Modeling and Analytical Solution of Chatter Stability for T-slot Milling

T-slot milling is one of the most common milling processes in industry. Despite recent advances in machining technology, productivity of T-slot milling is usually limited due to the process limitations such as high cutting forces and stability. If cutting conditions are not selected properly the process may result in the poor surface finish of the workpiece and the potential damage to the machine tool. Currently, the predication of chatter stability and determination of optimal cutting conditions based on the modeling of T-slot milling process is an effective way to improve the material removal rate(MRR) of a T-slot milling operation. Based on the geometrical model of the T-slot cutter, the dynamic cutting force model was presented in which the average directional cutting force coefficients were obtained by means of numerical approach, and leads to an analytical determination of stability lobes diagram(SLD) on the axial depth of cut. A new kind of SLD on the radial depth of cut was also created to satisfy the special requirement of T-slot milling. Thereafter, a dynamic simulation model of T-slot milling was implemented using Matlab software. In order to verify the effectiveness of the approach, the transfer functions of a typical cutting system in a vertical CNC machining center were measured in both feed and normal directions by an instrumented hammer and accelerators. Dynamic simulations were conducted to obtain the predicated SLD under specified cutting conditions with both the proposed model and CutPro?. Meanwhile, a set of cutting trials were conducted to reveal whether the cutting process under specified cutting conditions is stable or not. Both the simulation comparison and experimental verification demonstrated that the satisfactory coincidence between the simulated, the predicted and the experimental results. The chatter-free T-slot milling with higher MRR can be achieved under the cutting conditions determined according to the SLD simulation.     

MAXIMIZATION OF CHATTER-FREE MATERIAL REMOVAL RATE IN END MILLING USING ANALYTICAL METHODS

Chatter vibrations in milling, which develop due to dynamic interactions between the cutting tool and the workpiece, result in reduced productivity and part quality. Various numerical and analytical stability models have been considered in the previous publications, where mostly the stability limit of axial depth of cut is emphasized for chatter-free cutting. In this paper an analytical stability model is used, and a simple algorithm to determine the stability limit of radial depth of cut is presented. It is shown that, for the maximization of chatter-free material removal rate, radial depth of cut is of equal importance with the former. A method is proposed to determine the optimal combination of depths of cut, so that chatter-free material removal rate is maximized. The application of the method is demonstrated on a pocketing example where significant reduction in the machining time is obtained using the optimal parameters. The procedure can easily be integrated to a CAD/CAM or virtual machining environment in order to identify the optimal milling conditions automatically.     

MAXIMIZATION OF CHATTER-FREE MATERIAL REMOVAL RATE IN END MILLING USING ANALYTICAL METHODS

ABSTRACT

Chatter vibrations in milling, which develop due to dynamic interactions between the cutting tool and the workpiece, result in reduced productivity and part quality. Various numerical and analytical stability models have been considered in the previous publications, where mostly the stability limit of axial depth of cut is emphasized for chatter-free cutting. In this paper an analytical stability model is used, and a simple algorithm to determine the stability limit of radial depth of cut is presented. It is shown that, for the maximization of chatter-free material removal rate, radial depth of cut is of equal importance with the former. A method is proposed to determine the optimal combination of depths of cut, so that chatter-free material removal rate is maximized. The application of the method is demonstrated on a pocketing example where significant reduction in the machining time is obtained using the optimal parameters. The procedure can easily be integrated to a CAD/CAM or virtual machining environment in order to identify the optimal milling conditions automatically.     

A SIMPLIFIED SOLUTION FOR THE DEPTH OF CUT IN MULTI-PATH BALL END MILLING

Abstract

The axial depth of cut is an important factor in the dynamic cutting force analysis of milling. In multi-path ball end milling, it varies with the cutting edge position angle. General equations are derived from which the instant depth of cut in ball end milling can be calculated. Examples are given for four path increment modes. The cutting condition in each mode is discussed with respect to the depth of cut. The conditions needed to disengage the tip of the ball end mill from the cut are determined. The "step-up" increment mode has the most favorable cutting condition for cutter tip relief and high cutting velocity. In order to obtain an instant evaluation of the cutting stability, the equations of maximum depth of cut in ball end milling are derived. The exact solutions are obtained from the general equations for the instant depth of cut. More conservative estimates are obtained from the simplified solutions. The results in this paper can be used as a guide in NC part programming to select an optimal cutting strategy and to ensure a stable cutting process in ball end milling.     

