Virtual Design and Optimization of Machine Tool Spindles

An integrated digital model of spindle, tool holder, tool and cutting process is presented. The spindle is modeled using an in-house developed Finite Element system. The preload on the bearings and the influence of gyroscopic and centrifugal forces from all rotating parts due to speed are considered. The bearing stiffness, mode shapes, Frequency Response Function at any point on the spindle can be predicted. The static and dynamic deflections along the spindle shaft as well as contact forces on the bearings can be predicted with simulated cutting forces before physically building and testing the spindles. The spacing of the bearings are optimized to achieve either maximum dynamics stiffness or maximum chatter free depth of cut at the desired speed region for a given cutter geometry and work-piece material. It is possible to add constraints to model mounting of the spindle on the machine tool, as well as defining local springs and damping elements at any nodal point on the spindle. The model is verified experimentally.     

Modeling of spindle-bearing and machine tool systems for virtual simulation of milling operations

This paper presents a general, integrated model of the spindle bearing and machine tool system, consisting of a rotating shaft, tool holder, angular contact ball bearings, housing, and the machine tool mounting. The model allows virtual cutting of a work material with the numerical model of the spindle during the design stage. The proposed model predicts bearing stiffness, mode shapes, frequency response function (FRF), static and dynamic deflections along the cutter and spindle shaft, as well as contact forces on the bearings with simulated cutting forces before physically building and testing the spindles. The proposed models are verified experimentally by conducting comprehensive tests on an instrumented-industrial spindle. The study shows that the accuracy of predicting the performance of the spindles require integrated modeling of all spindle elements and mounting on the machine tool. The operating conditions of the spindle, such as bearing preload, spindle speeds, cutting conditions and work material properties affect the frequency and amplitude of vibrations during machining.     

Modelling and simulation of chatter in milling using a predictive force model

A predictive time domain chatter model is presented for the simulation and analysis of chatter in milling processes. The model is developed using a predictive milling force model, which represents the action of milling cutter by the simultaneous operations of a number of single-point cutting tools and predicts the milling forces from the fundamental workpiece material properties, tool geometry and cutting conditions. The instantaneous undeformed chip thickness is modelled to include the dynamic modulations caused by the tool vibrations so that the dynamic regeneration effect is taken into account. Runge–Kutta method is employed to solve the differential equations governing the dynamics of the milling system for accurate solutions. A Windows-based simulation system for chatter in milling is developed using the predictive model, which predicts chatter vibrations represented by the tool-work displacements and cutting force variations against cutter revolution in both numerical and graphic formats, from input of tool and workpiece material properties, cutter parameters, machine tool characteristics and cutting conditions. The system is verified with experimental results and good agreement is shown.     

立铣刀断屑槽对切削性能影响规律试验研究

采用析因试验法研究断屑槽结构的制备对整体式立铣刀切削性能的影响。选取2把断屑槽分布不同的刀具,以铣刀主轴转速、径向切削深度、每齿进给量为主要因素,建立正交铣削试验。结果表明：断屑槽分布密集的铣刀适合用于加工精度要求不高的零件;断屑槽分布稀释的铣刀,适合用于半精加工要求的工件;对比分析切屑形貌和表面质量,得到用断屑槽分布稀疏的刀具铣削工件时可获得较好的表面质量。     

Development of micro milling force model and cutting parameter optimization

Taking the minimum chip thickness effect,cutter deflection,and spindle run-out into account,a micro milling force model and a method to determine the optimal micro milling parameters were developed.The micro milling force model was derived as a function of the cutting coefficients and the instantaneous projected cutting area that was determined based on the machining parameters and the rotation trajectory of the cutter edges.When an allowable micro cutter deflection is defined,the maximum allowable cutting force can be determined.The optimal machining parameters can then be computed based on the cutting force model for better machining efficiency and accuracy.To verify the proposed cutting force model and the method to determine the optimal cutting parameters,micro-milling experiments were conducted,and the results show the feasibility and effectiveness of the model and method.     

