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.     

Theoretical and experimental study of the chatter vibration in wet and MQL machining conditions in turning process

Turning is one of the most commonly used cutting processes for manufacturing components in production engineering. The turning process, in some cases, is accompanied by intense relative movements between tool and workpiece, which is called chatter vibrations. Chatter has been identified as a detrimental problem that adversely impacts surface finish, tool life, process productivity, and dimensional accuracy of the machined part. Cooling/Lubrication in the turning process is normally done for some reasons, including friction and force reduction, temperature decrement, and surface finish improvement. Wet cooling is a traditional cooling/lubrication process that has been used in machining since the past. Besides, a variety of new cooling and lubricating approaches have been developed in recent years, such as the minimum quantity lubrication (MQL), cryogenic cooling, nanolubrication, etc., due to ecological issues. Despite the importance of cooling/lubrication in machining, there is a lack of research on chatter stability in the presence of cutting fluid in cutting processes. In this study, the chatter vibration in turning process for two cooling/lubrication conditions of conventional wet and MQL is investigated. An integrated theoretical model is used to predict both the metal cutting force and the chatter stability lobe diagram (SLD) in turning process. This model involves deriving a math equation for predicting metal cutting force for both wet and MQL conditions using experimental training force data and a Genetic Expression Programming (GEP)-based regression model. Also, the traditional single degree of freedom chatter model is used here for predicting the SLDs. The chatter model is discussed and verified with experimental tests. Then, the experimental results of the tool's acceleration signal, work surface texture, surface roughness, chip shape, and tool wear are presented and compared for wet and MQL conditions. The results of this study show that the cooling/lubrication systems such as wet or MQL have a considerable effect on the SLDs. Also, the predicted results of metal cutting force and SLD for both wet and MQL techniques are in good agreement with the experimental data. Therefore, it is recommended that for each lubrication condition including wet, or MQL, the SLD be determined to achieve higher machinability.     

基于有限元分析的滚齿SLD构建

针对稳定性耳垂线图(SLD)应用于滚齿颤振预测时存在动力学参数获取困难、切削深度难以确定等问题,建立了考虑滚刀刀杆柔性的三维滚齿系统动力学模型,通过滚刀极限切屑厚度与轴向进给量的关系计算滚齿系统动力学参数,并在此基础上绘制出滚齿SLD。设计了滚齿颤振实验方案,通过采集的实验数据分析平稳切削与颤振切削振动的特征量,确定颤振频率及颤振主体,证实了所建立的动力学模型及SLD的有效性。所提方法为滚齿工艺颤振预测、切削参数选取提供了一种新手段。     

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.     

Chatter stability of micro end milling by considering process nonlinearities and process damping

The micro end milling uses the miniature tools to fabricate complexity microstructures at high rotational speeds. The regenerative chatter, which causes tool wear and poor machining quality, is one of the challenges needed to be solved in the micro end milling process. In order to predict the chatter stability of micro end milling, this paper proposes a cutting forces model taking into account the process nonlinearities caused by tool run-out, trajectory of tool tip and intermittency of chip formation, and the process damping effect in the ploughing-dominant and shearing-dominant regimes. Since the elasto-plastic deformation of micro end milling leads to large process damping which will affect the process stability, the process damping is also included in the cutting forces model. The micro end milling process is modeled as a two degrees of freedom system with the dynamic parameters of tool-machine system obtained by the receptance coupling method. According to the calculated cutting forces, the time-domain simulation method is extended to predict the chatter stability lobes diagrams. Finally, the micro end milling experiments of cutting forces and machined surface quality have been investigated to validate the accuracy of the proposed model.     

Analysis of cutting force coefficients in high-speed ball end milling at varying rotational speeds

In high-speed ball end milling, cutting forces influence machinability, dimensional accuracy, tool failure, tool deflection, machine tool chatter, vibration, etc. Thus, an accurate prediction of cutting forces before actual machining is essential for a good insight into the process to produce good quality machined parts. In this article, an attempt has been made to determine specific cutting force coefficients in ball end milling based on a linear mechanistic model at a higher range of rotational speeds. The force coefficients have been determined based on average cutting force. Cutting force in one revolution of the cutter was recorded to avoid the cutter run-out condition (radial). Milling experiments have been conducted on aluminum alloy of grade Al2014-T6 at different spindle speeds and feeds. Thus, the dependence of specific cutting force coefficients on cutting speeds has been studied and analyzed. It is found that specific cutting force coefficients change with change in rotational speed while keeping other cutting parameters unchanged. Hence, simulated cutting forces at higher range of rotational speed might have considerable errors if specific cutting force coefficients evaluated at lower rotational speed are used. The specific cutting force coefficients obtained analytically have been validated through experiments.     

