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首页> 外文期刊>Applied Mathematical Modelling >Mathematical modeling of interrelationships among cutting angles,setting angles and working angles of single-point cutting tools
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Mathematical modeling of interrelationships among cutting angles,setting angles and working angles of single-point cutting tools

机译：单点切削刀具切削角度，设定角度和工作角度之间相互关系的数学建模

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摘要

The angles of a cutting tool play a key role in determining its cutting efficiency. However, once the tool has been mounted on a machine tool, setting errors inevitably cause the working angles of the tool to deviate slightly from the designed cutting angles. Accordingly, this study develops mathematical models to analyze the interrelationships among the tool angles, the setting angles and the working angles. In the proposed approach, a process of homogeneous coordinate transformation is employed to develop a kinematic model of the cutting tool such that the working angles can be derived given the tool angles and setting angles. Mathematical formulae are then developed to inversely derive the tool angles required to generate the specified working angles given prior knowledge of the setting angles. An illustrative numerical example is presented to demonstrate the validity of the proposed approach. Overall, the numerical results confirm that the methodology presented in this study provides a comprehensive, simple and versatile means of modeling a variety of conventional single-point cutting tools.
机译：切削刀具的角度在确定切削效率方面起着关键作用。但是，一旦将工具安装到机床上，设置错误就不可避免地导致工具的工作角度与设计的切削角度略有偏离。因此，本研究建立了数学模型来分析刀具角度，设定角度和工作角度之间的相互关系。在所提出的方法中，采用均匀坐标变换的过程来开发切削刀具的运动学模型，从而可以在给定刀具角度和设定角度的情况下得出工作角度。然后根据给定的设定角知识，开发出数学公式来反推生成特定工作角所需的刀具角。给出了一个说明性的数值示例，以证明所提出方法的有效性。总体而言，数值结果证实了本研究中提供的方法论为建模各种常规单点切削工具提供了一种全面，简单而通用的方法。

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