An improved cutting force model for micro milling considering machining dynamics

Micro milling, as a versatile micro machining process, is kinematically similar to conventional milling; however, it is significantly different from conventional milling with respect to chip formation mechanisms and uncut chip thickness modelling, due to the comparable size of the edge radius to the chip thickness, and the small per-tooth feeding. Considering tool runout and dynamic displacement between the tool and the workpiece, the contour of the workpiece left by previous tool paths is typically in a wavy form, and the wavy surface provides a feedback mechanism to cutting force generation because the instantaneous uncut chip thickness changes with both the vibration during the current tool path and the surface left by the previous tool paths. In this study, a more accurate uncut chip thickness model was established including the precise trochoidal trajectory of the cutting edge, tool runout and dynamic modulation caused by the machine tool system vibration. The dynamic regenerative effect is taken into account by considering the influence of all the previous cutting trajectories using numerical iteration; thus, the multiple time delays (MTD) are considered in this model. It is found that transient separation of the tool-workpiece occurring at a low feed per tooth, caused by MTD and the existing cutting force models, is no longer applicable when transient tool-workpiece separation occurs. Based on the proposed uncut chip thickness model, an improved cutting force model of micro milling is developed by full consideration of the ploughing effect and elastic recovery of the workpiece material. The proposed cutting force model is verified by micro end milling experiments, and the results show that the proposed model is capable of producing more accurate cutting force prediction than other existing models, particularly at small feed per tooth.     

铣削加工每齿进给量的决定因素研究及验证

研究了面铣刀的主偏角对切屑厚度和每齿进给量的影响,铣削中每齿进给量的决定因素,切削宽度与刀具直径的比值对切屑厚度的影响等问题进行理论分析,同时结合变速箱壳体铣削加工过程进行验证,解决了合理选择铣刀及切削参数以提升加工效率的问题。     

Mechanistic modeling of cutting forces in micro-end-milling considering tool run out,minimum chip thickness and tooth overlapping effects

This work proposed an improved mechanistic model for prediction of cutting forces in micro-milling process. The combined influences of tool run out, trochoidal trajectory of the tool center, overlapping of tooth, edge radius and minimum chip thickness are incorporated in this model to realize the exact cutting phenomenon. Moreover, an improved undeformed chip thickness algorithm has been presented by considering tool run out, minimum chip thickness and trajectory of all passing teeth for one complete revolution of the tool instead of only the current tooth trajectory. For estimation of tool run out, a model based on the geometry of the two fluted end mill cutter has been developed. Effects of trochoidal trajectory of the tool center and tool run out are found to be significant as each tooth has a different chip load. Further, the effect of minimum chip thickness is found to be significant at lower feed value. The proposed model has been validated by micro-milling experiments on Ti6Al4V-titanium alloys using uncoated flat end mill cutter. The predicted cutting forces were found to be in good agreement with the experimental cutting forces in both feed and cross feed directions.     

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.     

Micro slot milling of glass

Micro slot milling micro channels in a single pass vs two step upmilling has the benefit of higher productivity. This problem is approached by showing the theoretical benefits of more than two cutting edges. The acceptable feed per tooth and cutting depth at the maximum undeformed chip thickness for ductile-brittle transition and the benefit of upmilling versus downmilling and other parameters (tool wear, tool trajectory, tool deflection, air pressure/cutting oil) have been assessed by micro and macro-geometrical analyses versus surface finish/transparency, form error of the cross section shape in the micro scale (aspect ratio, tolerances, parallelism, flatness, straightness), chipping and productivity. Quantitative correlation between transparency and roughness is also proposed to estimate the acceptable amount of brittle mode.     

基于真实刀刃轨迹的立铣刀切削厚度模型

瞬时切削厚度是铣削加工建模研究的重要参数之一。通过分析刀刃切削轨迹,可以得到准确的瞬时切削厚度,但需要求解复杂的超越方程。通常对切削刀刃轨迹进行不同程度的简化来求解近似的瞬时切削厚度。为得到准确的瞬时切削厚度,提出一种新的切削厚度计算模型。基于立铣刀真实切削刀刃轨迹,对近似的切削厚度模型进行补偿,得到较传统计算方法更为准确的结果,计算过程也更为简单。通过切削力试验验证,该模型可以得到更好的动态切削力预测结果。     

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.     

