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.     

Instantaneous uncut chip thickness modeling for micro-end milling process

The prediction model of instantaneous uncut chip thickness is critical for micro-end milling process, which can directly affect the cutting forces, surface accuracy, and process stability of the micro-end milling process. This paper presents an instantaneous uncut chip thickness model systematically based on the actual trochoidal trajectory of tooth and the tool run-out in micro-end milling process. The variable entry and exit angles of tool, which are affected by the tool run-out, are concerned in the model. The related instantaneous uncut chip thickness is evaluated by considering the theoretical instantaneous uncut chip thickness and the minimum uncut chip thickness, which is formulated by two types of material removal mechanisms, in the elastic-plastic deformation region and the complete chip formation region, respectively. In comparison with the instantaneous chip thickness obtained from the conventional model, the feasibility of the proposed model can be proved by the related simulation results with variable process parameters including feed per tooth, radial depth of cut, and tool run-out. In addition, the predicted and measured cutting forces are compared with validate the accuracy of the proposed instantaneous uncut chip thickness model for the micro-end milling process.     

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.     

基于刀具磨损映射关系的微细铣削力理论建模与试验研究

微细铣削加工过程中,刀具直径小且磨损较快,刀具磨损对微细铣削力有着明显的非线性影响,同时刀具跳动又对刀具每齿的磨损表现出不同的影响效应,这些影响因素会导致加工过程的不稳定性和精度。然而,目前缺乏考虑具有刀具跳动和磨损效应的通用微细铣削力模型,研究了刀具跳动与刀具每齿磨损量之间的变化规律,提出了一种同时包括刀具跳动和刀具磨损效应的新型的微细铣削力模型。该模型中,根据刀具每齿磨损量与切削位置的几何关系,改进了瞬时切削厚度模型,基于不同切削刃所对应的受力情况,同时将刀具直径方向上磨损变化量与力模型系数相关联,从而来提高力模型的精确度。最后,通过不同铣削参数下的铣削试验,论证了所提出模型的准确性和有效性。利用所提出的模型,可以通过监测铣削力的大小来辨别刀具尺寸是否在可持续铣削的范围内,从而提高微铣削的加工精度和效率。     

Surface generation modeling of micro milling process with stochastic tool wear

Micro milling is widely used to manufacture miniature parts and features at high quality with low set-up cost. To achieve a higher quality of existing micro products and improve the milling performance, a reliable analytical model of surface generation is the prerequisite as it offers the foundation for surface topography and surface roughness optimization. In the micro milling process, the stochastic tool wear is inevitable, but the deep influence of tool wear hasn't been considered in the micro milling process operation and modeling. Therefore, an improved analytical surface generation model with stochastic tool wear is presented for the micro milling process. A probabilistic approach based on the particle filter algorithm is used to predict the stochastic tool wear progression, linking online measurement data of cutting forces and tool vibrations with the state of tool wear. Meanwhile, the influence of tool run-out is also considered since the uncut chip thickness can be comparable to feed per tooth compared with that in conventional milling. Based on the process kinematics, tool run-out and stochastic tool wear, the cutting edge trajectory for micro milling can be determined by a theoretical and empirical coupled method. At last, the analytical surface generation model is employed to predict the surface topography and surface roughness, along with the concept of the minimum chip thickness and elastic recovery. The micro milling experiment results validate the effectiveness of the presented analytical surface generation model under different machining conditions. The model can be a significant supplement for predicting machined surface prior to the costly micro milling operations, and provide a basis for machining parameters optimization.     

Tool wear rate prediction in ultrasonic vibration-assisted milling

Abstract

In the current study, a predictive model on tool flank wear rate during ultrasonic vibration-assisted milling is proposed. One benefit of ultrasonic vibration is the frequent separation between tool and workpiece as the cutting time is reduced. In order to account for this effect, three types of tool–workpiece separation criteria are checked based on the tool center instantaneous position and velocity. Type I criterion examines the instantaneous velocity of tool center under feed movement and vibration. If the tool is moving away from workpiece, there is no contact. Type II criterion examines the position of tool center. If the tool center is far from the uncut workpiece surface, there is no contact even though the tool is getting closer. Type III criterion describes the smaller chip size due to the overlaps between current and previous tool paths as a result of vibration. If any criterion is satisfied, the tool flank wear rate is zero. Otherwise, the flank wear rate is predicted considering abrasion, adhesion and diffusion. The proposed predictive tool flank wear rate model is validated through comparison to experimental measurements on SKD 61 steel with uncoated carbide tool. The proposed predictive model is able to match the measured tool flank wear rate with high accuracy of 10.9% average percentage error. In addition, based on the sensitivity analysis, smaller axial depth of milling, larger feed per tooth or higher cutting speed will result in higher flank wear rate. And the effect of vibration parameters is less significant.     

