Cycloid Approximation with Circle for the Calculation of Exit Angle

Manufacturers’ goal is to control, avoid or minimise burr during manufacturing. Burr control is used frequently, because it costs less and/or is less time-consuming. Based on the experimental results and simulations in the case of face milling it has been stated that exit order and planar exit angle have a significant influence on burr formation. A carefully planned tool path can provide constant exit angle. Setting the exit angle to an appropriate value or range, burr can be avoided or minimised. The exit angle can be determined approximately in a simple way, using a circle as a path of tool tip. The precise value of the error of the approximated calculation of exit angle has not been revealed yet. In this paper, this error is examined. The slope of a circle and the theoretically accurate cycloid curve can be expressed analytically. The difference between the two slopes can be calculated. Its maxima or minima give the value of the error which can be deducted into simple equations that are valid either for linear or circular feed. If the exit angle is changing, the chip thickness is also changing. With the help of the resulted expressions, a special workpiece contour can be designed, where the exit angle is constant and only the chip thickness is changing. In this way, the examination of the effect of the chip thickness on burr formation will be possible