外文翻译【原文】-基于有限元分析法的车床床身优化设计.pdf

Abstrac? ? ? ?The lathe-bed is a critically important part of a lathe, on which the performance of a machine tool depends largely. The optimization of a lathe-bed is hence an important issue in machine tool design. In this paper, we present three-dimensional modeling and finite element analysis methods for the optimization design of CNC lathes. We use PRO/E and PRO/MECHANICA to build three-dimensional modeling and to optimize the structure of lathe-beds. The final modal analysis shows that the presented optimal design is feasible and can produce a better structural performance. Keywords: Lathe-bed; optimization design; finite element analysis; modal analysis. I. FOREWORD As a supporting part of a lathe, the lathe-bed is generally used for placing such important components as lead rail and headstock 1. In order to meet the high requirements of computer numerical control (CNC) for speed, accuracy, productivity, reliability and automation degree, and compared with ordinary lathes, CNC lathes are superior in static and dynamic stiffness and vibration resistance 2. Due to the high complexity of lathe-beds with regard to structural shape, it will be very difficult to carry out calculations for its static/dynamic characteristics by means of conventional methods 3. With the maturity of finite element theory and the development of computer technique, it is a widely used method to perform a static/dynamic characteristic analysis by building three-dimensional modeling and performing finite element analysis with the software tool ANSYS 4. But this method is easy to lead to data loss and hence needs plenty of time for model repairing. We know that the software Pro/MECHANICA module by company PTC can perform structural analysis for Pro/ENGINEER model. In this paper, the structure design of a lathe-bed is first conducted, Pro/ENGINEER is used for modeling, and then Pro/MECHANICA is employed for finite element analysis. It is shown by the result that measures like finite element analysis can be employed for optimization design, thereby avoiding the inherent structural defects and disadvantages. Dongmei Li is with the Dept. of Mechanical Engineering, Guangdong Technical College of Water Resources and Electric Engineering, Tianhe, Guangzhou, China 510635 (email: ) Y. Guan is with the School of Mechanical and Automotive Engineering, South China University of Technology, Tianhe, Guangzhou, China 510640. Guan Xu and Weidong Mao are with Nanhai Zhongnan Machinery Co. Ltd, Foshan, Guangdong, China. Part of the work in this paper is supported by Guangdong-HongKong Technology Cooperation Funding (Foshan Project: 2008Z009). II. CONFIRMATION OF PART STRUCTURE AND DIMENSIONS OF LATHE-BED A. Structure and dimensions of lathe-bed According to layout modes, lathe-beds may be classified into upright lathe-beds, inclined lathe-beds, taper slide based upright lathe-beds and vertical lathe-beds. Among these types, the upright lathe-beds have the advantages of good manufacturability, easy processing, great assurance for the kinematic accuracy of cutting tools and great ability in bearing the gravity of work-pieces, etc. For this reason, upright lathe-bed is adopted in this paper for study. B. Design of strengthening ribs of a lathe-bed The strengthening ribs of a lathe-bed pertain to three basic types. The combination of strengthening ribs of different types will lead to different mechanical properties and different rib structures in different lathe parts 5. Different types of strengthening ribs will affect the flexibility, structural material, length of weld and other aspects to different extents. Since its load is not so great, the lathe-bed of a common CNC lathe does not require too high bending resisting stiffness and torsional stiffness. Provided a box structure, the lathe-beds structure will become complicated, thus making escape of chips difficult and the stiffness performance inferior to that of other kinds of layouts. Therefore, the lathe-bed of the lathe involved in this paper employs a herringbone rib with a thickness of 12mm. C. Design of batten wall pore To reduce the size of a lathe-bed and assure its stiffness requirement, a batten wall pore structure is designed. In order to assure adequate stiffness, the lathe has relevant requirements for the shape, location and size of the batten wall pore. From the point of view of stress, the lathe-bed is mainly imposed by a vertically upward force; moreover, the lathe-bed is not slender, so the direction of tangential stress should not be ignored. It is proved in the test that the influence of a structure for the stiffness will be greater when the batten wall pore is made in the direction vertical to the bending plane rather than in the direction parallel to, that is to say, the influence of structure for the stiffness will be the minimum when the batten wall pore is made in the direction parallel to the bending plane. And for the stress in the direction, which is imposed on the lathe-bed, the bending plane is an epiplastron, therefore, the batten wall Optimization Design of Lather-beds Based on FEA D. Li? Y. Guan? G. Xu and W. Mao 978-1-4244-3608-8/09/$25.00 2009 IEEE. 865 Proceedings of the 2009 IEEE International Conference on Information and Automation June 22 -25, 2009, Zhuhai/Macau, China pore should be designed in the epiplastron. When the batten wall pore is arranged at a place near the axis of center of bending, its impact on the bending resisting stiffness will be very small; and when it is arranged far away from the axis of center of bending and near the edge, the impact will be greater. For that reason, the batten wall pore should be arranged near the axis of center of bending, thereby weakening its impact on the lathe-beds stiffness. When in torsion, the shear stress function near the batten wall pore is associated with the shape of the batten wall pore. It is found in the finite element analysis made for different