From the machining center (MC) user's point of view, the authors propose a practical approach to estimate the trajectory error of a linear interpolation cutter path produced by the linear acceleration/deceleration (Acc/Dec) processing for a target MC in this paper. Firstly, a simple and convenient motion model is established for describing the behavior of the servo axes corresponding to the linear Acc/Dec procession of a linear segment, which can be applied to any linear segment regardless of length. Based on the model and a linearity assumption on the dynamics of servo system, a simulation method is developed to precisely calculate the cutter path trajectory in detail together with the servo axis speed from the motion parameters commanded in NC program. The algorithm not only has a very simple structure but also demonstrates high efficiency in actual calculation. In order to confirm the effect of the approach, verification experiments have been performed on the target MC, in which specially designed cutter paths were inspected by a cross grid measuring device with high resolution in non-contact state. These measured trajectories are compared and discussed with the ones simulated under the same motion parameters, from different perspectives. The examination results sufficiently demonstrate the effectiveness of the proposed model and simulation method. Therefore, as a useful tool, the approach provides a potential application possibility, i.e. beforehand estimating the influence of the NC Acc/Dec processing on cutter path accuracy or judging the motion conditions for the machining purpose without performing an actual machining with the target MC.

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In NC machining of planar contours, the cutter path is frequently approximated by linear interpolation to a contour curve as target. In this situation, the interpolation error should be measured along the normal direction of the contour curve, and it is desired that only the fewest linear segments are needed with respect to the specified accuracy. However, how to determine the parameters of segment to match these requirements has not been completely solved. This paper presents a new linear interpolation approach for this problem. The approach is named as the optimal linear interpolation method and has three features which include: (1) the interpolation error along the normal direction of object curve satisfies the specified accuracy, and the number of the required segments is the fewest simultaneously; (2) the connection between any two adjacent segments on generated cutter path is natural and smooth, and the generation of extremely short segment is avoided as much as possible; (3) the algorithm is simple and with a high computation efficiency. The effectiveness of the proposed approach has been sufficiently confirmed by applying it to two interpolation examples of planar cam contours. At the same time, the reduction effect of interpolation data has also been verified through comparing the segment number required by the proposed method and Nishioka's method, which is specially developed to precision machining of planar cam contour, relative to the same interpolation conditions.