Prediction of cutting force for ball end mill in sculptured surface based on analytic model of CWE and ICCE

Abstract

The force prediction is the precondition of improving equipment utilization ratio and optimizing process for CNC machining. Cutter-workpiece engagement (CWE) and in-cut cutting edge (ICCE) are the keys. In this article, a new analytic method of CWE and ICCE is proposed for ball end milling of sculptured surface and the prediction model of milling force is established. The sculptured surface is discretized into a series of infinitesimal inclined planes corresponding to cutter location points. The geometry relationships of cutter axis, feed direction and inclined plane are defined parametrically. The boundary curves and the boundary inflection points of the CWE are obtained by intersecting spatial standard curved surfaces with rotation transformation of coordinate system. The effective intersection points of the CWE and the cutter edge curve in X_c-Y_ctwo-dimensional plane are the upper and lower boundary points of ICCE. Based on the instantaneous chip thickness considering arbitrary feed direction, the force prediction model for ball end mill of three-axis surface milling is established. Simulation and experiment show that CWE and ICCE calculated by analytic method are well consistent with those of solid method. The predicted cutting forces match well with the measurements both in magnitude and variation trend.     

A solid modeler based ball-end milling process simulation

A system for geometric and physical simulation of the ball-end milling process using solid modeling is presented in this paper. A commercially available geometric engine is used to represent the cutting edge, cutter and updated part. The ball-end mill cutter modeled in this study is an insert type ball-end mill and the cutting edge is generated by intersecting an inclined plane with the cutter ball nose. The contact face between cutter and updated part is determined from the solid model of the updated part and cutter solid model. To determine cutting edge engagement for each tool rotational step, the intersections between the cutting edge with boundary of the contact face are determined. The engaged portion of the cutting edge for each tool rotational step is divided into small differential oblique cutting edge segments. Friction, shear angles and shear stresses are identified from orthogonal cutting data base available in the open literature. For each tool rotational position, the cutting force components are calculated by summing up the differential cutting forces. The instantaneous dynamic chip thickness is computed by summing up the rigid chip thickness, the tool deflection and the undulations left from the previous tooth, and then the dynamic cutting forces are obtained. For calculating the ploughing forces, Wu's model is extended to the ball-end milling process [21]. The total forces, including the cutting and ploughing forces, are applied to the structural vibratory model of the system and the dynamic deflections at the tool tip are predicted. The developed system is verified experimentally for various up-hill and down-hill angles.     

Theoretical modelling of cutting forces in helical end milling with cutter runout

A theoretical cutting force model for helical end milling with cutter runout is developed using a predictive machining theory, which predicts cutting forces from the input data of workpiece material properties, tool geometry and cutting conditions. In the model, a helical end milling cutter is discretized into a number of slices along the cutter axis to account for the helix angle effect. The cutting action for a tooth segment in the first slice is modelled as oblique cutting with end cutting edge effect and tool nose radius effect, whereas the cutting actions of other slices are modelled as oblique cutting without end cutting edge effect and tool nose radius effect. The influence of cutter runout on chip load is considered based on the true tooth trajectories. The total cutting force is the sum of the forces at all the cutting slices of the cutter. The model is verified with experimental milling tests.     

Analysis of cutting force coefficients in high-speed ball end milling at varying rotational speeds

In high-speed ball end milling, cutting forces influence machinability, dimensional accuracy, tool failure, tool deflection, machine tool chatter, vibration, etc. Thus, an accurate prediction of cutting forces before actual machining is essential for a good insight into the process to produce good quality machined parts. In this article, an attempt has been made to determine specific cutting force coefficients in ball end milling based on a linear mechanistic model at a higher range of rotational speeds. The force coefficients have been determined based on average cutting force. Cutting force in one revolution of the cutter was recorded to avoid the cutter run-out condition (radial). Milling experiments have been conducted on aluminum alloy of grade Al2014-T6 at different spindle speeds and feeds. Thus, the dependence of specific cutting force coefficients on cutting speeds has been studied and analyzed. It is found that specific cutting force coefficients change with change in rotational speed while keeping other cutting parameters unchanged. Hence, simulated cutting forces at higher range of rotational speed might have considerable errors if specific cutting force coefficients evaluated at lower rotational speed are used. The specific cutting force coefficients obtained analytically have been validated through experiments.     

