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The emergence of virtual axis CNC machine tools is considered to be the most revolutionary machine tool design breakthrough of this century. This new type of machine tool completely breaks the concept of the traditional machine tool structure, abandoning the fixed guide tool guide mode, and instead uses a six-bar parallel mechanism to drive, completely eliminating the cantilever structure, so that its rigidity can be increased by about five times compared with the conventional machine tool, so that the machining Accuracy and machining quality are greatly improved, and its feed rate and acceleration are several times higher than conventional machine tools, which is very advantageous for high speed and ultra high speed machining. In addition, the overall weight of the machine tool is small, the raw material consumption is small, the processing amount is small, and the mechanical structure is simple, the parts are generalized and the degree of standardization is high, which greatly facilitates the economical mass production of the machine tool manufacturer.
In view of the many advantages mentioned above, and the importance of promoting the development of machine tools, manufacturing and related disciplines and industries, its research and development has been widely recognized by countries all over the world, and has become a hot spot in the field of machine tool research in the world. For the analysis of the virtual axis machine tool, it can be seen that the biggest feature of this machine tool is the simple mechanical structure and complicated control. Therefore, in order to develop virtual axis CNC machine tools with Chinese characteristics in light of national conditions, we must first solve their control problems and research and develop a high-performance virtual axis machine tool numerical control system.
Because the virtual axis machine tool has six degrees of motion freedom, there is serious nonlinearity and deep coupling in the control relationship, so that the existing numerical control algorithm can not directly control it, and it is difficult to use the existing numerical control programming software to generate input information. Therefore, it has increased the difficulty of the development of its control system and affected the promotion and application of this new type of CNC machine tool.
In order to solve this problem, this paper proposes a direct control method for the trajectory of the virtual axis machine tool. The basic idea is to input the geometric information and process information of the machined part into the machine tool control system, and the control algorithm generates the cutting trajectory on the machined surface. The Tool Motion Control Directive, and the Journal of Instrumentation, was received in November 1998.
According to this, the control of the multi-degree-of-freedom movement of the machine tool is realized, thereby not only eliminating various problems caused by off-line programming of the virtual axis machine tool, but also effectively improving the machining precision and machining efficiency of the part, in order to fully utilize the virtual axis machine tool. Efficient and high-precision machining capabilities open up new avenues.
The basic principle of the direct control of the virtual axis machine tool trajectory is shown in Figure 1. The spindle unit of the machine is supported above the table by six variable length drive rods. The other end of the six drive rods is fixed to the base frame. Adjusting the length of the six drive rods allows the spindle and the tool to move in six degrees of freedom, including translational motion along three linear virtual axes X, Y, Z and rotational motion along three rotational virtual axes A, B.
Then, how to control the length of the six drive rods, in order to make the tool's motion track and attitude meet the processing requirements, this is the core problem of virtual axis machine control. The basic idea of ​​solving this problem is divided into three steps. The first step is to generate the tool motion trajectory in real time according to the input information in the virtual axis space, and solve the desired motion of each virtual axis. The second step is to virtualize the virtual axis. The desired amount of motion of the shaft is converted to the desired amount of motion of the real axis, ie the desired length of the six drive rods is calculated in real time. Finally, the required tool motion trajectory can be obtained by decoupling the follower control so that the actual length of the drive rod and the desired length are caused, as well as the real inverse virtual transformation implicitly realized by the machine structure.
According to the above ideas, this paper proposes a multi-level hierarchical control scheme, the principle is shown in Figure 2. The main modules are introduced below.
Cutting path planning The cutting path is the path that the cutting point of the tool should follow along the surface of the workpiece and is the basis for generating the tool trajectory. The cutting path planning solves how to solve the cutting path expression and determine the relevant parameters according to the input information of the numerical control system, such as the geometric information of the machined part and the process information. The following is an example of machining a free-form surface to introduce the solution process of the problem.
