Feed rate scheduling model considering transverse rupture strength of a tool for 3D ball-end milling

This paper presents an analytical model of off-line feed rate scheduling to determine desired feed rates for 3D ball-end milling. Off-line feed rate scheduling is presented as the advanced technology to regulate cutting forces through change of feed per tooth, which directly affects variation of uncut chip thickness. In this paper, the uncut chip thickness is calculated by following the movement of the position of the cutter center, which is determined by runout and cutter deflection. Also, since the developed cutting force model uses the cutting-condition-independent coefficients, off-line feed rate scheduling can be effectively performed regardless of continuous change of cutting conditions. Transverse rupture strength of the tool is used to determine the reference cutting force at which resultant cutting forces are regulated through feed rate scheduling. Experiments validated that the presented feed rate scheduling model reduced machining time drastically and regulated cutting forces at the reference cutting force.     

Integrated tool path and feed rate optimization for the finishing machining of 3D plane surfaces

An integrated approach for the concurrent optimization of tool path and feed rate for the finishing machining of 3D plane surfaces using ball-end milling is presented in this paper. This work is important, as the developed optimization approach is readily applicable to the finishing machining of sculptured surfaces. The concurrently optimized tool path and feed rate correspond to the maximum machining efficiency and satisfy the scallop height and machining error requirements. The cutter feed direction is employed as the optimization variable. For each cutter feed direction, tool path is determined according to the scallop height requirement and feed rate is maximized with the tolerance requirement by using a mechanistic cutting force model for three-dimensional ball-end milling. Optimization results have indicated that the shortest total tool path length, favored by most existing optimization approaches, does not result in maximum efficiency because the corresponding feed rate is often constrained by the specified tolerance. The optimum cutter feed direction is in general not unique but falls within an optimum range in the finishing machining of 3D plane surfaces.     

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

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.     

The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 1: Chip geometry analysis and cutting force prediction

The study of machining errors caused by tool deflection in the balkend milling process involves four issues, namely the chip geometry, the cutting force, the tool deflection and the deflection sensitivity of the surface geometry. In this paper, chip geometry and cutting force are investigated. The study on chip geometry includes the undeformed radial chip thickness, the chip engagement surface and the relationship between feed boundary and feed angle. For cutting force prediction, a rigid force model and a flexible force model are developed. Instantaneous cutting forces of a machining experiment for two 2D sculptured surfaces produced by the ball-end milling process are simulated using these force models and are verified by force measurements. This information is used in Part 2 of this paper, together with a tool deflection model and the deflection sensitivity of the surface geometry, to predict the machining errors of the machined sculptured surfaces.     

Increasing productivity in sculpture surface machining via off-line piecewise variable feedrate scheduling based on the force system model

Sculpture surface machining is a critical process commonly used in various industries such as the automobile, aerospace, die/mold industries. Since there is a lack of scientific tools in practical process planning stages, feedrates for CNC machining are selected based on the trial errors and previous experiences. In the selections of the process parameters, production-planning engineers are conservative in order to avoid undesirable results such as chipping, cutter breakage or over-cut due to excessive cutter deflection. Currently, commonly used CAD/CAM programs use only the geometric and volumetric analysis, but not the physics of the processes, and rely on experience based cutting tool database and users’ inputs for selection of the process parameters such as feed and speed. Usually, the feeds and cutting speeds are set individual constant values all along the roughing, semi-finishing, and finishing processes. Being too conservative and setting feedrate constant all along the tool path in machining of sculpture surfaces can be quite costly for the manufacturers. However, a force model based on the physics of the cutting process will be greatly beneficial for varying the feedrate piecewise along the tool path.The model presented here is the first stage in order to integrate the physics of the ball-end milling process into the selection of the feeds during the sculpture surface machining. Therefore, in this paper, an enhanced mathematical model is presented for the prediction of cutting force system in ball end milling of sculpture surfaces. This physical force model is used for selecting varying and ‘appropriate’ feed values along the tool path in order to decrease the cycle time in sculpture surface machining. The model is tested under various machining conditions, and some of the results are also presented in the paper.     