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.     

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.     

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。     

An experimental investigation on the machining characteristics of microscale end milling

This paper discusses an experimental approach to assess the machining characteristics in microscale end milling operation through a systematic experimentation procedure. Microchannels were machined on brass plates using a carbide end mill of 1?mm diameter to analyze the effect of chip load (feed per tooth) and cutting speed on the surface roughness, specific cutting pressure, and cutting forces during microend milling operation. The tangential and radial components of forces were analyzed with the help of a three-dimensional model using the force signals acquired through KISTLER dynamometer. Feed per tooth and the interaction of cutting speed and chip load were identified as the critical parameters affecting the surface roughness of microchannel. Applying the concept of elastic recovery on the side wall surface of microchannels, the minimum chip thickness during the above micromilling operation was evaluated as 0.97???m, and the result was validated by the drastic increase in specific cutting pressure and erratic behavior of cutting forces below a chip load of 1???m.     

Studies on high-efficiency and high-precision orthogonal turn-milling-The effects of relative cutting speed and tool axis offset on tool flank temperature

The cutting-edge temperature on the flank face in dry turn-milling of medium carbon steel (ISO C45) is measured using a two-color pyrometer with an optical fiber. In turn-milling, undeformed chip geometry is complex due to its dependence on several factors including diameter of the cutting tool, number of tooth, diameter of the workpiece, tool-work revolution speed ratio, depth of cut, feed per tooth, tool axis offset, and the cutting distance. In this study, the undeformed chip is analyzed and visualized by the 3D-CAD system, and the effects of the cutting parameters in turn-milling, especially relative cutting speed and tool axis offset on tool flank temperature, are investigated. It is interesting that the relative cutting speed does not significantly affect the tool flank temperature, where it increases by approximately 20 °C at most when relative cutting speed increases from 124 m/min to 217 m/min. In addition, tool flank temperature varies by approximately 40 °C when the tool axis offset is changed from 0 mm to 9.2 mm due to the change in the undeformed chip geometry.     

Application of a variable flow stress machining theory to helical end milling

A methodology of modeling chip geometry of flat helical end milling based on a variable flow stress machining theory is presented in this article. The proposed model is concerned with the variation of the width of cut thickness. The nonuniform chip thickness geometry is discretized into several segments based on the radial depth of cut. The chip geometry for each segment is considered to be constant by taking the average value of the maximum and minimum chip thickness. The maximum chip thickness for each chip segment is computed based on the current width of cut, feed per tooth and the cutter diameter. The subsequent radial depth of cut is subtracted from the discretized size of the width of cut to obtain the minimum chip thicknesses. The forces for each segment are summed to obtain the total forces acting on the system of the workpiece and the tool. The cutting forces can be predicted from input data of work material properties, cutter configuration and the cutting conditions used. The validation of the proposed model is achieved by correlating experimental results with the predicted results obtained.     

曲面铣削过程加工路径对切削力和磨损的影响研究

针对不同走刀路径下的复杂曲面加工过程进行球头铣刀铣削Cr12MoV加工复杂曲面研究,分析不同走刀路径下铣削力和刀具磨损的变化趋势。试验结果表明:通过对比分析直线铣削和曲面铣削过程中的最大未变形切屑厚度,可以得出单周期内曲面铣削的力大于直线铣削过程的力,铣削相同铣削层时环形走刀测得的切削力普遍大于往复走刀测得的切削力;以最小刀具磨损为优化目标,运用方差分析法分析得出不同走刀路径的影响刀具磨损的主次因素,同时利用残差分析方法建立球头铣刀加工复杂曲面刀具磨损预测模型,并通过试验进行验证。     

Three dimensional cutting force analysis in end milling

The analysis of cutting forces plays an important part in the design of machine tool systems as well as in the planning, optimization, and control of machining processes. This paper presents a three-dimensional model of cutting forces in peripheral end milling in terms of material properties, cutting parameters, machining configuration, and tool/work geometry. Based on the relationship of the local cutting force and the chip load, the total cutting force model is established via the angle domain convolution integration of the local forces in the feed, cross feed, and axial directions. The integration is taken along the cutter axis and summarized across the cutting flutes. The convolution integral leads to a periodic function of cutting forces in the angle domain and an explicit expression of the dynamic cutting force components in the frequency domain. The closed-form nature of the expressions allows the prediction and optimization of cutting forces to be performed without the need of numerical iterations. To assess the fidelity of the analytical model, experimental data from end milling tests are presented in the context of three dimensional time waveforms, power spectra, and phase angles, in comparison to the values predicted by the model.     