batten wall pores that prismatic pore is the best, followed by round pore and rectangular in turn. The lathe-bed employed in this paper has a prismatic batten wall pore, as shown in Fig. 1. According to the analysis, the larger the size of batten wall pore is, the weaker the stiffness is. The width and length of the prismatic batten wall pore are set as W and L respectively, and those of the upper surface of the lathe-bed are given as b and L1 respectively, then the expression W/b0.4 is gained in the test, which means the stiffness becomes weaker and weaker. Therefore, we set the value of W/b as 0.4, namely the value of W equals to 0.4b, in our case 113.6mm. Finally 113mm is taken. After analyzing the relation between the lengths of prismatic batten wall pores, it is found that the larger such length, the weaker the torsional stiffness of the lathe-bed. When the length L equals to 2W, the torsion deformation ratio is larger than that based on a non-porous box by half; and when the length L equals to 5W, the torsion deformation ratio is larger than that based on a non-porous box by more than one time. Therefore, the minimum proportion obtained is L=2W (namely 226mm). There are three pores which distribute evenly. Fig. 1: Prismatic Batten Wall Pore Fig. 2 Sectional View of Flange Part D. Design of connective structure of lathe-bed and foundation The connection between a lathe-bed and its foundation is a kind of permanent connection of which the main types are jaw seat type, flanging type and recessed type. The combining part of a connective structure of jaw seat type and the batten wall has poor stiffness and low contact stiffness. Cast easily, the connective structure of jaw seat type is applicable for the connection based on small lateral force. The partial stiffness of a connective structure of flanging type is higher than that of a connective structure of jaw seat type by 11.5 times. It has a simple structure, but it covers a larger space and does not have a good-looking appearance. It is suitable for the connection between larger work-pieces and that between larger work-pieces and foundations. The partial stiffness of a connective structure of recessed type is larger than that of a connective structure jaw seat type by 2.53 times and that of a connective structure of flanging type by more than 1.5 times. It is suitable for the connection between larger work-pieces and that between larger work-pieces and foundations. It covers a small area and has a good-looking appearance. But it is difficult in casting, thereby increasing the complexity in manufacturing. With a steel cast structure, the CNC lathe-bed has a poor welding performance. If a connective structure of recessed type is employed, the casting defect will increase the complexity in manufacturing, thereby leading to cost increment. If a connective structure of jaw seat type is adopted, the stiffness performance will be inferior to that of the other two types. Therefore, the conclusion drawn from analysis is that the connective structures of flanging type will be very ideal. The parameters of a structure of flanging type include the flange width b, flange thickness k, screw diameter d, screw hole linear eccentricity e, as shown in Fig. 2. The outline and internal structure of the lathe-bed from be obtained from the data above and are shown in Fig. 3 and Fig. 4. Fig. 3: Outline Drawing of Lathe-bed Fig. 4: Internal Structure and Dimensions of Lathe-bed III. FINITE ELEMENT ANALYSIS A. Finite element analysis for batten wall pore of lathe-bed The so-called finite element analysis is a kind of method 866 to decompose an object or system into multiple mutually connected and independent and simple points for analyzing. In this kind of analysis method, the number of the points is finite and therefore is called as finite elements 4. After the design of the lathe-bed is finished, the PRO/MECHANICA module of PRO/E is used to perform a simple finite element analysis for the design so as to verify the rationality of the design 5. Firstly, a hollow rectangular column with three geometric parameters and wall thickness are 100*100*300mm and 5mm respectively is prepared. A round window of a radius of 20mm is made on the opposite two faces of the column respectively. A vertically downward 3000N force is imposed on the two edges of upper surface respectively, by imitating the stress undertaken by the lathe-bed. The stress deformation nephogram of the model is found in the calculation and analysis to be as that described in (a) of Fig. 5. Then stress deformation analyses are respectively made for a rectangular window and a prismatic window which are made oppositely and have the same area as that of the round window. After that, we come to the maximum deformation nephograms as shown in (b) of Fig.5 and (c) in Fig. 5. (a): Stress Nephogram of Round Window (b): Stress Nephogram of Rectangular Window (c): Stress Nephogram of Prismatic Window Figure 5: Finite Element Analysis of Batten Wall Pore of Lathe-bed It can be observed from the above figure that when the round window is opened, the maximum deformation is 2.786?m, and when the rectangular window and prismatic window are opened, the maximum deformations are 2.806?m and 2.743?m respectively. So, it is clear that under the condition that the stress is constant, the choosing of a rectangular batten wall pore can reach a better bending resisting stiffness compared with the choosing of a rectangular batten wall pore of any other shape. It is verified in this way that applying a rectangular window as the batten wall pore is correct. When the lathe-bed window is made on the stress surface, the stress deformation nephograms of the batten wall pores of the said three shapes are given in Fig.6. According to the figure, the maximum deformations of the model, when a round window, a rectangular window and a prismatic are opened, are 2.694?m, 2.6912?m and2.6911?m respectively. Therefore, for the epiplastron, the