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Generating design method for machine tool motion function program
**Abstract**
This paper presents a systematic approach to analyzing the interaction between a tool and a workpiece, focusing on the relative motion described by the tool pose matrix. The tool pose matrix is implemented through a motion cascade matrix, enabling the design of the machine tool's movement function. The methodology outlines the main steps required to generate all possible movement programs for a machine tool. A three-axis machine tool example is used to demonstrate the effectiveness of the proposed method.
**Keywords:** Machine tool design, motion function, surface machining, kinematic synthesis, tool path planning
**1. Introduction**
Designing the motion function of a machine tool is a critical first step in the development process. Traditional methods rely heavily on existing examples and experience-based analogies, which often result in limited innovation and simplified designs. With the increasing demand for customized, small-batch products, there is a growing need for a theoretical framework that allows for the creation of motion functions without prior knowledge of specific machine configurations. This paper introduces a novel method based on the analysis of tool and workpiece surfaces to generate new machine tool motion functions. While this approach has been applied to two-dimensional surface processing, this study expands its application to three-coordinate systems, providing a detailed explanation of the entire design process.
**2. Description of Tool and Workpiece Information**
The foundation of the motion function design lies in the concept of the cutting surface of the tool [1]. This refers to the part of the tool that comes into contact with the surface being machined. Depending on the type of tool, the cutting surface can be a point, line, or plane. For instance, a cylindrical cutter’s cutting surface is a circular line around its axis, while an end mill has a flat circular cutting surface. These surfaces are created through rotational motion, and their description is essential for defining the relationship between the tool and the workpiece.
**2.1 Mathematical Description of the Cutting Surface**
The cutting surface is described using a homogeneous transformation matrix. In Figure 1, the coordinate system OP represents the cutting surface, and OC represents the local coordinate system of a point on it. The matrix [TPC] captures the position and orientation of the tool’s cutting surface within the OP frame. This mathematical model provides a structured way to represent the geometry of the cutting surface.
**2.2 Mathematical Description of the Machined Surface**
Similarly, the machined surface is described using a homogeneous matrix. In Figure 2, the coordinate system OW represents the workpiece, and OS represents a local coordinate system at a point on the machined surface. The matrix [WTS] defines the orientation and position of the machined surface relative to the workpiece.
**2.3 Determination of Tool Pose Conditions**
By aligning the OC and OS coordinate systems, the relative position and orientation of the tool and workpiece can be determined. This relationship is captured in the tool pose matrix [WTP], which is derived from the inverse of the tool’s cutting surface matrix. The matrix must also satisfy interference-free conditions to ensure that the tool does not collide with the workpiece during operation.
**3. Design Method of Machine Tool Motion Function**
Once the tool pose matrix [WTP] is established, the next challenge is determining the necessary motion units (e.g., translation or rotation) required to achieve the desired motion. This is done using a motion cascade matrix [TWP], which links the tool and workpiece coordinate systems. By solving the equation [TWP] = [WTP], various motion schemes can be generated. The hierarchical approach involves analyzing the motion required for both the generatrix (busbar) and wire (generator) of the surface, then combining these motions to form a complete motion program.
**4. Example Analysis**
To illustrate the method, a cylindrical cutter is used to machine a cylindrical surface. The generatrix is a circle defined by θZW, while the wire is a straight line along Z. The tool’s motion is described using a combination of rotational and translational movements. Several solutions are found, including combinations like W/XYZ/γp/T and W/XZγ/γp/T. These motion programs represent different ways to achieve the same machining task, offering flexibility in machine design.
**5. Conclusion**
This paper proposes a new method for designing machine tool motion functions based on the analysis of tool and workpiece surfaces. The approach uses the tool pose matrix and motion cascade matrix to systematically define the required motion units. The method has been successfully applied to a three-axis machine tool, demonstrating its versatility and effectiveness. It provides a solid theoretical foundation for future research in developing machine tools that do not depend on prior knowledge of specific configurations.