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Advanced Modeling and Optimization of Manufacturing Processes

The prediction of cutting forces is important for the planning and optimization of machining process in order to reduce machining damage. Helical milling is a kind of hole-machining technique with a milling tool feeding on a helical path into the workpiece, and thus, both the periphery cutting edges and the bottom cutting edges all participated in the machining process. In order to investigate the characteristics of discontinuous milling resulting in the time varying undeformed chip thickness and cutting forces direction, this paper establishes a novel analytic cutting force model of the helical milling based on the helical milling principle. Dynamic cutting forces are measured and analyzed under different cutting parameters for the titanium alloy (Ti–6Al–4V). Cutting force coefficients are identified and discussed based on the experimental test. Analytical model prediction is compared with experiment testing. It is noted that the analytical results are in good agreement with the experimental data; thus, the established cutting force model can be utilized as an effective tool to predict the change of cutting forces in helical milling process under different cutting conditions.

Prediction of cutting forces in helical milling process

Radial cutter runout is a common issue in milling processes and has a direct effect on milling stability due to variations of resulting chip load and forces. This paper presents a new method to effectively model and predict the instantaneous cutting forces in 5-axis milling processes with radial cutter runout based on tool motion analysis. First, the undeformed chip thickness model taking runout effect into account is established under continuous change of cutter axis orientation by means of the sweep traces of cutter edges. Second, the engaged cutting edge is determined and cutting coefficients are subsequently calibrated. Finally, the method of identifying runout parameters from the measured cutting forces is proposed, and mechanistic method is then applied to predict the cutting force. Since this method is completely based on the relative motion analysis of tool-part, it can reduce the prediction errors of cutting forces effectively and is suitable for generic rotation cutters. Several validation examples are given under different cutting conditions to prove its effectiveness and accuracy. The results reveal that the developed method can predict the cutter forces with a high accuracy and has the ability to be used in simulations and optimizations of five-axis machining.

Numerical simulation and prediction of cutting forces in five-axis milling processes with cutter run-out

This paper presents an approach to predict cutting force in 3-axis ball end milling of sculptured surface with Z-level contouring tool path. The variable feed turning angle is proposed to denote the angular position of feed direction within tool axis perpendicular plane. In order to precisely describe the variation of feed turning angle and cutter engagement, the whole process of sculptured surface milling is discretized at intervals of feed per tooth along tool path. Each segmented process is considered as a small steady-state cutting. For each segmented cutting, the feed turning angle is determined according to the position of its start/end points, and the cutter engagement is obtained using a new efficient Z-map method. Both the chip thickness model and cutting force model for steady-state machining are improved for involving the effect of varying feed turning angle and cutter engagement in sculptured surface machining. In validation experiment, a practical 3-axis ball end milling of sculptured surface with Z-level contouring tool path is operated. Comparisons of the predicted cutting forces and the measurements show the reliability of the proposed approach.

Cutting force prediction in ball end milling of sculptured surface with Z-level contouring tool path

The instantaneous uncut chip thickness and entry/exit angle of cutter/workpiece engagement continuously vary with tool path and workpiece geometry in 5-axis flank milling of sculptured surface, which results in the obvious time-varying characteristic for consecutive cutting forces. An accurate prediction method for cutting force in 5-axis flank milling of sculptured surface is proposed in this paper. Comprehensively considering curved tool path and actual tool motion process with cutter runout (offset and inclination) effects, an accurate representation model for instantaneous uncut chip thickness during cutter/workpiece engaging in 5-axis flank milling is presented firstly, which can reach a higher accuracy and efficiency with the aid of linear iteration process than the methods published. Then, based on the thin plate milling experiments, an efficient calibration procedure for cutter runout parameters and specific cutting force coefficients is given and further verified in practice. Finally, a series of validation experiments are conducted under different cutting conditions, and the results reveal that there is a very good agreement between the experimental and simulation data both in shape and magnitude and prove the effectiveness and accuracy of the proposed method.

An accurate prediction method of cutting forces in 5-axis flank milling of sculptured surface

This paper presents an approach for prediction of cutting forces in three-axis ball-end milling of a sculptured surface along an arbitrary tool path. The idea of differentiation is adopted to deal with the problems of varying feed direction, varying cutter engagement, and the consequent varying cutting forces in sculptured surface machining. Based on the differential idea, the whole process of sculptured surface milling is discretized at intervals of feed per tooth, and each segmented process is considered as a small steady-state cutting. For the discrete cuttings, mathematical models of feed turning angle and feed inclination angle are proposed according to the position of start/end points. By using an improved Z-map method, the detailed algorithms of determining the cutter–workpiece interface and the instantaneous in-cut edge segment for sculptured surface machining are suggested. A new integrative chip thickness model which involves the effects of feed turning angle, feed inclination angle, and cutter engagement is also presented. In validation experiment, two practical examples of a sculptured surface three-axis ball-end milling with arbitrary tool path are operated. Comparisons of the predicted cutting forces with the measurements show the effectiveness of the proposed approach.

Prediction of cutting force in ball-end milling of sculptured surface using improved Z-map

Cutting force prediction is important for the planning and optimization of machining process. This paper presents an approach to predict the cutting forces for the whole finishing process of generalized pocket machining. The equivalent feedrate is introduced to quantify the actual speed of cutting cross-section in prediction of cutting force for curved surface milling. For convenience, to analyze the process with varying feed direction and cutter engagement, the milling process for generalized pocket is discretized into a series of small processes. Each of the small processes is transformed into a steady-state machining, using a new approximation method. The cutting geometries of each discrete process, i.e., feed direction, equivalent feedrate per tooth, entry angle, and exit angle are calculated based on the information refined from NC code. An improved cutting force model which involves the effect of feed direction on cutting forces prediction is also presented. A machining example of a freeform pocket is performed, and the measured cutting forces are compared with the predictions. The results show that the proposed approach can effectively predict the variation of cutting forces in generalized pocket machining.

Cutting forces prediction in generalized pocket machining

Modeling of process geometry in peripheral milling of curved surfaces

This paper presents a flexible model for estimating the form error in three-axis ball-end milling of sculptured surface with z-level contouring tool path. At an interval of feed per tooth, the whole process of sculptured surface machining is treated as a combination of sequential small inclined surface milling. For ball-end milling of the inclined surface with z-level contouring tool path, at surface generation position, an analytical model is proposed to identify the feedback effect of tool deflection on cutting edge engagement. The deflection-dependent cutting edge engagement is determined by using an iterative procedure. And ultimately, the form error is obtained from the balanced tool deflection and associated surface inclination angle. In a validation experiment, the estimated form errors are compared with both the measurements and the predictions of a rigid model. It is shown that the proposed flexible model gives significant better predictions of the form error than rigid model. Good agreement between the predicted and measured form errors is demonstrated for the ball-end milling of sculptured surface with z-level contouring tool path.

Zhaocheng Wei

Papers

Cutting force prediction in ball end milling of sculptured surface with Z-level contouring tool path

Prediction of cutting force in ball-end milling of sculptured surface using improved Z-map

Cutting forces prediction in generalized pocket machining

Modeling of process geometry in peripheral milling of curved surfaces

Form error estimation in ball-end milling of sculptured surface with z-level contouring tool path