Error compensation in the end milling of pockets: a methodology
Introduction
End milling is a widely used machining process for the manufacture of dies and moulds, as well as high precision aerospace components. Among the factors causing machining errors in the milling process, cutting tool deflection is the most prominent factor. It is difficult to eliminate the deflections errors, but they can be compensated to a large extent by estimating the cutting forces and the corresponding deflection errors by using appropriate force and deflection models. In view of the complexity of the process, modeling of the milling process has been an important research topic. The early investigations focused on the estimation of average cutting forces [1], [2], [3], where as the current interests are concentrated in the areas of process stability, part geometry, surface texture, and robust tool condition monitoring [4], [5], [6], [7], [8], [9].
In the end milling of pockets, the tool deflection due to the cutting forces is the main cause of machining errors. The slender helical end mills used in pocket milling applications experience both static and dynamic deformations, which manifest as dimensional and surface finish errors on the machined part. The tool deflection error is closely related to the cutting tool stiffness [10]. For milling a complex shape or a simple rectangular pocket, the accuracy is mainly influenced by the deflection of end mills caused by variation of the cutting forces due to straight and corner cutting involved [11], [12]. The end milling force and deflection models based on input machining data (tool geometry, cutting conditions, and workpiece material properties) have proven to be applicable for generating accurate and reliable cutting force and deflection error data [13], [14].
For the compensation of deflection errors, fast and accurate estimation of cutting forces and deflection errors is necessary. The cutting force model for end milling applications and discrete deflection models presented in [11] are used for estimating the deflection errors in end milling of pockets consisting of straight and corner sections. It has been shown that the developed force and deflection models give accurate and reliable estimates of the end milling deflection errors. Using the data, a suitable compensation methodology has been developed to integrate the force and deflection models together with input cutting parameters for generating an optimized cutter path. Since the deflection error data required for compensation is voluminous and time consuming, a computerized methodology has been developed. The details of the compensation program algorithms and the path determination program with illustrations of the user interface are presented in this paper.
Section snippets
Determination of cutter path deflection errors
Error compensation of pockets requires determination of cutting forces and deflection errors. End milling cutter deflections can be determined by considering the end mill as a cantilever. The deflection of the end mill is determined according to the cutting forces exerted on the tool, assuming that the force is acting at the center position at the tip of the cutter. The deflection d can be given by:where P is the cutting force acting on the tool tip obtained from Eq. (2), L the
Error compensation scheme
With the calculated deflection errors, the compensated cutter path is determined by dividing the pocket into linear and corner sections.
Case study: slot milling
To implement the program presented, a rectangular pocket is machined as illustrated in Fig. 5. The first section of the program requires the user to input the cutter conditions, i.e. cutting parameters, the cutter geometry, feed per tooth, the designed cutter path of the concerned section. The essential input parameters for the force model and the deflection model are given below. The cutting conditions are set as follows:Workpiece material Aluminum alloy 6061 Strength of material, Sk 469 MPa End
Conclusions
In the presented error-compensation methodology, a cutting force model and appropriate deflection models are used to estimate the deflected cutter path. Based on an assumed preset tolerance value, an ideal compensated cutter path can be calculated so as to adjust the tool path within the limits of specified tolerance. The CPD program helps to determine the compensated cutter path based on the input cutting conditions. The case study presented shows the usefulness of the error compensation
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