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Research on the fast inspection algorithm of virtual axis machine tool workspace Li Tiemin, Li Tiemin, Wang Jinsong, using the single open chain method, can only find the value of all motion variables, including the motion coordinates of the driven hinge, so it is suitable for Quick inspection of the work space. Based on the actual virtual axis machine tool VAT1Y, the algorithm is applied and verified.
In this paper, the single-chain method is used to analyze the kinematics of the parallel mechanism, and a fast algorithm for the space inspection of the virtual axis machine tool is proposed.
The method can find the length of each branch and the angle of the driven hinge in the secondary calculation, improve the calculation speed, and ensure the real-time performance of the numerical control system.
1 Workspace inspection algorithm 1.1 Virtual axis machine tool workspace definition 6 Freedom virtual axis machine tool position available space 6 seats represent the position of the moving platform center in the machining coordinate system, [T represents the three attitude angles of the moving platform , defined here as the Euler angle.
According to the research focus, the working space of the virtual axis machine tool mainly has the following definitions: 1 Position space in a given position When the attitude of the moving platform is fixed, the center of the moving platform can reach the set of points.
The general way to determine the working space of a virtual axis machine is to search for the boundaries of the workspace by numerical calculations. This approach is useful for identifying the volume of the workspace and studying the distribution of the workspace. However, the working space size of the parallel structure machine depends on the direction of the end moving part. It is a 6-dimensional vector, and the working space is not a very regular shape. It is difficult to describe it with an analytical formula. The usual working space can be given. The boundary can only be made after fixing 3 degrees of freedom.
1.2 The rapid inspection algorithm for the virtual axis machine tool workspace The model is illustrated by the Stewart platform with hierarchical and structurally symmetric upper and lower platforms. The model is shown in Figure 1.
The working space of the parallel structure machine tool is affected by the telescopic range of the driving rod, the mechanism limitation of the driven hinge and the interference between the driving rods, but for the structure of the upper and lower layers, the first two factors are dominant, and The limit of the driven hinge has a strong directivity. The algorithm proposed in this paper is to test these two constraints.
When the kinematics model is established, the parallel structure is divided into six single open chains. Each single open chain starts from the origin of the static platform coordinate system and ends at the center of the corresponding ball joint on the moving platform, including a Hooke hinge. 1 drive lever and 1 ball hinge. Due to the symmetry of the machine structure, the motion analysis methods of the six single open chains are the same.
Set the moving platform and static platform coordinate system to E and E ', respectively, A is the hinge point center coordinate on the moving platform. According to Figure 1, the position of point A relative to the static platform coordinate system is vector i, relative to the position of the moving platform. The vector i , in the equation, is the attitude matrix of the coordinate system oxyz relative to the coordinate system o ′ x y y 'z ′, which is the three attitude angles T, and the function matrix o of U and V is the coordinate origin o of the coordinate system oxyz The coordinate system introduces homogeneous coordinates for the convenience of calculation, and the vectors are homogeneous coordinate vectors in the following analysis. It is seen from Fig. 1 that it is a homogeneous transformation matrix of the i-th drive chain, and describes the transmission transformation of the coordinate system established at the center of the i-th ball joint with respect to the static platform coordinate system. According to Equations 1 to 3, the transformation matrix of the position and orientation of the moving platform coordinate system with respect to the static platform coordinate system can be obtained.
To transform Equation 3, in Equation 5, the left side of the equation is a function of the tool pose x0, T, U, V and the machine structure parameters, and the right is a function of the three input variables θ. If a tool pose is given, the left form becomes a constant. If the left form is equal to [xT, then through Equations 6 to 9, it is possible to find all the variables of the Hook hinge and the servo leg in a certain pose. The two angle values ​​of the Hook hinge and the value of the leg length. In a similar way, the change values ​​of the three ball joints can also be obtained. However, in practical use, it is only necessary to find the angle between the actual position of the leg and the installation position of the ball joint in a certain posture, so that the verification of the hinge interference can be quickly performed. It can be seen from Fig. 1 that in the single open chain analysis, the z-axis of the coordinate system 3i always coincides with the leg vector, so that in the formula, j is the structural torsion angle of the static platform of the machine tool.
