The current researches on the tooth surface mathematical equations and the theory of gearing mainly pay attention to the ordinary type worm gear set（e.g., ZN, ZA, or ZK）. The research of forming mechanism and three-...The current researches on the tooth surface mathematical equations and the theory of gearing mainly pay attention to the ordinary type worm gear set（e.g., ZN, ZA, or ZK）. The research of forming mechanism and three-dimensional modeling method for the double pitch worm gear set is not enough. So there are some difficulties in mathematical model deducing and geometry modeling of double pitch ZN-type worm gear set based on generation mechanism. In order to establish the mathematical model and the precise geometric model of double pitch ZN-type worm gear set, the structural characteristics and generation mechanism of the double pitch ZN-type worm gear set are investigated. Mathematical model of the ZN-type worm gear set is derived based on its generation mechanism and the theory of gearing. According to the mathematical model of the worm gear set which has been developed, a geometry modeling method of the double pitch ZN-type worm and worm gear is presented. Furthermore, a geometrical precision calculate method is proposed to evaluate the geometrical quality of the double pitch worm gear set. As a result, the maximum error is less than 6′10–4 mm in magnitude, thus the model of the double pitch ZN-type worm gear set is available to meet the requirements of finite element analysis and engineering application. The derived mathematical model and the proposed geometrical modeling method are helpful to guiding the design, manufacture and contact analysis of the worm gear set.展开更多
The KAM theory can be used properly to describe the motion of the double pendulum if the gravity is treated as a perturbation. The existence of the KAM invariant closed curves represents that some characters of the “...The KAM theory can be used properly to describe the motion of the double pendulum if the gravity is treated as a perturbation. The existence of the KAM invariant closed curves represents that some characters of the “total generalized momentum” conservation of the gravity free system can be kept when the gravity is small in comparison with the total enery.展开更多
基金Supported by Major National Basic Research Program of China(973Program,Grant No.2011CB013400-05)PhD Programs Foundation of Ministry of Education of China(Grant No.20110191110005)
文摘The current researches on the tooth surface mathematical equations and the theory of gearing mainly pay attention to the ordinary type worm gear set（e.g., ZN, ZA, or ZK）. The research of forming mechanism and three-dimensional modeling method for the double pitch worm gear set is not enough. So there are some difficulties in mathematical model deducing and geometry modeling of double pitch ZN-type worm gear set based on generation mechanism. In order to establish the mathematical model and the precise geometric model of double pitch ZN-type worm gear set, the structural characteristics and generation mechanism of the double pitch ZN-type worm gear set are investigated. Mathematical model of the ZN-type worm gear set is derived based on its generation mechanism and the theory of gearing. According to the mathematical model of the worm gear set which has been developed, a geometry modeling method of the double pitch ZN-type worm and worm gear is presented. Furthermore, a geometrical precision calculate method is proposed to evaluate the geometrical quality of the double pitch worm gear set. As a result, the maximum error is less than 6′10–4 mm in magnitude, thus the model of the double pitch ZN-type worm gear set is available to meet the requirements of finite element analysis and engineering application. The derived mathematical model and the proposed geometrical modeling method are helpful to guiding the design, manufacture and contact analysis of the worm gear set.
基金The Natural Science Foundation of the Education Department of Henan Province (2009A1100032010A110005)+1 种基金the International Science and Technology Cooperation Project of Henan Provincethe Foundation of Henan University of Technology
文摘The KAM theory can be used properly to describe the motion of the double pendulum if the gravity is treated as a perturbation. The existence of the KAM invariant closed curves represents that some characters of the “total generalized momentum” conservation of the gravity free system can be kept when the gravity is small in comparison with the total enery.