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.     

Influence of size effect on burr formation in micro cutting

Burr is an important character of the surface quality for machined parts, and it is even more severe in micro cutting. Due to the uncut chip thickness and the cutting edge radius at the same range in micro cutting process, the tool extrudes the workpiece with negative rake angle. The workpiece flows along the direction of minimum resistance, and Poisson burr is formed. Based on the deformation analysis and experiment observations of micro cutting process, the factor for Poisson burr formation is analyzed. It is demonstrated that the ratio of the uncut chip thickness to the cutting edge radius plays an important role on the height of Poisson burr. Increasing the uncut chip thickness or decreasing the cutting edge radius makes the height of exit burr reduce. A new model of micro exit burr is established in this paper. Due to the size effect of specific cutting energy, the exit burr height increases. The minimum exit burr height will be obtained when the ratio of uncut the chip thickness to the cutting edge radius reaches 1. It is found that the curled radius of the exit burr plays an important role on the burr height.     

Cutter workpiece engagement region and surface topography prediction in five-axis ball-end milling

Based on the machining tool path and the true trajectory equation of the cutting edge relative to the workpiece, the engagement region between the cutter and workpiece is analyzed and a new model is developed for the numerical simulation of the machined surface topography in a multiaxis ball-end milling process. The influence of machining parameters such as the feed per tooth, the radial depth of cut, the angle orientation tool, the cutter runout, and the tool deflection upon the topography are taken into account in the model. Based on the cutter workpiece engagement, the cutting force model is established. The tool deflections are extracted and used in the surface topography model for simulation. The predicted force profiles were compared to the measured ones. A reasonable agreement between the experimental and the predicted results was found.     

Geometry of chip formation in circular end milling

Machining along continuous circular tool-path trajectories avoids tool stoppage and even feed rate variation. This helps particularly in high-speed milling by reducing the effect of the machine tool mechanical structure and cutting process dynamics. With the increase in popularity of this machining concept, the need for detailed study of a valid chip formation in circular end milling is becoming necessary for accurate kinematic and dynamic modeling of the cutting process. In this paper, chip formation during circular end milling is studied with a major focus on feed per tooth and undeformed chip thickness along with their analytical derivations and numerical solutions. At first, the difference in the feed per tooth formulation for end milling along linear and circular tool-path trajectories is presented. In the next step, valid formulation of the undeformed chip thickness in circular end milling is derived by considering an epitrochoidal tooth trajectory with a wide range of the tool-path radius. The complex transcendental equations encountered in the derivation are dealt with, by a case-based approach to obtain closed-form analytical solutions. The analytical solutions of undeformed chip thickness are validated with results of numerical simulations of tool and tooth trajectories for circular end milling and also compared to the linear end milling. The close resemblance between analytical and numerical calculations of the undeformed chip thickness in circular end milling suggests validity of the proposed analytical formulations. As a case study, the cutting forces in circular end milling are calculated based on the derived chip thickness formulations and an existing mechanistic model. The calculation results reiterate the need of taking into account adjusted feed per tooth and valid chip thickness formulations in circular end milling, especially for small tool-path radii, for more realistic process modeling.     

A numerical study of the effects of cutter runout on milling process geometry based on true tooth trajectory

Cutter runout is a common phenomenon affecting the cutting performances in milling operations. To date, most of the milling process models considering cutter runout were established based on the circular tooth path approximation, which brought errors into the runout estimation. In this paper, a new approach is presented for modelling the milling process geometry with cutter runout based on the true tooth trajectory of cutter in milling. The mathematical relationship between the trajectories generated by successive cutter teeth with runout is analysed. The milling process geometrical parameters, including the instantaneous undeformed chip thickness, the entry and exit angles of a cutting tooth, and the ideal peripheral machined workpiece surface roughness, are modelled according to the true tooth trajectories. Numerical method is used to solve the derived transcendental equations. A simulation study of the effects of cutter runout on milling process geometry is conducted using the models. It was found that the change of cutter radius for a tooth relative to its preceding one is the most important factor in evaluating the effects of cutter runout.     