Assuming that L is the normal vector of the installation vector mounting plane of the i-th ball joint on the moving platform, the length of the servo leg obtained by Equations 6 to 9 and Equation 14 for the integrated corner of the i-th ball joint with respect to the moving platform And the movement value of the Hook hinge and the ball joint can be used to calculate whether these variables are in the normal range of motion.
Using the single-open chain method, for the individual shape, as long as the inverse kinematics inverse transformation is solved, all the input variables can be obtained, which greatly improves the calculation speed and ensures the real-time performance of the numerical control system.
2 Application and verification of the algorithm The following is an example of a prototype of a virtual axis machine tool, VAT1Y, jointly developed by Tsinghua University and Tianjin University. Combined with the structural characteristics and control principle of the machine tool, the practicality of the above algorithm is explained and its effectiveness is described. Comparison. The structural model of VAT1Y can be used first. The trajectory planning module of the virtual axis machine usually uses the original part geometry information by means of AD software to generate the part and the offline processing part. The real-time processing part of the tool position correction information. The actual geometric dimension of the actual axis of the machine tool. Dimensional servo control system real axis motion instruction real axis precise interpolation based on single open chain virtual real map transformation virtual axis motion instruction virtual axis interpolation planning tool path file data preprocessing tool position file virtual axis trajectory planning part geometric information tool position file. Then, through the data preprocessing system of the machine tool, the tool position file of the traditional machine tool is converted into a specific track file format of the virtual axis machine tool, and the job verification such as the working space and the speed limit are performed according to the characteristics of the machine tool. If there is any problem, the error information is fed back to the trajectory planning module of the machine tool, and the tool position file is partially trimmed and then transmitted to the preprocessing system. Using the virtual axis interpolation plan, the tool path file generated by the preprocessing system suitable for the virtual axis machine tool is coarsely interpolated in the virtual axis space Cartesian space. According to the motion mapping relationship between the real axis and the imaginary axis, the motion instruction of the real axis is obtained. In order to achieve accurate motion trajectory, fine interpolation is applied to the movement process of the 6 drive rods of the real axis. Finally, the position command of each sampling period is transmitted to the servo system, and the machine tool is realized to realize the final virtual space machine tool space quick check algorithm. Research - Li Tiemin Wang Jin loose.
It can be seen from Fig. 2 that the inspection of the working space has been carried out in the offline processing stage of the system, but in the actual control of the machine tool, there may be a case of changing the length of the tool or jogging a long distance in real time, so in the real-time processing part It must have the function of job space verification, which can be achieved by a single-chain-based virtual real mapping algorithm.
The flow of the virtual and real mapping algorithm based on single open chain is as follows: 1 The system initializes the structural parameters of VAT1Y, including the 8 parameters of the model and the telescopic range of the legs, the limit deflection angle of the Hooke hinge and the ball joint.
Length change and angle change length change In the test leg length and hinge limit, the general method is to use the kinematic inverse solution to find the length of each servo rod in a certain position, and perform the range test of the leg length to establish the ball joint or the hook. The range of motion of the hinge is used to determine the angle between the servo leg and the moving platform or the static platform in the pose, and to determine the angle limit. By simply comparing the two algorithms, the single-turn angle change chain analysis method has a limited improvement on the speed of operation, but if the whole single-chain analysis method is directly started from the kinematics of the mechanism, it is only necessary to perform the inverse kinematics transformation. It is possible to find all the input variables, so that the result of the inverse kinematics in the virtual and real transformation can be directly used, and other calculations are avoided, so that the speed of the numerical control system can be significantly improved.
In the development of VAT1Y CNC system, the tool movement trajectory was tested in real time by the method described above. On the 166Hz industrial control 586 computer, the time required to complete the sub-test is less than 0.1s. It can be seen that the method can fully meet the virtual axis machine tool numerical control. The real-time requirements of the system.