资源描述
附录A 英文原文A mechanical structure-based design method and its implementation on a fly-cutting machine tool designYingchun Liang & Wanqun Chen & Yazhou Sun &Xichun Luo & Lihua Lu & Haitao LiuAbstract：The mechanical structure has a main influence of the machining performance and the servo performance. In this study, a mechanical structure-based design method is presented to design and optimize an ultra-precision fly-cutting machine tool. This method takes full account of the influence of mechanical components on the machining performance and servo performance at the design stage. The effect of the components structure on the roughness of machined surface is discussed, and an optimized structural form of the aerostatic spindle is given. The influence of the mechanical structure on the control system and electronic drives is discussed, and an integrated dynamic design model is built and used to optimize the hydrostatic slide. Furthermore, the impact of mechanical system dynamic performance of the machine tool on the processing topography is analyzed by the finite element model of the machine tool. This method provides a theoretical basis for the design and optimization of mechanical components and machine tools stiffness loop.Keywords：Mechanical structure；Design method；Integrated design；Machine dynamicsIntroduction：Increasing demands for optical devices in modern industries, such as digital cameras, high-energy solid-state lasers, and extra-large telescopes, has made it necessary to develop precision machine tool for optical parts machining 14. The machine tool development mainly contains the mechanical components design, the electronic drives system selection, and control system design 5, 6. The mechanical components design are always mainly from the mechanical point of view, the components are designed very robust to overcome the deformation. However, little attention has been paid to the influence of mechanical components structure on the machining performance. Furthermore, traditional methods for mechatronics design are often based on a sequential approach, where the mechanical structure is designed first, and then fitted with off-the-shelf electric motors, drive electronics, and sensors. Finally, a control system is designed and optimized for the already existing mechanical system 7, 8. Such a design method, that does not consider aspects from a control point of view during the design of the mechanical system, is unlikely to result in a system with optimal control performance. Moreover, to separately design and optimize each of the mechanical components will generally not result in a system that is optimal from a weight, dynamic response, or cost perspective. In addition, the dynamic loop stiffness of mechanical system is always designed as high as possible to improve the results of the machined surface, sometimes it helps and other times it makes things worse. If the designers choose the dynamic loop stiffness at random, or at least without considering its effect on the processing topography, it will lead a bad machining result, especially to the large optical parts machining.In this paper, a mechanical structure-based design method is proposed as shown in Fig. 1. At the design stage, the influence of mechanical components structure on the machining performance is fully considered, which helps the designer to choose the design parameters. To reach the optimal design of an integrated mechatronic system, the mechanical system, the control system, and electronic drives system are treated as a whole, considering aspects from all involved engineering domains concurrently, and therefore enables global optimization.Fig. 1 The outline of the mechanical structure-based design methodAt last, the mechanical system dynamic performance of the machine tool on the processing topography is analyzed from the finite element model of the machine tool. The proposed design method is implemented on a fly-cutting machining tool design. 2 Implementation of the mechanical structure based design method on a fly-cutting machine tool 2.1 Structural design of spindle considering its influence on the surface topography Spindle is the key element of the ultra-precision machine tool. Many effects have been paid to the influence of its static and dynamic performance on the machining results 9, 10. However, little attention has been focuses on the influence of the designed spindle structure on the surface topography of the workpiece. An et al. 11 pointed out that there was a relationship between tilting motions of spindle and medium-frequency waviness errors of workpiece surface in fly-cutting machining. Furthermore, the 3D locus of the diamond-cutting tool is given as following:Where, R denotes the radius of cutting tool locus, z denotes angular velocity component, denotes the initial angle, f denotes the feed rate of machine table, KT denotes angular