航空薄壁件铣削加工铣削力预测方法研究

铣削加工中铣削力是导致加工变形的直接原因,而航空薄壁件加工中,加工变形是加工误差产生的主要因素.本文以航空薄壁件铣削加工过程的铣削力为研究对象,通过确定铣削力模型和切削系数参数,建立了刚性和考虑刀具工件变形耦合的柔性预测两种模型.在柔性模型中,采用预扭Timoshenko梁单元的刀具/工件独立建模的方法建立有限元模型,利用Python语言在通用有限元软件Abaqus下迭代求解.实验验证表明预测模型具有很高的准确性和有效性.     

Modelling the cutting edge radius size effect for force prediction in micro milling

This paper presents a theoretical model for cutting force prediction in micro milling, taking into account the cutting edge radius size effect, the tool run out and the deviation of the chip flow angle from the inclination angle. A parameterization according to the uncut chip thickness to cutting edge radius ratio is used for the parameters involved in the force calculation. The model was verified by means of cutting force measurements in micro milling. The results show good agreement between predicted and measured forces. It is also demonstrated that the use of the Stabler's rule is a reasonable approximation and that micro end mill run out is effectively compensated by the deflections induced by the cutting forces.     

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.     

A three-dimensional analytical cutting force model for micro end milling operation

In the present day manufacturing arena one of the most important fields of interest lies in the manufacturing of miniaturized components. End milling with fine-grained carbide micro end mills could be an efficient and economical means for medium and small lot production of micro components. Analysis of the cutting force in micro end milling plays a vital role in characterizing the cutting process, in estimating the tool life and in optimizing the process. A new approach to analytical three-dimensional cutting force modeling has been introduced in this paper. The model determines the theoretical chip area at any specific angular position of the tool cutting edge by considering the geometry of the path of the cutting edge and relates this with tangential cutting force. A greater proportion of the helix face of the cutter participating in the cutting process differs the cutting force profile in micro end milling operations a bit from that in conventional end milling operations. This is because of the reason that the depth-of-cut to tool diameter ratio is much higher in micro end milling than the conventional one. The analytical cutting force expressions developed in this model have been simulated for a set of cutting conditions and are found to be well in harmony with experimental results.     

行星复合铣削及其刀具研究

行星复合铣削方法是复合加工方法的一种实现形式,该加工方法所产生的切削力较普通端铣加工的切削力有大幅度的降低,从而能有效地降低切削热、减少工件变形、提高刀具寿命。行星复合铣削方法切削力大幅度地降低的主要原因是该方法的切削轨迹使其能将厚切削层分解为细小的切削层,而该方法中的立铣刀的螺旋角和半径对实际切削力的影响很小。行星复合铣削方法在刀盘低速旋转时就能实现高速切削,有效地避开了高速旋转刀盘的动平衡问题,结合其切削力小的优势,通过增大刀盘直径并增加立铣刀数量来提高加工效率。行星铣刀采用行星轮系结构,能够达到行星复合铣削方法切削轨迹要求,具有扭矩大、运转可靠等优势。     

Time domain model of plunge milling operation

Plunge milling operations are used to remove excess material rapidly in roughing operations. The cutter is fed in the direction of spindle axis which has the highest structural rigidity. This paper presents time domain modeling of mechanics and dynamics of plunge milling process. The cutter is assumed to be flexible in lateral, axial, and torsional directions. The rigid body feed motion of the cutter and structural vibrations of the tool are combined to evaluate time varying dynamic chip load distribution along the cutting edge. The cutting forces in lateral and axial directions and torque are predicted by considering the feed, radial engagement, tool geometry, spindle speed, and the regeneration of the chip load due to vibrations. The mathematical model is experimentally validated by comparing simulated forces and vibrations against measurements collected from plunge milling tests. The study shows that the lateral forces and vibrations exist only if the inserts are not symmetric, and the primary source of chatter is the torsional–axial vibrations of the plunge mill. The chatter vibrations can be reduced by increasing the torsional stiffness with strengthened flute cavities.     

