On cutting parameters selection for plunge milling of heat-resistant-super-alloys based on precise cutting geometry

In plunge milling operation the tool is fed in the direction of the spindle axis which has the highest structural rigidity, leading to the excess high cutting efficiency. Plunge milling operation is one of the most effective methods and widely used for mass material removal in rough/semi-rough process while machining high strength steel and heat-resistant-super-alloys. Cutting parameters selection plays great role in plunge milling process since the cutting force as well as the milling stability lobe is sensitive to the machining parameters. However, the intensive studies of this issue are insufficient by researchers and engineers. In this paper a new cutting model is developed to predict the plunge milling force based on the more precise plunge milling geometry. In this model, the step of cut as well as radial cutting width is taken into account for chip thickness calculation. Frequency domain method is employed to estimate the stability of the machining process. Based on the prediction of the cutting force and milling stability, we present a strategy to optimize the cutting parameters of plunge milling process. Cutting tests of heat-resistant-super-alloys with double inserts are conducted to validate the developed cutting force and cutting parameters optimization models.     

A chatter free calibration method for determining cutter runout and cutting force coefficients in ball-end milling

The accuracy of cutting force coefficients plays an important role in predicting reliable cutting force, stability lobes as well as surface location error in ball-end milling. In order to avoid chatter risk of the traditional calibration test with an entire-ball-immersed cutting depth, a cylindrical surface milling method is proposed to calibrate the cutting force coefficients with the characteristics of low cutting depth and varying lead angle. A dual-cubic-polynomial function is also presented to describe the non-uniform cutting force coefficients of the ball part cutting edge and the nonlinear chip size effect on cutting force. The variation of the maximum chip thickness versus the lead angle is established with the consideration of cutter runout. According to the dependence of chip thickness on lead angle, a runout identification method is introduced by seeking the critical lead angle at which one of the cutter flutes is just thoroughly out of cut. Then, a lumped equivalent method is adopted for the low cutting depth condition so that the dual-cubic-polynomial model can be calibrated for the chip size effect and the cutting force coefficients respectively. The accuracy of the proposed calibration method has been validated experimentally with a series of milling tests. The stability examinations indicate that the proposed method has an evident chatter-free advantage, compared with that of varying cutting depth method.     

Experimental research on cutting force variation during regenerative chatter vibration in a plain milling operation

A plain milling operation is characterized by a transient and intermittent cutting process, in which undeformed chip thickness varies continuously. The reverse is the case in variations of undeformed chip thickness in the processes of up- and down-milling. In the present study, the property of regenerative chatter vibration in a plain milling operation is investigated from the viewpoint of cutting force variation. With primary chatter vibration, the vibration energy supply is closely related to the collision of the cutting tool flank against the workpiece surface during vibration, which is induced by the bending vibration or the torsional vibration of the arbor. In addition to this factor, the regenerative effect is considered to be one of the main causes of the chatter excitation in regenerative chatter vibration. The simulation result of the cutting force variation during regenerative chatter vibration agrees well with the experimental result, when considering these factors. It is shown that the regenerative chatter vibration in the-down-milling process occurs more easily than in the up-milling process.     

On the dynamics of ball end milling: modeling of cutting forces and stability analysis

This paper presents a dynamic force model and a stability analysis for ball end milling. The concept of the equivalent orthogonal cutting conditions, applied to modeling of the mechanics of ball end milling, is extended to include the dynamics of cutting forces. The tool is divided into very thin slices and the cutting force applied to each slice is calculated and summed for all the teeth engaged. To calculate the instantaneous chip thickness of each tooth slice, the method of regenerative chip load calculation which accounts for the effects of both the surface undulations and the instantaneous deflection is used. To include the effect of the interference of the flank face of the tool with the finished surface of the work, the plowing force is also considered in the developed model. Experimental cutting forces are obtained using a five-axis milling machine with a rotary dynamometer. The developed dynamic model is capable of generating force and torque patterns with very good agreement with the experimental data. Stability of the ball end milling in the semi-finishing operation of die cavities is also studied in this paper. The tangential and radial forces predicted by the method of equivalent orthogonal condition are fitted by the equations F_t = K_t(Z)bh_av and F_r = K_r(Z)F_t, where b is the depth of cut and h_av is the average chip thickness along the cutting edge and Z is the tool axis coordinate. The polynomial functions K_t(Z) and K_r(Z) are the cutting force constants. The interdependency of the axial and radial depths of cut in ball end milling results in an iterative solution of the characteristic equation for the critical width of cut and spindle speed. In addition, due to different cutting characteristics of the cutting edge at different heights of the ball nose, stability lobes are represented by surfaces. Comparison of the time domain simulation for the shoulder removal process in die cavity machining with the analytical predictions shows that the proposed method is capable of accurate prediction of the stability lobes.     