A SIMPLIFIED SOLUTION FOR THE DEPTH OF CUT IN MULTI-PATH BALL END MILLING

The axial depth of cut is an important factor in the dynamic cutting force analysis of milling. In multi-path ball end milling, it varies with the cutting edge position angle. General equations are derived from which the instant depth of cut in ball end milling can be calculated. Examples are given for four path increment modes. The cutting condition in each mode is discussed with respect to the depth of cut. The conditions needed to disengage the tip of the ball end mill from the cut are determined. The "step-up" increment mode has the most favorable cutting condition for cutter tip relief and high cutting velocity. In order to obtain an instant evaluation of the cutting stability, the equations of maximum depth of cut in ball end milling are derived. The exact solutions are obtained from the general equations for the instant depth of cut. More conservative estimates are obtained from the simplified solutions. The results in this paper can be used as a guide in NC part programming to select an optimal cutting strategy and to ensure a stable cutting process in ball end milling.     

Prediction of dynamic cutting force and regenerative chatter stability in inserted cutters milling

Currently, the modeling of cutting process mainly focuses on two aspects: one is the setup of the universal cutting force model that can be adapted to a broader cutting condition; the other is the setup of the exact cutting force model that can accurately reflect a true cutting process. However, there is little research on the prediction of chatter stablity in milling. Based on the generalized mathematical model of inserted cutters introduced by ENGIN, an improved geometrical, mechanical and dynamic model for the vast variety of inserted cutters widely used in engineering applications is presented, in which the average directional cutting force coefficients are obtained by means of a numerical approach, thus leading to an analytical determination of stability lobes diagram (SLD) on the axial depth of cut. A new kind of SLD on the radial depth of cut is also created to satisfy the special requirement of inserted cutter milling. The corresponding algorithms used for predicting cutting forces, vibrations, dimensional surface finish and stability lobes in inserted cutter milling under different cutting conditions are put forward. Thereafter, a dynamic simulation module of inserted cutter milling is implemented by using hybrid program of Matlab with Visual Basic. Verification tests are conducted on a vertical machine center for Aluminum alloy LC4 by using two different types of inserted cutters, and the effectiveness of the model and the algorithm is verified by the good agreement of simulation result with that of cutting tests under different cutting conditions. The proposed model can predict the cutting process accurately under a variety of cutting conditions, and a high efficient and chatter-free milling operation can be achieved by a cutting condition optimization in industry applications.     

平底立铣刀在多刃切削时的切削力变化规律研究

为揭示平底立铣刀在多刃铣削时的切削力变化规律,理论推导了多刃切削的水平方向公称切削力的数学表达式,发现这些公称切削力是旋转角的简谐函数,其常数项与同时参与切削的刃数成正比。将切削力表达式的系数做归一化处理,采用仿真方法,得到各常用齿数平底立铣刀在单刃、多刃连续切削时的公称切削力量纲一均值和刀齿频率幅值,结果表明：切削宽度方向的公称切削力均值在多刃切削时显著增大,而其刀齿频率幅值在多刃切削时有时增大,有时减小。开展了4齿平底立铣刀的切削测力试验,试验结果与理论推导和仿真结果相符。研究结果表明：与单刃连续切削相比,多刃切削的切削宽度方向的静态切削力显著增大;多刃切削在水平方向存在着更平稳和更不平稳两种可能;偶数齿铣刀的多刃切削最平稳。研究结论可为铣削加工中优选浸入角参数提供参考。     

Study of fuzzy stochastic limited cutting width on chatter

Fuzzy mathematical theory is applied to drawing the fuzzy stability lobes in which each lobe is characterized by a membership grade of experiential distribution of testing data in the theoretical distribution set of chatter signal. The judgement of limit value of free-chatter cutting width is spread over the fuzzy domain in this paper. The fuzzy combination relationship between the spindle speed and the depth of cut in milling is also addressed. According to the limit width, a safety criterion on which the cutting process is stable is developed. Also, the concept and definition of safety criterion for the cutting process stability operation for fuzzy stochastic meaning are given. Analysis indicates that the fuzzy stability lobes have definite physical significance. First, they can tell us in which status the cutting process is for the drawn lobe. Second, they reflect the probability distribution of the limit value of cut width in the fuzzy domain with respect to the identification of chatter status (fuzzy event). Meanwhile, it indicates that there is a transition between unstable lobes and stable lobes in a stability threshold graph with the influence of both fuzzy stochastic parametric excitation and fuzzy stochastic external excitation. Testing value curves of the fuzzy allowed domain of the limited cutting width are developed via experiment.     