球头铣刀铣削斜面的三维有限元仿真研究

在能源动力、汽车、航空航天、模具制造等关键零部件的加工过程中,球头铣刀因其特有的刀具几何结构,常作为零件加工的最终成型刀具。考虑到在球头铣刀立铣加工中不同的刀具与工件相对姿态会对切削过程产生不同的影响,本文研究切屑形成和不同走刀方式下切削过程中各物理量(切削力、切削温度等)的变化情况,结合有限元仿真技术在切削加工中的应用,建立硬质合金球头铣刀铣削斜面的有限元模型,模拟相同切削参数下,八种不同走刀方式的球头铣削过程,分析刀具切入切出工件时切屑的形成过程,探究切削力和切削温度的变化规律。仿真结果表明:不同的走刀方式,平均切削合力各不相同,同时切屑和工件的最大切削温度也出现较大差异,而斜坡上坡逆铣的走刀方式所对应的平均切削合力和最大切削温度均最优。     

Prediction of chatter in NC machining based on a dynamic cutting force model for ball end milling

Ball end milling is one of the most widely used cutting processes in the automotive, aerospace, die/mold, and machine parts industries, and the chatter generated under unsuitable cutting conditions is an extremely serious problem as it causes excessive tool wear, noise, tool breakage, and deterioration of the surface quality. Due to the critical nature of detecting and preventing chatter, we propose a dynamic cutting force model for ball end milling that can precisely predict the cutting force for both stable and unstable cutting states because our uncut chip thickness model considers the back-side cutting effect in unstable cutting states. Furthermore, the dynamic cutting force model considers both tool runout and the penetration effect to improve the accuracy of its predictions. We developed software for calculating the cutting configuration and predicting the dynamic cutting force in general NC machining as well as single-path cutting. The chatter in ball end milling can be detected from the calculated cutting forces and their frequency spectra. A comparison of the predicted and measured cutting forces demonstrated that the proposed method provides accurate results.     

Identification of cutter offset in end milling without a prior knowledge of cutting coefficients

This paper presents a method for the identification of cutter offset through milling force without requiring the specific cutting coefficients to be known as priori. The total milling force in the presence of cutter offset is first obtained on the basis of dual cutting mechanisms, where the local force is comprised of a constant plowing force and a linear shearing force proportional to the chip load under the cutter offset. The total milling force is synthesized through convolution and is shown to be the sum of three force components: the nominal chip shearing force component, the plowing force components and the offset related shearing force component. Fourier analysis of these force components reveals the effects of offset geometry and yields formulas for the identification of offset geometry. The identification process requires only two cutting tests and the evaluation of two algebraic expressions; the shearing constants are found from the average forces of cutting tests and the offset geometry is identified from the force component at the spindle frequency. Through numerical simulation and experimental results, the efficacy of the identification method is demonstrated; the effects of feed per tooth and cutting depths on the accuracy of the model are investigated and criteria for the appropriate selection of these parameters are suggested.     

Cutting process in glass peripheral milling

Peripheral glass milling for trimmings of several devices and touch panels is studied with measuring cutting forces and observing surface damages. Peripheral millings were performed to cut the end faces of 1 mm thick glass plates. In order to discuss the typical cutting force in glass milling, the cutting forces were compared with those of 0.45% carbon steel (AISI 1045) at high feed rates in a large radial depth of cut. The differences of the cutting force in glass milling from that of metal milling are: (1) the change in the cutting force does not correspond to the uncut chip thickness; and (2) the maximum cutting force does not change with the feed rate. A model is proposed to predict the cutting forces in glass millings, which are performed in ductile, ductile/brittle complex and brittle modes. The cutting force depends on the uncut chip thickness in a ductile mode. In a brittle mode, the mean value of the cutting force does not change though the vibration component becomes large. Because the uncut chip thickness changes with the dynamic displacement of the cutting edge, the cutting process is performed in a ductile/brittle complex mode when the cutting mode changes in ductile–brittle transition. The critical uncut chip thickness at the transition from a ductile to a ductile/brittle complex mode and that of the transition from a ductile/brittle complex to brittle mode are determined in the rate of the cutting force change. The force model is verified by the cutting forces in up- and down-cutting milling operations. Then, the surface finishing and crack propagation in up- and down-cutting millings were analyzed to define the cutter path in glass trimming. Cracks propagate to the surface to be finally finished in down-cutting; while cracks propagate to the chip to be removed in up-cutting. The cutter path in up-cutting milling should be selected to finish the fine surfaces.     

