【正文】 lement method (FEM) model. So the virtual prototype built based on VPT can simulate most of the pump performances, and the simulation results of the virtual prototype are very close to the test results of the physics prototype. Sometimes the simulation can even replace physics test and save the development cost[1]. Hydraulic virtual prototype technology integrate the advanced 3D CAD modeling method and hydraulic simulation technology to predict performance and study characteristics of a machine[1]. Because of the plicated structure and nonlinear characteristics of the hydraulicsolid coupling, it is timeconsuming and expensive with traditional tryanderror design way, and the analysis results of traditional way are not accurate enough[2]. The virtual prototype of hydraulic machine, such as the axial piston pump, is a better way to predict the performance of hydraulic ponent[3]. With the mercial hydraulic and dynamic softwares, a virtual prototype of piston pump was made by Aachen Technique University, Germany, in 2002[4]. The hydraulic characteristics and frictions between the key tribopairs were analyzed[5?6]. In order to optimize the incline angle of the swash plate, a virtual prototype of a bent axis piston pump was made in 2003[7]. The concept of virtual prototype of piston pump was proposed in 2004, the output pressure and flow ripple, the strain and stress of the key parts were all analyzed[8]. It is very useful for the optimization of pump. The flow ripple of a swash plate piston pump was studied using VPT in 2006[9]. All these researches proved the effectivity of this technology, but these models are still simple and need further improving.In this research, a virtual prototype of axial piston pump is developed, which bines 3D model, flexible FEM model and hydraulic modeling together. The performance of the pump is analyzed, and the optimization of the index angle of swash plate by VPT shows the potential of improving products.2 Modeling of the Piston PumpThe validity of the simulation results lay on the rationality of its model, so the modeling of piston pump is crucial. The virtual prototype of piston pump connects several different models, including hydraulic system, 3D structural model and FEM parts model, which are built respectively and connected each other in simulation. Analysis of dynamic relationshipsBefore building the dynamic model and making the interfaces to connect other models, the real kinetic relationships and motion parameters of the necessary parts should be analyzed. There are several hypotheses as follows.(1) In order to simply the simulation, only necessary parts are considered. Some accessories models, such as mechanism of variable displacement and slipper holddown, are ignored.(2) The rotation of middle shaft is stable and the speed is defined as constant.(3) The angle of swash plate changes in a defined work range by rotation drive.(4) The oil film between piston and cylinder, swash plate and slipper, cylinder and valve plate is stable, and its friction coefficient is constant.As shown in Fig. 1, the middle shaft of swash plate type piston pump rotates around its axis and drives the cylinder, pistons and correspond slippers rotating at a same speed[10?11].The coordinates of point B′ of intersection between the center line of piston and the surface of swash plate is described as follows: (1)From Eq. (1), it is shown that piston moves along zaxis and rotates around the middle shaft. The track of point B can describe the motion of the piston. Based on Eq. (1), the speed and accelerate of point B′ are as follows: (2)The slipper is connected with piston by spherical joint. The track of point B in the spherical joint can describe the motion of slipper. The coordinates of the point B are (3)The motion track of the slipper is ellipse, the vector diameter ρ is (4)The angle θ between ρ and the Langaxis of ellipse is (5)The rotation speed of the point B around the point O is (6)The velocity of the point B is (7)Based on the equations above, the motion of basic parts can be defined. Structural and dynamic modelAs for swash plate type piston pump, showed in Fig. 2(a), the 3D structural model (Fig. 2(b)) was made in a erical CAD software. To simplify the analysis, only necessary parts model were made. The joints and constraints between connecting parts were added. According to the real dynamic relationship between different parts, the proper joints and motion parameters are shown in Table 1 and Table 2. In the dynamic software, all these joints and motions were added to corresponding parts.