通用立铣刀真实切削轨迹下五轴铣削力计算

针对五轴铣削中刀具位姿变化和刀具类型差异所导致的铣削力预测难的问题，提出通用立铣刀五轴铣削力计算方法。基于通用立铣刀结构形式，建立通用立铣刀几何模型；综合考虑刀齿真实运动轨迹和刀具姿态变化，构建刀具瞬时切屑厚度模型；将刀具沿轴线方向等分成若干切削刃微元，并根据线性切削力假设建立刀具微元铣削力；将微元铣削力从刀具坐标系转换至工件坐标系下，并沿刀具轴向铣削深度进行积分，获得通用立铣刀的五轴铣削力模型；最后，在混联五轴数控加工实验平台上开展了铣削力测试。实测结果表明:所提铣削力计算方法正确有效，可作为后续五轴铣削工艺参数优选的理论依据。     

A chip formation based analytic force model for oblique cutting

An oblique cutting force model has been developed using an analytic orthogonal force model. The force model uses a thermo-visco-plastic material constitutive law to represent the shear stress during deformation of the material. The strains and strain rates used for defining the shear stress were obtained from chip formation and morphology derived from orthogonal cutting tests and has been extended to oblique cutting. A time domain simulation using the in-cut chip geometry to define the chip load area has been developed. The oblique force model was used to predict the cutting forces during ball milling of hardened AISI D2 tool steel. The predicted forces were verified experimentally and showed good correlation.     

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.     

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.     

Prediction of cutting forces in three and five-axis ball-end milling with tool indentation effect

Simulation of multi-axis ball-end milling of dies, molds and aerospace parts with free-form surfaces is highly desirable in order to optimize the machining processes in virtual environment ahead of costly trials. This paper presents a mechanics model that predicts the cutting forces in feed (x), normal (y) and axial (z) directions by modeling the chip thickness distribution, and cutting and indentation mechanics. The shearing forces are based on commonly known cutting mechanics models. The indentation of the cutting edge into the work material is modeled analytically by considering elasto-plastic deformation of the work material pressed by a rigid cutting tool edge with a positive or negative rake angle. The distribution of chip thickness and geometry of indentation zone are evaluated by considering five-axis motion of the tool along the toolpath. The proposed model has been experimentally validated in plunge indentation, as well as in three and five-axis ball-end milling of free-form surfaces. The prediction of axial (z) cutting forces is shown to be improved significantly when the proposed indentation model is integrated into the mechanics of ball-end milling.     

A model for thread milling cutting forces

This paper presents a mechanistic model for prediction of the thread milling forces. The mechanics of cutting for thread milling is analyzed similar to the end milling process but with modified cutting edge geometry. The chip thickness and cutting force models are developed considering the unique geometry of the tool. The model has been calibrated for 6061 Aluminum and validated. The effects of tool and thread geometry have been studied using the model.     

Mechanistic modeling of five-axis machining with a general end mill considering cutter runout

The accurate and fast prediction of cutting forces in five-axis milling of free-form surfaces remains a challenge due to difficulties in determining the varying cutter-workpiece engagement (CWE) boundaries and the instantaneous uncut chip thickness (IUCT) along the tool path. This paper proposes an approach to predict the cutting forces in five-axis milling process with a general end mill considering the cutter runout effect that is inevitable in the practical machining operations. Based on the analytical model of cutting edge combined with runout parameters, the expression of the rotary surface formed by each cutting edge undergoing general spatial motion is firstly derived. Then by extracting the feasible contact arc along the tool axis, a new arc-surface intersection method is developed to determine the CWE boundaries fast and precisely. Next, the circular tooth trajectory (CTT) model is developed for the calculation of the IUCT with a slight sacrifice of accuracy. In comparison with the true IUCT calculated by the trochoidal tooth trajectory model, the approximation error introduced by the circular assumption is negligible while the computational efficiency improves a lot. Finally, combining with the calibrated cutting coefficients and runout parameters, comprehensive formulation of the cutting force system is set up. Simulations and experimental validations of a five-axis flank milling process show that the novel CTT model possesses obvious advantages in computing efficiency and accuracy over the existing approaches. Rough machining of a turbo impeller is further carried out to test the practicability and effectiveness of the proposed mechanistic model.     

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.     

Five-axis milling mechanics for complex free form surfaces

Accurate and fast prediction of machining forces is important in high performance cutting of free form surfaces that are commonly used in aerospace, automotive, biomedical and die/mold industries. This paper presents a novel and generalized approach for prediction of cutting forces in five-axis machining of parts with complex free form surfaces. Engagement simulations between cutter and part are performed precisely along the tool path by a recently developed boundary representation method. Moreover, mathematical model for five-axis milling mechanics is developed for any given solid model of parts with complex free form surfaces. Theoretical simulations and experimental validations show that cutting forces are predicted fast and precisely for five-axis machining of complex free form surfaces.     