Surface roughness variation of thin wall milling, related to modal interactions

High-speed milling operations of thin walls are often limited by the so-called regenerative effect that causes poor surface finish. The aim of this paper is to examine the link between chatter instability and surface roughness evolution for thin wall milling. Firstly, the linear stability lobes theory for the thin wall milling optimisation was used. Then, in order to consider the modal interactions, an explicit numerical model was developed. The resulting nonlinear system of delay differential equations is solved by numerical integration. The model takes into account the coupling mode, the modal shape, the fact that the tool may leave the cut and the ploughing effect. Dedicated experiments are carried out in order to confirm this modelling. This paper presents surface roughness and chatter frequency measurements. The stability lobes are validated by thin wall milling. Finally, the modal behaviour and the mode coupling give a new interpretation of the complex surface finish deterioration often observed during thin wall milling.     

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.     

Generalized modeling of drilling vibrations. Part II: Chatter stability in frequency domain

A time domain model of the drilling process and hole formation mechanism is presented in Part I, and the general solution of drilling chatter stability in frequency domain is presented in this paper. The drill's flexibility in torsional, axial and lateral directions are considered in determining the regenerative chip thickness. Stability is modelled as a fourth order eigenvalue problem with a regenerative delay term. The critical radial depth of cut and spindle speed are analytically determined from the eigenvalues of the characteristics equation of the dynamic drilling process in frequency domain. The method is compared against the extensive numerical solutions in time domain which were presented in Part I, cutting experiments and previously published partial stability laws. The time domain model presented in Part I of the paper considers tool geometry dependent mechanics, all vibration directions and the true kinematics of drilling, while allowing for nonlinearities such as tool jumping out of cut and nonlinear cutting force models. It is shown that accurate prediction of drilling stability requires modeling of drill/hole surface contact stiffness and damping which is still a research challenge.     

Time domain model of plunge milling operation

Plunge milling operations are used to remove excess material rapidly in roughing operations. The cutter is fed in the direction of spindle axis which has the highest structural rigidity. This paper presents time domain modeling of mechanics and dynamics of plunge milling process. The cutter is assumed to be flexible in lateral, axial, and torsional directions. The rigid body feed motion of the cutter and structural vibrations of the tool are combined to evaluate time varying dynamic chip load distribution along the cutting edge. The cutting forces in lateral and axial directions and torque are predicted by considering the feed, radial engagement, tool geometry, spindle speed, and the regeneration of the chip load due to vibrations. The mathematical model is experimentally validated by comparing simulated forces and vibrations against measurements collected from plunge milling tests. The study shows that the lateral forces and vibrations exist only if the inserts are not symmetric, and the primary source of chatter is the torsional–axial vibrations of the plunge mill. The chatter vibrations can be reduced by increasing the torsional stiffness with strengthened flute cavities.     

Mechanics and dynamics of general milling cutters.: Part I: helical end mills

A variety of helical end mill geometry is used in the industry. Helical cylindrical, helical ball, taper helical ball, bull nosed and special purpose end mills are widely used in aerospace, automotive and die machining industry. While the geometry of each cutter may be different, the mechanics and dynamics of the milling process at each cutting edge point are common. This paper presents a generalized mathematical model of most helical end mills used in the industry. The end mill geometry is modeled by helical flutes wrapped around a parametric envelope. The coordinates of a cutting edge point along the parametric helical flute are mathematically expressed. The chip thickness at each cutting point is evaluated by using the true kinematics of milling including the structural vibrations of both cutter and workpiece. By integrating the process along each cutting edge, which is in contact with the workpiece, the cutting forces, vibrations, dimensional surface finish and chatter stability lobes for an arbitrary end mill can be predicted. The predicted and measured cutting forces, surface roughness and stability lobes for ball, helical tapered ball, and bull nosed end mills are provided to illustrate the viability of the proposed generalized end mill analysis.     

Extension of Tlusty׳s law for the identification of chatter stability lobes in multi-dimensional cutting processes

Chatter vibrations in cutting processes are studied in the present paper. A unified approach for the calculation of the stability lobes for turning, boring, drilling and milling processes in the frequency domain is presented. The method can be used for a fast and reliable identification of the stability lobes and can take into account nonlinear shearing forces, as well as process damping forces. The applicability of Tlusty׳s law, which is a simple scalar relationship between the real part of the oriented transfer function of the structure and the limiting chip width, is extended to milling and any other multi-dimensional chatter problem without neglecting the coupled dynamics. The given analysis is suitable for getting a deep understanding of the chatter stability dependent on the parameters of the cutting process and the structure. Basic examples based on experimental data of real machine tools include the dependence of the stability behavior on the rotational direction in turning, the effect of axial–torsional structural coupling in drilling, and the dynamics of slot milling.     

