Chip volume prediction using a numerical control verification model

This paper presents a prediction model of chip volume per tooth in milling operations using a numerical control (NC) verification model that can describe actual cutting. This is important from the viewpoint of cutting force calculation and prediction of the chip load on a cutter tooth. In this paper, the cutter swept volumes along the path were calculated from the information obtained from NC codes as well as the feed-rate. The chip volume per tooth was kinetically modeled for the machining state of free-formed surfaces with flat, ball and round endmills, respectively. To investigate the effectiveness of the proposed model, simulation studies were conducted. Following this simulation, the chip volume per tooth precisely mimicked real machining.     

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.     

CNC machine tool surface interpolator for ball-end milling of free-form surfaces

This paper presents a new type of CNC machine tool interpolator that is capable of generating the cutter path for ball-end milling of a free-form surface. The surface interpolator comprises on-line algorithms for cutter-contact (CC) path scheduling, CC path interpolation, and tool offsetting. The interpolator algorithms for iso-parametric, iso-scallop and iso-planar machining methods are developed, respectively. The proposed surface interpolator method gains the advantages for minimizing the data loaded to the CNC machine tool and maintaining the desired feedrate and position accuracy along the CC path.     

Modeling of process geometry in peripheral milling of curved surfaces

This paper presents an approach for modeling of the process geometry in peripheral milling of curved surfaces. The modeled process geometry involves feed direction, equivalent feedrate and cutter entry/exit angle. The equivalent feedrate, which is defined at the centroid of cutting cross-section, is proposed to measure the actual machining feedrate. The milling process of curved surface is discretized at intervals of feed per tooth for describing the variation of process geometry. The mathematical models for calculating the process geometry of each segmented cutting process are presented. Two same curved surfaces are machined. The tool paths are carried out with NURBS interpolation and traditional consecutive small line segments interpolation, respectively. The simulated and measured results are presented for the verification of the proposed method.     

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.     

Machining accuracy improvement in five-axis flank milling of ruled surfaces

The aim of this study is to develop a new adjustment method for improving machining accuracy of tool path in five-axis flank milling of ruled surfaces. This method considers interpolation sampling time of the five-axis machine tools controller in NC tool path planning. The actual interpolation position and orientation between G01 commands are estimated with the first differential approximation of Taylor expansion. The tool swept volume is modeled using the envelope surface and compared with the design surface to determine the deviation, which corresponds to the machining error induced by the linear interpolation. We propose a feedrate adjustment rule that automatically controls the tool motion at feedrate-sensitive corners based on a bisection method, thus limiting the maximum machining errors and improving the machining accuracy. Experimental cuts are conducted on different ruled surfaces to verify the effectiveness of the proposed method. The result shows that it can enhance the machining quality in five-axis flank milling in both simulation and practical operation.     

NURBS interpolator for constant material removal rate in open NC machine tools

Conventionally used linear or circular interpolators are undesirable for the precision machining of 3D free-form surfaces for the following reasons: the transmission errors due to the huge number of point data, discontinuity of curve segmentation, and unsmooth motion speed. In this regard, modern CNC machine tools are designed with a function for machining arbitrary parametric curves. However, these systems do not consider controlling feedrate adaptively, which dominates the quality of the machining process. This paper proposes a NURBS interpolator based on the adaptive feedrate control for the constant material removal rate. This is accomplished by varying feedrate using the curvature of a surface. The curvature-compensated feedrate system has important potential applications in ensuring part accuracy and protecting the cutting tool. The simulated and experimental results show it is applicable to real machining.     

Feedrate scheduling for indexable end milling process based on an improved cutting force model

In CNC machining, an optimal process plan is needed for higher productivity and machining performance. This paper proposes a mechanistic cutting force model to perform feedrate scheduling that is useful in process planning for indexable end milling. Indexable end mills, which consist of inserts and a cutter body, have been widely used in the roughing of parts in the mold industry. The geometry and distribution of inserts compose a discontinuous cutting edge on the cutter body, and tool geometry of indexable end mill varies with axial position due to the geometry and distribution of inserts. Thus, an algorithm that calculates tool geometry data at an arbitrary axial position was developed. The developed cutting force model uses cutting-condition-independent cutting force coefficients and considers run out, cutter deflection, geometry variation and size effect for accurate cutting force prediction. Through feedrate scheduling, NC code is optimized to regulate cutting forces at given reference force. Experiments with general NC codes show the effectiveness of feedrate scheduling in process planning.     

