Keywords: exercise program sports design sports creation machine tools
1 Introduction
The function design of the machine tool movement is the first work to be done in the design of the machine tool. The design method of the traditional machine tool function is based on the existing design examples of the machine tool and is based on experience and analog design. This method is simple, but its innovation is poor, which is the main reason for the simplification of current machine tool products. With the economic development, the market demand for products is multi-category, small-batch, in order to quickly and economically meet the needs of the market, it is necessary to theoretically study and establish a design method that does not rely on prior knowledge of machine tool movement functions. This is of great significance for the brand-new machine tool design. This paper introduces a method based on machining the surface information of the tool and the workpiece and analyzing the machine tool's motion function through analysis, that is, the method of creating a new type of machine tool's motion function. The application of this method in two-dimensional surface processing has been introduced in [1]. This article will introduce the further research results of this method, and take a three-coordinate machine tool as an example to introduce the whole process of the design of the motion function program in detail.
2 tool workpiece information description method
The basis of the design method of the motion function of the generatrix machine tool is the concept of the tool cutting surface [1]. The tool cutting surface refers to the surface on the tool that can be in contact with the surface to be machined. It is a generalized surface, which can be points, lines, Faces (varies depending on the type of cutting face). For the case of the outer cylindrical surface machined by a chip cutter as shown in Fig. 1, the cutting surface of the tool is a circular line around the tool axis; if it is a cylindrical milling cutter, the cutting surface is a cylindrical surface; if it is an end mill, the cutting is performed. The surface is a flat circle, and so on. At this time, the cutting surface of the tool is created by the turning motion of the tool itself, and the cutting surface of the cutting tool only needs one turning motion.
Fig.1 Schematic diagram of outer cylindrical surface of plate cutter
2.1 Mathematical description of the cutting surface of the tool The form of the homogeneous function matrix [2] is used to describe the cutting surface of the tool. In Figure 1, OP is the coordinate system of the cutting surface, OC is the coordinate system of the point on the cutting surface, and the XC coordinates point to the tool. Physical material direction, r is the radius of gyration of the tool. This describes the cutting surface of the tool in the OP coordinate system as follows:
(1)
Among them, CγP=cos(γP), SγP=sin(γP), {xC}C is the coordinate array of the midpoint of the OC coordinate system, {xC}P is the coordinate array of the midpoint of the OP coordinate system, [TPC] is Tool cutting surface description matrix.
2.2 The mathematical description of the machined surface is still described in the form of a homogeneous function matrix. In Figure 2, OW is the workpiece coordinate system. OS is the coordinate system at a point on the machining surface. Take the XS coordinate to point to the outside normal of the machining surface, and the YS coordinate is the tangential direction of the busbar of the machining surface. In this way, the description of the machining surface in the OW coordinate system can be obtained:
(2)
In the formula [WTS] - description matrix of the machined surface
Figure 2 Workpiece Surface Description Coordinate System
2.3 Determination of tool pose conditions With the concept of tool cutting surface, the process of creating a machined surface can be described as creating a machined surface by moving or rotating the tool cutting surface relative to the machined surface. In this process, the tool should be in contact with the surface to be machined, and there should be no interference, that is, satisfying certain contact conditions and interference conditions, so that there is a certain position and posture requirement between the tool (OP) and the workpiece (OW). This relative relationship can be described by the tool pose matrix [WTP].
The contact condition of the cutting surface and the machined surface is that the OC coordinate system coincides with the OS coordinate system, so that the position and orientation matrix of the tool relative to the workpiece can be derived:
[WTP]=[WTS].[TPC]-1 (3)
From the above formula can be seen: [WTP] contains the information of the tool and the workpiece. [WTP] is a condition that should be satisfied during the process of machine tool movement. D. In addition, the necessary interference check is performed on the tool pose matrix obtained above, mainly to check whether other points on the blade edge interfere with the machined surface. If no interference occurs, it means that the requested tool pose matrix is ​​feasible.
3 machine tool movement function design method
With the pose matrix of the tool, the problem that needs to be solved now is how to determine the number, sequence, etc. of the necessary motion units between the tool and the workpiece in the machining process by [WTP]. This article mainly studies the serial machine tool motion function design problem. We use the motion cascade matrix [TWP] between OP and OW to implement [WTP] (as shown in figure 3), ie [TWP]=[WTP] (4)
Fig. 3 Relationship between tool pose matrix and motion cascade matrix
The motion function of the machine tool can be obtained by solving the above equation. Each motion unit arrangement in [TWP] represents a motion scheme. This is a multi-solution inverse kinematics problem, and direct solution is very difficult. Based on the characteristics of tandem movement and the creation principle of machining surface, this paper presents a hierarchical analysis method. If the surface to be machined is S(u,v), it is a bus when v=const, and a wire when u=const. The resolution steps are as follows:
(1) Determine the busbars and wires of the surface to be machined;
(2) Analysis of the motion function when creating a processing bus:
Determine the tool pose matrix [WTP]u when creating a bus, and set the motion cascade matrix [TWP]u according to the characteristics of [WTP]u, and make [TWP]u=[WTP]u (5)
Solving equation (5), if the solved motion unit is a function of u, it indicates that the motion unit is necessary, otherwise the set motion unit is redundant. From this it is possible to determine the required movement unit when creating the bus.