stiffness of spindles, denotes the precession angular velocity, M denotes torque generated by the unbalance mass, R denotes the distance between the tool tip with the spindle centroid, C denotes the axial inertia tensor, and A the radial inertia tensor. Equation (1) shows that the periods and amplitudes of waviness are mainly affected by C and A. In this design, to reduce the effect of the medium-frequency waviness and the simulation surface of the medium-frequency waviness, the structure of the spindle designed as shown in Fig. 2 has the same axial and radial inertia tensor, which makes the tool tip displacement in Z direction to be reduced as:Equation (2) shows that the angular stiffness of spindle KT also has an important influence of the tool tip displacement in the Z direction. A larger angular stiffness of the spindle can reduce the tool tip displacement effectively. To improve the angular stiffness, the aerostatic bearing with a large support surface is adopted and the film gap is optimized as shown in Fig. 3. It shows that the bearing stiffness in each direction primarily increases and then decreases as film gap increases. The maximum stiffness in axial, radial, and angular are all obtained at 15 m, 2,188 N/m, 640 N/m, and 1167.5 Nm/arcsec, respectively. Therefore, the 15 m is selected as the bearing film gap. Figure 4 shows the simulation results based on Eq. (1), which shows the roughness at less than 3 nm. The simulation conditions are as follows, the depth of cut is 5 m, tool nose radius is 5mm, the feed rate is 10 m/s, and the angular stiffness of the spindle is 1,167.5 Nm/arcsec, respectively.2.2 Integrated dynamic design and optimization of the hydrostatic slideThe performance of the slide directly affects the profile accuracy. To satisfy the targeting specification with a flatness of less than 3 m in 415415 mm2, a slide with good static, dynamic, and servo performance is needed. In this study, the integrated design of a hydrostatic slide system is presented. A design methodology that influences the mechanical and electronic systems of the electric driver, which enables global optimization, has been developed. Furthermore, the control performance of the hydrostatic slide system is evaluated and optimized, such that the physical system design and the controller design are integrated.Fig. 2 The structure of the spindleFig. 3 The relationship between stiffness and film gapThe semi-closed type is used to improve the stiffness of the slide and reduce the difficulty of assembly. In addition, the linear motor is adopted to enhance the transmission accuracy and structure compactness. The direction of the driving force must be aligned to the centroid of the slider to reduce the kinematic error during installation of the linear motor on the slide. As shown in Fig. 5a, the hydrostatic slide is composed of a carriage, guide, oil supply system, linear motor, and linear encoder whose resolution is 5 nm. Figure 5b shows the force analysis of the carriage driven by the linear motor; the motion equation can be calculated as:Where, kf is the motor thrust coefficient; i is q axis current in the linear motor (A); m is the weight of moving parts (kilograms); B is the viscosity of the oil in hydrostatic slide (newton seconds per square meter); FL is interference force (newtons). After Laplace transform, the corresponding transfer function can be formulated as:The scheme of transfer function of the linear feeding system is established as shown in Fig. 6 and simulation analysis is carried out by Simulink. The difference between the traditional method and the integrated method for hydrostatic slide design is determined. Figure 7 shows the step response under interference force of 1 N and the step response of the position loop at the same gain coefficient, respectively, designed by the traditional method. Fig. 4 The surface roughness of simulation It can be seen that the stiffness of the linear feed system can meet the requirement (about 166 N/m), but the system shocking has a larger overshoot with a longer rise time (40ms), and this problem has not been resolved by debugging the control parameters. This is because the rise time and the maximum overshoot are a pair of contradictory indicators in a traditional control system; thus, when the overshoot decreases, the rise time will increase. However, in the integrated design method, optimizing the mechanical systems provides great convenience to the control process and improves the slide performance. It can decrease the maximum overshoot while increasing the rise time. The weight of the carriage has a larger influence on the dynamic performance, and reducing it without changing the electrical equipment does not only increase the acceleration but also improve the response ability. Thus, decreasing the weight of the carriage in the initial stage of the design will benefit the servo performance