曲面铣削过程加工路径对切削力和磨损的影响研究

针对不同走刀路径下的复杂曲面加工过程进行球头铣刀铣削Cr12MoV加工复杂曲面研究,分析不同走刀路径下铣削力和刀具磨损的变化趋势。试验结果表明:通过对比分析直线铣削和曲面铣削过程中的最大未变形切屑厚度,可以得出单周期内曲面铣削的力大于直线铣削过程的力,铣削相同铣削层时环形走刀测得的切削力普遍大于往复走刀测得的切削力;以最小刀具磨损为优化目标,运用方差分析法分析得出不同走刀路径的影响刀具磨损的主次因素,同时利用残差分析方法建立球头铣刀加工复杂曲面刀具磨损预测模型,并通过试验进行验证。     

Mechanistic modelling of the milling process using complex tool geometry

Mechanistic models of the milling process must calculate the chip geometry and the cutter edge contact length in order to predict milling forces accurately. This task becomes increasingly difficult for the machining of three dimensional parts using complex tool geometry, such as bull nose cutters. In this paper, a mechanistic model of the milling process based on an adaptive and local depth buffer of the computer graphics card is compared to a traditional simulation method. Results are compared using a 3-axis wedge shaped cut – a tool path with a known chip geometry – in order to accommodate the traditional method. Effects of cutter nose radius on the cutting and edge forces are considered. It is verified that there is little difference (1.4% at most) in the predicted force values of the two methods, thereby validating the adaptive depth buffer approach. The numerical simulations are also verified using experimental cutting tests of aluminium, and found to agree closely (within 12%).     

球头铣刀高速铣削斜面的三维数值模拟研究

用球头铣刀高速铣削斜面是在三轴加工中心上加工模具时的一种走刀方式。根据球头铣刀高速铣削斜面的特点,建立了在垂直向上和向下、水平向上和向下四种走刀方式下高速铣削45°斜面,以及在垂直向下走刀方式下高速铣削30°、60°、75°斜面的三维有限元模型,以分析不同走刀方式下铣削斜面以及铣削不同角度斜面时切削力和切削温度的变化规律。模拟结果表明,在铣削45°斜面时,采用向上走刀方式较向下走刀方式的切削力幅值小、波动大,且切削温度高;采用垂直向下走刀方式铣削大角度斜面时也出现类似情况。对切削力的实测结果验证了该模型的可靠性。     

Cutting parameter and tool path style effects on cutting force and tool deflection in machining of convex and concave inclined surfaces

Convex and concave inclined surfaces are frequently encountered in the machining of components in industries such as aerospace, aircraft, automotive, biomedical, and precision machinery manufacturing and mold industries. Tool path styles, generated by different cutting strategies, result in various cutting forces and tool deflection values that might lead to poor surface integrities. In cost-effective manufacturing, it is helpful to make known their effects on machinability. Thus, the first aim of this study is to investigate optimum cutting parameter values in ball end milling of EN X40CrMoV5-1 tool steel with three coated cutters. The parameters taken into consideration are cutting speed, feed rate, step over, and tool path style. The second aim of the study is to determine the effects of tool path styles in ball end milling of inclined surfaces. As a result, the most effective parameter within the selected cutting parameters and cutting styles for both inclined surfaces and different coatings was step over. In terms of tool coatings, the most rapidly deteriorating coating was TiC coating for cutting forces in both inclined surfaces and for tool deflection in convex inclined surface. In addition, the response surface methodology is employed to predict surface roughness values, depending on the cutting forces obtained. The model generated gives highly accurate results.     

球头铣刀切削力计算机预报模型的数值仿真

借助建立的铣刀切削力、扭矩和切削功率的计算机预报模型 ,对平前刀面球头铣刀的切削性能进行了数值仿真研究 ;通过分析各种切削参数对切削性能的影响规律 ,获得了不同切削条件下球头铣刀切削力和扭矩的特征和变化趋势     

基于Z-MAP方法的球头铣刀铣削力的建模

瞬时刚性切削力的建模是铣削加工物理仿真的基础,然而,球头铣刀的刀齿形状复杂,加工过程中姿态多变,瞬时刚性铣削力的建模难度较大。在考虑刀具姿态调整的情况下,通过齐次坐标变换建立了刀齿的运动轨迹,提出了一种识别刀具和工件瞬时接触区的改进Z-MAP算法,通过计算当前刀齿的参考线与工件的边界面或刀齿扫掠面的交点求出瞬时未变形切屑厚度,并采用非线性回归的方法辨识了切削力系数,在此基础上使用微元积分法建立了瞬时切削力的计算模型。为了验证仿真模型的可靠性,分别进行了垂直加工和倾斜加工试验,试验和仿真结果具有较高的一致性,表明该建模仿真方法是有效的,可以为实际加工中参数的选择和优化提供理论依据。     

A new method for cutting force prediction in peripheral milling of complex curved surface

The instantaneous uncut chip thickness and entry/exit angle of tool/workpiece engagement vary with tool path, workpiece geometry and cutting parameters in peripheral milling of complex curved surface, leading to the strong time-varying characteristic for instantaneous cutting forces. A new method for cutting force prediction in peripheral milling of complex curved surface is proposed in this paper. Considering the tool path, cutter runout, tool type(constant/nonconstant pitch cutter) and tool actual motion, a representation model of instantaneous uncut chip thickness and entry/exit angle of tool/ workpiece engagement is established firstly, which can reach better accuracy than the traditional models. Then, an approach for identifying of cutter runout parameters and calibrating of specific cutting force coefficients is presented. Finally, peripheral milling experiments are carried out with two types of tool, and the results indicate that the predicted cutting forces are highly consistent with the experimental values in the aspect of variation tendency and amplitude.     