Influence of ultrasonic vibrations on side milling of AISI 420 stainless steel

Characteristics of one-dimensional ultrasonic-assisted side milling of AISI 420 stainless steel have been investigated in this paper. Cutting force in ultrasonic-assisted milling (UAM) has been modeled, and new relations for critical cutting speed and undeformed chip thickness have been presented. Based on analytic relations, it can be inferred that in successive end mill revolutions, contrary to conventional milling (CM), cutting forces in UAM have different magnitudes. In order to experimentally investigate the cutting forces and the workpiece surface roughness, CM and UAM processes have been applied and compared in certain cutting conditions. Experimental results indicate that the average of cutting forces in UAM is less than in CM, and depending on cutting parameters, workpiece surface roughness in UAM can improve. During small value of feed, the influence of ultrasonic vibrations on the decrease of cutting forces is more noticeable in up milling, while during larger feed, employing UAM is more effective in down milling. It seems that for low feed rates, high cutting speeds and up milling process, the effect of ultrasonic vibrations on the surface roughness is more noticeable.     

微细铣削氧化锆陶瓷铣削力特征分析

针对硬态氧化锆陶瓷的微细精密加工问题,采用金刚石涂层微铣刀进行了微细铣削试验。介绍了微细铣削陶瓷材料时加工区的几何特征,分析了可能产生单齿铣削的原因。通过测力仪记录了铣削力信号,对特征力信号进行了描述和分析,研究了铣削参数以及刀具磨损对铣削力大小的影响。结果表明,微细铣削陶瓷材料时,由于每齿进给量非常小,故铣削过程易产生单齿铣削现象;铣削力轴向分量Fz的值最大,随着每齿进给量的增大,Fz呈明显上升趋势;随铣削路程的增加,刀具磨损加剧,铣削力也随之增大,受刀具磨损影响产生一定波动,特别是Fz,其增加幅度明显大于Fx和Fy的增加幅度。     

Prediction of cutting forces in helical milling process

The prediction of cutting forces is important for the planning and optimization of machining process in order to reduce machining damage. Helical milling is a kind of hole-machining technique with a milling tool feeding on a helical path into the workpiece, and thus, both the periphery cutting edges and the bottom cutting edges all participated in the machining process. In order to investigate the characteristics of discontinuous milling resulting in the time varying undeformed chip thickness and cutting forces direction, this paper establishes a novel analytic cutting force model of the helical milling based on the helical milling principle. Dynamic cutting forces are measured and analyzed under different cutting parameters for the titanium alloy (Ti–6Al–4V). Cutting force coefficients are identified and discussed based on the experimental test. Analytical model prediction is compared with experiment testing. It is noted that the analytical results are in good agreement with the experimental data; thus, the established cutting force model can be utilized as an effective tool to predict the change of cutting forces in helical milling process under different cutting conditions.     

A study of the effect of tool cutting edge radius on ductile cutting of silicon wafers

Ductile mode cutting of silicon wafers can be achieved under certain cutting conditions and tool geometry. An experimental investigation of the critical undeformed chip thickness in relation to the tool cutting edge radius for the brittle-ductile transition of chip formation in cutting of silicon wafers is presented in this paper. Experimental tests for cutting of silicon wafers using diamond tools of different cutting edge radii for a range of undeformed chip thickness are conducted on an ultra-precision lathe. Both ductile and brittle mode of chip formation processes are observed in the cutting tests. The results indicate that ductile cutting of silicon can be achieved at certain values of the undeformed chip thickness, which depends on the tool cutting edge radius. It is found that in cutting of silicon wafers with a certain tool cutting edge radius there is a critical value of undeformed chip thickness beyond which the chip formation changes from ductile mode to brittle mode. The ductile-brittle transition of chip formation varies with the tool cutting edge radius. Within the range of cutting conditions in the present study, it has also been found that the larger the cutting edge radius, the larger the critical undeformed chip thickness for the ductile-brittle transition in the chip formation.