and reduce the trouble of the control staff. In addition to the gravity of the carriage and workpiece, the carriage also bears the electromagnetic attraction between stator and rotor (about 0.2 MPa). The deformation of the carriage is shown in Fig. 8a. If the carriage is not rigid enough, it will reduce the gap between the stator and rotor, damaging the linear motor. Therefore, an appropriate structure should be used to meet the strength and stiffness requirements rather than reducing the weight randomly in the design of the carriage.Figure 8b shows the structural parameters of the carriage, where a, b, c, and d account for stiffness and bearing as described by hydrostatic theory, so these four parameters remain unchanged in the optimization process. e, f , g, h, and i account for the design variables, while the vertical deformation is less than 20m as the state variable and the lightest weight as the optimal objective (the density of the carriage is unchanged so that the lightest weight is equivalent to the minimum volume). The optimization model can be calculated as. Fig. 5 Hydrostatic slide: as tructure of the hydrostatic slide and b force analyses of the worktableFig. 6 Block diagram of the linear feeding systemFig. 7 The response of the slide: a the step response under interference force and b the step response of the positionFig. 8 Optimization of the carriage structure: a deformation of the carriage, b carriage structure, c optimization iteration curveFig. 9 The FEM of mechanical structureFigure 8c shows that the weight of the carriage being reduced from 436 to 225 kg after optimization. Figure 7 shows that the system stiffness has a slight increase after optimization. At the same time, the amplitude of the transient process and the oscillation frequency are reduced. After optimization, the rise time decreases from 40ms to 20ms, and the maximum overshoot reduces from 18 % to zero. It demonstrates that the dynamic quality is highly improved. 2.3 Dynamics modeling and analysis of machine tool To predict the influence of mechanical system dynamic performance on the processing topography, the finite element model (FEM) of the whole machine tool is established. The joint characteristics of the machine tool, such as the bolt joint and the bearing connection have great impact on the dynamic performance 12, 13. Therefore, the modeling approach of the junction directly determines the accuracy of the whole model of the machine tool. In this study, the Conta173 and Targe170 are applied to the contact components. The spring elements are used for the noncontact components, such as the aerostatic spindle and hydrostatic slide. The Prets179 elements are used to simulate the bolt joint which can exert the preload by the node K. The FEM of the whole machine is shown in Fig. 9.After establishing the FEM of the whole machine tool, harmonic response analysis is carried out in X, Y, and Z directions. The harmonic response analysis is able to give the response of the machine tool in different frequency excitation. The cutting force F0 of 1 N is assumed and the frequency range from 0 to 600 Hz with 2 Hz intervals is chosen to give an adequate response curve.Figure 10 provides the harmonic response of relative displacement between cutting tool and workpiece in three directions. The maximum dynamic compliance in X direction about 0.078 m/N occurs at 200 Hz, which corresponds to a dynamic loop stiffness of 12.8 N/m. The maximum dynamic compliance in Y direction at 0.018 m/N occurs at 234 Hz, which corresponds to a dynamic loop stiffness of 55.6 N/m. The dynamics of this machine tool in sensitive direction (Z direction) are dominated by a structure resonance at 255 Hz; the dynamic loop stiffness is 35.7 N/m. The relevant modal parameters are determined by the frequency response function in Fig. 10a. The static stiffness is 500MN/m, and the damping factor is 3 %. 2.4 Performance prediction and the dynamic loop stiffness optimization of the machine toolFly-cutting is a typical intermittent machining technique. The intermittent cutting force has an important influence on the surface texture. In this particular example, the size of the workpiece is 415415 mm2, and cutting occurs during 48.8 to 131.2. Figure 11 shows a sample cutting force over two revolutions of the fly-cutting. The cutting force is inputted to the machine tool system as the input signal, the output is the displacement of the cutting tool. The predicted surface texture can be obtained by transforming output signal from time domain to the spatial domain as shown in Fig. 11. According to the machining requirements of the potassium dihydrogen phosphate crystal, the maximum amplitude of the vertical stripes should be less than 15 nm, and the period greater than 33 mm 14, 15. Considering the two indicators above, the appropriate range of the stiffness for dominant resonant frequency is given from 125 to 800 N/m. It provides a theoretical basis for the stiffness loop design of the mechanical system. The stiffness is 500 N/m is designed for the mechanical structure system and the prediction surface is given in Fig. 11.Fig. 10 Harmonic response of the machine tool: a Z, b X and c Y directionsFig. 