Pre_deformationf_省略_ofMachineCenters_SUN.pdf

CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol 27 No 3 2014 528 DOI 10 3901 CJME 2014 03 528 available online at Pre deformation for Assembly Performance of Machine Centers SUN Yongping1 WANG Delun1 DONG Huimin1 XUE Runiu2 and YU Shudong3 1 Department of Mechanical Engineering Dalian University of Technology Dalian 116024 China 2 Dalian Machine Tool Group Co Ltd Dalian 116600 China 3 Department of Mechanical and Industrial Engineering Ryerson University Toronto M5B 2K3 Canada Received April 7 2013 revised March 3 2014 accepted March 30 2014 Abstract The current research of machine center accuracy in workspace mainly focuses on the poor geometric error subjected to thermal and gravity load while in operation however there are little researches focusing on the effect of machine center elastic deformations on workspace volume Therefore a method called pre deformation for assembly performance is presented This method is technically based on the characteristics of machine tool assembly and collaborative computer aided engineering CAE analysis The research goal is to enhance assembly performance including straightness positioning and angular errors to realize the precision of the machine tool design A vertical machine center is taken as an example to illustrate the proposed method The concept of travel error is defined to obtain the law of the guide surface The machine center assembly performance is analyzed under cold condition and thermal balance condition to establish the function of pre deformation Then the guide surface in normal direction is processed with the pre deformation function and the machine tool assembly performance is measured using a laser interferometer The measuring results show that the straightness deviation of the Z component in the Y direction is 158 9 of the allowable value primarily because of the gravity of the spindle head and the straightness of the X and Y components is minimal When the machine tool is processed in pre deformation the straightness of the Z axis moving component is reduced to 91 2 This research proposes a pre deformation machine center assembly method which has sufficient capacity to improving assembly accuracy of machine centers Keywords machine tool assembly accuracy travel error pre deformation design performance test 1 Introduction The rapid development of the manufacturing industry has increased the demand for precision heavy and highly reliable CNC machine centers which requires a flexible manufacturing line for machines 1 In a machine tool production line assembly is a key process for achieving machine center accuracy 2 3 The fitting assembly method is the main approach used in the assembly stage By applying this method the repair link is adjusted based on worker experience Thus this step is becoming a bottleneck in mass production Moreover machine centers are subject to thermal and gravity load while in operation during which volumetric performance varies based on the coordinate position 4 5 Consequently assembly accuracy and efficiency are affected In such case the variation of deformation must be analyzed to enhance the machine assembly cycle and improve efficiency Recent research on machine assembly mainly focused on Corresponding author E mail dlunwang Supported by National Key Technology Support Program of China Grant No 2011BAF11B03 and National Science and Technology Major Projects of China Grant No 2012ZX04010 011 Chinese Mechanical Engineering Society and Springer Verlag Berlin Heidelberg 2014 design for manufacture and assembly DFMA and computer aided assembly process plan CAAPP This research status mainly focuses on three areas 1 DFMA During the component design stage DFMA reduces assembly costs component count and overall costs while improving the reliability of the product 6 Boothroyd and Dewhurst developed the methodologies and computer solutions for DFMA 7 8 The concept has been applied in commercial design software 2 CAAPP CAAPP is the function of determining how a product will be made to satisfy the requirements specified at the most economical cost 9 Ref 10 lays the foundation for computer aided assembly sequence planning studies The design method is widely used in process planning design 3 Geometric error compensation GEC Schultschik established the kinematic error vector model which contains 18 motion errors 11 KIM 12 developed a new volumetric accuracy analysis method based on the generalized geometric error models KIRIDENA et al 13 discussed an approach for modeling the effects of the positioning errors of a machine s axes on the accuracy of the cutting tool in its work space No study has been conducted on pre deformation with most involving only CHINESE JOURNAL OF MECHANICAL ENGINEERING 529 machine tool geometric error modeling However although considerable research has been conducted on DFMA and CAAPP the output of the former and the input of the latter lack the elastic deformation trajectory of moving components This condition results in volumetric error in the workspace Volumetric performance represents the overall errors of a machine center Therefore this factor has become an important index representing the quality of a machine tool If the machine center structure is designed using DFMA and CAAPP assembly accuracy will not reach up to the allowance In such case workers have to use the fitting assembly method which restricts assembly efficiency In this paper pre deformation for assembly performance PFAP method which compensates for volumetric error is presented to improve the accuracy and performance of the machine center assembly The concept of travel error of moving component is defined and the machine center assembly performance is analyzed under cold condition and thermal balance condition such that the expression of pre deformation is established Then the guide surfaces in normal direction of the X Y and Z axes are processed with the pre deformation function and the