A new method of cutting force measurement based on command voltages of active electro-magnetic bearings

In this paper, a new indirect method of measuring dynamic cutting forces is proposed. Milling tests have been performed on a five-axis machine, Gambin 120CR, fitted out with an electro-spindle with magnetic bearings developed by the company S2M, and named SMB30. These bearings are not affected by friction and wear. An experimental approach has been developed to determine the cutting forces as a function of the measured command voltages of the milling spindle’s magnetic bearings. The spindle is treated as a “black box”, where the transfer functions linking the unknown cutting force with command voltages are established experimentally. The cutting forces calculated from the command voltages of magnetic bearings are in good agreement with the ones measured with a Kistler four-component dynamometer. This indirect method of cutting force determination provides a useful way to estimate tool wear and monitor product quality in high-speed milling on-line.     

Process simulation using finite element method — prediction of cutting forces, tool stresses and temperatures in high-speed flat end milling

End milling of die/mold steels is a highly demanding operation because of the temperatures and stresses generated on the cutting tool due to high workpiece hardness. Modeling and simulation of cutting processes have the potential for improving cutting tool designs and selecting optimum conditions, especially in advanced applications such as high-speed milling. The main objective of this study was to develop a methodology for simulating the cutting process in flat end milling operation and predicting chip flow, cutting forces, tool stresses and temperatures using finite element analysis (FEA). As an application, machining of P-20 mold steel at 30 HRC hardness using uncoated carbide tooling was investigated. Using the commercially available software DEFORM-2D™, previously developed flow stress data of the workpiece material and friction at the chip–tool contact at high deformation rates and temperatures were used. A modular representation of undeformed chip geometry was used by utilizing plane strain and axisymmetric workpiece deformation models in order to predict chip formation at the primary and secondary cutting edges of the flat end milling insert. Dry machining experiments for slot milling were conducted using single insert flat end mills with a straight cutting edge (i.e. null helix angle). Comparisons of predicted cutting forces with the measured forces showed reasonable agreement and indicate that the tool stresses and temperatures are also predicted with acceptable accuracy. The highest tool temperatures were predicted at the primary cutting edge of the flat end mill insert regardless of cutting conditions. These temperatures increase wear development at the primary cutting edge. However, the highest tool stresses were predicted at the secondary (around corner radius) cutting edge.     

On the dynamics of ball end milling: modeling of cutting forces and stability analysis

This paper presents a dynamic force model and a stability analysis for ball end milling. The concept of the equivalent orthogonal cutting conditions, applied to modeling of the mechanics of ball end milling, is extended to include the dynamics of cutting forces. The tool is divided into very thin slices and the cutting force applied to each slice is calculated and summed for all the teeth engaged. To calculate the instantaneous chip thickness of each tooth slice, the method of regenerative chip load calculation which accounts for the effects of both the surface undulations and the instantaneous deflection is used. To include the effect of the interference of the flank face of the tool with the finished surface of the work, the plowing force is also considered in the developed model. Experimental cutting forces are obtained using a five-axis milling machine with a rotary dynamometer. The developed dynamic model is capable of generating force and torque patterns with very good agreement with the experimental data. Stability of the ball end milling in the semi-finishing operation of die cavities is also studied in this paper. The tangential and radial forces predicted by the method of equivalent orthogonal condition are fitted by the equations F_t = K_t(Z)bh_av and F_r = K_r(Z)F_t, where b is the depth of cut and h_av is the average chip thickness along the cutting edge and Z is the tool axis coordinate. The polynomial functions K_t(Z) and K_r(Z) are the cutting force constants. The interdependency of the axial and radial depths of cut in ball end milling results in an iterative solution of the characteristic equation for the critical width of cut and spindle speed. In addition, due to different cutting characteristics of the cutting edge at different heights of the ball nose, stability lobes are represented by surfaces. Comparison of the time domain simulation for the shoulder removal process in die cavity machining with the analytical predictions shows that the proposed method is capable of accurate prediction of the stability lobes.     

Three-dimensional cutting process analysis with different cutting velocities

This paper uses the large deformation large strain finite-element theory, the updated Lagrangian formulation and the incremental theory approach to develop a 3D elastic-plastic analytical model that examines metal cutting on the tool tip and twin nodes on the machined face. The geometric position and the critical value of strain energy density, combined with twin node treatment, are also introduced to serve as the continuous chip separation criterion.

Finally, the 3D low-velocity cutting condition of mild steel was explored to analyze changes in the appearances of the workpiece and the chip, the distribution of stress and strain, and the progress of changes in the cutting force. The impact of different cutting velocities and the initial conditions of the residual stress were studied to understand the impact of various cutting conditions on the machined workpiece. The numerical average cutting forces are compared with the experimental cutting forces with the different low-cutting velocities to verify that the 3D cutting model that has been developed is reasonable.     

