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.     

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.     

Process geometry modeling with cutter runout for milling of curved surfaces

Prediction of cutting forces and machined surface error in peripheral milling of curved geometries is non-trivial due to varying workpiece curvature along tool path. The complexity in this case, arises due to continuously changing process geometry as workpiece curvature varies along tool path. In the presence of cutter runout, the situation is further complicated owing to changing radii of cutting points. The present work attempts to model process geometry in machining of curved geometries and in the presence of cutter runout. A mathematical model computing process geometry parameters which include cutter/workpiece engagements and instantaneous uncut chip thickness in the presence of cutter runout is presented. The developed model is more realistic as it accounts for interaction of cutting tooth trajectory with that of preceding teeth trajectories in computing process geometry. Computer simulation studies carried for this purpose has shown that it is essential to account for teeth trajectory interactions for accurate prediction of process geometry parameters. This aspect is further confirmed with machining experiments, which were conducted to validate this aspect. From the outcomes of present work, it is clearly seen that the computation of process geometry during machining of curved geometries and in presence of cutter runout is not straightforward and requires a systematic approach as presented in this paper.     

Theoretical modelling and simulation of cutting forces in face milling with cutter runout

A new approach to theoretical modelling and simulation of cutting forces in face milling is presented. Based on a predictive machining theory, the action of a milling cutter is modeled as the simultaneous actions of a number of single-point cutting tools. The milling forces are predicted from the workpiece material properties, cutter parameters, tooth geometry, cutting conditions and types of milling. The properties of the workpiece material are considered as functions of strain, strain-rate and temperature in the cutting region. It takes into account the effect of the intermittent contact between each milling tooth and the workpiece on the temperature in the cutting region. It also takes into account the effect of cutter runout on the undeformed chip thickness. Milling experiments have been conducted to verify the proposed model. Good agreements between the experimental and simulated results are presented.     

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.     

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 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.     

Dynamic response analysis in end milling using pre-twisted beam finite elements

This paper develops an analytical model for estimating the dynamic responses in end milling, i.e. dynamic milling cutter deflections and cutting forces, by using the finite-element method along with an adequate end milling-cutting force model. The whole cutting system includes the spindle, the bearings and the cutter. The spindle is modelled structurally with the Timoshenko-beam element, the milling cutter with the pre-twisted Timoshenko-beam element due to its special geometry, and the bearings with lumped springs and dampers. Because the damping matrix in the resulting finite-element equation of motion for the whole cutting system is not one of proportional damping due to the presence of bearing damping, the state-vector approach and the convolution integral is used to find the solution of the equation of motion. To assure the accuracy of prediction of the dynamic response, the associated cutting force model should be sufficiently precise. Since the dynamic cutting force is proportional to the chip thickness, a quite accurate alogorithm for the calculation of the variation of the chip thickness due to geometry, run-out and spindle-tool viration is developed. A number of dynamic cutting forces and tool deflections obtained from the present model for various cutting conditions are compared with the experimental and analytical results available in the literature, good agreement being demonstrated for these comparisons. The present model is useful, therefore, for the prediction of end milling instability. Also, the tool deflections obtained using the pre-twisted beam element are found to be smaller than those obtained using the straight beam element without pre-twist angle. Hence neglecting the pre-twist angle in the structural model of the milling cutter may overestimate the tool deflections.     

Modelling the machining dynamics of peripheral milling

The machining dynamics involves the dynamic cutting forces, the structural modal analysis of a cutting system, the vibrations of the cutter and workpiece, and their correlation. This paper presents a new approach modelling and predicting the machining dynamics for peripheral milling. First, a machining dynamics model is developed based on the regenerative vibrations of the cutter and workpiece excited by the dynamic cutting forces, which are mathematically modelled and experimentally verified by the authors [Liu, X., Cheng, K., Webb, D., Luo, X.-C. Improved dynamic cutting force model in peripheral milling—Part 1: Theoretical model and simulation. Int. J. Adv Manufact Tech, 2002, 20, 631–638; Liu, X., Cheng, K., Webb, D., Longstaff, A. P., Widiyarto, H. M., Jiang, X.-Q., Blunt, L., Ford, D. Improved dynamic cutting force model in peripheral milling—Part 2: Experimental verification and prediction. Int. J. Adv Manufact Tech, 2004, 24, 794–805]. Then, the mechanism of surface generation is analysed and formulated based on the geometry and kinematics of the cutter. Thereafter a simulation model of the machining dynamics is implemented using Simulink. In order to verify the effectiveness of the approach, the transfer functions of a typical cutting system in a vertical CNC machine centre were measured in both normal and feed directions by an instrumented hammer and accelerometers. Then a set of well-designed cutting trials was carried out to record and analyse the dynamic cutting forces, the vibrations of the spindle head and workpiece, and the surface roughness and waviness. Corresponding simulations of the machining processes of these cutting trials based on the machining dynamics model are investigated and the simulation results are analysed and compared to the measurements. It is shown that the proposed machining dynamics model can well predict the dynamic cutting forces, the vibrations of the cutter and workpiece. There is a reasonable agreement between the measured and predicted roughness/waviness of the machined surface. Therefore the proposed approach is proven to be a feasible and practical approach analysing machining dynamics and surface roughness/waviness for shop floor applications.     

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.     

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.     

