Milling Force Prediction Model Research Articles

Milling Force Modeling Methods for Slot Milling Cutters

The slot milling cutter is primarily used for machining the tongue and groove of the steam turbine rotor, which is a critical operation in the manufacturing process of the steam turbine rotor. It is challenging to predict the milling force of a groove milling cutter due to variations in rake, rake angles and cutting speeds of the main cutting edge. Firstly, based on a limited amount of experimental data on turning, we have developed an equivalent turning force model that takes into account the impact of the rounded cutting edge radius, the tool’s tip radius and the feed rate on tool’s geometric angle. It provides a more accurate frontal angle for the identification method of the Johnson–Cook material constitutive equation. Secondly, the physical parameters, such as shear stress, shear strain and strain rate on the main shear plane, are calculated through the analysis of experimental data and application of the orthogonal cutting theory. Thirdly, the range of initial constitutive parameters of the material was determined through the split Hopkinson pressure bar (SHPB) test. The objective function was defined as the minimum error between the theoretical and experimental values. The optimal values of the Johnson–Cook constitutive equation parameters A, B, C, n and m are obtained through a global search using a genetic algorithm. Finally, the shear stress is determined by the governing equations of deformation, temperature and material. The axial force, torque and bending moment of each micro-segment are calculated and summed using the unit cutting force vector of each micro-segment. As a result, a milling force prediction model for slot milling cutters is established, and its validity is verified through experiments.

A Ti-6Al-4V Milling Force Prediction Model Based on the Taylor Factor Model and Microstructure Evolution of the Milling Surface.

In this paper, a milling force prediction model considering the Taylor factor is established, and the Ti-6Al-4V milling force predicted by the model under different milling parameters is presented. In the study, the milling experiment of Ti-6Al-4V was carried out, the milling force was collected by the dynamometer, and the microstructure evolution of the milling surface before and after milling was observed by EBSD. Through the comparative analysis of the experimental results and the model prediction results, the reliability of the prediction model proposed in this study was verified, and the influences of the milling parameters on the milling force were further analyzed. Finally, based on the EBSD observation results, the effects of the milling parameters on the microstructure evolution of the milling surface were studied. The results show that both the tangential milling force and normal milling force increase with the increase in the milling depth and feed rate. Among the milling parameters selected in this study, the milling depth has the greatest influence on the milling force. The average errors of the tangential milling force and normal milling force predicted by the milling force model are less than 10%, indicating that the milling force prediction model established in this paper considering Taylor factor is suitable for the prediction of the Ti-6Al-4V milling force. With the change in the milling parameters, the grain structure, grain size, grain boundary distribution, phase distribution, and micro-texture of the material surface change to varying degrees, and the plastic deformation of the milling surface is largely coordinated by the slip.

Surface profile and milling force prediction for milling thin-walled workpiece based on equivalent 3D undeformed chip thickness model

With the development of the aviation manufacturing industry, the application range of thin-walled parts is rapidly increasing. Accurate machining process and surface topography prediction are the keys to ensuring machining quality. This article is based on the relative geometric relationship between the real motion trajectory of the milling cutter and the workpiece; the undeformed chip thickness equation and the two-dimensional surface contour feature algorithm are established. By introducing the parameters of milling cutter critical height, milling cutter helix angle, and lag angle parameters, the three-dimensional surface profile prediction model and the equivalent three-dimensional model considering the chip formation process are derived. And the calculation equations of the instantaneous chip cross-sectional area and the blade-workpiece contact length of the three phases of chip formation are established, respectively. The multiple linear regression method was used to fit the orthogonal test results of titanium alloy Ti-6Al-4 V, so as to complete the dynamic milling force identification, and finally establish the milling force prediction model. The accuracy of the prediction model was verified by the single factor method, and the influence of different parameters on the milling process of thin-walled parts was observed. The results show that the established model has high accuracy in predicting the surface profile and milling force of thin-walled parts. This study provides guidance for efficient prediction of the milling process of thin-walled parts.

Research on Milling Characteristics of Titanium Alloy TC4 with Variable Helical End Milling Cutter

The application of variable helical end mills to the milling of titanium alloys can suppress the regeneration effect during the machining process and ensure the stability of milling. However, due to their special geometry, their milling characteristics are also different. In this paper, the process of milling titanium alloy with a variable helix end mill is taken as the research object, and the milling force, milling stability and machining effect during the machining process are deeply studied. Firstly, the feed per tooth and cutting thickness model of the variable helical end mill were established, the milling force prediction model of the variable helical end mill was deduced, and the instantaneous milling force and its variation law were obtained by solution. Secondly, the finite element analysis model of the variable helix end mill for machining titanium alloy was established, and the influence of the variable helix angle structure on the milling force was obtained. Then, the dynamic equation of milling with a variable helix end mill was established, the stability lobe diagram of variable helix milling is was and drawn, and the influence of variable helix angle on milling stability was analyzed. Lastly, a variable helix end mill milling experiment was designed to verify the accuracy of the theoretical model and finite element simulation; the influence of the variable helix angle structure on the surface roughness was analyzed, and the influence of machining parameters on the milling force when using a variable helix end mill was investigated.