基于正向杜邦指标线的五坐标侧铣加工

为实现叶轮类零件的多坐标侧铣加工,通过引入正向杜邦指标线,利用鼓锥形刀对自由曲面的五坐标侧铣加工进行研究。针对具有严格凸切削刃的侧铣加工刀具,提出不发生局部干涉的充要条件是切触点处刀具曲面的正向杜邦指标线位于被加工曲面的正向杜邦指标线之内。给出利用鼓锥形刀侧铣加工自由曲面时实施干涉检查的判断准则以及消除干涉的修正方法,推导出具有严格凸切削刃的刀具在给定的残留高度下侧铣加工带宽的计算方法。在此基础上,利用等残留高度法实现鼓锥形刀侧铣加工自由曲面无干涉刀具轨迹的生成。算例表明,在相同残留高度下,鼓锥形刀侧铣较之球头刀加工效率提高37.44%,说明侧铣加工是提高切削效率和加工质量的一种有效途径。     

球头铣刀切削力模型的建立

在考虑刀具的瞬时变形和刀具变形的再生反馈对切削厚度的影响的基础上,建立了包含主轴偏心、刀具磨损、刀具振动和工件振动的球头铣刀动力学模型,并通过试验验证了所建立模型的正确性。切削力模型的建立对实现球头铣刀切削力的预报具有重要的现实意义,并为进一步提高表面加工质量奠定了基础。     

Process modeling and toolpath optimization for five-axis ball-end milling based on tool motion analysis

In free-form surface machining, the prediction of five-axis ball-end milling forces is quite a challenge due to difficulties of determining the underformed chip thickness and engaged cutting edge. Part and tool deflections under high cutting forces may result in poor part quality. To solve these concerns, this paper presents process modeling and optimization method for five-axis milling based on tool motion analysis. The method selected for geometric stock modeling is the dexel approach, and the extracted cutter workpiece engagements are used as input to a force prediction. The cutter entry?Cexit angles and depth of cuts are found and used to calculate the instantaneous cutting forces. The process is optimized by varying the feed as the tool?Cworkpiece engagements vary along the toolpath, and the unified model provides a powerful tool for analyzing five-axis milling. The new feedrate profiles are shown to considerably reduce the machining time while avoiding process faults.     

凸曲面拼接模具球头铣刀的瞬时铣削力预测

在曲面模具拼接区域球头铣刀铣削过程中,刀具载荷变化大,瞬态铣削力有突变现象,影响模具拼接区域的加工精度和表面质量。为了预测拼接区域球头铣刀的瞬态铣削力,首先,建立考虑冲击振动的球头铣刀三维次摆线轨迹方程,得到瞬时未变形切屑厚度模型;然后,基于铣削微元的思想,建立凸曲面双硬度拼接模具球头铣刀的瞬态铣削力模型,该模型能够综合考虑拼接区冲击振动、硬度变化、刀具工件切触角度变化对瞬态铣削力的影响;最后,进行凸曲面拼接区域球头铣刀铣削加工实验。实验结果表明,预报的瞬态铣削力和实验测量结果在幅值上和变化趋势上具有一致性,在平稳切削时最大铣削力预测误差值基本在15%以内,验证了该模型能有效地预报凸曲面模具拼接区域球头铣刀的瞬态铣削力。     

On the machining characteristics of H13 tool steel in different hardness states in ball end milling

This paper investigates and compares the machining characteristics of AISI H13 tool steel in hardness states of 41 and 20 HRC in the ball end milling process. The machining characteristics are illustrated through three types of process outputs from the milling experiments: the milling force, the chip form, and the surface roughness. Characteristic differences in these process outputs are shown to reflect the hardness effect of the tool steel on the ball end milling process. The mechanistic phenomena of the milling process are revealed by the six shearing and ploughing cutting constants extracted from the milling forces. The experimental results show that all the cutting constants of the softer tool steel are greater than those of the hard steel, indicating that higher cutting and frictional energies are required in the chip shearing as well as in the nose ploughing processes of the softer tool steel. The higher cutting energy is also attested by the more severely deformed, shorter, and thicker chips of the softer steel. Surface roughness of the hard steel is shown to be considerably better than that of the soft steel at all cutting speeds and feed rates and is independent of cutting speed, whereas the surface roughness of the softer steel is significantly improved with increasing cutting speed.     

