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.     

Chatter stability prediction in milling using time-varying uncertainties

The chatter stability in milling severely affects productivity and quality of machining. Tool wear causes both the cutting coefficient and the process damping coefficient, but also other parameters to change with cutting time. This variation greatly reduces the accuracy of chatter prediction using conventional methods. To solve this problem, we consider the cutting coefficients of the milling system to be both random and time-varying variables and we use the gamma process to predict cutting coefficients for different cutting times. In this paper, a time-varying reliability analysis is introduced to predict chatter stability and chatter reliability in milling. The relationship between stability and reliability is investigated for given depths and spindle speeds in the milling process. We also study the time-varying chatter stability and time-varying chatter reliability methods theoretically and with experiments. The results of this study show that the proposed method can be used to predict chatter with high accuracy for different cutting times.     

Chatter stability for micromilling processes with flat end mill

A mechanistic model is developed to predict micromilling forces with flat end mill for both shearing and ploughing-dominant cutting regimes. The model assumes that there is a critical chip thickness that determines whether a chip will form or not. Numerical method is extended to predict the chatter stability in micro end milling, which is performed based on the proposed cutting force model. The simulating procedure for predicting stability and cutting forces is presented in detail, and the stability diagram is constructed. The validation experiments are conducted to verify the simulation results. Both experimental cutting forces measured and machined workpiece surface scanned through digital microscope are analyzed and used to verify the proposed model.     

Cutting force model considering tool edge geometry for micro end milling process

The analysis of the cutting force in micro end milling plays an important role in characterizing the cutting process, as the tool wear and surface texture depend on the cutting forces. Because the depth of cut is larger than the tool edge radius in conventional cutting, the effect of the tool edge radius can be ignored. However, in micro cutting, this radius has an influence on the cutting mechanism. In this study, an analytical cutting force model for micro end milling is proposed for predicting the cutting forces. The cutting force model, which considers the edge radius of the micro end mill, is simulated. The validity is investigated through the newly developed tool dynamometer for the micro end milling process. The predicted cutting forces were consistent with the experimental results.     

Time domain coupled simulation of machine tool dynamics and cutting forces considering the influences of nonlinear friction characteristics and process damping

A higher machining ability is always required for NC machine tools to achieve higher productivity. The self-oscillated vibration called “chatter” is a well-known and significant problem that increases the metal removal rate. The generation process of the chatter vibration can be described as a relationship between cutting force and machine tool dynamics. The characteristics of machine tool feed drives are influenced by the nonlinear friction characteristics of the linear guides. Hence, the nonlinear friction characteristics are expected to affect the machining ability of machines. The influence of the contact between the cutting edge and the workpiece (i.e., process damping) on to the machining ability has also been investigated. This study tries to clarify the influence of the nonlinear friction characteristics of linear guides and ball screws and process damping onto milling operations. A vertical-type machining center is modeled by a multi-body dynamics model with nonlinear friction models. The influence of process damping onto the machine tool dynamics is modeled as stiffness and damping between the tool and the workpiece based on the evaluated frequency response during the milling operation. A time domain-coupled simulation approach between the machine tool behavior and the cutting forces is performed by using the machine tool dynamics model. The simulation results confirm that the nonlinear frictions influence the cutting forces with an effect to suppress the chatter vibration. Furthermore, the influence of process damping can be evaluated by the proposed measurement method and estimated by a time domain simulation.     

Investigation on chatter stability of thin-walled parts in milling based on process damping with relative transfer functions

Chatter usually occurs in cutting of thin-walled workpiece due to poor structural stiffness, which results in poor surface quality and damaged tool. Aiming at process damping caused by interference between a tool flank face and a machined surface of thin-walled part, the dynamic model and critical condition of stability are proposed by the relative transfer functions, when both the tool structure and the machined workpiece have similar dynamic behaviors in this paper. Using the frequency method to solve the stability of the cutting chatter, it can be seen that the process damping can significantly improve the stability of the low speed region. Moreover, the stability domain is different and more exact than the one that derives from the simple superposition of the tool and the workpiece lobe diagrams. The correctness of the model is validated by experiments. These conclusions provide a theoretical foundation and reference for the milling mechanism research.     