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.     

Improved dynamic cutting force model in ball-end milling. Part I: theoretical modelling and experimental calibration

An accurate cutting force model of ball-end milling is essential for precision prediction and compensation of tool deflection that dominantly determines the dimensional accuracy of the machined surface. This paper presents an improved theoretical dynamic cutting force model for ball-end milling. The three-dimensional instantaneous cutting forces acting on a single flute of a helical ball-end mill are integrated from the differential cutting force components on sliced elements of the flute along the cutter-axis direction. The size effect of undeformed chip thickness and the influence of the effective rake angle are considered in the formulation of the differential cutting forces based on the theory of oblique cutting. A set of half immersion slot milling tests is performed with a one-tooth solid carbide helical ball-end mill for the calibration of the cutting force coefficients. The recorded dynamic cutting forces are averaged to fit the theoretical model and yield the cutting force coefficients. The measured and simulated dynamic cutting forces are compared using the experimental calibrated cutting force coefficients, and there is a reasonable agreement. A further experimental verification of the dynamic cutting force model will be presented in a follow-up paper.     

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.     

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.     

Cutting force prediction for ball nose milling of inclined surface

Ball nose milling of complex surfaces is common in the die/mould and aerospace industries. A significant influential factor in complex surface machining by ball nose milling for part accuracy and tool life is the cutting force. There has been little research on cutting force model for ball nose milling on inclined planes. Using such a model ,and by considering the inclination of the tangential plane at the point of contact of the ball nose model, it is possible to predict the cutting force at the particular cutting contact point of the ball nose cutter on a sculptured surface. Hence, this paper presents a cutting force model for ball nose milling on inclined planes for given cutting conditions assuming a fresh or sharp cutter. The development of the cutting force model involves the determination of two associated coefficients: cutting and edge coefficients for a given tool and workpiece combination. A method is proposed for the determination of the coefficients using the inclined plane milling data. The geometry for chip thickness is considered based on inclined surface machining with overlapping of previous pass. The average and maximum cutting forces are considered. These two forces have been observed to be more dominating force-based parameters or features with high correlation with tool wear. The developed cutting force model is verified for various cutting conditions.     

On modeling of cutting forces in micro-end milling operation

Micro-end milling is used for manufacturing of complex miniaturized components precisely in wide range of materials. It is important to predict cutting forces accurately as it plays vital role in controlling tool and workpiece deflections as well as tool wear and breakage. The present study attempts to incorporate process characteristics such as edge radius of cutting tool, effective rake and clearance angles, minimum chip thickness, and elastic recovery of work material collectively while predicting cutting forces using mechanistic model. To incorporate these process characteristics effectively, it is proposed to divide cutting zone into two regions: shearing- and ploughing-dominant regions. The methodology estimates cutting forces in each partitioned zone separately and then combines the same to obtain total cutting force at a given cutter rotation angle. The results of proposed model are validated by performing machining experiments over a wide range of cutting conditions. The paper also highlights the importance of incorporating elastic recovery of work material and effective rake and clearance angle while predicting cutting forces. It has been observed that the proposed methodology predicts the magnitude and profile of cutting forces accurately for micro-end milling operation.     

Critical speed analysis for nonlinear effects of rotor system and ball end milling

The critical speed analysis for nonlinear effects of rotor-bearing system and ball end milling are studied in this paper. The nonlinear cutting force can be calculated by using the Tlusty proposed 3/4 rule for chip thickness. The rotor system is supported by bearings with nonlinear spring effects. The critical speeds obtained from this study are compared with two sets of experimental data to validate the proposed four cases. The effects of design parameters on system dynamic behaviors, including critical speeds and tool displacements under the dynamic cutting forces, are numerically investigated in the time domain. The results show that the critical speeds of system are proportional to the corresponding system natural frequencies, but inversely to the cycle number of tool vibration multiplying by the number of flutes during the cutting time from one flute to another. For the linear system and the nonlinear system with small depth-of-cut under linear cutting force milling, their critical speeds are almost identical. With large feed-per-tooth, the differences of the critical speeds become larger between linear and nonlinear rotor systems and so are the dynamic responses at critical speeds milling. The critical speed under nonlinear cutting force milling is found to be always higher than that under linear cutting force. Furthermore, the chatter stability lobes are studied for various cutting conditions. The intervals between critical speeds increase gradually, and the axial depths of cut of nonlinear system for stability are lower than those of linear system.     