Effect of tilted plate vibration on solidification and microstructural and mechanical properties of semisolid cast and heat-treated A356 Al alloy

To optimize the machining process, finding the minimum uncut chip thickness is of paramount importance in micro-scale machining. However, strong dependency of the minimum uncut chip thickness to the tool geometry, workpiece material, tool-work friction, and process condition makes its evaluation complicated. The paper focuses on determination of the minimum uncut chip thickness experimentally during micro-end milling of titanium alloy Ti-6Al-4V with respect to influences of cutting parameters and lubricating systems. Experiments were carried out on a CNC machining center Kern Evo with two flute end mills of 0.8 and 2 mm diameters being used in the tests for micro- and macro-milling, respectively. It was found that the micro-milling caused more size effect than macro-milling due to higher surface micro-hardness and specific cutting forces. The specific cutting force depended strongly on feed rate (f _z) and lubricating system, followed by depth of cut (a _p) and cutting speed (v _c), mainly in the micro-scale. All output parameters were inversely proportional to the specific cutting force. Finally, depending on different process parameters during micro-milling of Ti-6Al-4V, the minimum uncut chip thickness was found to vary between 0.15 and 0.49 of the tool edge radius.     

An Improved Method for the Determination of 3D Cutting Force Coefficients and Runout Parameters in End Milling

A simple improved method is suggested for determining constant cutting force coefficients, irrespective of the cutting condition and cutter rotation angle. This can be achieved through the combination of experimentally deternimed cutting forces with those from simulation, performed by a mechanistic cutting force model and a geometric uncut chip thickness model. Additionally, this study presents an approach that estimates runout-related parameters, and the runout offset and its location angle, using only one measurement of cutting force. This method of estimating 3D end milling force coefficients was experimentally verified for a wide range of cutting conditions, and gave significantly better predictions of cutting forces than any other methods. The estimated value of the runout offset also agreed well with the measured value.     

Calculations of chip thickness and cutting forces in flexible end milling

In the end milling process of a flexible workpiece, it is well recognized that the precise determination of the instantaneous uncut chip thickness (IUCT) is essential for the cutting force calculation. This paper will present a general method that incorporates simultaneously the cutter/workpiece deflections and the immersion angle variation into the calculation of the IUCT and cutting forces. Contributions are twofold. Firstly, considering the regeneration model, a new scheme for the IUCT calculation is determined based on the relative positions between two adjacent tooth path centers. Secondly, a general approach is established to perform numerical validations. On one hand, the engagement/separation of the cutter from the workpiece is instantaneously identified. On the other hand, the calculation of the IUCT is iteratively performed. To demonstrate the validity of the method, several examples are used to show the convergence history of the cutting force and the IUCT during the flexible end milling process. Both theoretical analyses and numerical results show that the regeneration mechanism is short lived and will disappear after several tooth periods in flexible static end milling process .     

ANALYTICAL MODELING OF MICRO END-MILLING FORCES WITH EDGE RADIUS AND MATERIAL STRENGTHENING EFFECTS

The study aims at developing a predictive analytical force model for the micro end-milling operation taking into account the material strengthening as well as the edge radius effects that come into play at the micro level. The mechanistic models for macro end-milling process have been extensively reported in literature and such models predominantly use milling force coefficients which are empirically determined from end-milling experiments. The proposed model for micro end-milling is based on determination of milling force coefficients from fundamental oblique cutting approach. The edge radius effect has been accounted by analyzing the rubbing action similar to the rolling of a cylinder over work surface. Johnson-Cook material model has been modified based on the strain gradient plasticity theory incorporating the increase in material strength with decreasing uncut chip thickness. From the micro orthogonal cutting experiments, a good agreement between the experimental and predicted shear strength values is observed. The force model is validated against measured forces in end-milling experiments carried out on the KERN Evo 5 axis micro machining center. The feed and lateral forces are predicted within 10% deviation on an average.     