If the surface to be machined is represented by a bicubic spline surface, the geometric information input to the control system can be given by the geometric coefficient matrix P. The expression is: where the control point of the P-B spline patch is based on P. The expression of the machined surface is established: S ( u, v ) in the formula - the position vector of any point on the B-spline surface - the component of the constant matrix S ( u, v) in the X, Y, Z coordinate direction is called the coordinate The function, whose expression is: P in the formula - the process information required for the matrix cutting path planning consisting of the components of the elements in the geometric coefficient matrix P: the starting position, the direction of the cutting, the way of the cutting, and the traveling Direction, tool size, allow instrumentation journal errors, etc. Based on this information, the cutting plane for each cut can be determined from the initial position: the curves obtained by intersecting these mutually parallel planes with the machined surface of the part are the cutting paths on the surface of the workpiece. The first cutting path obtained by intersecting the jth cutting plane with the machining surface of the part is shown in Fig. 3. The uv domain expression is: 4 The cutting path generates the cutting trajectory in real time. The key problem to be solved is (5) The given time-independent cutting path is converted to a discretized cutting trajectory associated with time. The idea of ​​accomplishing this task is to generate an interpolation straight line segment L k , . . . according to a given feed speed and tolerance, and use it to approximate the cutting path to gradually obtain the coordinate values ​​of the discrete points k , . . . Obviously, this is a direct interpolation of free-form surfaces.
Since the interpolation calculation is not a static geometric calculation, it must not only make the distance between the current interpolation point and the front interpolation point meet the requirements of feed rate and acceleration and deceleration, but also ensure the interpolation straight line between the two points. The error between the interpolated surface and the interpolated surface is within a given tolerance. In order to meet the above requirements, this paper adopts the direct interpolation algorithm with the instantaneous feed rate as the control target and the allowable error as the constraint condition. The basic process is as follows.
First, the instantaneous feed rate F is given by the acceleration/deceleration calculation, and the desired chord length in the current sampling period (the length of the interpolation straight line segment without constraint) is calculated by the following formula.
δL - the desired chord length (mm) T - sampling period (milliseconds) At the same time, according to the allowable error, calculate the constrained chord length according to the error relationship in Figure 4: where e - the allowable between the actual cutting trajectory and the desired cutting trajectory Error r - the average radius of curvature of the ball cutter radius to the desired trajectory between the points. If the desired chord length is less than the constraint chord length, the current interpolation straight line segment length is 1; otherwise, ΔL is taken, and then the chord length varies according to the parameter. Sensitivity, select (8) or (9) to calculate the value of u (or v) at point P and then substituting u) into equation (5) to solve the actual value of the other variable at P.
Because the interpolation frequency is higher, the arc length is very close to the chord length in each sampling period, so in the actual calculation, du / ds ≈ Δu / ΔL. Let u take the increment Δu, and then find the corresponding ΔL. To obtain the same reason, you can also find the final, and substitute u and the coordinate function expression (3) to get the coordinate value X of the P point. (u 5 Tool movement track calculation Tool movement track refers to a point on the tool ( For example, the movement path of the ball head. The machining path of the tool needs to be completed in two steps. The first step is to obtain the unit normal vector N ( u, v ) of the cutting point according to the geometric information of the machining surface. The expression is: In the second step, the tool motion trajectory corresponding to the cutting trajectory is obtained according to the tool information and the obtained normal vector information. When the ball end milling cutter is used, the tool radius r is offset along the normal direction to obtain the tool knives. The ball virtual axis machine tool tool motion track directly controls the tool motion track represented by the heart coordinate function.
In the formula, N - the unit of the unit vector N in the X, Y, and Z coordinate axes, the value at the point is substituted into the above formula, and the coordinate value of the point corresponding to the point on the tool path is obtained, that is, the motion of the linear virtual axis. Control instruction.
It can be seen from equation (11) that different sizes of tools are used, although the generated tool movement trajectories are different, but the cutting trajectory can be kept unchanged. This means that this tool path direct control method can easily realize real-time compensation of 3D tool size.
6 Tool motion attitude calculation In the virtual axis machine tool, the tool axis vector L can be used to describe the tool attitude. The task of tool motion attitude calculation is to calculate the value of the tool axis vector L at that time from the known unit normal vector N of the workpiece surface at the current cutting point according to the machine structure and machining requirements.
In the general processing of curved surfaces, ball-end milling cutters are often used. In order to ensure the machining quality of the surface of the parts, the cutting speed is constant. This requires that the tool axis is centered on the normal of the cutting point, the center of the tool is the apex and the half-angle is φ. Conical surface. At the same time, in order to make the machine tool in a better stress condition during the machining process, the angle between the tool axis and the Z axis of the machine tool should be as small as possible. Therefore, the following method is used to solve the tool attitude.
