A dynamic model of a helical gear rotor system is proposed.Firstly,a generally distributed dynamic model of a helical gear pair with tooth profile errors is developed.The gear mesh is represented by a pair of cylinder...A dynamic model of a helical gear rotor system is proposed.Firstly,a generally distributed dynamic model of a helical gear pair with tooth profile errors is developed.The gear mesh is represented by a pair of cylinders connected by a series of springs and the stiffness of each spring is equal to the effective mesh stiffness.Combining the gear dynamic model with the rotor-bearing system model,the gear-rotor-bearing dynamic model is developed.Then three cases are presented to analyze the dynamic responses of gear systems.The results reveal that the gear dynamic model is effective and advanced for general gear systems,narrow-faced gear,wide-faced gear and gear with tooth profile errors.Finally,the responses of an example helical gear system are also studied to demonstrate the influence of the lead crown reliefs and misalignments.The results show that both of the lead crown relief and misalignment soften the gear mesh stiffness and the responses of the gear system increase with the increasing lead crown reliefs and misalignments.展开更多
Continuously variable transmission(CVT)of noncircular gear has the technical advantages of large bearing capacity and high transmission efficiency.The key technology of CVT with noncircular gear has been broken throug...Continuously variable transmission(CVT)of noncircular gear has the technical advantages of large bearing capacity and high transmission efficiency.The key technology of CVT with noncircular gear has been broken through some countries,and is in the stage of deep application research.Although the characteristics and design methods of noncircular gear pairs have been continuously studied in China,the noncircular gear CVT is still in the preliminary exploration and research stage.The linear functional noncircular gear pair,whose transmission ratio is a linear function in the working section,to realize continuously variable transmission was the research object in this paper.According to the required transmission ratio in the working section,the transmission ratio function in the non-working section was constructed by using a polynomial.And then the influence of pitch curve parameters in the working section on which in the non-working section was also analyzed to obtain the pitch curve suitable for transmission of this gear pair.In addition,for improving the stability and bearing capacity of gear transmission,the noncircular gear pair transmission with high contact ratio was designed.Furthermore,the accurate value of the contact tooth length was calculated based on the gear principle and the characteristics of the involute tooth profile,from this the contact tooth length error was calculated by comparing the accurate value with its actual value obtained by the rolling experiment.Finally,an indirect method to verify the contact ratio by detecting the contact length error of the tooth profile was proposed.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
When the noncircular gear pair is applied to the continuously variable transmission （CVT） with gear, the transmission ratio function is discontinuous. In accordance with this unique characteristic, a new approach to...When the noncircular gear pair is applied to the continuously variable transmission （CVT） with gear, the transmission ratio function is discontinuous. In accordance with this unique characteristic, a new approach to design and analyze noncircular gears with discontinuous pitch curve is proposed. The design courses of various noncircular gear pairs with discontinuous pitch curve are unified based on the numerical algorithm of spline fitting and ＂fairing boundary condition＂. According to the particularity of discontinuous pitch curve, the rules and procedures for teeth distribution are recommended. It is explained in detail why the undercut is formed and how to manage the undercut based on meshing principle.In addition, the calculation formulas for each tooth profile segment are also derived. If the tooth profile data are calculated, the measurement and the incision process for noncircular gear can be conducted and the CAD simulation can be achieved easily. To ensure the continuity of the transmission, the transmission interference of the tooth which is located at the pitch curve joint point is managed by utilizing Bezier curve with CAD software. And the contact ratio of gear pair is obtained. The case study shows that this approach is successful and opens up a new way for the design of noncircular gear.展开更多
基金Projects(51605361,51505357) supported by the National Natural Science Foundation of ChinaProjects(XJS16041,JB160411) supported by the Fundamental Research Funds for the Central Universities,China
文摘A dynamic model of a helical gear rotor system is proposed.Firstly,a generally distributed dynamic model of a helical gear pair with tooth profile errors is developed.The gear mesh is represented by a pair of cylinders connected by a series of springs and the stiffness of each spring is equal to the effective mesh stiffness.Combining the gear dynamic model with the rotor-bearing system model,the gear-rotor-bearing dynamic model is developed.Then three cases are presented to analyze the dynamic responses of gear systems.The results reveal that the gear dynamic model is effective and advanced for general gear systems,narrow-faced gear,wide-faced gear and gear with tooth profile errors.Finally,the responses of an example helical gear system are also studied to demonstrate the influence of the lead crown reliefs and misalignments.The results show that both of the lead crown relief and misalignment soften the gear mesh stiffness and the responses of the gear system increase with the increasing lead crown reliefs and misalignments.
基金Supported by National Natural Science Foundation of China(Grant No.51675060)Equipment Pre-Research Project(Grant No.3010519404)+2 种基金Chongqing University Graduate Student Research Innovation Project(Grant No.CYB19011)National Natural Science Foundation of China(Grant No.U1864210)Scientific Research Foundation of Binzhou University(Grant No.2022Y2).
文摘Continuously variable transmission(CVT)of noncircular gear has the technical advantages of large bearing capacity and high transmission efficiency.The key technology of CVT with noncircular gear has been broken through some countries,and is in the stage of deep application research.Although the characteristics and design methods of noncircular gear pairs have been continuously studied in China,the noncircular gear CVT is still in the preliminary exploration and research stage.The linear functional noncircular gear pair,whose transmission ratio is a linear function in the working section,to realize continuously variable transmission was the research object in this paper.According to the required transmission ratio in the working section,the transmission ratio function in the non-working section was constructed by using a polynomial.And then the influence of pitch curve parameters in the working section on which in the non-working section was also analyzed to obtain the pitch curve suitable for transmission of this gear pair.In addition,for improving the stability and bearing capacity of gear transmission,the noncircular gear pair transmission with high contact ratio was designed.Furthermore,the accurate value of the contact tooth length was calculated based on the gear principle and the characteristics of the involute tooth profile,from this the contact tooth length error was calculated by comparing the accurate value with its actual value obtained by the rolling experiment.Finally,an indirect method to verify the contact ratio by detecting the contact length error of the tooth profile was proposed.
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When the noncircular gear pair is applied to the continuously variable transmission （CVT） with gear, the transmission ratio function is discontinuous. In accordance with this unique characteristic, a new approach to design and analyze noncircular gears with discontinuous pitch curve is proposed. The design courses of various noncircular gear pairs with discontinuous pitch curve are unified based on the numerical algorithm of spline fitting and ＂fairing boundary condition＂. According to the particularity of discontinuous pitch curve, the rules and procedures for teeth distribution are recommended. It is explained in detail why the undercut is formed and how to manage the undercut based on meshing principle.In addition, the calculation formulas for each tooth profile segment are also derived. If the tooth profile data are calculated, the measurement and the incision process for noncircular gear can be conducted and the CAD simulation can be achieved easily. To ensure the continuity of the transmission, the transmission interference of the tooth which is located at the pitch curve joint point is managed by utilizing Bezier curve with CAD software. And the contact ratio of gear pair is obtained. The case study shows that this approach is successful and opens up a new way for the design of noncircular gear.