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.     

Chatter prediction utilizing stability lobes with process damping in finish milling of titanium alloy thin-walled workpiece

Machining chatter often becomes a big hindrance to high productivity and surface quality in actual milling process, especially for the thin-walled workpiece made of titanium alloy due to poor structural stiffness. Aiming at this issue, the stability lobes are usually employed to predict if chatter may occur in advance. For obtaining the stability lobes in milling to avoid chatter, this article introduces an extended dynamic model of milling system considering regeneration, helix angle, and process damping into the high-order time domain algorithm which can guarantee both high computational efficiency and accuracy. Via stability lobes, the reasonability and accuracy of the proposed method are verified globally utilizing specific examples in literature. More convincingly, the time-domain numerical simulation is also implemented to predict vibration displacement for partial stability verification. In this extended model, process damping is well-known as an effective approach to improve the stability at low spindle speeds, and particularly, titanium alloy as typical difficult-to-machine material is generally machined at low spindle speeds as well due to its poor machinability. Therefore, the proposed method can be employed to obtain the 3D stability lobes in finish milling of the thin-walled workpiece made of titanium alloy, Ti-6Al-4V. Verification experiments are also conducted and the results show a close agreement between the stability lobes and experiments.     

A novel chatter stability criterion for the modelling and simulation of the dynamic milling process in the time domain

The modelling of the dynamic processes in milling and the determination of chatter-free cutting conditions are becoming increasingly important in order to facilitate the effective planning of machining operations. In this study, a new chatter stability criterion is proposed, which can be used for a time domain milling process simulation and a model-based milling process control. A predictive time domain model is presented for the simulation and analysis of the dynamic cutting process and chatter in milling. The instantaneous undeformed chip thickness is modelled to include the dynamic modulations caused by the tool vibrations so that the dynamic regeneration effect is taken into account. The cutting force is determined by using a predictive machining theory. A numerical method is employed to solve the differential equations governing the dynamics of the milling system. The work proposes that the ratio of the predicted maximum dynamic cutting force to the predicted maximum static cutting force can be used as a criterion for the chatter stability. Comparisons between the simulation and experimental results are given to verify the new model.     

Hybrid model- and signal-based chatter detection in the milling process

Chatter causes machining instability and reduces productivity in the metal cutting process. It has negative effects on the surface finish, dimensional accuracy, tool life and machine life. Chatter identification is therefore necessary to control, prevent, or eliminate chatter and to determine the stable machining condition. Previous studies of chatter detection used either model-based or signal-based methods, and each of them has its drawback. Model-based methods use cutting dynamics to develop stability lobe diagram to predict the occurrence of chatter, but the off-line stability estimation couldn’t detect chatter in real time. Signal-based methods apply mostly Fourier analysis to the cutting or vibration signals to identify chatter, but they are heuristic methods and do not consider the cutting dynamics. In this study, the model-based and signal-based chatter detection methods were thoroughly investigated. As a result, a hybrid model- and signal-based chatter detection method was proposed. By analyzing the residual between the force measurement and the output of the cutting force model, milling chatter could be detected and identified efficiently during the milling process.

     

Built-up edge effects on process outputs of titanium alloy micro milling

Built-up edge (BUE) is generally known to cause surface finish problems in the micro milling process. The loose particles from the BUE may be deposited on the machined surface, causing surface roughness to increase. On the other hand, a stable BUE formation may protect the tool from rapid tool wear, which hinders the productivity of the micro milling process. Despite its common presence in practice, the influence of BUE on the process outputs of micro milling has not been studied in detail. This paper investigates the relationship between BUE formation and process outputs in micro milling of titanium alloy Ti6Al4V using an experimental approach. Micro end mills used in this study are fabricated to have a single straight edge using wire electrical discharge machining. An initial experimental effort was conducted to study the relationship between micro cutting tool geometry, surface roughness, and micro milling process forces and hence conditions to form stable BUE on the tool tip have been identified. The influence of micro milling process conditions on BUE size, and their combined effect on forces, surface roughness, and burr formation is investigated. Long-term micro milling experiment was performed to observe the protective effect of BUE on tool life. The results show that tailored micro cutting tools having stable BUE can be designed to machine titanium alloys with long tool life with acceptable surface quality.     

