International Journal of Machine Tools and Manufacture
Prediction of cutting forces in helical end milling fiber reinforced polymers
Introduction
Machining of composites is a major manufacturing activity in the aircraft and automotive industries. Edge trimming, milling, drilling, turning and grinding are frequently used to finish composite parts and bring them to the assembly requirements. Because of the inhomogeneous nature of composite materials, their response to machining may involve undesirable consequences such as rapid tool wear, fiber pullout, surface burning and smearing, pitting and delamination. All of these responses are directly related to the cutting tool forces applied to the workpiece edge. Delamination in particular is strongly dependent on the cutting force component normal to the stacking plane in unidirectional and multidirectional laminate composites. In drilling, for example, delamination is directly related to the thrust force component. In edge trimming and milling with helical tools, delamination is caused by the tensile axial cutting force component. Therefore, it is of great technological and practical interest to be able to predict the cutting forces in machining composites. Accurate prediction of the cutting forces allows the development of process control schemes for avoiding delamination by controlling and regulating the cutting process parameters that lead to high thrust and axial cutting forces.
There have been several studies in the literature on modeling of cutting forces in milling of metals. Of the different predictive modeling techniques used, mechanistic modeling method is the most robust, simple and efficient technique. Because of these features, mechanistic modeling has gained popularity in the past two decades and found wide applications in the simulation of simple and complex milling operations [1], [2], [3], [4], [5], [6], [7]. Such models attempt to correlate the cutting forces to the in-process chip geometry by way of experimentally determined cutting force coefficients (or specific cutting energies). The underlying assumption behind the mechanistic models is that the cutting forces are proportional to the uncut chip area by means of the cutting force coefficients. However, there are still some problems yet to be overcome in creating mechanistic force modeling systems. One problem is the lack of cutting force coefficients for oblique cutting, as most of the work published is for orthogonal cutting. Another major impediment is the lack of cutting force coefficients for different tool/workpiece combinations, such as fiber reinforced composites, as such data are obtained through extensive cutting experiments and calibration of the model parameters. In addition, this problem is further complicated by the highly nonlinear and inhomogeneous nature of composite materials as compared with metals. This makes the generation of specific cutting energy data for composites more challenging. Our review of the literature indicated that there has been very little evidence of work that attempts to model the cutting forces in milling fiber reinforced composites. An early mechanistic model for orthogonal milling of unidirectional composites was developed by Puw and Hocheng [8] using specific cutting energy data obtained from linear orthogonal cutting tests. However, this model was capable of predicting cutting forces only for two fiber orientations, parallel and perpendicular to the direction of the feed. Later, a more comprehensive model for orthogonal milling of unidirectional composites at various fiber orientations was developed by Sheikh-Ahmad et al. [9]. The limitation of these two models to milling with a simple straight cutting edge with no inclination is apparent and there is a need to account for more complex cutting tool geometries, such as helical end mills.
This paper provides a methodology that combines the mechanistic modeling techniques from metal machining and neural network approximation in order to obtain a predictive cutting force model for helical end milling of carbon fiber reinforced polymers (CFRP). The neural networks predictive capabilities are used to capture the highly nonlinear behavior of the specific cutting energies of the composite workpiece material. Cutting with a helical mill provides conditions of oblique cutting, as opposed to orthogonal cutting, and hence some transformation is necessary to apply orthogonal cutting knowledge to helical milling. Section 2 of this paper discusses relevant mechanistic models and orthogonal to oblique transformation performed in metal machining research. Section 3 discusses the application of artificial neural networks to model and predict the cutting force coefficients in orthogonal cutting of CFRP over the entire range of fiber orientations. Finally, Section 4 describes the development of a predictive cutting force model that combines metal cutting mechanistic techniques and artificial neural network orthogonal cutting data base in order to predict cutting forces in helical end milling. Verification of this model is provided by comparison with experimental data as discussed in 5 Experimental verification, 6 Results and discussion.
Section snippets
Previous mechanistic models
A mechanistic model for the prediction of cutting forces in helical end milling of metals was developed by Kline et al. [1]. This model was used to study problems of cornering and forging cuts. The mechanistic model was based upon the relationship between the cutting forces and the chip load. In this model, the cutter was divided into a stack of thin disk elements along the axis. Each disk element has a finite thickness. The cutting action of each disk was treated as an orthogonal cutting edge
ANN orthogonal machining data base
In the past few years, artificial neural network (ANN) was proven to be an efficient modeling tool and has become increasingly popular in the predictive modeling of several machining processes [14], [15], [16], [17], [18], [19], [20]. ANNs give an implicit relationship between the input(s) and output(s) by learning from a data set that represents the behavior of a system. The capacity of artificial neural networks to capture nonlinear relationships in a relatively efficient manner has motivated
Mechanistic model for helical milling of CFRP
The cutting force prediction model presented in this study has been developed based on the approaches of Lin et al. [11] and Li et al. [12], with the significant difference that the current model does not rely on the same basic material properties common in metal cutting to determine the elemental cutting forces because such quantities do not exist in the literature. Instead, the cutting force coefficients are imported directly from the ANN orthogonal cutting data base and the elemental cutting
Experimental verification
To verify the predictive cutting force model, a series of edge milling operations of CFRP material were performed on a vertical machining center, under dry cutting conditions, with a helical tool and in an up-milling configuration. Two-flute end milling cutter with 30° helix angle was used to machine the CFRP laminates. The cutting forces in the feed, normal and axial directions were measured using a Kistler (Type 9257 B) platform piezoelectric dynamometer attached between the workpiece and the
Results and discussion
Samples of the cutting forces obtained during helical milling of the unidirectional and multidirectional laminates are shown in Fig. 8, Fig. 9, Fig. 10. The directions of forces Fx, Fy and Fz are along the normal, feed and axial directions, respectively, as shown in Fig. 3. The force signals represent the tool engagement in one revolution. The data sampling rate was 20,000 samples/s. Each force signal was obtained by averaging four one-revolution engagements at different time periods in the
Conclusions
A methodology has been presented for simulating helical end milling of fiber reinforced polymer composites. The methodology utilizes mechanistic modeling approaches from metal cutting and the transformation of specific cutting energy data from orthogonal cutting to oblique cutting. The helical end mill is treated as a stack of finite thickness disks with oblique cutting edges. The cutting forces for each disk are calculated using the mechanistic and transformation techniques from metal cutting,
Acknowledgement
The authors would like to acknowledge the support of the National Science Foundation for the funding of this research (DMI-973347).
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