performance of a machine tool is measured using a laser interferometer Although pre deformation method has been widely applied in production practice its application in machine tool assembly is not clear This paper is significant in the process improvement and structure design of precision machine tools 2 Theory and Design Procedure 2 1 Design theory for pre deformation The machine center is composed of the X Y and Z axis sub systems The table is the moving component of the X axis the table saddle is the moving component of the Y axis and the spindle head is the moving component of the Z axis 14 The functional point presents the relative motion between the component of the machine that carries the cutting tool and that which carries the work piece The configuration and working volume of the vertical machine center VMC are shown in Fig 1 Fig 1 Configuration and working volume of the vertical machine center The working volume of VMC is defined by the travel of the machine linear axes for machining operations with dimensions of 850 mm 510 mm 510 mm The X Y and Z axis sub systems are connected to bearings and ball screws The column and bed are bolted to each other at the joints Meanwhile the internal weighted system of the column can reduce loading on the spindle As shown in Figs 2 a 2 c the machine center structures during travel differ in terms of working volume Fig 2 Three different coordinates of vertical machine center When one component moves along its linear axis the sustain component appears with a different degree of elastic deformation The straightness positioning and angular errors are then generated The concept of pre deformation is thus presented The fundamental theory is to process the guide surface in the contrary geometric error function during the cutting stage When moving components move along their linear axis geometric error could be compensated and high accuracy and performance could be achieved 2 2 Procedure of pre deformation The PFAP method for a machine center has three steps 1 establishment of the model and features of assembly 2 collaborative computer aided engineering CAE calculation and 3 contribution and variation analysis The criterion for pre deformation could be the basis for the improvement of the machine tool structure The flow chart of pre deformation for an assembly machine center is shown in Fig 3 Fig 3 Flow chart of pre deformation for assembly YSUN Yongping et al Pre deformation for Assembly Performance of Machine Centers Y 530 The key point in pre deformation is obtaining the variation of the function of geometric errors PFAP has the following features 1 Precision compensation function Based on the method of PFAP the geometry errors caused by the structures are compensated with high accuracy thus improving assembly performance 2 High efficiency mass production The surface of a slide guide is processed by the grinder rather than through the manual fitting assembly method This process could reduce the machine assembly cycle and improve efficiency 3 Weight reduction structure design A designer could realize a lighter component structure by using the PFAP method A green design that avoids the heavy structure of moving components is achieved 3 Modeling Assembly Features The geometric error of a machine component along its axis of motion corresponds to six deflections which is analogous to the six degrees of freedom of a body in space This condition could ensure assembly accuracy by checking the geometric error under a quasi static condition Quasi static errors are defined as errors that slowly vary with time and are related to the geometry of the machine center A typical linear moving component table in the X direction 15 is shown in Fig 4 Fig 4 Three translator and three rotary deflections of a table with one axis of movement As shown in Fig 4 error motions are identified by the letter E followed by a subscript where the first letter is the name of the axis corresponding to the direction of the error motion and the second letter is the name of the axis of motion The linear error motion along the X direction is called the linear positioning error which is expressed by EX X The other two translational error motions are called straightness errors which are expressed by EY X and EZ X The angular error motion around the A B and C axes are EA X EB X and EC X respectively Based on Fig 4 18 geometric VMC errors are shown in Table 1 Table 1 Geometric errors of translator and rotary axis in the machine center assembly process E X EX X EY X EZ X EA X EB X EC X E Y EX Y EY Y EZ Y EA Y EB Y EC Y E Z EX Z EY Z EZ Z EA Z EB Z EC Z The variation of the deviation of the Y and Z directions of the table saddle with X axis movement is shown in Fig 5 Fig 5 Moving trajectory of the travel error of the X axis moving component Definition 1 The machine center travel error is a function of coordinate position If we consider a point where the coordinate is P0 x y z in a numerical control system with an actual position P x y z the translation axial error vector is shown in Eq 1 Exxyyzz 1 The travel error could be curve fitted by four order polynomial data fitting and could be expressed in Eq 2 2 12 n n Ei jk jk jk j iX Y Z A B C jx y z 2 where E Error of moving component X Y Z Direction of error A B C Rotation in the X Y Z axes j Component of machine tool x y z Travel of the X Y Z axes 4 Coordinate CAE Calculation The coordinate CAE analysis is a computer aided analysis that calculates the deformation of a machine tool under both cold condition and thermal balance condition Under cold condition a machine tool is subject to gravity in standard ambient temperature 20 C 16 17 Under thermal balance condition the machine tool is subject to thermal mechanical loading in thermal equilibrium The framework of the pre deformation of the coordinate CAE analysis of a machine tool is shown in Fig 6 As shown in Fig 6 the solid model is built based on a 2D drawing The element distribution of a machine tool is controlled