二维振动辅助微细铣削切削力建模与试验研究

基于力学解析法与斜角切削微元力模型,综合考虑刀具偏心、尺度效应与累积作用对瞬时切削厚度的影响,结合二维振动辅助微细铣削运动学特性,根据剪切区与犁耕区切削力大小不同的特点,建立了二维振动辅助微细铣削切削力模型.为实现振动辅助加工的目的,基于自行设计并优化的非谐振式二维柔顺振动平台,对铝合金Al6061进行了相应的二维振动...     

Development of an automatic arc welding system using SMAW process

In end milling of pockets, variable radial depth of cut is generally encountered as the end mill enters and exits the corner, which has a significant influence on the cutting forces and further affects the contour accuracy of the milled pockets. This paper proposes an approach for predicting the cutting forces in end milling of pockets. A mathematical model is presented to describe the geometric relationship between an end mill and the corner profile. The milling process of corners 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. For the cutting force prediction, an analytical model of cutting forces for the steady-state machining conditions is introduced for each segmented process with given radial depth of cut. The predicted cutting forces can be calculated in terms of tool/workpiece geometry, cutting parameters and workpiece material properties, as well as the relative position of the tool to workpiece. Experiments of pocket milling are conducted for the verification of the proposed method.     

Chatter prediction based on frequency domain solution in CNC pocket milling

Chatter has been a problem in CNC machining process especially during pocket milling process using an end mill with low stiffness. Since an iterative time-domain chatter solution consumes a computing time along tool paths, a fast chatter prediction algorithm for pocket milling process is required by machine shop-floor for detecting chatter prior to real machining process. This paper proposes the systematic solution based on integration of a stability law in frequency domain with geometric information of material removal for a given set of tool paths. The change of immersion angle and spindle speed determines the variation of the stable cutting depth along cornering cut path. This proposed solution transforms the milling stability theory toward the practical methodology for the stability prediction over the NC pocket milling.     

Active suppression of chatter in peripheral milling. Part II. Application of fuzzy control

In this paper, a feasibility study is conducted where fuzzy logic control is investigated to actively vary spindle speed modulation parameters for chatter suppression. A justification for using fuzzy control is given, as well as a brief synopsis of the fuzzy inferencing mechanism. Proportional and proportional-integral fuzzy control algorithms are developed. The set point in these controllers is established from experimental observations and measurements of the machined surfaces. Controller performance is tested by simulating changes in the axial depth of cut from a stable depth to 20% and 50% beyond the stable limit for constant speed cutting. It was found that both controllers were able to regulate the vibration in the milling process, however, the proportional-integral controller generally exhibited more desirable performance characteristics.     

Cutting dynamics and process-structure interactions applied to milling

Cutting dynamics should not be restricted only to self-excited chatter vibrations. Transient disturbances are superimposed on stable working conditions and these dynamic components provide useful information on the real behaviour of the whole machining process. Cutting dynamics therefore include the analysis of such signals in the entire frequency range. An introduction to the basic dynamics of milling processes is presented.Milling is a cutting operation during which the periodic sequence of cutting edges generates periodic time signals with discrete force and vibration spectra. A single cutting pulse from the series of successive cuts leads to an aperiodic time function and thus to a continuous spectrum. Since the dynamic behaviour is known at all frequencies a study of the influence of various cutting conditions and the interactions between the cutting process and the machine tool structure is possible. The discrete spectrum of a real cut involving many teeth can be deduced from the corresponding single cutting pulse.A simple cutting force model was assumed in the theoretical analysis in order to give an initial rough idea of the fundamental properties of the milling pulses (frequency content of the spectra, spatial excitation locus and excitation ratio) as a function of the most important parameters (total cutting angle, up and down milling, symmetrical and asymmetrical cut and number of teeth). The computed results were compared with experimentally obtained data.     

