@article{aed3c6d82a98407babc7084f233a2d27,
title = "Simulation of NC machining with cutter deflection by modelling deformed swept volumes",
abstract = "Most research on the representation of swept volumes has been limited to motion of rigid objects. In this study, a Sweep Differential Equation (SDE) approach is presented for the representation of deformed swept volumes associated with flexible objects. The deformed swept volume analysis is integrated with machining mechanics to account for cutter deflection in NC simulation. End milling is modeled and analyzed and the cutter deflections are computed and integrated with an SDE based software program which is developed in C++ for the generation of deformed swept volumes. It is shown that this approach constitutes an effective NC simulation technique with capabilities for geometric verification and machining tolerance checking.",
keywords = "Machining, Numerical control (NC), Simulation",
author = "Leu, {Ming C.} and Feng Lu and Denis Blackmore",
note = "Funding Information: 4. The boundary of the deformed swept volume is input to ProiEngineer for cutter swept volume visualization. Boolean subtraction of the cutter swept volume from the workpiece is used for material removal simulation and machining error checking. 4.3 Integration with Advanced Cutting Force Prediction Programs As discussed before. there are more accurate models and software programs for cutting force prediction developed by many researchers. These software programs can be integrated with our program. For NC machining simulation and verification purposes, we may not need to use the details of the cutting forces generated by these programs. For rough cut. the material which is left on the machined surface from the current pass is of main concern. Therefore, it is reasonable to calculate the average cutting force in each turn of the cutter for the deformed cutter swept volume generation. In this way, the time needed for computing the deformed cutter swept volume can be dramatically reduced. As depicted in Figure 6(a), this provides a good approximation for the removal of material. For finish cut, the machined surface needs to satisfy tolerance requirements. The average surface error is not suitable for this checking. Thus, the maximum and minimum cutting forces are used to calculate the deformed cutter swept volume and check the tolerance satisfaction accordingly. As shown in Figure 6(b), the real machined surface lies between the maximum/minimum deformation contours. Therefore, tolerance satisfaction by the maximumlminimum surface deformation also implies tolerance satisfaction by the actual machined surface. 5. Simulation Example To illustrate the SDE approach for the deformed swept volume representation and its application to NC simulation and verification, an example is now given. This is a milling simulation for the generation of a mouse shell mold. The mold is designed with ProlMold. The CL data are generated using ProlManufacturing. Two NC machining sequences are used. The first is rough milling for material removal. and the second is trajectory milling along the mold side for finish milling. Figure 7 illustrates the material removal simulation for the rough cut, where the top-left shows the cutter swept volume together with the workpiece, the top-right shows the workpiece after the material removal, the bottom-left shows the second pass with a stepover of 0.2”, and the bottom-right shows the workpiece after the rough cut. Figure 8 illustrates the simulation for the finish cut process, where the top-left shows the boundary of the undeformed cutter swept volume, the top-right shows the undeformed cutter swept volume together with the workpiece, the bottom-left shows the material removed in the finish cut, and the bottom-right shows the machined part at the end. The areas of the machined surface which have errors exceeding tolerances can be indicated (by using different colors, for example). By modifying the machining parameters, such as reducing the cut depth in the finish cut, the machining error can be reduced to satisfy the tolerance constraint. 6. Conclusions We have described how to implement the generation of deformed swept volumes with the SDE approach in NC machining simulation and verification. Linear and nonlinear cutter deflections are calculated with the established cutting force models. By using the deformed cutter swept volume, we have developed an algorithm for more accurate prediction of cutting force and deflection. The computer program developed using this algorithm has been integrated with a commercial CAD/CAM system (ProIEngineer) to take advantage of its capabilities for visualization and Boolean operation. Prediction of machined surface errors is carried out by indicating the portion of the machined surface whose deformation exceeds the error tolerance. Besides using a simple cutter force model built into our program, the program can be integrated with the results of advanced cutting force models available from other researchers. The applicability of the NC simulation and verification program based on the SDE approach is demonstrated for a mold milling process. ACKNOWLDEGMENT This work was supported by NSF research grant DMS- 9588088 and by the Center for Manufacturing Systems at NJIT. Ming C. Leu was on leave at the National Science Foundation as the Program Director for Manufacturing Machines and Equipment when the work was done. REFERENCES Armarego. E.J., and Deshpande, N.P., 1991, Computerized end milling force prediction with cutting model allowing eccentricity and cutter deflections, Annals of CIRP, 40: 25-29.",
year = "1998",
doi = "10.1016/s0007-8506(07)62870-4",
language = "English (US)",
volume = "47",
pages = "441--446",
journal = "CIRP Annals - Manufacturing Technology",
issn = "0007-8506",
publisher = "Elsevier USA",
number = "1",
}