Zhang Yanhong's principle of adjusting the parameters of the machine tool into the adjustment parameters of the machine tool Zhang Yanhong, Wu Lianyin, Wei Hongqin, Wang Xiaoyu (Institute of Numerical Control Technology, Xi'an Jiaotong University, Xi'an 710049, China), the principle of the number is simple, only two times of vector rotation is required. The transformation method, and derives the conversion formula expressed by explicit expression. Through the derivation, the exact solution of the high-order Taylor expansion polynomial coefficients of each motion axis of FreeFor machine tool can be obtained. The conversion method has clear principle and simple conversion, and the expression formula expressed by the explicit expression can meet the requirements of real-time interpolation of the numerical control system, which is different from other transformation methods.
Introduction The introduction of the FreeFor gear milling machine is a major revolution in the gear machining process. It not only greatly simplifies the machine structure, but also achieves numerical control, and can improve the machining accuracy, quality and meshing performance of the gears, and accurately simulate the traditional machining methods. The tooth type is not limited, it is an efficient and versatile CNC cutting machine. First proposed and put into practice is the Gleason's universal spiral bevel gear and hyperbolic gear cutting machine, also known as FreeFor machine. Several domestic manufacturers have introduced such machine tools, but they rely on the processing software provided by the foreign parties, and cannot independently develop products. At present, the machine tool developed by Professor Wang Xiaoyu and the Qin Machine Tool Factory of Xi'an Jiaotong University has been basically developed on the basis of independent copyright software, and the overall performance will be even better than that of similar foreign products. Under the condition of ensuring the relative position and motion between the workpiece and the tool, the traditional machine parameters are transformed into the parameters of the motion axis of the Free For machine. The coordinated movement of the six axes can be processed to the same tooth shape as the conventional machine. Gears. The correct conversion is the guarantee for the correct tooth shape of the FreeFor machine. This paper analyzes the principle of transforming the most complicated knife-turning gear adjustment parameters into FreeFor adjustment parameters in the traditional machine tool, and deduces the corresponding Conversion formula.
The transformation method proposed by the literature is complex and computationally intensive, and it is impossible to use it for real-time control. Although the conversion formula proposed in the literature is simple, it can not guarantee the relative motion relationship between the cutter head and the workpiece. The geometry and motion principle are wrong. The literature gives a general form of polynomial interpolation, which can meet the requirements of high-precision real-time control, but does not give the conversion principle and related formulas. In this paper, through the research on the motion of FreeFor milling machine, a new transformation method is proposed, and the exact solution and the exact solution of the coefficients of each motion axis polynomial expression are derived.
1 Introduction to FreeFor Gear Milling Machine This machine realizes all the movements required for gear machining with a six-axis CNC axis. It eliminates the cradle, knife tilt and eccentric mechanism. It has six linkage axes: three translation axes X , Y, Z three rotation axes A, B, . The structure is shown in Figure 1. The six axes provide six degrees of freedom for flexible control of the position and movement of the workpiece and tool in space. When machining on a FreeFor machine, the motion of the tool and the workpiece is decomposed into linear motions in the X, Y, and Z directions and A, B, and three rotary motions. The axis of the cutter head is parallel to the Z axis, and the workpiece axis is parallel to the X Z plane. The expression of each motion axis can be expressed by a high-order polynomial, and the improvement improves the machining accuracy. For example, the X-axis can be expressed as a fourth-order polynomial. The five coefficients in the equation can be obtained by deriving at the reference point. Therefore, the tooth surface of the workpiece machined by the FreeFor type gear can reach the fourth-order contact with the tooth surface of the conventional machine tool. . The workpiece and the cutter head are driven by six CNC axes, and the actual development motion is completed by the composite space motion.
Mechanical Science and Technology 2 Introduction to Knife-Dip Machine Tool Knife-type machine tool is a movement of the production wheel and workpiece formed by the rotation of the cutter head. The schematic diagram of the turret machine tool with the cutter axis F and the tool angle is simplified as shown in Fig. 2. The symbols in the figure are: O is the center of the shaker A is the workpiece axis V is the installation root cone angle O is the cutter center O is the workpiece root cone vertex x is the horizontal wheel is the vertical wheel position S is the knife radius q is the knife position angle.
Taking the tool position polar angle q at the reference point of the tooth surface as the reference point, and letting it turn the angle h= t, then at the time t, the tool position polar angle t. At this time, the vector of the cutter head axis is represented as the workpiece root cone. The relative position between the apex and the center of the cutter head is the vector represented by the workpiece axis A as the three vectors to determine the relative position and motion of the workpiece and the tool at any time.
