture system simulation. The virtual gear product can be achieved in the accomplished software.展开更多
The tooth surface shape of hypoid gear is very complicated, and tooth surface accuracy of hypoid gear can be measured by using the latticed measurement and scanning measurement. Advantages and disadvantages of the two...The tooth surface shape of hypoid gear is very complicated, and tooth surface accuracy of hypoid gear can be measured by using the latticed measurement and scanning measurement. Advantages and disadvantages of the two measurement patterns are compared and application of their measurement data on hypoid gear＇s quality management is analyzed. How to use these measurement data to simulate the dynamical performance of hypoid gear is researched, and the intelligent predicton of the dynamical performance indexes of contact spot, root stress, vibration exciting forces and load distribution and hertz contact stress on the tooth surface are carried out. This research work has an important guiding sense to design and ma- chine hypoid gear with low vibration and noise.展开更多
Improving vehicle transmission efficiency and reducing vehicle fuel consumption is currently one of the main objectives in the automotive field. Reducing gear churning power losses has significant influence on the dec...Improving vehicle transmission efficiency and reducing vehicle fuel consumption is currently one of the main objectives in the automotive field. Reducing gear churning power losses has significant influence on the decreasing vehicle fuel consumption. Based on the two phase flow theory, a 2D two-phase model of the simplified hypoid gear is established to predict the churning losses in different conditions, the VOF method is introduced to track the volume fraction of the free surface, a standard k-ε model is also built to calculate complex turbulence. The oil distributions at the different rotational speed, the different immersion depth and the different viscosity as well as the churning losses of the hypoid gear are obtained and discussed in detail. In general, the churning power losses increase with the increase of the speed, the immersion depth and the viscosity, while the rotational speed shows the greatest influence on the churning losses. It is hoped that this investigation will be helpful in automotive industry applications.展开更多
A digital model is presented for the purpose of design, manufacture and measurement of hypoid gear, based on the non-uniform rational B-spline surface （NURBS） method. The digital model and the function-oriented acti...A digital model is presented for the purpose of design, manufacture and measurement of hypoid gear, based on the non-uniform rational B-spline surface （NURBS） method. The digital model and the function-oriented active design technique are combined to form a new design method for hypoid gears. The method is well adaptable to CNC bevel gear cutting machines and CNC-controlled gear inspection machines, and can be used to create the initial machine tool cutting location data or program measurement path. The presented example verifies the method is correct.展开更多
Distinguishing with traditional tooth profile of spiral bevel and hypoid gear, it proposed a new tooth profile namely the spherical involute. Firstly, a new theory of forming the spherical involute tooth profile was p...Distinguishing with traditional tooth profile of spiral bevel and hypoid gear, it proposed a new tooth profile namely the spherical involute. Firstly, a new theory of forming the spherical involute tooth profile was proposed. Then, this theory was applied to complete parametric derivation of each part of its tooth profile. For enhancing the precision, the SWEEP method used for formation of each part of tooth surface and G1 stitching schema for obtaining a unified tooth surface are put forward and made the application in the accurate modeling. Lastly, owing to the higher accuracy of tooth surface of outputted model, it gave some optimization approaches. Given numerical example about the model can show that this designed gear with spherical involute tooth profile can achieve fast and accurate parametric modeling and provide a foundation for tooth contact analysis （TCA） in digitized design and manufacture.展开更多
A very useful new method of tooth contact finite element analysis(TCFEA) for spiralbevel and hypoid gears is presented, combines 3-d finite element contact stress analysis withLTCA (Loaded Tooth Contact Analysis). The...A very useful new method of tooth contact finite element analysis(TCFEA) for spiralbevel and hypoid gears is presented, combines 3-d finite element contact stress analysis withLTCA (Loaded Tooth Contact Analysis). The TCFEA uses mixed finite element method to ana-lyze the 3-d contact stress. The related formulas are derived and an efficient analyzing method asseveral pairs of teeth in contact occurs is presented, which greatly reduce the computationalamount. It is of great significance that the tooth stress. geometry. contact condition and load areall considered in the same model. Finally the related experimental results are used to verify thesolution of TCFEA .展开更多