Development of a novel boring tool with anisotropic dynamic stiffness to avoid chatter vibration in cutting: Part 2: Analytical and experimental verification of the proposed method

In this study, we developed prototypes of boring tools with anisotropic dynamic stiffness, and their chatter stability was investigated analytically and experimentally. In Part 1, a novel design of boring tools with an anisotropic structure was proposed to improve the nominal stiffness in boring operation, thus resulting in higher chatter stability in simulation. In this part (Part 2), anisotropic boring tools with a holder length-to-diameter ratio (L/D) of 4 and 10 designed in Part 1 were prototyped, and their frequency response functions were evaluated. Then, the chatter stabilities were evaluated through turning experiments. With respect to a L/D4 boring tool with anisotropic structure, the nominal dynamic stiffness was significantly improved within the range of machining conditions that satisfies the appropriate combination of cutting force ratio and chip flow direction, compared to a conventional tool with isotropic structure. We confirmed that the proposed boring tool with an anisotropic structure increases the critical radial depth of cut by approximately 17 times compared with conventional tools. Even with an L/D10 anisotropic boring tool, a similar effect was observed wherein the dynamic stiffness of the tool was improved. In contrast, the effect of improving the dynamic stiffness was insufficient; thus, chatter free cutting could not be realized. Analytical investigations verified the importance of further improvement of dynamic characteristics. To realize stable boring with L/D10 boring tools, it is necessary to further reduce the system compliance while also improving the similarity of the frequency response function.     

Specific cutting force coefficients modeling of end milling by neural network

In a high precision vertical machining center, the estimation of cutting forces is important for many reasons such as prediction of chatter vibration, surface roughness and so on. The cutting forces are difficult to predict because they are very complex and time variant. In order to predict the cutting forces of end-milling processes for various cutting conditions, their mathematical model is important and the model is based on chip load, cutting geometry, and the relationship between cutting forces and chip loads. Specific cutting force coefficients of the model have been obtained as interpolation function types by averaging forces of cutting tests. In this paper the coefficients are obtained by neural network and the results of the conventional method and those of the proposed method are compared. The results show that the neural network method gives more correct values than the function type and that in the learning stage as the omitted number of experimental data increase the average errors increase as well.     

动态切削力对切削颤振的影响

以外圆车削实验为依据,建立加工过程中刀具振动的非线性动力学模型,并采用数值分析方法,研究切削力中的动态分量对切削颤振的影响.结果表明,随速度变化的切削力分量对颤振幅值影响较小,而且会在短时间内被系统内的结构阻尼所衰减.而与加速度成非线性关系的切削力分量对颤振的影响却很显著,而且加速度系数有临界值存在,当超过这个临界值后,颤振的理论幅度将急剧增大.     

A solid modeler based ball-end milling process simulation

A system for geometric and physical simulation of the ball-end milling process using solid modeling is presented in this paper. A commercially available geometric engine is used to represent the cutting edge, cutter and updated part. The ball-end mill cutter modeled in this study is an insert type ball-end mill and the cutting edge is generated by intersecting an inclined plane with the cutter ball nose. The contact face between cutter and updated part is determined from the solid model of the updated part and cutter solid model. To determine cutting edge engagement for each tool rotational step, the intersections between the cutting edge with boundary of the contact face are determined. The engaged portion of the cutting edge for each tool rotational step is divided into small differential oblique cutting edge segments. Friction, shear angles and shear stresses are identified from orthogonal cutting data base available in the open literature. For each tool rotational position, the cutting force components are calculated by summing up the differential cutting forces. The instantaneous dynamic chip thickness is computed by summing up the rigid chip thickness, the tool deflection and the undulations left from the previous tooth, and then the dynamic cutting forces are obtained. For calculating the ploughing forces, Wu's model is extended to the ball-end milling process [21]. The total forces, including the cutting and ploughing forces, are applied to the structural vibratory model of the system and the dynamic deflections at the tool tip are predicted. The developed system is verified experimentally for various up-hill and down-hill angles.     

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.     

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.