Machineability in NURBS interpolator considering constant material removal rate

Increasing demands on precision machining of three-dimensional free-form surfaces have necessitated that the tool move smoothly and at varying feedrates. To achieve this, parametric interpolators, such as the Non-Uniform Rational B-Spline (NURBS) interpolator, have been introduced in CNC machining systems. Such interpolators reduce the data burden in the Numerical Control (NC) code, increase data transfer rate into the NC controller, and finally give smooth motion while machining. In this research, a new concept to control cutting load in a NURBS interpolator based on the degree of curvature was tried. This protects the cutting tool and improves machineability. To prove the system, cutting force and surface topography were evaluated. From the experimental results, the interpolator is adequate for machining a free-form surface.     

基于反求工程的自由曲面数控加工

介绍了以反求工程为技术支撑的自由曲面数控加工的基本原理和全过程，并对其中的数字化扫描、CAD建模及刀具轨迹生成等关键技术作了进一步的分析。最后描述了采用逆向工程技术进行国际象棋的棋子——马从模型到成品零件数控加工的实例。     

Machining of free-form surfaces. Part I: Analytical chip load

In the machining simulations of 3D free-form surfaces with ball-end mill, determinations of instantaneously changing tool-workpiece engagement regions and chip load play very critical roles in force and surface quality predictions. Cutting force models for ball-end milling are based on the undeformed chip load. Undeformed chip load can be constructed from the boundaries of instantaneous engagement region between the ball-end mill and workpiece. In order to predict the cutting forces accurately, precise determination of the varying engagement regions is important. In the literature, there are two main engagement region constructing methods; one is the Z-mapping and the other one is using solid modeler based on Boolean operation method. Both methods construct the engagement region within accuracy limits, on the other hand the computational time for these methods are long such that it is not possible to calculate the forces at the same time of CL-point construction. This paper presents development of a new analytical method for fast and accurate determination of the instantaneous engagement regions in the 3D machining of monotonic free-form surfaces. The analytical tool is grid size independent, thus it is much faster than discretization and Boolean methods. In addition to that, the analytical tool gives the most precise and exact engagement regions.     

Development of a reference cutting force model for rough milling feedrate scheduling using FEM analysis

Recently developed feedrate scheduling systems regulate cutting forces at the desired level by changing the feedrate to reduce the machining time and to avoid undesirable situations. For effective scheduling, an optimized criterion is required to adjust the feedrate. In this study, a method to obtain the most appropriate reference cutting force for rough milling was developed. The reference cutting force was determined by considering the transverse rupture strength of the tool material and the area of the rupture surface. A finite element method analysis was performed to accurately calculate the area of the rupture surface. Using the analyzed results, the effect of various cutting parameters on the chipping phenomenon was determined. The calculation method for the reference cutting force considered the area of the rupture surface, the effect of the rake angle, and the axial depth of the cut. The reference cutting force calculated using the developed model was applied to feedrate scheduling for pocket machining. The experimental results clearly show that the reference cutting force obtained from the proposed method met the desired constraints that guarantee higher productivity without tool failure.     

模具数控磨削技术开发研究

研究了模具研腔的数控磨削加工技术,开发了安装于数控铣床主轴上的Ｔ／Ｄ牵引驱动增速装置和各种ＣＢＮ磨头,利用开发的增速器和ＣＢＮ磨头可进行平面、斜同、竖直面及空间自由曲面的磨削加工,为在ＮＣ机床和加工中心实现一次装夹完成模具的铣削和磨削加工提供了新的工艺装备和工艺条件。     

Feed-rate optimization with jerk constraints for generating minimum-time trajectories

Competitive pressure requires manufacturers to simultaneously address increasingly stringent constraints on both productivity and quality. From the perspective of numerically controlled (NC) machine tools, this means higher machining performance in terms of speed and accuracy. Conventional approaches to programming NC operations involve selecting a constant feedrate for a given operation to produce acceptable performance (operation time and contouring accuracy).In this paper, we examine the possibility of scheduling or varying the feedrate by taking into consideration the geometry of the contour that the machine is expected to follow and the physical capabilities of the machine (i.e., its maximum velocity, acceleration and jerk constraints). Previous work by the authors has addressed the efficient, off-line computation of time-optimal trajectories with constraints on velocity and acceleration. This paper introduces additional constraints on the permissible jerk (rate of change of acceleration) on the machine's axis. From a practical perspective, excessive jerk leads to excitation of vibrations in components in the machine assembly, accelerated wear in the transmission and bearing elements, noisy operations and large contouring errors at discontinuities (such as corners) in the machining path.The introduction of jerk into the feedrate scheduling problem makes generating computationally efficient solutions while simultaneously guaranteeing optimality a challenging problem. This paper approaches this problem as an extension of our previous bi-directional scan algorithm [23] and [29]. A new acceleration-continuation procedure is added to the feedrate optimization algorithm to address jerk constraints and remove discontinuities in the acceleration profile. The algorithm maintains computational efficiency and supports the incorporation of a variety of state-dependent (such as position, velocity, acceleration and jerk) constraints. By carefully organizing the local search and acceleration continuity enforcing steps, a globally optimal solution is achieved. Singularities, or critical points, and critical curves on the trajectory, which are difficult to deal within optimal control approaches, are treated in a natural way in this algorithm. Several application examples and tests are performed to verify the effectiveness of this approach for high-speed contouring.     