To minimize quenching distortion and dispersion, carburizing and quenching process conditions must be optimized; this includes the parts racking design used for quenching. We investigated some factors affecting carbur...To minimize quenching distortion and dispersion, carburizing and quenching process conditions must be optimized; this includes the parts racking design used for quenching. We investigated some factors affecting carburized quenching distortion with an experiment using a hypoid gear having a shaft and with numerical simulation methods. The experimental results and those obtained from simulation were generally in agreement. Focusing on the surface temperature distribution in the gear, we studied quenching distortion characteristics in terms of changes in tooth profile and helix deviation. In our experiments, distortions occur during quenching in 373 K oil after austenitized temperature treatments conducted with various attitudes. We calculated the distortions by simulating the carburized oil-quenching process for the hypoid gear. Our results show large differences between the cooling rates of the tooth toe, middle section, and heel edges, and these greatly influence the change in tooth profile and helix deviation. We found that reducing the differences in temperatures on the gear surfaces during quenching is most important for minimizing the quench distortion of the hypoid gear.展开更多
基金Project(2011CB706800-G)supported by the National Basic Research Program of ChinaProject(51375159)supported by the National Natural Science Foundation of China+1 种基金Project(20120162110004)supported by the Postdoctoral Science Foundation of ChinaProject(2015JJ5020)supported by the Science Foundation of Hunan Province,China
文摘In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of spiral bevel and hypoid gears were investigated analytically. Firstly, a mathematical model of spiral bevel and hypoid gears with circular blade profile was established according to the cutting characteristics of the duplex helical method. Based on a hypoid gear drive, the tooth bearings and the functions of transmission errors of four design cases were analyzed respectively by the use of the tooth contact analysis(TCA), and the contact stresses of the four design cases were analyzed and compared using simulation software. Finally, the curvature radius of the circular profile blade was optimized. The results show that the contact stresses are availably reduced, and the areas of edge contact and severe contact stresses can be avoided by selecting appropriate circular blade profile. In addition, the convex and concave sides are separately modified by the use of different curvature radii of inside and outside blades, which can increase the flexibility of the duplex helical method.
基金Projects(52075552,51575533,51805555,11662004)supported by the National Natural Science Foundation of China。
文摘In this work,synchronous cutting of concave and convex surfaces was achieved using the duplex helical method for the hypoid gear,and the problem of tooth surface error correction was studied.First,the mathematical model of the hypoid gears machined by the duplex helical method was established.Second,the coordinates of discrete points on the tooth surface were obtained by measurement center,and the normal errors of the discrete points were calculated.Third,a tooth surface error correction model is established,and the tooth surface error was corrected using the Levenberg-Marquard algorithm with trust region strategy and least square method.Finally,grinding experiments were carried out on the machining parameters obtained by Levenberg-Marquard algorithm with trust region strategy,which had a better effect on tooth surface error correction than the least square method.After the tooth surface error is corrected,the maximum absolute error is reduced from 30.9μm before correction to 6.8μm,the root mean square of the concave error is reduced from 15.1 to 2.1μm,the root mean square of the convex error is reduced from 10.8 to 1.8μm,and the sum of squared errors of the concave and convex surfaces was reduced from 15471 to 358μm^(2).It is verified that the Levenberg-Marquard algorithm with trust region strategy has a good accuracy for the tooth surface error correction of hypoid gear machined by duplex helical method.
基金This project is supported by National Natural Science Foundation of China (No. 59775087).
文摘It is known that manufacture of hypoid gears is difficult and complicated,the reason lies on the limitation of traditional mechanical machine tools. With the development ofNC machine tools, there should be new ways of cutting this kind of gear. Therefore, an idea togenerate gears with conjugating tooth surfaces is proposed, based on the 'flexibility'characteristic of NC that means various motions, in a sense, can be performed, arbitrarily on NCmachine tools. Using this method, the direction of the contact path on tooth surfaces can becontrolled, and also, theoretically, the generated tooth surfaces can transmit motion at specifictransmission ratio curve.
基金Supported by Natural Science Foundation of China (No. 50475117).
文摘A virtual computerized numerical control C CNC） processing system is built for spiral bevel and hypoid gears. The pre-designed process of the solution to locate the way of realization is investigated. A kind of combined programming method and principle of solid modeling are chosen. Multienvironmental programming thought and the inter-connected mechanisms between different environments are applied in the proposed system. The problems of data exchange and compatibility of modules are settled. Environment of the system is founded with object oriented programming thought. AutoCAD is located as the graphic environment. Matlab is used for editing the computation module. Virtual C ＋＋6.0 is the realization environment of the main module. Windows is the platform for realizing the multi-environmental method. Through establishing the virtual system based windows message handling mechanism and the component object model, the application of multienvironmental programming is realized in the manufacture system simulation. The virtual gear product can be achieved in the accomplished software.