by the program The boundary and material properties are defined by the features of the machine tool The cold condition and thermal balance condition are then calculated CHINESE JOURNAL OF MECHANICAL ENGINEERING 531 Fig 6 Flow chart of coordinate CAE analysis of VMC 5 Error Contribution and Variation Analysis 5 1 Error contribution analysis Different loadings could have different degrees of impact on machine tool travel error Machine centers are subject to thermal and gravity load while in operation Thus 33 disperse position structures of working volume were calculated In order to determine the influence of different loadings on travel error The conditions are gravity thermal loading and thermo mechanical couple loading T M Most of the travel errors are shown in Table 2 Table 2 Summarizing of translator and rotary travel error Travel error Allowance Cold T M Variation ratio R EY X m 20 0 17 0 65 3 2 EZ X m 20 1 49 1 38 7 5 EA X 12 2 20 1 94 18 3 EB X 12 0 19 1 49 12 4 X axis moving component EC X 12 0 50 1 74 14 5 EX Y m 15 1 82 0 1 12 1 EZ Y m 15 1 35 1 56 10 4 EA Y 12 1 28 0 67 10 7 EB Y 12 0 01 0 66 5 5 Y axis moving component EC Y 12 0 32 0 92 7 7 EX Z m 15 5 32 0 67 35 5 EY Z m 15 23 33 23 84 158 9 EA Z 12 13 79 12 51 114 9 EB Z 12 0 87 4 59 38 3 Z axis moving component EC Z 12 0 19 3 51 29 3 It is shown in Table 2 that the maximum geometric variation ratio of the X and Y axes is 18 3 of the allowance 18 whereas for the Z axis the maximum value is 158 9 EY Z and EA Z both exceeded the allowance which can be attributed to the bending moment of the G structure loop Thus we should analyze the degree of influence in further detail As shown in Table 3 the deformation in Y direction of Z component under thermal condition is approximately equal to the difference of the thermal balance and cold conditions The maximum difference of variation and thermal condition is only 0 696 m in the 0 coordinate under thermal condition The results show that the deformation changes uniformly in the Z axis under thermal loading and that travel error is mainly caused by gravity Table 3 Comparison of different conditions of the deformation in Y direction of Z component m Travel Z axis GravityT M Vary Thermal Subtraction 0 24 137 56 02431 887 31 763 0 124 102 29 648 61 76532 117 31 852 0 265 204 34 612 66 77732 165 31 787 0 378 306 39 331 71 17231 841 31 285 0 556 408 43 936 75 47131 535 30 928 0 607 550 48 043 79 86431 821 31 125 0 696 5 2 Volumetric performance 5 2 1 Counter map of working volume First 121 positions of the XY plane and 11 positions of the Z axis are calculated under cold condition and thermal balance condition to obtain the variation of the working volume As shown in Figs 7 and 8 a 3D gray map surface of travel error in XY plane is presented when the coordinate of the Z axis is 255 Fig 7 Travel error of XY plane under cold condition m Fig 8 Travel error of XY plane under thermal balance condition m As shown in Figs 7 and 8 the variation of travel error in the XY plane presents a half cylinder under cold condition with a maximum of 4 25 m On the other hand under thermal balance condition the XY plane presents an inclined surface with a maximum of 3 69 m The travel error variations can be attributed to the asymmetric arrangement caused by the heat source in the fixed end A YSUN Yongping et al Pre deformation for Assembly Performance of Machine Centers Y 532 3D gray map surface of travel error in the YZ plane is presented in Figs 9 and 10 in which the table is in between the X and Y axes Fig 9 Travel error of YZ plane under cold condition m Fig 10 Travel error of YZ plane under thermal balance condition m As indicated in Figs 9 and 10 the variation of travel error in the XY plane presents an inclined surface under cold condition and thermal balance condition with a maximum of 23 9 m The gradient of cold condition is very similar to that of the thermal balance condition 5 2 2 Travel error components From the above analysis the travel error in the Z axis exceeded the allowance whereas the travel error of the X and Y axes in the Z direction are in the sensitive direction Thus the travel error of the Z axis in the Y direction as well as the travel error of the X Y component in the Z direction should be discussed further The deviation of the travel error can be attributed to the straightness When straightness is analyzed the other axes are assumed to be located near the center travel of the machine tool axes As illustrated in Fig 11 the travel error under cold condition and thermal balance condition of the X axis is contrasted Under cold condition the maximum elastic deformation is at the 0 and 850 coordinates The straightness reaches the minimum at the 425 coordinate and presents as a convex shape in during travel Under thermal balance condition the travel error presents an asymmetric shape and is caused by the DB bearing arrangement The straightness values are only 1 38 m and 1 49 m with a difference of only 0 11 m Fig 11 Straightness deviations of X component in Z direction As shown in Fig 12 the travel error in the Y axis is contrasted Under cold condition the straightness is 1 16 m and presents an uphill uptrend shape Under thermal balance condition the straightness is 1 35 m and likewise presents an uphill shape The two conditions both exhibit an uphill uptrend shape and the variation of straightness is only 0 21 m Fig 12 Straightness deviations of Y component in Z direction As indicated in Fig 13 the travel error in the Z axis is contrasted Under cold condition the straightness is 23 33 m and presents an uphill uptrend shape Under thermal balance condition the straightness is 23 84 m and likewise presents an uphill shape Both conditions exhibit an uphill downtrend shape with a difference of only 0 51 m Other travel errors of the vertical machine center are shown in Appendix Fig 13 Straightness deviations of Z component in Y direction CHINESE JOURNAL OF MECHANICAL ENGINEERING 533 5 3 Pre deformation of machine ce