In order to verify the validity of the design for the orthogonal variable transmission ratio face gear pair, a five-axis CNC machine tool was used to machine this gear. The cutter tooth profile coordinate system, orthogonal variable ratio face gear machining coordinates, the model for the round-corner at tooth tip, the contact line model and CNC machining models were established by using space gear meshing theory and the machining principle of five-axis CNC machine tools. The method of machining this gear along the contact line has been obtained through the combination of the envelope method and milling principle. Cutter tooth profile equations, coordinate transformation matrices between the non-circular gear tooth surface and orthogonal variable transmission ratio gear tooth surface, transition surface equations and five-axis motion equations were derived. The rolling experiment and tooth surface measurement experiment were conducted on the gear, which was processed by a five-axis CNC machine. The results show that the tooth surface accuracy of the orthogonal variable transmission ratio face gear is high. The design of the orthogonal variable transmission ratio face gear, and its processing method using a five-axis NC machine have been verified.Key words : Face gear, CNC machining, Variable transmission ratio, Design, Drive IntroductionOrthogonal variable transmission ratio face gear drive is a gear drive where a non-circular gear and an orthogonal variable ratio face gear are engaged with a 90 degrees' intersecting axis. The orthogonal variable transmission ratio face gear combines the features of non-cylindrical gear and bevel gear and it allows variable transmission ratio between intersecting axis. The driving wheel is an on-cylindrical gear, and the driven one is a face gear. The gear pair can realize given variable transmission ratio. The Orthogonal variable transmission ratio face gear pair is shown in Figure1. In this research report, OVTR face gear is stand for orthogonal variable transmission ratio face gear. Fig. 1 OVTR face gear pairIn face gear drive, a cylindrical gear is engaged with a bevel gear (Litvin, et al., 1992). In 1940's, Buckingham introduced face gear in his book. Today, the face gear transmission structure is mainly used in the shunt transmission structure of the helicopter's main gear transmission system (George, 2002). Its narrow range of applications is attributed to reasons such as complexity of design, poor precision and difficulties in teeth grinding. the development and application of the face gear transmission.DARPA in the U.S. investigated the face gear transmission technique in TRP project, with the aim to apply this technique to the new generation Apache helicopter gunship. The study included the manufacturing and experiment of carburized face gear. Saga University in Japan used a large helical hob with less gear to machine face gear (Ohshima, et al., 2009). U.S. Processing and Treatment Center improved the hob and made it possible to process small face gears and imp...

As a new type of face gear, curve-face gear combines the common characteristics of non-cylindrical gear, bevel gear, and face gear [1]. It can be used in engineering machinery, agricultural machinery, textile machinery and high-powered spacecraft, etc.[2], and will be developed towards high speeds and heavy loads [3]. Therefore, the research on the dynamic characteristics of curve-face gear has increasingly become prominent.The research of the nonlinear vibration characteristics of gears mainly focuses on the bevel gear, spur gear, face gear and planetary gear drive; the analytical approach of the system generally uses finite element method (FEM), and the Runge-Kutta method is applied to solve the differential equations of the system. For the simulation and vibration-based condition monitoring of a geared system, a system with an appropriate number of degrees of freedom (DOFs) was modelled [4]. An investigation of the performance of statistical fault detection indicators for three different series of crack propagation scenarios was presented [5]. From the vibration signal, the numbers of teeth on all gears, the calculation of tooth mesh frequencies and rotational speeds of all shafts were determined [6]. The dynamic behaviour of a single-stage spur gear reducer in a transient regime was studied [7]. However, for the rotary system with mass eccentricity, the Lagrange equation with generalized coordinates expression is over FEM, as it only relates to the kinetic energy and the potential energy of the system. Therefore, for the mechanical system composed of particles and rigid bodies, the system equation can be obtained quickly by using the Lagrange equation. However, due to the differential calculation of Lagrange function L, its simulation process is complex. To overcome the disadvantage of this modelling method, a new modelling method combined Lagrange equation and bond-graph is proposed. When the generalized coordinates, the parameter equation, the force input, and the velocity conversion matrix are determined, the mathematical simulation of the system can be obtained. Compared with the classical method, the modelling process of the Lagrange bond-graph is more regular, and the solving process is more efficient [8].Recently, few studies were available for the curve-face gear drive. Due to the time-varying characteristics of non-circular gears, the vibration response of this type of gear is much complex than that of normal gears. For general gears, the excitations of the vibration response are mainly time-varying mesh stiffness, tooth transmission error, and meshing impact, etc. The dynamic model of a spur gear pair, considering the backlash, time-varying stiffness, Dynamic Model and Analysis of Nonlinear VibrationCharacteristic of a Curve-Face Gear Drive

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The compound transmission mechanism of curve-face gear is a new type of gear transmission based on the cam mechanism and the curve-face gear pair. It combines the transmission characteristics of the cam mechanism and noncircular bevel gear. When the compound transmission mechanism of curve-face gear is engaged in the meshing transmission, the rotating center of the cylindrical gear is fixed and used as the driving wheel, and the curve-face gear can generate the helical motion around the axis. In this paper, the meshing characteristics and motion laws of the compound transmission mechanism of the curve-face gear are studied based on the theory of screw. Based on the meshing theory of gears, the coordinate system of conjugate surfaces is established, the basic meshing theory and equation are obtained. On this basis, combined with the principle of the cam, the transmission principle is analyzed by the screw theory. The tooth surface equation of the compound transmission mechanism of curve-face gear is deduced based on the meshing theory and the related knowledge of geometry. The motion law of the curve-face gear and the change of the motion law with the change of the basic parameters of the gear pair with different design parameters are calculated and analyzed. An experimental platform is built to verify the law of motion, and the experimental results are compared with the theoretical values. The correctness of the theoretical analysis is verified, which provides a new way for the research of the compound transmission mechanism of the curve-face gear.

Curve-face gear drive is a new type of variable transmission ratio gear pair between the intersecting axes based on the face gear pair. And tooth width is one of the main geometrical factors of curve-face gear which affects the intensity of tooth root. This article uses the method of boundary function and geometric approximate evaluation to investigate the undercutting and pointing conditions of curve-face gear considering the tooth profile difference. The equations of tooth profile distribution angle and engagement angle are derived using the coordinate transformation theory. On this basis, the equations of the theoretic undercutting and pointing conditions are deduced, and the undercutting inner diameter and pointing outer diameter of the tooth profile are simulated using mathematical software. Then, the corresponding phenomenon of undercutting and pointing of curve-face gear are analyzed. In the end, the feasibility of the theoretical calculation is received by the experiment of curve-face gear.

The curve-face gear pair is a new type of face gear pair with a variable transmission ratio. Concerning the complexity of its tooth surface, based on the coordinate transformation principle and the spatial meshing theory, a discrete algorithm of this tooth surface was proposed. The determination rule of the limiting points on the tooth surface was analyzed by introducing the generating method and tooth surface characteristics of this gear tooth. Through the corresponding limiting angles and the distribution law of the contact line, the gear tooth surface was discretized, and the theoretical data points of the tooth surface were obtained. The variations in gear tooth surface in a meshing cycle and under different parameters were analyzed. By comparing the virtual tooth model and the corresponding rolling experiment, the correctness of the tooth surface discrete algorithm of the curve-face gear was verified.