数控加工模具型腔中的数据处理

模具型腔在数控加工中需要一套控制刀具运动轨迹的算法，本文给出了从模具型面的几何描述，加工数据的生成到形成Ｇ格式指令进行数控加工这一生产过程的数据处理，实验和现场加工的结果表明：该数据处理算法成功地解决了模具型面的加工制造问题。     

Swept volumes of toroidal cutters using generating curves

Modelling the volume swept by a tool as it moves from one programmed position to another in three, four and five-axis milling is a challenging task. In this paper, a technique for generating the volume swept by a toroidal cutter in its motion along a given tool path, is presented. This technique is based on identifying “generating curves” along the path and connecting them into a solid model of the swept volume. The swept volume simulations are verified experimentally for three test pieces. These are also compared with the simulation results from the Z-map technique. The results of the experimental verification show the method to be accurate to within 10 μm for the three test pieces. Furthermore, the computation time for the new technique is significantly less than the Z-map method. It is concluded that the proposed method has the potential of allowing fast simulation and verification of multi-axis tool paths.     

A realtime curvature-smooth interpolation scheme and motion planning for CNC machining of short line segments

G01 codes generated by CAM (Computer Aided Manufacturing) system are the most common form of tool path in CNC (Computer Numerical Control) machining. For the piecewise linear path, tangential and curvature discontinuities bring about large fluctuation of feedrate and acceleration, which produces vibration of machine tool. In recent studies, the methods for G² (curvature-continuous) tool-path smoothing and jerk-limiting feedrate scheduling were developed. However there still exist the deficiencies when these methods are employed in CNC machining. It is difficult to simultaneously ensure that the tool path is chord-error-constrained and G01-point-interpolated in real time. In addition, heavy computational load hinders realtime processing in CNC system. Recently the scholars experimentally found the potential of G³ (curvature-smooth) trajectory and jerk-continuous motion in reducing the vibration of machinery. This work proposes a realtime tool-path smoothing algorithm, generating G³ interpolative tool path composed by mixed linear and quartic Bezier segments. The purpose of the smoothing scheme is the simultaneous considerations of G³ continuity, confined chord error, G01 points interpolated, and realtime performance. And the tool path generated is optimized in curvature variation energy (CVE) and analytical curvature extrema is available. To reduce the vibration, a high-efficient algorithm of jerk-continuous (JC) feedrate scheduling for G³ tool path is provided. Finally, a realtime tool-path processing scheme is developed, including G³ interpolation and motion planning functions. As shown in the simulation, the contour error, curvature of tool path, feedrate fluctuation and machining time are reduced compared with G² transition scheme. The experiment on a machine tool is conducted to demonstrate the advantages of the proposed algorithm in vibration reduction and surface quality, compared with G² transition scheme.     

自由曲面数控加工智能选刀方法的研究与开发

由于自由曲面的几何复杂性,其数控加工的刀具干涉判别和刀具选取往往依靠数控机床编程工程师的经脸,致使加工的安全性、精度、效率及可靠性得不到有效保证.采用改进的遗传算法获取自由曲面的点云数据,在自主开发的系统中重构自由曲面.研究自由曲面加工刀位面生成的几何机理,根据刀具类型和几何尺寸,自动生成自由曲面数控加工的刀位面,可视化判别是否发生刀具干涉.将改进的快速排序算法应用到智能选刀模块,通过对常用类型和尺寸的刀具进行干涉排查,在避免干涉的前提下,智能选取最优化的加工刀具.对三种加工方案进行了测试,验证了智能选刀方法的正确性.     

基于Free-form型锥齿轮机床的齿面制造技术

介绍了一种基于Free-form型机床切齿加工理论的点啮合齿面制造技术。提供了Free-form型机床3轴联动切齿加工基本方程及详细的计算公式。直接以工件齿轮的转角为运动参数,将机床其它各轴的运动表达为工件齿轮转角的函数。阐明了机床运动函数及其它切齿参数的确定方法。