window shape doesnt great impact on the lathe-beds stiffness. Nevertheless, a rectangular window which will produce a very little impact is chosen in the design to be the epiplastron window of the lathe-bed. Fig.6 Deformation Nephogram of Epiplastron Window B. Finite element analysis of rib plate of lathe-bed The rib structure of a lathe-bed varies a lot. Now, we will take a vertically longitudinal reinforcing rib, a vertically transverse reinforcing rib, a vertically grass character rib and a herringbone rib respectively for comparison. Firstly, a hollow rectangular column whose geometric sizes and wall thickness are 100 * 100 * 500mm and 5mm respectively is prepared. The interior of the column is respectively filled with the three kinds of rib structures needing verification, with a uniform rib plate thickness of 10mm. A vertically downward 3000N force is imposed on the two edges of upper surface respectively, by imitating the stress undertaken by the lathe-bed, in order to limit the two end faces of the fixed model. It is found in calculation and analysis that the stress deformation nephograms of the four kinds of reinforcing rib layouts of the model are as given in Fig.7. Fig. 7 Deformation Nephograms of Various Rib Plate Structure Layouts It can be seen from the above figure that the maximum deformation of the model with a (upper left) vertically longitudinal rib plate structure is 9.07?m; that of the model with a (lower left) herringbone rib plate structure is 7.46?m; that of the model with a (upper right) vertically transverse rib plate structure is 7.88?m; and that of the model with a (lower right) grass character rib plate structure is 6.01?m. Therefore, it is clear that the bending resisting stiffness of the herringbone rib plate structure of the lathe-bed is better 867 than that of the purely vertically transverse rib plate structure and purely vertical rib plate structure but inferior to that of the grass character rib plate structure combined by transverse and vertical rib plates. Nevertheless, the model with a herringbone rib plate structure can save a lot of materials than the model with a grass character rib plate structure. The weights of the model in the case of application of the aforementioned two kinds of rib plate structures are given in Table 1. It can be observed from the table that the weight of the ribs of herringbone rib plate structure is lighter than that of the ribs of grass character rib plate structure by 1.25kg. Therefore we choose the herringbone rib plate structure in the design, in order to meet the requirement of decreasing the lathe-beds weight. TABLE 1 COMPARISON TABLE OF WEIGHTS OF HERRINGBONE RIB AND GRASS CHARACTER RIB Title Herringbone Rib Grass Character Rib Weight (kg) 4.137 5.387 IV. MODAL ANALYSIS OF LATHE-BED A. Modal analysis It is a fact that lathe is instability and vibration in operation, it is necessary to perform a modal analysis for the lathe-bed in order to reduce the vibration of the lathe, to assure its stability and to improve the accuracy of processed parts. The modal analysis of lathe-bed is employed for confirming the vibration feature of the design structure or machine parts. The vibration feature is a key parameter to design of a structure bearing a dynamic load. The main task of modal analysis is to study the free vibration of damping free systems and particularly the natural frequencies of the structure, thereby enabling the designers to keep off these frequencies or to minimize the motivation on them and ultimately eliminating the excessively serious vibrations or noise 8. Modal analysis mainly functions in the three aspects as follows: firstly, to keep the structure away from resonance vibration or from a particular frequency; secondly, to enable us to understand the impacts of the structure for the dynamic loads of different types; and thirdly, to facilitate the estimations and solving of some control parameters such as time step in other kinetic analysis. On lots of occasions, modal analysis plays a critical role. For example, a lot of machines need to avoid resonance vibration. Modal analysis enables us to know the natural vibration frequency and mode of vibration of a structure so that necessary measures can be taken to avoid the unnecessary energy losses due to resonance vibration. The vibration characteristic of a structure determines its responding conditions for various dynamic loads. B. Process of dynamic analysis When defining the material properties, choose “Model” in “Structure” of Pro/MECHANICA, then choose “Materials” and clit the chosen material and press “Edit” for editing. For the material previously chosen HT300 whose density, elastic modulus and Poissons ratio are 7.3e-9tonne/mm3, 2e+11N/ m2 and 0.3 respectively in accordance with relevant data. Then the above information can be used for defining the material properties 9. In order to achieve believable results, the paper chooses Multi-Pass Adaptive way to inspect the convergence property. With the same task, the Multi-Pass Adaptive way will realize comparisons of different channels, thereby making judgment on whether or a higher calculation order is necessary. The Multi-Pass Adaptive way can provide a convergence curve to control the analysis quality and set convergence property at the sensitive zones as well 10. The analysis results are given in Fig.8. (a) First-order mode of vibration: frequency 479.02Hz (b) Second-order mode of vibration: frequency 06.58Hz (c) Third-order mode of vibration: frequency 554.65Hz (d) Fourth-order mode of vibration: frequency 737.20Hz Fig. 8 First- to Fourth-Order Modes of Vibration in Pro/M Analysis According to the calculation result, within the scope of 800Hz, the lathe-bed has frequencies of four orders and all of its natural frequencies are above 450Hz, much higher than the normal working frequency. So, the lathe-bed is sound in stiffness, vibration resistance and processing stability, thereby assuring