Optimized feed scheduling in three axes machining. Part I: Fundamentals of the optimized feed scheduling strategy

An optimized feed scheduling strategy is proposed in this paper to maximize the metal removal rate in 3-axis machining while guaranteeing the machining accuracy. The tool path is assumed defined by a cubic parametric form. In part I of this paper, the fundamentals of this strategy are presented. This strategy integrates the feed drive dynamics, described by the acceleration/deceleration (Acc/Dec) profile, with the minimum-time trajectory planning in order to achieve the desired feed rate at the appropriate position. An optimum use of the feed drive capabilities is considered to track the changes in the cutting geometry along the tool path and to ensure an acceptable contour error. Therefore, this strategy combines different constraints and various criteria in modifying the feed rate to maintain a near-constant cutting force resulting in a highly non-linear problem. The constraints include the cutting force magnitude, the feed rate boundaries, the contour error and the characteristics of the (Acc/Dec) profile of the different feed drive systems. The criteria are the maximum production rate, the machining accuracy and safety. In part II of this paper, the effectiveness of this strategy is demonstrated using ball end mill operation on a workpiece that provides variable cutting geometry along a non-linear tool path. The performance of this strategy in terms of productivity, machining safety, and machining accuracy, is compared to a feed scheduling strategy based on control points as well as to milling with constant feed rate.     

Optimized feed scheduling in three axes machining: Part II: Experimental validation

The optimized feed scheduling strategy, developed in part I of this paper, considers an optimal use of the feed drive systems. The low frequency dynamics of the different feed drive systems of the machine tool are identified. The resulting transfer functions are transformed into FIR filter and integrated with the planning of the tool trajectory. The effectiveness of the proposed feed scheduling strategy is demonstrated using ball end milling of a workpiece that provides variable cutting conditions along a nonlinear tool path. The performance of this strategy in terms of productivity, machining safety, and machining accuracy, is compared to a feed scheduling strategy based on control points. The proposed strategy has significantly improved the tracking and trajectory following characteristics. It achieves a good prediction of the feed rate of the different axes and consequently a better regulation of the cutting force. In addition, by increasing the feed rate, while respecting the different constraints, it improves the tool path accuracy and enhances the productivity.     

Feedrate scheduling strategies for free-form surfaces

Free-form machining is one of the commonly used manufacturing processes for several industries such as automobile, aerospace, die and mold industries. In 3D complicated free-form surfaces, it is critical, but often difficult, to select applicable cutting conditions to achieve high productivity while maintaining high quality of parts. It is essential to optimize the feedrate in order to improve the machining efficiency of the ball-end milling. Conservative constant feedrate values have been mostly used up to now since there was a lock of physical models and optimization tools for the machining processes.The common approach used in feedrate scheduling is material removal rate (MRR) model. In the MRR based approach, feedrate is inversely proportional to either average or instantaneous volumetric removal rate. Commonly used CAM programs and NC code generators based on only the geometric and volumetric analysis, but they do not concern the physics of the free-form machining process yet. The new approach that is also introduced in this paper is based on the mechanics of the process. In other words, the force-based models in which feedrate is set to values which keep either average or instantaneous machining forces to prescribed values. In this study, both feedrate scheduling strategies are compared theoretically and experimentally for 3D ball-end milling of free-form surfaces. It is shown that MRR based feedrate strategy outputs higher feedrate values compared to force based feedrate strategy. High feedrate values of the MRR strategy increase the cutting forces extensively which can be damaging to the part quality and to the CNC Machine.When the new force based feedrate-scheduling strategy introduced in this paper is used, it is shown that the machining time can be decreased significantly along the tool path. The force-based feedrate scheduling strategy is tested under various cutting conditions and some of the results are presented in the paper.     

Feedrate optimization for freeform milling considering constraints from the feed drive system and process mechanics

This paper presents a new and comprehensive strategy for planning minimum cycle time tool trajectories subject to both machining process related constraints, and also limitations of the feed drive control system. The machining process is considered by computing the workpiece-tool engagement along the toolpath and setting local feed limits to maintain a specified resultant cutting force. The drive constraints are considered by limiting the velocity, acceleration, and jerk magnitudes commanded to each actuator. Feed profiling is realized with uninterrupted acceleration transitions, capable of spanning multiple toolpath segments. Effectiveness of the proposed strategy is demonstrated in sculptured surface machining experiments.     

雕刻表面球形铣削的分段变进给率加工

雕刻表面球形铣削加工中,根据刀头的受力模型,可以计算整个刀具路径上刀头的受力.刀具路径上加工深度变化时,若采用恒进给率,则刀具受力是变化的,为了安全保险起见,往往按最大受力来选择较低的恒进给率,整个加工效率很低.采用变进给率加工,即加工深度小时提高进给率,使刀具在整个路径上受力均匀.本文给出了路径上力的计算仿真方法,以及分段进给率的计算方法,可以指导实际的加工过程,这样既保证了加工过程的安全,又提高了生产率.     