高速铣削时颤振的诊断和稳定加工区域的预报

给出一种通过测量加工过程中的噪声来诊断高速铣削时颤振的方法.先测量环境噪声,然后测量加工噪声.理论分析和试验结果表明,如果加工噪声的主谐振频率接近其中一个环境噪声主谐振频率或者是齿频的整数倍,那么系统无颤振,否则有颤振.建立系统结构和铣削过程动力学特征参数的数学模型.根据测出的颤振频率,通过所建模型可解出系统的固有频率、阻尼比和过程参数,并计算出稳定极限曲线.试验证明,该方法能较好地预报高速铣削时的稳定加工区域.     

Extension of process damping to milling with low radial immersion

This paper investigates the stabilizing effect of process damping at low cutting speeds for regenerative machine tool vibrations of milling processes. The process damping is induced by a velocity-dependent cutting force model, which takes into account that the actual cutting velocity is different from the nominal one during machine tool vibrations. The chip thickness and the cutting force are calculated according to the direction of the actual cutting velocity. This results in an additional damping term in the governing delay-differential equation, which is time-periodic for milling and inversely proportional to the cutting speed. In the literature, this term is often assumed to be constant and is considered to improve stability properties at low spindle speeds. In this paper, it is shown that the velocity-dependent cutting force model captures the improvement in the low-speed stability only for turning operations and milling with large radial immersion, while it results in a negative process damping term for low-immersion milling. Consequently, an extended process damping model is needed to explain the low-speed stability improvement for low radial immersion milling.     

Stability charts with large curve-flute end-mills for thin-walled workpieces

The development of advanced performance materials by foundrymen allows new designs of components with similar mechanical resistance but lower thicknesses. This accentuates the well-known problems in machining cutting systems (static form errors, forced vibrations, and chatter), which appear increasingly early. These problems are particularly severe in the case of rotating parts in the field of aeronautics. Currently, the machining time for impellers and blisks can be improved so that new cutting tools with innovative features are continually developed. Barrel type or curved end mills will have a significant impact on the manufacturing of aircraft components during incoming years. In this paper, a time domain method is proposed for the first time to predict stability in milling operations when using these tools. The dynamic cutting forces are first obtained and then used to plot stability contour maps. Key aspects, such as tool orientation angles, several dynamic modes, and runout were also considered. Finally, chatter tests were performed for a low-stiffness mechanical system to validate the model. The presented maps indicate chatter severity and may be used for chatter prediction and productivity improvement.     

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.     

Milling force vibration analysis in high-speed-milling titanium alloy using variable pitch angle mill

Chatter may cause fast wear of tools and poor surface quality of the workpieces at high cutting speed and it will happen on different process parameters; how do we select the suitable cutting speed to suppress the chatter? In this paper, a signal analysis method for milling force and acceleration is adopted to identify chatter, which can obtain the results not only in frequency of chatter but also in the contribution for milling force at different frequencies. Through the milling experiment, the machining vibration behaviors of milling Ti–6Al–4V with variable pitch end mill were investigated. Milling force and acceleration signals obtained from experiment were analyzed and compared at stable and unstable milling processes. The experimental results show that when the chatter occurs, milling forces were found to increase dramatically by 61.9–66.8% compared with that of at stable cutting; machining surface quality became poor and machined surface roughness increases by 34.2–40.5% compared with that of at stable cutting.     

