高速鉆床動(dòng)力學(xué)分析翻譯中英文-文庫(kù)吧資料
2024-08-31 17:19本頁(yè)面
【正文】 ems (US NSF Grant EEC9592125) at the University of Michigan and the valuable input fromthe Center’s industrial partners.中文翻譯高速鉆床的動(dòng)力學(xué)分析摘要通常情況下，術(shù)語(yǔ)“高速鉆床”就是指具有較高切削速率的鉆床。 is the maximum fluctuation of residual vibrations of the tool tip after the pointtopoint positioning. Set and start the calculation from c6=0. The optimization results in c6=10mm/s . Consequently, c5=10mm/s , c4 =10mm/s , c3=10mm/s , c2=c1=c0=0. It can be seen that the optimization calculation brought the design variable c6 to the boundary. If further loosing the limit for c6, the objective will continue reduce in value, but the maximum value of acceleration of the input motion will bee too big. The optimal input motions after the optimization are shown in Fig. 9. The corresponding residual vibration of the tool tip is shown in Fig. 10. It is seen from paring Fig. 8 and Fig. 10 that the amplitude and tool tip residual vibration was reduced by 30 times after optimization. Smaller residual vibration will be very useful for increasing the positioning accuracy. It should be mentioned that only link elasticity is included in above calculation. The residual vibration after optimization will still be very small if the pliance from other sources such as bearings and drive systems caused it 10 times higher than the result shown in Fig. 10.5. Input power reduction by adding spring elementsReducing the input power is one of many considerations in machine tool design. For the PKM we studied, two linear motors are the input units which drive the PKM module to perform drilling and positioning operations. One factor to be considered in selecting a linear motor is its maximum required power. The input power of the PKM module is determined by the input forces multiplying the input velocities of the two linear motors. Omitting the friction in the joints, the input forces are determined from balancing the drilling force and inertia forces of the links and the spindle unit. Adding an energy storage element such as a spring to the PKM may be possible to reduce the input power if the stiffness and the initial (free) length of the spring are selected properly. The reduction of the maximum input power results in smaller linear motors to drive the PKM module. This will in turn reduce the energy consumption and the size of the machine structure. A linear spring can be added in the middle of the two links as shown in Fig. 11(a). Or two torsional springs can be added at points B and C as shown in Fig. 11(b). The synthesis process is the same for the linear or torsional springs. We will take the linear spring as an example to illustrate the design process. The generalized force in Eq. (10) has the form ofwhere l0 and k are the initial length and the stiffness of the linear spring. The input power of the linear motors is determined byIn order to reduce the input power, we set the optimization objective as follows:where v is a vector of design variables including the length and the stiffness of the spring, . For the PKM module we studied, the mass properties are listed in Table 1. The initial values of the design variables are set as . The domains for design variables are set as [lmin。 here). The input motion of the linear motors with constant acceleration and deceleration is shown in Fig. 7, in which the maximum velocity is 1500 mm/s, the positioning time is s. Assuming the material damping ratio as , the residual vibration of the tool tip is shown in Fig. 8. In order to reduce the residual vibration and make the positioning motion smoother, a six order polynomial input motion function is built as Eq. (19)where the coeffcients ci are the design variables which have to be determined by minimizing the residual vibration of the tool tip. Selecting the boundary conditions as that when t=0, sin=0, vin=0, ain=0。 are the linear 1 2 3 4 5 6 and angular deformations of the node at the element local coordinate system. Detailed derivations can be found in [14]. Typically, a pliant mechanism is discretized into many elements as in finite element analysis. Each element is associated with a mass and a stiffness matrix. Each element has its own local coordinate system. We bine the element mass and stiffness matrices of all elements and perform coordinate transformations necessary to transform the element local coordinate systemto global coordinate system. This gives the systemmass [M] and stiffness [K] matrices. Capturing the damping characteristics in a pliant systemis not so straightforward. Even though, in many applications, damping may be small but its effect on the systemstability and dynamic response, especially in the resonance region, can be significant. The damping matrix [C] can be written as a linear bination of the mass and stiffness matrices [15] to form the proportional damping [C] which is expressed aswhere a and b are two positive coefficients which are usually determined by experiment. An alternate method [16] of representing the dam
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