Stability prediction in radial immersion for milling with symmetric structure

In this study, an analytical approach is presented to find stability limits in terms of radial immersion for a given axial depth of cut, and vice versa. Under the assumption of axis-symmetric structure and using the zero order force model, the direction coefficient matrix is decoupled to reduce the 2D milling system to a 1D stability problem. The effect of the radial immersion and radial cutting coefficient on the system stability are explicitly represented through the eigenvalue function of the directional coefficient matrix. The resulting characteristic equation allows the limiting radial immersion be solved for a given axial immersion. A procedure is presented in obtaining the radial stability diagram, in which additional unstable island and secondary lobes are shown to exist besides the traditional lobes. Stability diagrams in both axial and radial immersion are presented to demonstrate the physical insights offered by the presented method. The model is validated by comparing with results from the existing analytical and numerical models.     

Active control of high frequency chatter with machine tool feed drives in turning

This paper presents a new active vibration control strategy to mitigate high frequency regenerative chatter vibrations using machine tool feed drives. Rather than modal damping, proposed approach aims to control regenerative process dynamics to shape the Stability Lobe diagram (SLD) and attain higher material removal rates. The controller is designed as a feedback filter whose parameters are optimized to compensate regeneration. The proposed strategy is applied to actively control orthogonal (plunge) turning dynamics where >2.5 [kHz] chatter vibrations are suppressed by a fast tool servo (FTS) drive system. Stability lobes are shaped locally to reach up to 4x higher material removal rates.     

Chatter Stability of Metal Cutting and Grinding

This paper reviews fundamental modeling of chatter vibrations in metal cutting and grinding processes. The avoidance of chatter vibrations in industry is also presented. The fundamentals of orthogonal chatter stability law and lobes are reviewed for single point machining operations where the process is one dimensional and time invariant. The application of orthogonal stability to turning and boring operations is presented while discussing the process nonlinearities that make the solution difficult in frequency domain. Modeling of drilling vibrations is discussed. The dynamic modeling and chatter stability of milling is presented. Various stability models are compared against experimentally validated time domain simulation model results. The dynamic time domain model of transverse and plunge grinding operations is presented with experimental results. Off-line and real-time chatter suppression techniques are summarized along with their practical applications and limitations in industry. The paper presents a series of research topics, which have yet to be studied for effective use of chatter prediction and suppression techniques in industry.     

航空铝合金7075-T651高速铣削锯齿形切屑的形成机理研究

目的分析航空铝合金高速铣削锯齿形切屑的形成过程及机理,为提高工件表面质量、延长刀具使用寿命提供理论依据。方法考虑航空铝合金在高速铣削过程中铣削厚度变化的特点,选用合理的本构模型及材料断裂准则,将三维铣削简化为二维变厚度的正交切削热力耦合有限元模型,对锯齿形切屑的形成过程进行有限元模拟,并经铣削试验验证有限元模型的准确性。结果在2～16 m/s的切削速度范围内,铣削力、切削温度、锯齿形切屑形貌均得到了准确的仿真。随着切削速度的增加,切屑厚度、切屑连续部分高度和剪切带间距都有减小的趋势,相反,剪切角随切削速度的增加而增大。切削速度为16m/s时,锯齿形切屑在切屑厚度较大的一侧出现,并随着切屑厚度减小而逐渐消失,变为均匀带状切屑,准确仿真了切削厚度变化下锯齿形切屑形貌。结论提出考虑剪切带宽度变化的三阶段锯齿形切屑形成模型,通过剪切带内外的应变、应变率和温度的变化分析了绝热剪切过程,并使用分割强度比参数量化锯齿形切屑应变程度,控制锯齿形切屑形态。     

Chatter avoidance in the milling of thin floors with bull-nose end mills: Model and stability diagrams

The milling of thin parts is a high added value operation where the machinist has to face the chatter problem. The study of the stability of these operations is a complex task due to the changing modal parameters as the part loses mass during the machining and the complex shape of the tools that are used. The present work proposes a methodology for chatter avoidance in the milling of flexible thin floors with a bull-nose end mill. First, a stability model for the milling of compliant systems in the tool axis direction with bull-nose end mills is presented. The contribution is the averaging method used to be able to use a linear model to predict the stability of the operation. Then, the procedure for the calculation of stability diagrams for the milling of thin floors is presented. The method is based on the estimation of the modal parameters of the part and the corresponding stability lobes during the machining. As in thin floor milling the depth of cut is already defined by the floor thickness previous to milling, the use of stability diagrams that relate the tool position along the tool-path with the spindle speed is proposed. Hence, the sequence of spindle speeds that the tool must have during the milling can be selected. Finally, this methodology has been validated by means of experimental tests.     