Cusp error reduction under high speed micro/meso- scale milling with ultrasonic vibration assistance

In the conventional use of vibration assisted machining, vibratory motion is mostly applied to the continuous machining processes such as turning where the cutting speed is much lower than the vibration speed. Even the recent articles on vibration assisted milling processes are also quite limited to low spindle speed less than 3k RPM. This study investigates vibration assistance that is applied to the workpiece in a high speed micro/meso-scale intermittent milling system where the cutting speed is much higher than the vibration speed. In addition to this, the vibration effect is analyzed considering feed and cross-feed directional application separately, which gives an idea of a right vibration assistance direction for surface quality improvement. To validate this, a one-directional ultrasonic vibration assisted milling system with ultrasonic frequency at 40 kHz and with amplitudes of a few microns is designed and its effect on the machined surface quality is investigated at high spindle RPMs over 15k. As a result, cusp heights are found to be reduced with ultrasonic vibratory motion of cutting edge in high cutting speed. Furthermore, the machined surface quality clearly tells that feed directional vibration assistance is able to generate better surface quality with reduced wavy burrs than cross-feed directional vibration assistance.     

Effect of machining parameters on the milling process of 2.5D C/SiC ceramic matrix composites

Abstract

The C/SiC ceramic matrix composites are widely used for high-value components in the nuclear, aerospace and aircraft industries. The cutting mechanism of machining C/SiC ceramic matrix composites is one of the most challenging problems in composites application. Therefore, the effects of machining parameters on the machinability of milling 2.5D C/SiC ceramic matrix composites is are investigated in this article. The related milling experiments has been carried out based on the C/SiC ceramic matrix composites fixed in two different machining directions. For two different machining directions, the influences of spindle speed, feed rate and depth of cut on cutting forces and surface roughness are studied, and the chip formation mechanism is discussed further. It can be seen from the experiment results that the measured cutting forces of the machining direction B are greater than those of the in machining direction A under the same machining conditions. The machining parameters, which include spindle speed, feed rate, depth of cut and machining direction, have an important influence on the cutting force and surface roughness. This research provides an important guidance for improving the machining efficiency, controlling and optimizing the machined surface quality of C/SiC ceramic matrix composites in the milling process.     

基于铣削均匀性的切削参数优化

分析了高速铣削加工切屑形成过程中刀具—工件的接触行为,提出了考虑轴向切削深度和径向切削深度的铣削均匀性模型。在此基础上,以恒定的金属去除率为约束条件、铣削均匀性系数为优化目标,建立了切削参数的优化模型。通过对航空铝合金进行高速铣削试验,验证了铣削均匀性理论及优化模型的合理性。结果表明,对于航空铝合金的高速铣削加工,采用大径向切深—小轴向切深有利于提高铣削均匀性,减小切削力。     

高速铣削时铣削力的研究

基于数控机床动力学测试分析和仿真系统,求得加工时的切削稳定域,确定加工参数的范围。在其它参数不变的情况下,通过对求得的切削力和功率的分析,得到转速高的铣削力相对较小,刀具螺旋角对铣削力的影响较小,切宽与铣削力不呈线性关系,切深与铣削力呈线性关系。文中对高速加工参数的选择有一定的指导意义。     

A coupled dynamics,multiple degree of freedom process damping model,Part 2: Milling

Self-excited vibration, or chatter, is an important consideration in machining operations due to its direct influence on part quality, tool life, and machining cost. At low machining speeds, a phenomenon referred to as process damping enables stable cutting at higher depths of cut than predicted with traditional analytical models. This paper describes an analytical stability model for milling operations which includes a process damping force that depends on the surface normal velocity, depth of cut, cutting speed, and an empirical process damping coefficient. Model validation is completed using time domain simulation and milling experiments. The results indicate that the multiple degree of freedom model is able to predict the stability boundary using a single process damping coefficient.     

高强度钢高速加工时切削力尺度效应特征规律研究

在切削速度118m/min～463m/min,每齿进给量0.078mm/z～0.2mm/z,切削深度0.2mm～1mm范围内,研究高速端面铣削某新型高强度钢材料(>42HRc、抗拉强度σb>1.2GPa)过程中切削力的变化规律,考察切削用量对铣削力的交互影响与尺度效应规律,并从切削变形机理上进行讨论与分析,使用残差分析与最小二乘法等统计方法,建立切削力与切削用量经验公式。研究结果表明:高速铣削时,切削深度、每齿进给量和两者之间的交互作用为对主切削力有显著影响的效应因素;该类型高强度钢的单位铣削力为45调质钢的1.0729倍～1.7917倍;非自由切削过程在高速切削条件下将会引发切削力的尺度效应。