Optimization of machining parameters using genetic algorithm and experimental validation for end-milling operations

Optimization of cutting parameters is valuable in terms of providing high precision and efficient machining. Optimization of machining parameters for milling is an important step to minimize the machining time and cutting force, increase productivity and tool life and obtain better surface finish. In this work a mathematical model has been developed based on both the material behavior and the machine dynamics to determine cutting force for milling operations. The system used for optimization is based on powerful artificial intelligence called genetic algorithms (GA). The machining time is considered as the objective function and constraints are tool life, limits of feed rate, depth of cut, cutting speed, surface roughness, cutting force and amplitude of vibrations while maintaining a constant material removal rate. The result of the work shows how a complex optimization problem is handled by a genetic algorithm and converges very quickly. Experimental end milling tests have been performed on mild steel to measure surface roughness, cutting force using milling tool dynamometer and vibration using a FFT (fast Fourier transform) analyzer for the optimized cutting parameters in a Universal milling machine using an HSS cutter. From the estimated surface roughness value of 0.71 μm, the optimal cutting parameters that have given a maximum material removal rate of 6.0×10³ mm³/min with less amplitude of vibration at the work piece support 1.66 μm maximum displacement. The good agreement between the GA cutting forces and measured cutting forces clearly demonstrates the accuracy and effectiveness of the model presented and program developed. The obtained results indicate that the optimized parameters are capable of machining the work piece more efficiently with better surface finish.     

New mathematical method for the determination of cutter runout parameters in flat-end milling

The cutting force prediction is essential to optimize the process parameters of machining such as feed rate optimization, etc. Due to the significant influences of the runout effect on cutting force variation in milling process, it is necessary to incorporate the cutter runout parameters into the prediction model of cutting forces. However, the determination of cutter runout parameters is still a challenge task until now. In this paper, cutting process geometry models, such as uncut chip thickness and pitch angle, are established based on the true trajectory of the cutting edge considering the cutter runout effect. A new algorithm is then presented to compute the cutter runout parameters for flat-end mill utilizing the sampled data of cutting forces and derived process geometry parameters. Further, three-axis and five-axis milling experiments were conducted on a machining centre, and resulting cutting forces were sampled by a three-component dynamometer. After computing the corresponding cutter runout parameters, cutter forces are simulated embracing the cutter runout parameters obtained from the proposed algorithm. The predicted cutting forces show good agreements with the sampled data both in magnitude and shape, which validates the feasibility and effectivity of the proposed new algorithm of determining cutter runout parameters and the new way to accurately predict cutting forces. The proposed method for computing the cutter runout parameters provides the significant references for the cutting force prediction in the cutting process.     

Prediction of cutting forces and machining error in ball end milling of curved surfaces -I theoretical analysis

This paper presents a theoretical model by which cutting forces and machining error in ball end milling of curved surfaces can be predicted. The actual trochoidal paths of the cutting edges are considered in the evaluation of the chip geometry. The cutting forces are evaluated based on the theory of oblique cutting. The machining errors resulting from force induced tool deflections are calculated at various parts of the machined surface. The influences of various cutting conditions, cutting styles and cutting modes on cutting forces and machining error are investigated. The results of this study show that in contouring, the cutting force component which influences the machining error decreases with increase in milling position angle; while in ramping, the two force components which influence machining error are hardly affected by the milling position angle. It is further seen that in contouring, down cross-feed yields higher accuracy than up cross-feed, while in ramping, right cross-feed yields higher accuracy than left cross-feed. The machining error generally decreases with increase in milling position angle.     

Extracting cutting constants via harmonic force components for a general helical end mill

Mechanistic cutting constants serve well in predicting milling forces, monitoring the milling process as well as in helping to understand the mechanistic phenomena of a machining process for a unique pair of workpiece and cutter materials under various types of cutting edge geometry. This paper presents a unified approach in identifying the six shearing and ploughing cutting constants for a general helical end mill from the dynamic components of the measured milling forces in a single cutting test. The identification model is first presented assuming the milling force is measured with a known phase angle of the cutter spindle. When the phase angle of the cutter rotation is not available, as is the case for most milling machines, it is shown that the true phase angle can be identified through the theoretical phase relationship between the different harmonic components of the milling forces measured with an arbitrary phase angle. The numerical simulation and the experimental results for ball and cylindrical end mills are presented to demonstrate and validate the identification methods.