(3) Analysis of the motion function when creating a processing wire:
The method is the same as above;
(4) Synthesis of motion units for generatrix bus and wire:
The motion unit of the generatrix busbar and the generatrix conductor is integrated to form a combined type of basic movement unit when creating a machining surface.
(5) Extend the basic movement unit of the created surface to create all possible movement function programs.
The symbol of the motion unit used in this paper and its relationship with the coordinates are shown in Figure 4.
Figure 4 Motion unit and datum coordinate system
4 Example analysis
As shown in Fig. 1, a cylindrical cutter is used to machine the cylindrical surface, and OW, OP, OS, and OC coordinate systems are respectively established, wherein the processing bus is a circle described by θZW; the wire is a straight line described by Z; and γP is a cutting motion of the tool. Angle; R is the radius of the cylinder being machined. According to the method described above, the machine tool function is analyzed.
(1) Tool orientation matrix for generatrix bus:
(6)
Where CθZW-γP=cos(θZW-γP)
SθZW-γP=sin(θZW-γP)
Taking into account the features of the pose and position terms of equation (6), set the following motion cascade matrix: 
(7)
Among them, b1, a2, a3, b3, aP, bP are the translational coordinate transformations between the motion coordinate systems, and the X, Y translations are contained in X, Y.
By [TWP]u=[WTP]u,
(8)
There are four motion variables X, Y, γ, and γP in the above equation, but there are only three equations. Therefore, it is a multi-solution equation group with the following three solutions:
Solution 1: Let γ = 0, then γP, X, and Y are functions of θZW uniquely determined by the system of equations.
Solution 2: Let X=0, then the system of equations can uniquely determine that γ, γp, and Y are functions of θZW.
Solution 3: Let Y=0, then the equation can uniquely define γ, γP, and X as a function of θZW.
These three sets of solutions can be written in the form of a sport combination:
W/XY/γP/T, W/Xγ/γP/T, W/Yγ/γP/T
The above motion combination represents the combination of the motion units from the tool to the workpiece, where the left side of the equation “W†represents the workpiece, the right side “T†represents the tool, and the middle motion unit represents the relative motion combination between OW and OP. .
The equation above includes the case of linear motion. For the motion of an all-rotational motion unit, taking into account the features of equation (6), a double-gamma motion cascade matrix can be set. Similarly, the motion combination W/γγ/ can be obtained. γP/T.
(2) Motion analysis when creating a wire: The tool pose matrix when creating a wire is
(9)
It can be seen that the pose item in the above equation is not variable, so only one motion unit is needed to create a wire: Z.
(3) Integrate the motion unit of the generatrix generatrix and the wire to obtain the motion combination required for creating a cylindrical surface:
W/XYZ/γp/T, W/XZγ/γp/T, W/YZγ/γp/T, W/γγZ/γp/T
Which W / XYZ / γp / T, W / XZγ / γp / T is the same, take one of them.
(4) Machine tool motion function plan generation: The combined expression obtained by the above formula only represents the number and nature of relative motions between OP and OW. Arranging the motion units in this formula can obtain various solutions. Under the condition of satisfying formula (4), the following 15 kinds of schemes can be obtained (indicated by the ingenious motion formula):
W/XYZ/γp/T, W/XZY/γp/T, W/YXZ/γp/T, W/YZX/γp/T, W/ZXY/γp/T, W/ZYX/γp/T,
W/XZγ/γp/T, W/XγZ/γp/T, W/ZXγ/γp/T, W/ZγX/γp/T, W/γXZ/γp/T, W/γZX/γp/T,
W/Zγγ/γp/T, W/γZγ/γp/T, W/γγZ/γp/T
These 15 kinds of motion programs are all possible motion schemes when the cutter cutter creates a cylindrical surface, representing the required motion unit combination arrangement scheme between the cutter and the workpiece.
Based on the above-mentioned motion function plan, when the structural scheme of the machine tool is created, the motion function needs to be assigned to it, that is, with the base as a reference, the motion unit is assigned to the tool side and the workpiece side, and thus A variety of kinematic structures can be obtained. For example, for Genesis Sports W/XYZ/γp/T, there are four methods for assigning the kinematic function. The base is indicated by “.â€, and there are W/.XYZ/γp/T. W/X .YZ/γp/T,W/XY .Z/γp/T,W/XYZ ./γp/T
Therefore, from the above 15 kinds of invented sports formula can get 60 kinds of movement structure, and then, based on the 60 kinds of movement structure based on the overall structure of the machine tool layout program, you can get a variety of possible machine structure layout program, For specific designs.
In the above, the method for designing and planning a machine tool motion function program was only described by taking a cylindrical cutter as an example. This method is versatile and equally applicable to other types of tools and machining surfaces. For the parts group processing situation, the movement function of the machine tool can be planned through the motion synthesis.
5 Conclusion
This paper presents a method for the creation of a kinematics program for a machine tool using tools and workpieces as input information. By defining the cutting face of the tool, a tool pose matrix is ​​used to describe the relationship between the relative motion between the machined surface and the tool, a method of implementing the position and orientation of the tool using the motion cascade matrix, and a method to analyze the motion function of the machine tool are presented. The analysis of the example shows that the method proposed in this paper is versatile and can effectively create all possible machine tool motion programs. It provides a theoretical basis for establishing a new machine tool motion function design method that does not rely on prior knowledge. .
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