Cutting force prediction of sculptured surface ball-end milling using Z-map

The cutting force in ball-end milling of sculptured surfaces is calculated. In sculptured surface machining, a simple method to determine the cutter contact area is necessary since cutting geometry is complicated and cutter contact area changes continuously. In this study, the cutter contact area is determined from the Z-map of the surface geometry and current cutter location. To determine cutting edge element engagement, the cutting edge elements are projected onto the cutter plane normal to the Z-axis and compared with the cutter contact area obtained from the Z-map. Cutting forces acting on the engaged cutting edge elements are calculated using an empirical method. Empirical cutting mechanism parameters are set as functions of cutting edge element position angle in order to consider the cutting action variation along the cutting edge. The relationship between undeformed chip geometry and the cutter feed inclination angle is also analyzed. The resultant cutting force is calculated by numerical integration of cutting forces acting on the engaged cutting edge elements. A series of experiments were performed to verify the proposed cutting force estimation model. It is shown that the proposed method predicts cutting force effectively for any geometry including sculptured surfaces with cusp marks and a hole.     

Integrated planning for precision machining of complex surfaces. Part 1: Cutting-path and feedrate optimization

In order to achieve higher productivity and product quality simultaneously for sculptured surface productions, two advanced strategies are proposed for machining planning, namely a cutting-path-adaptive-feedrate strategy and a control surface strategy. In the cutting-path-adaptive-feedrate strategy, machining time is reduced by cutting along low-force-low-error machining directions and by maximizing feedrates. In the control surface strategy, machining errors are minimized by using a compensated control surface based on predicted machining errors. In part 1 of this paper, the cutting-path-adaptive-feedrate strategy, which improves the productivity of sculptured surface machining when subjected to both force and dimensional constraints, is described. In this proposed strategy, a new machining-planning aid called a maximum feedrate map is developed. In this map, the maximum allowable feedrates, subjected to the specified constraints, at each control point along various machining directions, are determined using a surface generation model. These local maximum-feedrate boundaries indicate the acceptable range of feedrates that a part programmer can use in the NC programming. In addition, the maximum feedrate map also provides the part programmer an important aid in selecting the cutting directions. In order to illustrate the application of the maximum feedrate map and to examine the capability of the proposed cutting-path-adaptive-feedrate strategy in improving the productivity of sculptured surface machining, simulation studies of a two-dimensional curved surface are performed and the results are presented in this paper. The applications of the proposed strategy to real three-dimensional complex surfaces (e.g. a turbine blade die) along with experimental verifications are presented in part 2 of this paper. In part 3 of this paper the control surface strategy and its applications to the finish milling of three-dimensional complex surfaces are discussed.     

The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 2: Surface generation model and experimental verification

This paper presents a surface generation model for sculptured surface productions using the ball-end milling process. In this model, machining errors caused by tool deflections are studied. As shown in Part 1 of this paper, instantaneous horizontal cutting forces can be evaluated from the cutting geometries using mechanistic force models. In this paper, a tool deflection model is developed to calculate the corresponding horizontal tool deflection at the surface generation points on the cutter. The sensitivity of the machining errors to tool deflections, both in magnitude and direction, has been analyzed via the deflection sensitivity of the surface geometry. Machining errors are then determined from the tool deflection and the deflection sensitivity of the designed surface. The ability of this model in predicting dimensional errors for sculptured surfaces produced by the ball-end milling process has been verified by a machining experiment. In addition to providing a means to predict dimensional accuracy prior to actual cutting, this surface generation model can also be used as a tool for quality control and machining planning.     

Feed optimization for five-axis CNC machine tools with drive constraints

Real time control of five-axis machine tools requires smooth generation of feed, acceleration and jerk in CNC systems without violating the physical limits of the drives. This paper presents a feed scheduling algorithm for CNC systems to minimize the machining time for five-axis contour machining of sculptured surfaces. The variation of the feed along the five-axis tool-path is expressed in a cubic B-spline form. The velocity, acceleration and jerk limits of the five axes are considered in finding the most optimal feed along the tool-path in order to ensure smooth and linear operation of the servo drives with minimal tracking error. The time optimal feed motion is obtained by iteratively modulating the feed control points of the B-spline to maximize the feed along the tool-path without violating the programmed feed and the drives’ physical limits. Long tool-paths are handled efficiently by applying a moving window technique. The improvement in the productivity and linear operation of the five drives is demonstrated with five-axis simulations and experiments on a CNC machine tool.     