The tool coordinate system whose origin is located at the center of the tool is established, and its coordinate axis X is parallel to the X, Y, and Z axes of the machine coordinate system. The center of the tool is made into a plane to include the Z axis and the normal of the cutting point, and then the point of the tool point is straight on the plane, and the angle between the line and the normal of the cutting point is equal to the half of the cone of the tool axis. Angle φ, this line is the feasible tool axis.
The three components L z of the tool axis vector L are obtained by the following equation, that is, the tool posture at the current time is quantitatively determined.
It should be pointed out that when the normal of the cutting point is close to the Z axis, the transition processing is required, and the algorithm is cumbersome, and another special article will be introduced.
Real-axis motion control Real-axis motion control includes two steps of real-axis motion calculation and decoupling follow-up control. The main task of the real axis motion calculation is to solve the desired amount of motion of the six drive rods according to the virtual axis motion command. The realization process is as follows: when the initial state is set, the tool axis is parallel to the Z axis, and the tool attitude = L. The corresponding dynamic platform attitude (represented by the rotation coordinate A of the winding axis) is A = 0. According to the structure of the moving platform, The initial position of the end point (moving end point) of the six-drive rod supporting the moving platform in the tool coordinate system is obtained: if the tool posture becomes L zk at time k, the rotation angle of the moving platform around the X-axis can be obtained: the corresponding rotation The transformation matrix is: the same can be used to find the rotation angle of the moving platform around the Yt axis: the corresponding rotation transformation matrix is: because the rotation angle of the moving platform around the Z axis is zero, so the rotation transformation matrix: thus the time can be calculated The position of the six-drive rod end point in the tool coordinate system: then, at this moment, the coordinate values ​​of the six-drive rod end point in the machine coordinate system are: according to the six-drive rod end point coordinates obtained above and according to the machine structure Know the static endpoint coordinates, press ( 21 )
The desired value of the length of each drive rod instrumentation journal can be obtained, thereby obtaining the real axis motion command value.
In the formula, the coordinate value of the static end point of the six-drive rod in the machine coordinate system is finally realized. By decoupling the follow-up control to ensure the actual length and the desired length of the drive rod, real-axis linkage control that meets the requirements of the tool path can be realized. The implementation method has been described in detail in the article.
Simulation Experiment Results In order to verify the correctness and feasibility of the proposed method, several simulation experiments were carried out. The experiment was carried out on a CNC system developed with the Pentium microcomputer as the core. The system uses a direct control algorithm for the trajectory of the virtual axis machine tool with a frequency of 266 Hz in a language 32-bit assembly language mixed programming.
shape. In the figure, the intersection of the curves is the shape point of the free-form surface, a total of 361. Figure 6 shows the tool motion trajectory and tool motion attitude (represented by the tool axis vector) generated by the control software. For clarity, the tool path and attitude in the figure are displayed in an interlaced manner. The illustrated results and data sampling results show that the proposed method is correct.
After testing, the time taken to complete the real-time control calculation cycle (calculating the interpolated straight line segment on the surface and the corresponding tool path point coordinate value and the real axis motion amount) is about 3 s. Thus, in the sampling period of the numerical control system The remaining 2s, that is, 40 machine hours can be used to complete other functions of the CNC system, such as graphic display, human-computer interaction, information processing, and switching control. This shows that this tool path direct control method can be realized in the N system based on high-end microcomputer.
Conclusion The biggest feature of virtual axis machine tools is the simple mechanical structure and complicated control. Therefore, in order to develop a virtual axis CNC machine tool with Chinese characteristics in light of national conditions, it is necessary to first solve its control problem and research and develop a high-performance virtual axis machine tool numerical control system.
Aiming at the particularity of virtual axis machine tool control, this paper proposes a direct control method for the tool path of virtual axis machine tool. This method can directly generate the tool desired track and virtual axis motion command according to the part geometry information and machining process information, and through virtual and real mapping. Realize the linkage control of the real axis, thus effectively ensuring that the actual trajectory of the tool is consistent with the desired trajectory, which opens up a new way for the efficient control of the virtual axis machine tool.
Theoretical analysis and simulation experiments prove that the principles and methods proposed in this paper are feasible, which lays a necessary theoretical and technical foundation for the development of a new generation of virtual axis machine tool numerical control system.