球头铣刀动力学模型及其铣削加工稳定性的研究

根据螺旋刃球头铣刀的几何模型,考虑切削加工时刀齿的有交切削区及再生效应,建立球头铣刀的单刃切削力模型;进行模态实验和参数识别,建立螺旋刃球头铣刀的动力学模型;在Matlab环境下,基于龙格-库塔法对球头铣刀铣削加工过程稳定性进行仿真,结果表明:该模型能很好地描述切削过程中的稳定性及振动等动学特性,对于实际铣削加工过程及实验机的优化设计具有指导意义。     

Prediction of cutting force distribution and its influence on dimensional accuracy in peripheral milling

Cutting force has a significant influence on the dimensional accuracy due to tool and workpiece deflection in peripheral milling. In this paper, the authors present an improved theoretical dynamic cutting force model for peripheral milling, which includes the size effect of undeformed chip thickness, the influence of the effective rake angle and the chip flow angle. The cutting force coefficients in the model were calibrated with the cutting forces measured by Yucesan [18] in tests on a titanium alloy, and the model was proved to be more accurate than the previous models. Based on the model, a few case studies are presented to investigate the cutting force distribution in cutting tests of the titanium alloy. The simulation results indicate that the cutting force distribution in the cut-in process has a significant influence on the dimensional accuracy of the finished part. Suggestions about how to select the cutter and the cutting parameters were given to get an ideal cutting force distribution, so as to reduce the machining error, meanwhile keeping a high productivity.     

铝合金6061-T6三维铣削加工有限元仿真及实验

为了获得6061-T6铝合金材料在铣削过程中铣削参数对铣刀切削性能的影响,使用有限元软件AdvantEdge建立有限元模型,研究了铣削深度、铣削宽度和主轴转速对切削力及温度的影响。根据仿真结果分析可得,铣削参数对切削力的影响铣削深度﹥铣削宽度﹥主轴转速;对温度的影响铣削宽度﹥铣削深度﹥主轴转速。通过实验对比,发现仿真结果与实验结果误差不超过30%,且切削力的走向基本一致,说明仿真结果是可信的。     

Numerical simulation and prediction of cutting forces in five-axis milling processes with cutter run-out

Radial cutter runout is a common issue in milling processes and has a direct effect on milling stability due to variations of resulting chip load and forces. This paper presents a new method to effectively model and predict the instantaneous cutting forces in 5-axis milling processes with radial cutter runout based on tool motion analysis. First, the undeformed chip thickness model taking runout effect into account is established under continuous change of cutter axis orientation by means of the sweep traces of cutter edges. Second, the engaged cutting edge is determined and cutting coefficients are subsequently calibrated. Finally, the method of identifying runout parameters from the measured cutting forces is proposed, and mechanistic method is then applied to predict the cutting force. Since this method is completely based on the relative motion analysis of tool-part, it can reduce the prediction errors of cutting forces effectively and is suitable for generic rotation cutters. Several validation examples are given under different cutting conditions to prove its effectiveness and accuracy. The results reveal that the developed method can predict the cutter forces with a high accuracy and has the ability to be used in simulations and optimizations of five-axis machining.     

Milling force prediction using a dynamic shear length model

Modelling of cutting forces in milling is often needed in machining automation. In this paper, a new method for the determination of the cutting forces in face milling is presented, which applies a predictive machining theory originally developed for orthogonal cutting to milling operations, with a dynamic shear length model developed and incorporated. The proposed dynamic shear length model is developed based on the analysis for the true tooth trajectories of a milling cutter, taking into account of the characteristic wavy surface effects in milling. The prediction for the cutting forces is carried out at each step of the angular increment of cutter rotation from input data of fundamental workpiece material properties, tool geometry and cutting conditions. Cutting forces at a cutter tooth can be predicted once the shear angle, shear length, shear plane area, and the shear flow stress along the shear length have been determined. The milling force prediction using the dynamic shear length model is verified through milling experimental tests. The sensitivity of the difference between the static and dynamic shear length models with respect to the feed per tooth and the cutter diameter is discussed.