Estimation and experimental validation of cutting forces in ball-end milling of sculptured surfaces

Chip thickness calculation has a key important effect on the prediction accuracy of accompanied cutting forces in milling process. This paper presents a mechanistic method for estimating cutting force in ball-end milling of sculptured surfaces for any cases of toolpaths and varying feedrate by incorporation into a new chip thickness model. Based on the given cutter location path and feedrate scheduling strategy, the trace modeling of the cutting edge used to determine the undeformed chip area is resulted from the relative part-tool motion in milling. Issues, such as the selection of the tooth tip and the computation of the preceding cutting path for the tooth tip, are also discussed in detail to ensure the accuracy of chip thickness calculation. Under different chip thicknesses cutting coefficients are regressed with good agreements to calibrated values. Validation tests are carried out on a sculptured surface with curved toolpaths under practical cutting conditions. Comparisons of simulated and experimental results show the effectiveness of the proposed method.     

Development of 3 DOF Ultrasonic Vibration Tool for Elliptical Vibration Cutting of Sculptured Surfaces

A new machining method is proposed to obtain sculptured mirror surfaces by applying elliptical vibration cutting. The tool is vibrated elliptically unlike rotated end mills and fed along the sculptured surface in the proposed method. A 3 DOF ultrasonic vibration tool is developed, which can generate an arbitrary ultrasonic elliptical vibration in the 3D space so that it is suitable to machine the 3D sculptured surfaces. A precision machine tool is also developed, and the proposed method is successfully applied to mirror surface machining of hardened die steel.     

Virtual prediction and constraint of contour errors induced by cutting force disturbances on multi-axis CNC machine tools

This paper presents a strategy to virtually predict and constrain the contouring errors contributed by cutting force disturbances on feed drives. The tracking errors on each feed drive are predicted as a linear function of tangential feed by evaluating the product of estimated power spectrum of cutting forces and disturbance frequency response function along the tool path in virtual CAM environment. The corresponding tool tip contouring and tool axis orientation errors are estimated and constrained by scaling the feed along the tool path. The algorithm is experimentally illustrated to improve the machining accuracy on a 5 Axis CNC machine tool.     

Development of a virtual machining system, part 3: cutting process simulation in transient cuts

In Parts 1 and 2 of this three-part paper, a mechanistic cutting force model was developed and machined surface errors for steady cuts under fixed cutting conditions were predicted. The virtual machining system aims to simulate and analyze the machining and the machined states in a general flat end-milling process. This frequently involves transient as well as steady cuts. Therefore, a method for simulating the cutting process of transient cuts needs to be developed to realize the virtual machining system concept. For this purpose, this paper presents a moving edge-node (ME) Z-map model for the cutting configuration calculation. The simulation results of four representative transient cuts in two-dimensional pocket milling and an application of off-line feed-rate scheduling are also given.

In transient cuts, the cutting configurations that are used to predict the cutting force vary during the machining operation. The cutting force model (Part 1) and surface error prediction method (Part 2) were developed for steady cuts; these are extended to transient situations using the ME Z-map model to calculate the varying cutting configurations efficiently. The cutting force and surface errors are then predicted. To validate the feasibility of the proposed scheme, the measured and predicted cutting forces for transient test cuts were compared. The predicted surface error maps for transient cuts were constructed using a computer simulation. Also, off-line feed-rate scheduling is shown to be more accurately performed by applying the instantaneous cutting coefficients that were defined in Part I.     

Smooth trajectory generation for five-axis machine tools

This paper presents a smooth spline interpolation technique for five-axis machining of sculptured surfaces. The tool tip and orientation locations generated by the CAM system are first fitted to quintic splines independently to achieve geometric jerk continuity while decoupling the relative changes in position and orientation of the cutter along the curved path. The non-linear relationship between spline parameters and displacements along the path is approximated with ninth order and seventh order feed correction splines for position and orientation, respectively. The high order feed correction splines allow minimum deviation from the reference axis commands while preserving continuous jerk on three translational and two rotary drives. The proposed method has been experimentally demonstrated to show improvements in reducing the excitation of inertial vibrations while improving tracking accuracy in five-axis machining of curved paths found in dies, molds and aerospace parts.     

A model for cutting forces generated during machining with self-propelled rotary tools

In this paper, a force model for self-propelled rotary tool is presented. Conventional oblique cutting force predictions were reviewed and extended to predict the cutting forces generated during machining with the self-propelled rotary tools. The model presented is based on Oxley's analysis and was verified by cutting tests using a typical self-propelled tool. Good agreement was obtained between the predicted and the experimentally measured forces under a wide range of cutting conditions. The effect of different cutting conditions on the friction coefficient along the chip/tool interface and tool rake face normal force were also presented and discussed.