An improved methodology for the experimental evaluation of tool runout in peripheral milling

The modeling of cutting forces plays an important role in the progress of research and technology in most machining processes. In particular, peripheral milling is a cutting process difficult to model due to the large number of variables involved. Among these variables, tool runout affects process performance by modifying milling force patterns, shortening the tool life and machine components, and by degrading workpiece quality. In this paper, a methodology to evaluate tool runout in peripheral milling is presented. The use of a boring toolholder is proposed to make controllable changes in the tool offset that modifies tool runout. In addition, the proposed methodology has been validated by means of a piezoactuator-based system that allows tool runout compensation through controlling workpiece displacement. Experimental and simulated results presented in this paper reveal the practical applications of this methodology for researchers and engineers involved in the practice of milling and its modeling.     

微铣削中考虑刀具跳动的瞬时切厚解析计算方法

通过研究刀具实际切削过程中的余摆线轨迹及其影响,提出一种新的瞬时切厚解析计算方法,并针对两齿、四齿的情况给出瞬时切厚的具体计算公式。在两齿和四齿铣槽工况下,分析刀具跳动量和跳动角度对各齿切削过程的影响。该方法考虑刀具的综合径向跳动(包括主轴跳动,刀具制造安装误差等综合形成的径向跳动值),适用于微铣削中任意齿数刀具瞬时切厚的计算。通过与宏观铣削中的传统切厚计算公式、BAO模型和Newton-Raphson等数值法对比,量化指出了微细铣削加工与传统宏观铣削加工的一些不同,同时验证了提出的方法具有计算简洁、精度高和通用性强的优势。基于该模型进行了微铣削铣槽试验中切削力的预测,预测结果和试验结果相符良好,验证了模型的正确性和实用意义。     

Investigating the cutting phenomena in free-form milling using a ball-end cutting tool for die and mold manufacturing

This paper presents an investigation of nonplanar tool-workpiece interactions in free-form milling using a ball-end cutting tool, a technique that is widely applied in the manufacturing of dies and molds. The influence of the cutting speed on the cutting forces, surface quality of the workpiece, and chip formation was evaluated by considering the specific alterations of the contact between tool-surface along the cutting time. A trigonometric equation was developed for identifying the tool-workpiece contact along the toolpath and the point where the tool tip leaves the contact with the workpiece. The experimental validation was carried out in a machining center using a carbide ball-end cutting tool and a workpiece of AISI P20 steel. The experimental results demonstrated the negative effect of the engagement of the tool tip into the cut on machining performance. The length of this engagement depends on the tool and workpiece curvature radii and stock material. When the tool tip center is in the cut region, the material is removed by shearing together with plastic deformation. Such conditions increase the cutting force and surface roughness and lead to an unstable machining process, what was also confirmed by the chips collected.     

Improved dynamic cutting force model in peripheral milling. Part II: experimental verification and prediction

Cutting trials reveal that a measure of cutter run-out is always unavoidable in peripheral milling. This paper improves and extends the dynamic cutting force model of peripheral milling based on the theoretical analytical model presented in Part I [1], by taking into account the influence of the cutter run-out on the undeformed chip thickness. A set of slot milling tests with a single-fluted helical end-mill was carried out at different feed rates, while the 3D cutting force coefficients were calibrated using the averaged cutting forces. The measured and predicted cutting forces were compared using the experimentally identified force coefficients. The results indicate that the model provides a good prediction when the feed rate is limited to a specified interval, and the recorded cutting force curves give a different trend compared to other published results [8]. Subsequently, a series of peripheral milling tests with different helical end-mill were performed at different cutting parameters to validate the proposed dynamic cutting force model, and the cutting conditions were simulated and compared with the experimental results. The result demonstrates that only when the vibration between the cutter and workpiece is faint, the predicted and measured cutting forces are in good agreement.     

Improved analytical chip thickness model for milling

In this paper an analytic expression for chip thickness in milling was formulated while considering the cycloidal motion of the teeth, runout, and uneven teeth spacing. In order to generalize the equation, the cutting parameters associated with milling (linear feed, tool rotational speed, and radius) were combined into a single, non-dimensional parameter. The new parameter allowed abstraction of the milling process and enabled selection of the maximum possible chip thickness in milling. Equations for entry and exit angles of a cut were also developed. The chip thickness values given by the new model were compared to prior models and showed lower error levels.