An approach to calculate grinding wheel path for complex end mill groove grinding based on an optimization algorithm

Applying complex groove with variable helical angle, rake angle, core radius or groove width along tool axis is an essential way to improve the cutting performance of solid end mills. However, the usage of complex groove is limited due to the lack of an effective way to calculate wheel path for its machining, because the previous envelope theory or trial-and-error method that used for simple constant groove can no longer be used for complex groove. In this paper, a general model is established to calculate the wheel path for complex groove machining based on a mathematical optimization model, which have three constraints and one objective. First, the complex groove is defined by four curves, namely the edge curve, rake curve, core curve and flank curve, so that the variable helical angle, rake angle, core radius and groove width can be expressed by mathematical formulas. Second, the grinding wheel path is expressed as a series of its position vectors, including three location parameters and three posture parameters. Then, these vectors are calculated by searching the minimum machining error of groove width with three constraints: contact constraint to meet the rake and core radius requirements, groove width constraint to prevent the overcut with the adjacent edge and non-interfere constraint to prohibit the interfere with the current edge. Finally, the accuracy and efficiency of the model are validated by five experiments with different designed complex grooves.