3 Conversion principle and formula (1) Conversion principle As can be seen from the above two sections, in a conventional machine tool with a knife tilting mechanism, the tool axis is not parallel to the Z axis. In a FreeFor machine, the tool axis is parallel to the Z axis and the workpiece axis is parallel to the X Z plane. In order to be able to machine the same tooth profile as a knife-type machine in a FreeFor machine, the relative position and relative motion of the workpiece and tool must be the same as for a knife-type machine. To this end, this paper proposes a simple conversion method: the workpiece in the traditional machine tool and the cutter head as a rigid body are rotated around the workpiece axis A by a ΔT angle so that the tool axis is parallel to the XZ plane, and then the Y axis is rotated by ΔU angle to make the knife The axis is parallel to the Z axis. In this way, the relative positional relationship of the tool tilting machine is converted to the FreeFor machine while keeping the relative position of the workpiece and the tool unchanged. In two rotations, the A axis is always in the plane. The relative position and motion relationship between the cutter head and the workpiece after transformation can be represented by the vector of the tool axis, the workpiece axis vector and the root cone apex O to the center O of the cutter head. Before they are converted, f, a, and R are expressed as ΔT angle around the workpiece axis A, and then expressed by f around the y-axis around the Y-axis.
(2) Any straight line nk) of the origin of the coordinate system given by the conversion matrix, l, and n are the cosines of the direction of the straight line l, then the homogeneous transformation matrix of the θ angle rotated counterclockwise around the line is (3) transformation The transformation formula sought in this section is the expression of f after two rotations, and then the expression of each motion axis can be obtained. Therefore, we must first find the angles ΔT and ΔU that are rotated twice. Then, by using the transformation matrix formula of the upper section, we can obtain the transformation matrix ( aΔT ) R and obtain the expression of the converted f. ΔT and ΔU can be obtained by the vector relationship of two rotations, respectively.
First, find the angle of ΔT. Figure 3 is a schematic diagram of f rotating ΔT to f around the A axis. In the figure, the plane determined by the vectors a and f is the XZ plane, and the converted cutter axis is in the XZ plane, where l is the modulus of the vector l, l= (a×j )? f, from which ΔT can be determined as the second f rotation around the Y axis, so that the tool axis is parallel to the axis. Since the tool axis is perpendicular to the X axis after rotation, the angle between the A axis and the tool axis is always the same, so the U angle shown in Fig. 4 is the angle between the workpiece axis and the X axis after conversion, and thus ΔT and ΔU are obtained. After that, the expression of f after conversion can be obtained: in the FreeFor machining system, the coordinate system with the O as the reference origin and the coordinate axes X, Y, Z and the original coordinate axis is established, then O is in the new coordinate. The position in the system is: xi yj zk. It can be determined that the expressions in the FreeFor machine are Zhang Yanhong, etc.: The principle of the tool adjustment parameter is converted to the FreeFor machine tool adjustment parameter. The angle at which the workpiece turns when engaged at time t is a function of t. Its order derivative is the angular velocity of the workpiece in a knife-type machine.
The coefficients of the polynomial expressions of the respective axes can be obtained by deriving at the reference point. Taking the X-axis as an example, the coefficients in equation (1) are solved as follows: the expression coefficients of the remaining axes Y, Z, A, B are found to be the same as the X-axis.
The coefficients for the X, Y, and Z axes can also be obtained by the motion relationship before and after the conversion. The following is a brief description: the motion of the converted R can be seen as the relative motion of the R before the transformation, and the workpiece is rotated around the A axis. The rotation of the ΔT angle and the angle ΔU around the Y axis is the implicated motion. The absolute motion of R and its derivatives are obtained from the superposition of the two motions, and the coefficients of the X, Y, and Z axes are obtained.
(Note that due to the implicated motion as the rotation, there is a Coriolis acceleration when the superposition is superimposed). This method is also easy to implement on a computer.
4 Conclusion The principle of this transformation is simple. It can meet the real-time control of numerical control on the computer. Because the formula is expressly expressed, it can be easily obtained by deriving the coefficients of the expression, which is more accurate than the difference method. It is an accurate and efficient method. Conversion method.
[References] Technology and Machine Tools, 1997 Yuan Zhonghu et al. Deadlock avoidance control for class parallel mutual exclusion manufacturing systems [5] Wu Naiqi. Deadlock avoidance under multipath conditions in flexible manufacturing systems, Part 1: System modeling [J]. Information and Control, 1997, 26 (6): Mechanical Science and Technology
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