Force prediction and stability analysis of plunge milling of systems with rigid and flexible workpiece

Time domain simulation model is developed to study the dynamics of plunge milling process for system with rigid and flexible workpiece. The model predicts the cutting forces, system vibration as a function of workpiece and tool dynamics, tool setting errors, and tool kinematics and geometry. A horizontal approach is used to compute the chip area to consider the contribution of the main and side edge in the cutting zone and to deal with any geometric shape of the insert. The dynamic chip area is evaluated based on the interaction of the insert main and side cutting edges with the workpiece geometry determined by the pilot hole and surface left by the previous insert. For the case of system with a flexible workpiece, the workpiece dynamics, as well as its variation in the axial direction with respect to hole location, is considered in the simulation. Cutting tests with single and double inserts were carried out to validate the simulation model and predicted stability lobe for both systems with rigid and flexible workpiece and to check the correctness of the cutting coefficient model. Good agreement was found between the measured and the predicted cutting forces and vibration signals and power spectra. This indicates the ability of the model to accurately predict cutting forces, system vibration, and process stability for process planning prior to machining. The results show dominance of workpiece dynamics in the axial direction for systems with flexible workpiece due to its flexibility as compared to the tool axial rigidity. On the other hand, chatter behavior was found to occur due to tool lateral modes for case of rigid workpiece.     

Incomplete mesh-based tool path generation for optimum zigzag milling

The majority of mechanical parts are manufactured by milling machines. Hence, geometrically efficient algorithms for tool path generation and physical considerations for better machining productivity with guarantee of machining safety are the most important issues in milling tasks. In this paper, we present an optimized path-generation algorithm for zigzag milling, which is commonly used in the roughing stage as well as in the finishing stage, based on an incomplete two-manifold mesh model, namely, an inexact polyhedron that is widely used in recent commercialized CAM software systems. First of all, a geometrically efficient tool path generation algorithm using an intersection points-graph is introduced. Although the tool path obtained from geometric information has been successful to make a desirable shape, it seldom considers physical process concerns like cutting forces and chatter. In order to cope with these problems, an optimized tool path that maintains constant MRR in order to achieve constant cutting forces and to avoid chatter vibrations at all times is introduced and the result is verified. Additional tool path segments are appended to the basic tool path by using a pixel-based simulation technique. The algorithm was implemented for two-dimensional contiguous end-milling operations with flat end mills and cutting tests were conducted by measuring the spindle current, (which reflect machining situations) to verify the significance of the proposed method.     

Development and evaluation of tool dynamometer for measuring high frequency cutting forces in micro milling

A tool dynamometer is developed for measuring the high frequency cutting forces, and evaluated in micro milling of aluminum 6061-T6 using a tungsten carbide (WC) micro end mill. To improve the accuracy and productivity of the machining process, it is essential to monitor and control the machining process by measuring cutting forces. In order to improve the precision and quality of machined parts, high-speed machining with smaller micro tools is required, causing higher frequency cutting forces. The first natural frequency of tool dynamometers is high enough to precisely measure the high cutting forces. We investigate dynamic characteristics of the tool dynamometer theoretically and experimentally. The measurable frequency range of the developed tool dynamometer was higher than the commercial tool dynamometer, and the measured cutting force signals were not distorted at high-speed of above 60,000 rpm. The results showed that the developed dynamometer is able to measure the static and dynamic force components in high-speed micro milling.     

Extraction of 5-axis milling conditions from CAM data for process simulation

5-axis milling is widely used in machining of parts with free-form surfaces and complex geometries. Although in general 5-axis milling increases the process capability, it also brings additional challenges due to complex process geometry and mechanics. In milling, cutting forces, tool deflections, and chatter vibrations may reduce part quality and productivity. By use of process simulations, the undesired results can be identified and overcome, and part quality and productivity can be increased. However, machining conditions and geometry, especially the tool–work engagement limits, are needed in process models which are used in these simulations. Due to the complexity of the process geometry and continuous variation of tool–work engagement, this information is not readily available for a complete 5-axis milling cycle. In this study, an analytical method is presented for the identification of these parameters from computer-aided manufacturing data. In this procedure, depths of cut, lead, and tilt angles, which determine the tool–workpiece engagement boundaries, are directly obtained the cutter location file analytically in a very fast manner. The proposed simulation approach is demonstrated on machining of parts with relatively complex geometries.