Process stabilization with an adaptronic spindle system

For economical reasons it is necessary to reduce the machining time and to increase the process automation. This leads to the need for fast machine tools with high process stability in order to enhance the material removal rate. However, the machine often does not limit the process stability but the tool because of its compliance. This paper presents a new possibility of expanding the stable process range of long and slender end mills with an adaptronic spindle system. The system is able to position the spindle dynamically in the range of microns with three piezo actuators. In order to disturb the regenerative effect, which leads to an instable process, the chip thickness is modulated by a dynamic spindle actuation. This is realized by a superposition of vibrations of the tool in feed direction. In milling tests the degree of stabilization is verified for different superpositions. Hence, the stable process range could be improved for spindle speeds up to 5,000?rpm.     

Mechanics and dynamics of general milling cutters. Part II: inserted cutters

Inserted cutters are widely used in roughing and finishing of parts. The insert geometry and distribution of inserts on the cutter body vary significantly in industry depending on the application. This paper presents a generalized mathematical model of inserted cutters for the purpose of predicting cutting forces, vibrations, dimensional surface finish and stability lobes in milling. In this paper, the edge geometry is defined in the local coordinate system of each insert, and placed and oriented on the cutter body using the cutter's global coordinate system. The cutting edge locations are defined mathematically, and used in predicting the chip thickness distribution along the cutting zone. Each insert may have a different geometry, such as rectangular, convex triangular or a mathematically definable edge. Each insert can be placed on the cutter body mathematically by providing the coordinates of the insert center with respect to the cutter body center. The inserts can be oriented by rotating them around the cutter body, thus each insert may be assigned to have different lead and axial rake angles. By solving the mechanics and dynamics of cutting at each edge point, and integrating them over the contact zone, it is shown that the milling process can be predicted for any inserted cutter. A sample of inserted cutter modeling and analysis examples are provided with experimental verifications.     

A study on instantaneous cutting force coefficients in face milling

In this paper, the characteristics of instantaneous cutting force coefficients in face milling are studied. In order to estimate instantaneous cutting force coefficients in face milling, the relationships between instantaneous cutting force coefficients and measured cutting force signals are derived. A series of experiments are then conducted to study the natures of instantaneous cutting force coefficients. The relationships between instantaneous cutting force coefficients and other cutting parameters are also established. It is found that the normal force coefficient is mainly affected by chip thickness and cutting speed; the vertical force coefficient is mainly affected by chip thickness, cutting edge length and cutting speed; and that the horizontal force coefficient is not only affected by chip thickness, cutting speed and length of cut, but also the variation rate of chip thickness.     

RCPM—A new method for robust chatter prediction in milling

The reliability of conventional chatter prediction algorithms is limited by the inaccuracy of machining system dynamic models. In this paper, a new probabilistic algorithm for a robust analysis of stability in milling, which performs the stability analysis on an uncertain dynamic milling model, is presented. In this approach, model parameters are considered as random variables, and robust analysis of stability is carried out in order to estimate system's probability of instability for a given combination of cutting parameters. By doing so, probabilistic instead of deterministic stability lobes are obtained, and a new criterion for system stability based on level curves and gradient of the probabilistic lobes can be applied to identify optimal robust stable cutting conditions. Experimental validation consisted of different phases: firstly, machining system dynamics were estimated by means of pulse tests. Secondly, cutting force coefficients were determined by performing cutting tests. Eventually, chatter tests were performed and the experimental stability lobes were compared with the predicted robust stable regions.     

Prediction of plastic surface defects for 5-axis ball end milling of Ti-6Al-4 V with rounded cutting edges using a material removal simulation

The resulting surface quality after 5-axis ball end milling is of superior importance because finish milling is often the last process step determining the functional performance of a component. However, the prediction of surface topography is still a challenging task. Especially in ball end milling with the characteristic sickle shaped chip cross section, ploughing effects in the area of low chip thickness result in plastic deformation and surface defects (also known as burr). This paper provides a new approach to predict those surface defects by considering the minimum chip thickness for complex milling engagement conditions within a virtual process design. This allows the choice of suitable process parameters without extensive experimental efforts.