航空铝合金7075-T651高速铣削锯齿形切屑的形成机理研究

目的分析航空铝合金高速铣削锯齿形切屑的形成过程及机理,为提高工件表面质量、延长刀具使用寿命提供理论依据。方法考虑航空铝合金在高速铣削过程中铣削厚度变化的特点,选用合理的本构模型及材料断裂准则,将三维铣削简化为二维变厚度的正交切削热力耦合有限元模型,对锯齿形切屑的形成过程进行有限元模拟,并经铣削试验验证有限元模型的准确性。结果在2～16 m/s的切削速度范围内,铣削力、切削温度、锯齿形切屑形貌均得到了准确的仿真。随着切削速度的增加,切屑厚度、切屑连续部分高度和剪切带间距都有减小的趋势,相反,剪切角随切削速度的增加而增大。切削速度为16m/s时,锯齿形切屑在切屑厚度较大的一侧出现,并随着切屑厚度减小而逐渐消失,变为均匀带状切屑,准确仿真了切削厚度变化下锯齿形切屑形貌。结论提出考虑剪切带宽度变化的三阶段锯齿形切屑形成模型,通过剪切带内外的应变、应变率和温度的变化分析了绝热剪切过程,并使用分割强度比参数量化锯齿形切屑应变程度,控制锯齿形切屑形态。     

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.     

An improved cutting force and surface topography prediction model in end milling

During the milling operation, the cutting forces will induce vibration on the cutting tool, the workpiece, and the fixtures, which will affect the surface integrity of the final part and consequently the product's quality. In this paper, a generic and improved model is introduced to simultaneously predict the conventional cutting forces along with 3D surface topography during side milling operation. The model incorporates the effects of tool runout, tool deflection, system dynamics, flank face wear, and the tool tilting on the surface roughness. An improved technique to calculate the instantaneous chip thickness is also presented. The model predictions on cutting forces and surface roughness and topography agreed well with experimental results.     

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.     

Improved modelling of cutting force coefficients in peripheral milling

Titanium is one of the most widely used metals in the aircraft and turbine manufacturing industries. Accurate prediction of cutting forces is important in controlling the dimensional accuracy of thin walled aerospace components. In this paper, a general three-dimensional mechanistic model for peripheral milling processes is presented. The effects of chip thickness, rake angle and cutting geometry on chip flow, rake face friction and pressure, and cutting forces are analyzed. A set of closed form expressions with experimentally estimated cutting force factors are presented for the prediction of cutting forces. The model is verified experimentally in the peripheral milling of a titanium alloy. For a given set of cutting conditions and tool geometry, the model predicts the cutting forces accurately for the chip thickness and rake angle ranges tested.     

A new dynamic model for drilling and reaming processes

This paper presents a new computer simulation model for drilling and reaming processes. The model is made of four parts: the force model for the cutting lips, the force model for the chisel edge, the dynamic model for the machine tool (including the cutter) and the regenerative correlation between the force and machine tool vibration. The models for the forces and the machine tool are similar to the existing models. The key to the model is the regeneration correlation between the cutting forces and the machine tool vibration. It uses a new 3D chip formation model to describe the interaction between the cutter and the workpiece. The model can predict the dynamic forces and chatter limit. It also reveals several interesting phenomena, such as how the feed and the point angle of the drill affect the chatter limit. The model is implemented using C++ language with an interface to I-DEAS™ CAE software system. The simulation results are validated experimentally by both drilling and reaming under various cutting conditions. The experiment results show that the simulation is accurate with average error about 10%. A number of research issues are also proposed for the future work.     

Precise prediction of forces in milling circular corners

Pocket corner is the most typical characters of aerospace structure components. To achieve high-quality product and stable machining operation, manufacturer constantly seek to control the cutting forces in pocket corner milling process. This paper presents the cutting force in corner milling considering the precision instantaneous achievements of tool engagement angle and undeformed chip thickness. To achieve the actual milling tool engagement angle in corner milling process, the details of tool–corner engagement relationship are analyzed considering the elements of tool trajectory, tool radius, and corner radius. The actual undeformed chip thicknesses in up and down milling operations are approached on account of the trochoid paths of adjacent teeth by a presented iteration algorithm. Error analysis shows that the presented models of tool engagement angle and undeformed chip thickness have higher precision comparing with the traditional models. Combined with the cutting force coefficients fitted by a series of slot milling tests, the predicted cutting force in milling titanium pocket with different corner structure and milling parameters are achieved, and the prediction accuracy of the model was validated experimentally and the obtained predict and the experiment results were found in good agreement.