Sculpture surface machining: a generalized model of ball-end milling force system

A new mechanistic model is presented for the prediction of a cutting force system in ball-end milling of sculpture surfaces. The model has the ability to calculate the workpiece/cutter intersection domain automatically for a given cutter location (CL) file, cutter and workpiece geometries. Furthermore, an analytical approach is used to determine the instantaneous chip load (with and without runout) and cutting forces. In addition to predicting the cutting forces, the model also employs a Boolean approach for a given cutter, workpiece geometries, and CL file to determine the surface topography and scallop height variations along the workpiece surface which can be visualized in 3-D. The results of model validation experiments on machining Ti-6A1-4V are also reported. Comparisons of the predicted and measured forces as well as surface topography show good agreement.     

Prediction of cutting forces in milling of circular corner profiles

This paper proposes an approach to predict the cutting forces in peripheral milling of circular corner profiles in which varying radial depth of cut is encountered. The geometric relationship between an end mill and the corner profile is investigated and a mathematical model is presented to describe the different phases of the cutter/workpiece contact. The milling process for circular corner is discretized into a series of steady-state cutting processes, each with different radial depth of cut determined by the instantaneous position of the end mill relative to the workpiece. A time domain analytical model of cutting forces for the steady-state machining conditions is introduced to each segmented process for the cutting force prediction. The predicted cutting forces can be calculated in terms of tool/workpiece geometry, cutting parameters and workpirece material property, as well as the relative position of the tool to workpiece. Experiments are conducted and the measured forces are compared to the predictions for the verification of the proposed method.     

Tool temperatures and crack development in milling cutters

This paper presents a theoretical and experimental study of the dynamic temperature field on a milling cutter tooth. A finite element model is developed to simulate the heat cycle of the cutting tooth by a time-varying heat flux. Forced convection effect has been investigated at exit. Experiments on simulating thermal process of face milling by heating cemented carbide teeth with laser pulses have also been conducted; the dynamic temperature field on a cutting tooth was measured. It has been shown that when the tooth is disengaged its temperature does not decrease to a level which will induce tensile stresses on the rake face. Thus, thermal cracks are not initiated during this stage of cutting. In this paper the authors propose that thermal cracks develop cyclically with increases in the temperature gradient at each entry of the cutter into the workpiece.     

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.     

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。     

Simulation of flank milling processes

The paper presents prediction of cutting forces when flank milling ruled surfaces with tapered, helical, ball end mills. The geometric model of the workpiece is imported from standard CAD systems, and the tapered helical ball end mill is modeled as the combination of sphere and cone primitives in ACIS^© solid modeling environment. The intersection of cutter and part with a ruled surface is evaluated, and the cutter entry into and exit angles from the work material are modeled, and stored as a function of tool center coordinates along the path. The cutter entry and exit angles, the immersion angles, are used as boundary conditions in predicting the cutting forces along the path. The methodology allows prediction of cutting load distribution on the tool and part, as well optimization of machining cycle times by scheduling the feedrate in such a way that torque, power and static deflections can be maintained at safe levels.     

An improved process simulation system for ball-end milling of sculptured surfaces

A simulation system is developed in this paper, which deals with the geometry and mechanics of machining with ball-end milling cutters. The geometry of the workpiece, the cutter, and the cutter/workpiece engagement is modeled using a geometric simulation system. This module uses a commercial solid modeler (ACIS) as a geometric engine and automatically extracts the critical geometric information required for the physical simulation system. To calculate the instantaneous cutting forces, a new mechanistic force model is developed. This force model takes into account the variations of the cutting coefficients along the cutting edge, and considers the variations of the rake angle and the chip flow direction on the rake face. The calibration of the developed model is performed for half-immersion ball-end milling operation. The applicability of the developed system is verified experimentally for various up-hill angles. It is shown that as the up-hill angle increases, the ball-nose tip engagement decreases which in turn significantly affects the magnitude of the resultant forces. Also, lower cutting forces and powers are experienced if cutting with the vicinity of the tool tip is avoided.     

Mechanistic model for prediction of cutting forces in micro end-milling and experimental comparison

Micro end milling is an important process in the manufacture of micro and meso scale products and has an advantage of creating more complex geometry in a wider variety of materials in comparison with other micro-machining methods. In this paper, a new methodology for predicting the cutting coefficients considering the edge radius and material strengthening effects is presented. Further a mechanistic model is developed to predict the cutting forces in micro end milling operation taking into account overlapping tooth engagements. The mechanistic model, derived from basics considering material property and principles of metal cutting, is valid for a wider range of cutting parameters. The model is validated with the results from micro slot end-milling of mild steel carried out on the basis of full factorial design. On comparing the amplitudes of cutting forces, it is seen that mechanistic model predicts the transverse force with an average absolute error of 12.29%, while a higher prediction error of 19.49% is obtained for feed force. Additionally the mechanistic model is able to predict the variations in the cutting forces with rotation of the cutter and average absolute deviations of 13% and 11% are obtained for feed and transverse forces, respectively.     

复杂型面数控加工中的切削力预测

球头铣刀加工水平面的切削力的预测模型已经非常成熟,而对于球头铣刀加工复杂型面切削力预测的研究却很少。文章提出一种模型来预测复杂型面加工过程中的切削力。此模型通过坐标转换．使零件坐标系统与刀具坐标系统一致,并根据具体的材料,刀具,切削条件,加工方向以及表面斜率的一套参数来预测切削力。这个模型将为复杂型面加工条件的选择提供参考,并提高加工效率。