11 The mechanical system dynamic performance of the machine tool on the processing topographyThis stiffness can be achieved by optimization the contact stiffness between the contact components such as changing the value of contact area and preload. 3 Preliminary machining test The ultra-precision fly-cutting machine tool is built in Fig. 12 according to the analysis above. The low-speed feed experiment under the control instructions 10 m/s and 500ms sampling period is conducted to verify the stability of the low-speed performance of the hydrostatic slide system as shown in Fig. 13. It can be seen that feed speed of the slide undulates within a range of 0.1 m/s, and actual position coincides well with feed system command position. It shows that low-speed stability of the control system is excellent. Furthermore, the machining test is carried out on this machine tool. The machining parameters such as spindle speed and feed and tool nose radius are consistent with the simulation parameters. The experimental results are examined by a 3D rough surface tester, Wyko RST-plus (Veeco Metrology Group, Santa Barbara, CA, USA), which has a 500-mm vertical measurement range and 3-nm vertical resolution. The measurement result with only tip, tilt, and piston removed are shown in Fig. 14. Figure 14a shows the vertical stripes in the cutting direction, with amplitude at 10 nm and period at 58 mm. Figure 14b shows the roughness of the machined surface, and the roughness values is 2.8 nm. The test results agree well with the simulation result which demonstrates the feasibility of the proposed design method.4 Conclusions1. The mechanical structure-based design method is presented and implemented on a fly-cutting machine tool design; the theoretical basis is provided for the mechanical structure system design. The following major conclusions are drawn.The effect of the components structure on the roughness of machined surface is discussed; an optimized structural form of the spindle is designed which can reduce the roughness of the workpiece.Fig. 12 Ultraprecision fly-cutting machine toolFig. 13 The speed and displacement curves of the slide under 10 m/sFig. 14 The 3D topography of the workpiece: a the measuring vertical stripes of the workpiece and b surface roughness of machined surface2. An integrated dynamic model considering the influence of the mechanical structure on the control system and electronic drives is built and used to optimize the slide of the machine tool. Collaborative optimization of rise time and maximum overshoot are achieved; the rise time from 40 ms decreases to 20 ms while the maximum overshoot reduces from 18 % to zero.3. The influence of the mechanical structure system on the surface topography is analyzed. The relationship between the machine dynamic characteristics and surface topography was established at the design stage. The appropriate range of the stiffness (125800 N/m) for dominant resonant frequency is given, which provides a benchmark and guiding significance for the design of the machine tool. AcknowledgmentsThe authors gratefully acknowledge financial support from the National Science Fund for Distinguished Young Scholars of China (grant number 50925521), The Sino-UK Higher Education Research Partnership for PhD Studies program, and China Scholarship Council (CSC).References1 Wybranski B (2004) Micro production technologies .mstNews 2:43452 Comley P, Morantz P, Shore P, Tonnellier X (2011) Grinding meter scale mirror segments for the E-ELT ground based telescope. Ann CIRP 60(1):3793823 Shore P, Morantz P, Luo X, Tonnellier X, Collins R, Roberts A, Miller R and Read R (2005) Large optix ultra-precision grinding/ measuring system. In: Proceedings of SPIE-The International Society for Optical Engineering, Q, pp. 184 LuoXC, ChengK,DaveW, FrankW(2005)Design of ultraprecision machine tools with applications to manufacture of miniature and micro components. J Mater Process Technol 167(23):5155285 Cheng K (2009) Machining dynamicsfundamentals. Appl Pract 10:2833206 Huo DH, Cheng K, Wardle F (2010) Design of a five-axis ultraprecision micro-milling machine-UltraMill. Part 1: holistic design approach, design considerations and specifications. Int J Adv Manuf Technol 47(912):8678777 Chen CY, Cheng CC (2005) Integrated design for a mechatronic feed drive system of machine tools. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Monterey, CA8 Kono D, Lorenzer T, Weikert S, Wegener K (2010) Evaluation of modeling approaches formachine tool design. Precis Eng 34(3):399 4079 Zhang SJ, To S, Cheung CF, Wang
展开阅读全文