Solid ceramic mills are a promising technological solution for cutting heat-resistant materials. Although nanostructured cutting ceramics has a number of valuable physical and mechanical properties providing high operational performance of mills, it has low strength. The design of a solid ceramic mills is formed by smooth surfaces without stress concentrators to ensure operability and to reduce the probability of failure. The most important structural element of solid ceramic end mill is a helical groove with a negative rake angle needed to increase surface strength. This groove can be machined with standard grinding wheels of type 1A1 or 1V1. However, the application of grinding wheels of a standard shape requires the use of reduced cutting parameters to prevent chipping on the forming sections of the cutter. Chipping can be caused by too short length of the contact line and the stress concentration at the end point of the profile of the grinding wheel, which is typically fully responsible for shaping the front surface and its transition to the tooth back. In this paper, in order to increase the contact line, we develop a new approach to designing grinding wheels for machining helical grooves of solid mills and determining rational technological and operational parameters for there use. A new approach is developed based on the fundamental principles of analytical geometry and linear algebra, numerical methods and basic axioms of the shaping theory. In this study, we have identified the key relationships between parameters determining the position of the grinding wheel relative to the workpiece and the geometrical parameters of a solid ceramic mills. The developed approach allowing to determine the specific design of the grinding wheel, depending on the initial parameters of the mill and the trajectory of the axis of the wheel relative to the mill, was implemented in the MathCAD environment.

固态陶瓷磨是一种用于切割耐热材料的有前途的技术解决方案。尽管纳米结构切割陶瓷具有许多有价值的物理和机械性能，可提供轧机的高运行性能，但强度却很低。坚固的陶瓷磨机的设计是由没有应力集中器的光滑表面形成的，以确保可操作性并减少故障的可能性。固态陶瓷立铣刀最重要的结构元素是具有负前角的螺旋凹槽，需要增加表面强度。该凹槽可以用1A1或1V1型标准砂轮加工。但是，使用标准形状的砂轮需要使用减少的切割参数，以防止在切割机的成型部分上碎裂。切屑的产生可能是由于接触线的长度太短以及砂轮轮廓的终点处的应力集中而引起的，这通常完全负责使前表面成形以及过渡到齿背。在本文中，为了增加接触线，我们开发了一种新的方法来设计用于加工实心轧机螺旋凹槽的砂轮，并确定合理的技术和操作参数。基于解析几何和线性代数的基本原理，数值方法和成形理论的基本公理，开发了一种新方法。在这项研究中，我们确定了确定砂轮相对于工件位置的参数与实体陶瓷磨机的几何参数之间的关键关系。