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.     

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.     

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。     

Effect of cutter runout on process geometry and forces in peripheral milling of curved surfaces with variable curvature

This paper presents a novel method for cutting force modeling related to peripheral milling of curved surfaces including the effect of cutter runout, which often changes the rotation radii of cutting points. Emphasis is put on how to efficiently incorporate the continuously changing workpiece geometry along the tool path into the calculation procedure of tool position, feed direction, instantaneous uncut chip thickness (IUCT) and entry/exit angles, which are required in the calculation of cutting force. Mathematical models are derived in detail to calculate these process parameters in occurrence of cutter runout. On the basis of developed models, some key techniques related to the prediction of the instantaneous cutting forces in peripheral milling of curved surfaces are suggested together with a whole simulation procedure. Experiments are performed to verify the predicted cutting forces; meanwhile, the efficiency of the proposed method is highlighted by a comparative study of the existing method taken from the literature.     

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.     

Dynamic analysis of runout correction in milling

Tool runout and its effects is an important area of research within modelling, simulation, and control of milling forces. Tool runout causes tool cutting edges to experience uneven forces during milling. This fact also affects tool life and deteriorates workpiece surface quality. In this article a procedure, in order to diminish the effects of tool runout, is presented. The procedure is based on chip thickness modification by means of the fast correction of the tool feed rate. Dynamic feed rate modification is provided by superposing our own design of a fast feed system driven by a piezoelectric actuator to the conventional feed drive of the CNC machine tool. Previously, a model of the dynamic behaviour of the system was developed to analyze the influence of fast feed rate modification on cutting forces. The model incorporates the piezoelectric actuator response as well as the structural dynamics of the tool and the designed Fast Feed Drive System (FFDS). Simulated and experimental results presented in this paper show the effectiveness and benefits of this new tool runout correction procedure.     

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.     

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.     

Experimental studies of cutting force variation in face milling

The purpose of this paper is to present a developed cutting force model for multi-toothed cutting processes, including a complete set of parameters influencing the cutting force variation that has been shown to occur in face milling, and to analyse to what extent these parameters influence the total cutting force variation for a selected tool geometry. The scope is to model and analyse the cutting forces for each individual tooth on the tool, to be able to draw conclusions about how the cutting action for an individual tooth is affected by its neighbours.A previously developed cutting force model for multi-toothed cutting processes is supplemented with three new parameters; eccentricity of the spindle, continuous cutting edge deterioration and load inflicted tool deflection influencing the cutting force variation. A previously developed milling force sensor is used to experimentally analyse the cutting force variation, and to give input to the cutting force simulation performed with the developed cutting force model.The experimental results from the case studied in this paper show that there are mainly three factors influencing the cutting force variation for a tool with new inserts. Radial and axial cutting edge position causes approximately 50% of the force variation for the case studied in this paper. Approximately 40% arises from eccentricity and the remaining 10% is the result of spindle deflection during machining. The experimental results presented in this paper show a new type of cutting force diagrams where the force variation for each individual tooth when two cutting edges are engaged in the workpiece at the same time. The wear studies performed shows a redistribution of the individual main cutting forces dependent on the wear propagation for each tooth.     

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.     

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.     

The effect of runout on the milling tool vibration and surface quality

When milling with tools of a high length to diameter ratio, there is often a non negligible runout. Since those tools tend towards chatter because of their low stiffness, the effect of runout on the dynamic behavior of the tool must be considered. Runout adds an additional dynamic component to the tool vibration and thus to the dynamicly changing cutting forces. Furthermore runout affects the surface quality even in stable machining. This paper analyzes the effect of runout by simulation of the dynamic milling process and compares the results to experimental data. One aspect is the difference of the vibration patterns with and without runout. Furthermore, a method for the analysis of timeseries is presented in order to distinguish between chatter and runout. Another topic is the expected surface quality resulting from stable processes with runout. This surface is modeled, examined and compared to the one produced by a process without runout.     

A cutting force model for finishing processes using helical end mills with significant runout

Analytical cutting force models play an important role in a wide array of simulation approaches of milling processes. The accuracy of the simulated processes directly depends on the predictive power of the applied cutting force model, which may vary under specific circumstances. End milling processes with small radial cutting depths, e.g. finishing processes, are particularly problematic. In this case, the tool runout, which is usually neglected in established cutting force models, can become quite significant. Within this article, well-known cutting force models are implemented for runout-prone finishing processes and modified by integrating additional parameters. A method is presented for how these additional runout parameters can be efficiently determined alongside commonly used cutting coefficients. For this purpose, a large number of milling experiments have been performed where the cutting forces were directly measured using a stationary dynamometer. The measured cutting forces were compared with the simulated cutting forces to verify and assess the modified model. By using the presented model and calibration method, cutting forces can be accurately predicted even for small radial cutting depths and significant tool runout.     

High-speed five-axis milling of hardened tool steel

This paper investigates critical issues related to high-speed five-axis milling of hardened D2 tool steel (hardness HRc 63). A forging die cavity was designed to represent the typical features in dies and molds and to simulate several effects resulting from complex tool path generation. Cutting tool materials used were coated carbide for the roughing and semi-finishing processes and polycrystalline cubic boron nitride (PCBN) for the finishing process. The effects of complex tool paths on several critical machining issues such as chip morphology, cutting forces, tool wear mechanisms, tool life and surface integrity were also investigated. The main tool failure mode was chipping due to the machine tool dynamics. A five-axis analytical force model that includes the cutter location (CL) data file for computing the chip load has been developed. The effect of instantaneous tilt angle variation on the forces was also included. Verification of the force model has been performed and adopted as a basis for explaining the difficulties involved with high-speed five-axis milling of D2 tool steel.     

A multi-sensor strategy for tool failure detection in milling

A multi-sensor monitoring strategy for detecting tool failure during the milling process is presented. In this strategy, both cutting forces and acoustic emission signals are used to monitor the tool condition. A feature extracting algorithm is developed based on a first order auto-regressive (AR) model for the cutting force signals. This AR(1) model is obtained by using average tooth period and revolution difference methods. Acoustic emission (AE) monitoring indices are developed and used in determining the setting threshold level on-line. This approach was beneficial in minimizing false alarms due to tool runout, cutting transients and variations of cutting conditions. The proposed monitoring system has been verified experimentally by end milling Inconel 718 with whisker reinforced ceramic tools at spindle speeds up to 3000 rpm.     

基于改进瞬时刚性力模型的机床铣削加工监测

针对用于切削力预测的瞬时刚性力模型所需参数较多且依赖初步切削实验的问题,提出一种不需要切削实验的新型切削力预测方法,实现在实际工厂中监测机床铣削加工过程。在斜角切削模型和正交切削理论的基础上,对传统的瞬时刚性力模型进行改进,减少切削力预测所需的切削参数。改进后的模型仅需在铣削操作开始时从测量的主轴电机扭矩得到的剪切角参数,无需任何额外的传感器就可以实现铣削力预测。在所提模型中,刀具跳动的影响可通过每个切削刃处的旋转半径偏差表示,以精确预测切削力。为验证该模型的有效性,进行切削实验。结果表明：切削力的预测值与实测值吻合较好,在实际加工过程中,无需任何实验铣削或任何额外的力传感器就可以准确了解机床加工状态。     

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.     

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.