基金National Natural Science Foundation of China（No. 50976108）
文摘The tooth surface shape of hypoid gear is very complicated, and tooth surface accuracy of hypoid gear can be measured by using the latticed measurement and scanning measurement. Advantages and disadvantages of the two measurement patterns are compared and application of their measurement data on hypoid gear＇s quality management is analyzed. How to use these measurement data to simulate the dynamical performance of hypoid gear is researched, and the intelligent predicton of the dynamical performance indexes of contact spot, root stress, vibration exciting forces and load distribution and hertz contact stress on the tooth surface are carried out. This research work has an important guiding sense to design and ma- chine hypoid gear with low vibration and noise.
文摘Improving vehicle transmission efficiency and reducing vehicle fuel consumption is currently one of the main objectives in the automotive field. Reducing gear churning power losses has significant influence on the decreasing vehicle fuel consumption. Based on the two phase flow theory, a 2D two-phase model of the simplified hypoid gear is established to predict the churning losses in different conditions, the VOF method is introduced to track the volume fraction of the free surface, a standard k-ε model is also built to calculate complex turbulence. The oil distributions at the different rotational speed, the different immersion depth and the different viscosity as well as the churning losses of the hypoid gear are obtained and discussed in detail. In general, the churning power losses increase with the increase of the speed, the immersion depth and the viscosity, while the rotational speed shows the greatest influence on the churning losses. It is hoped that this investigation will be helpful in automotive industry applications.
基金This project is supported by National Natural Science Foundation of China (NO.59775009)
文摘A digital model is presented for the purpose of design, manufacture and measurement of hypoid gear, based on the non-uniform rational B-spline surface （NURBS） method. The digital model and the function-oriented active design technique are combined to form a new design method for hypoid gears. The method is well adaptable to CNC bevel gear cutting machines and CNC-controlled gear inspection machines, and can be used to create the initial machine tool cutting location data or program measurement path. The presented example verifies the method is correct.
文摘Distinguishing with traditional tooth profile of spiral bevel and hypoid gear, it proposed a new tooth profile namely the spherical involute. Firstly, a new theory of forming the spherical involute tooth profile was proposed. Then, this theory was applied to complete parametric derivation of each part of its tooth profile. For enhancing the precision, the SWEEP method used for formation of each part of tooth surface and G1 stitching schema for obtaining a unified tooth surface are put forward and made the application in the accurate modeling. Lastly, owing to the higher accuracy of tooth surface of outputted model, it gave some optimization approaches. Given numerical example about the model can show that this designed gear with spherical involute tooth profile can achieve fast and accurate parametric modeling and provide a foundation for tooth contact analysis （TCA） in digitized design and manufacture.
文摘A very useful new method of tooth contact finite element analysis(TCFEA) for spiralbevel and hypoid gears is presented, combines 3-d finite element contact stress analysis withLTCA (Loaded Tooth Contact Analysis). The TCFEA uses mixed finite element method to ana-lyze the 3-d contact stress. The related formulas are derived and an efficient analyzing method asseveral pairs of teeth in contact occurs is presented, which greatly reduce the computationalamount. It is of great significance that the tooth stress. geometry. contact condition and load areall considered in the same model. Finally the related experimental results are used to verify thesolution of TCFEA .
文摘To minimize quenching distortion and dispersion, carburizing and quenching process conditions must be optimized; this includes the parts racking design used for quenching. We investigated some factors affecting carburized quenching distortion with an experiment using a hypoid gear having a shaft and with numerical simulation methods. The experimental results and those obtained from simulation were generally in agreement. Focusing on the surface temperature distribution in the gear, we studied quenching distortion characteristics in terms of changes in tooth profile and helix deviation. In our experiments, distortions occur during quenching in 373 K oil after austenitized temperature treatments conducted with various attitudes. We calculated the distortions by simulating the carburized oil-quenching process for the hypoid gear. Our results show large differences between the cooling rates of the tooth toe, middle section, and heel edges, and these greatly influence the change in tooth profile and helix deviation. We found that reducing the differences in temperatures on the gear surfaces during quenching is most important for minimizing the quench distortion of the hypoid gear.
