International Journal of Machine Tools and Manufacture
Feedrate scheduling for free-form surface using an NC verification model
Introduction
Virtual machining simulation enables NC programmers and machining operators to visually detect errors in a machining program by using a computer graphics display; it has become an important function of CAD/CAM systems for the purpose of program verification. Many verification models have been developed for the simulation of NC machining [1], [2], [3]; however, virtual machining simulators currently being used on the shop floor only predict geometrical errors for the free-form surfaces from NC codes. These simulators cannot predict the chip load per tooth because the cutter-swept volume is calculated along the entire tool path of an NC command using the start and end coordinates without considering the actual cutter movement.
Researchers have recently attempted to integrate various errors and predict the cutting force and surface roughness in virtual machining. Yeung et al. reported on tracking and contouring error estimation in a virtual CNC system [4] and Ko et al. studied the cutting force and machined surface error in a virtual machining system [5], [6]. An NC verification model that can predict the chip volume per tooth for a free-form surface was also presented [7]. In order to obtain a constant chip load in the machining of a free-form surface, another issue in virtual machining that must be considered is feedrate scheduling. Two methods exist for conducting feedrate scheduling: one is based on the material removal rate (MRR) [8], [9], [10] and the other is based on the cutting force [11], [12], [13], [14]. The cutting force in flat-end milling can be rapidly calculated because the uncut chip thickness can be easily obtained from the cutting conditions and the geometry of the workpiece. However, in ball-end milling for free-form surfaces, the calculation of the uncut chip thickness and the cutting force is time consuming because the depth of the cut changes with the surface curvature, feedrate, and cusp height formed by the previous tool path [15].
In the machining of a free-form surface using a high-speed machine tool, the verification of the machined surface and the feedrate scheduling should be rapidly conducted in the same simulator because high-speed machine tools are becoming faster as a result of modern technology. However, feedrate scheduling based on the cutting force with NC verification for a free-form surface is time consuming. When the grid interval of the z-map in virtual machining for a free-form surface is so large that calculating the cutting force is hard, even predicting chip volume per tooth takes a very long time, and a significant amount of time is required to verify the machined surface for a free-form surface even with a large grid interval [7]. If the grid interval is small, the uncut chip thickness for the cutting force can be obtained with comparative precision; however, calculating the cutting force for a free-form surface using existing CAD/CAM systems is time consuming [15].
Feedrate scheduling based on the cutting force is more precise than that based on MRR; eventually, the cutting force should be used in feedrate scheduling for free-form surfaces [11], [12], [13], [14]. However, in this research, feedrate scheduling based on the chip volume per tooth for a free-form surface was studied considering both the verification of the machined surface and the calculation time because an NC verification model for a free-form surface should be used to obtain the chip volume per tooth not only in roughing but also in finishing operations. The NC verification model used here describes the actual machining.
It is desirable to consider the travel length of the acceleration/deceleration period in feedrate scheduling because the desired feedrate can be achieved after acceleration/deceleration. Tounsi et al. identified the acceleration/deceleration of the feed drive systems used in CNC machines [16]. A method that generates a new NC command in an NC block is presented to compensate for the travel length of acceleration/deceleration.
In conventional feedrate scheduling, the feedrate is generated from CAM only in existing NC blocks. However, with the scheduled feedrate in the NC block, the chip volume per tooth varies with every passing tooth due to the curvature of the free-form surface as well as the cusp height formed by the previous tool path. A strategy for generating new NC commands at a set number of rotations between two existing NC blocks in order to obtain a constant chip volume per tooth is also presented.
Section snippets
Chip volume prediction using the NC verification model
Verifying the machined surface of the free-form surface in modern CAD/CAM systems is an indispensable operation, and an NC verification model should also provide the uncut chip thickness for the cutting force or the MRR for feedrate scheduling. The general simulators consider only x, y, and z coordinates of NC codes and verify the machined surface geometrically [1], [2], [3]. In this case, cutter-swept volumes are calculated along the entire tool path of an NC command block using the start and
Feedrate scheduling strategy
Two methods for feedrate scheduling are used and compared. The first conducts feedrate scheduling based on the chip volume per NC block, and the other is based on the chip volume per tooth. In this research, the machined surface of the free-form surface is verified and a new NC file with the scheduled feedrate is simultaneously generated.
Simulation results
Feedrate scheduling is simulated using the NC verification model. The NC codes are generated using CAM software. First, feedrate scheduling based on the chip volume per NC block is performed, and a new feedrate is inserted in every existing NC block. When the feedrate exhibits a sharp change between two consecutive NC blocks, a new NC block is inserted between them. Fig. 1 shows an example with a concave surface that is the same as that used in Ref. [7], and the feed direction is also depicted.
Experiments
Experiments were conducted to validate feedrate scheduling with a high-speed machine tool. The workpiece was made as shown in Fig. 9. It demonstrates region III of Fig. 1 where the cutting was carried out on the plain bottom with one NC block, and the chip volume per tooth is very high at the end of the NC block, as shown in Fig. 6. Cutting forces were measured with and without feedrate scheduling for the purpose of comparison. The workpiece type and the experimental conditions are listed in
Conclusions
An NC verification model that can describe actual cutting motions is used to conduct feedrate scheduling for free-form surface. Feedrate scheduling is conducted using not only chip volume per tooth, but also per NC block. Conducting feedrate scheduling based on chip volume per tooth, a strategy for generating new NC commands at a set number of rotations between two existing NC blocks is also proposed.
The calculation times for both the verification and feedrate scheduling based on NC blocks in
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