Research on machining error prediction of open blade under dynamic loading

The instantaneous cutting contact relationship between tool and workpiece is changing with the change of curvature profile of open blade impeller. This leads to a strong nonlinear characteristic of the dynamic cutting load change during the machining of this type of parts, which affects the machining accuracy of the blade. This paper proposes a method to predict the machining error of ball-end milling under dynamic load. This method considers the influence of the curvature change of blade profile. Based on the analysis of the instantaneous cutting contact of complex surface in ball-end milling, a prediction model of the instantaneous undeformed cutting thickness of ball-end milling under the influence of surface curvature changes is constructed. Based on this model, the correction of the prediction model of machining complex surface milling force is realized. The prediction of the machining error when the complex surface is thin-walled impeller is processed under dynamic load. Finally, the effectiveness and accuracy of the method are verified through ball-end milling experiments. The research can provide guidance for the control and compensation of milling machining errors of complex-shaped thin-walled open blade.

Theoretical model of instantaneous milling force for CFRP milling with a ball-end milling cutter: Considering spatial dimension and temporal dimension discontinuity effects

Milling force is a crucial parameter that impacts the surface quality of weakly rigid, curved carbon fiber reinforced polymer (CFRP) components. However, the cutting edge of ball-end milling cutter suitable for curvature processing has different cutting conditions at any point in the spatial dimension. Further, the cutting force can only be generated within the effective cutting range, which causes the cutting force to be discontinuous in both spatial and temporal dimensions. The above problems greatly increase the difficulty of calculating the CFRP milling force. To address this issue, in this study, a novel theoretical prediction model of instantaneous milling force for the milling of CFRP component by a ball-end milling cutter is established considering the discontinuity effects in spatial and temporal dimensions. The theoretical model has a maximum peak error of less than 18% compared with the experimental results. The impacts of different cutting parameters on the milling force are further discussed, which indicates that lower feed speed, axial cutting depth, and higher spindle speed should be selected to reduce the cutting force. This model could be helpful to determine the cutting parameters and tool selection for the high-performance milling of curved CFRP parts with excellent processing quality.

A Hybrid SVR Model Based on Support Vector Regression and Differential Evolution for Milling Force Prediction of Titanium Alloy

Prediction of milling force plays an important role in milling process of titanium alloy. In this paper, the milling process of titanium alloy is studied, and the material quality is affected directly by the milling force. Support vector regression (SVR) has shown a prominent performance for many practical applications. Although there is some literature about parameter optimization techniques of SVR model, it still needs further research and improvement on the performance and accuracy of this model. We present a hybrid milling force prediction model, namely DE&SVR, which hybridizes the SVR with differential evolution (DE) to enhance the prediction accuracy for milling force of titanium alloy. The main advantage of hybrid model is that the DE is adopted to optimize the kernel parameters of the SVR. The main parameters affecting milling force, such as the milling depth, feeding speed, and cutting speed, are considered in this study. The results have shown that the hybrid model yields better prediction accuracy, and the percentage prediction milling force deviation is found to be less than 3.5% for all the cases tested, <span style="font-style: italic;">NRMSE</span> is only 0.0200, and <span style="font-style: italic;">MAPE</span> is only 1.4791%. Thus, this methodology can be widely applied to the fields of material processing optimization.

Force model of freeform surface multi-axis machining with fillet end mill based on analytical contact analysis

In the multi-axis machining of freeform surface, compared with ball end mill, the fillet end mill has higher machining efficiency under the same residual height and has been widely used. As the most important physical quantity in machining process, milling force has always been the focus of research. In this paper, the contact geometry between fillet end mill and freeform surface is analyzed by analytical method, and then the milling force prediction model of multi-axis machining is established. Based on differential discretization, the cutter location point of multi-axis machining of freeform surface is approximate to multi-axis machining of oblique plane, which simplifies the research object. The inclination angle is defined to describe the relationship among cutter axis, feed, and workpiece in cutter coordinate system. The space range of the cutting edge element participating in material cutting is constructed by the swept surface of previous tool path, the to-be machined surface and the feed direction surface, and the in-cut cutting edge is determined by judging the cutting edge element one by one. Considering cutter run-out, the element cutting forces on the cylindrical and fillet surfaces of fillet end mill are derived, and all the element forces within in-cut cutting edge are summed by vector to obtain the overall milling force of fillet end mill. Simulation results show that, compared with the solid method, this contact analysis method between cutter and workpiece can take both efficiency and accuracy into account. In the machining experiment, the measured force and predicted force are consistent in trend and amplitude, which verifies the effectiveness of the milling force prediction model.

Establishment of instantaneous milling force prediction model for multi-directional CFRP laminate

Carbon fiber reinforced polymer (CFRP) is widely used in the aerospace field due to its light weight and high strength. The CFRP milling process is prone to damage such as burrs and tears. The cutting force is closely related to the damage of CFRP and tool wear. In this paper, a back propagation (BP) neural network model of cutting force and edge force coefficients was established. The model considers the effects of instantaneous uncut chip thickness, fiber cutting angle, spindle speed, and axial depth of cut. The unidirectional CFRP laminate instantaneous milling model considering the cutting edge force was further established. The instantaneous milling force prediction model was extended to multi-directional CFRP laminates. And the relationship between the damage mechanism of CFRP and the instantaneous milling force was analyzed. Experiments have proved that the instantaneous milling force prediction model built in this paper has high accuracy.

A method for predicting ball-end cutter milling force and its probabilistic characteristics

Ball-end milling is widely used in industrial applications, such as mold manufacturing and aerospace industries. One of many difficulties in milling research is the milling force, which is often crucial to the component’s processing efficiency and quality. In this paper, a method for predicting ball-end cutter milling force and its probabilistic characteristics is presented. First, a model of milling force prediction is established by integrating the differential milling forces. Then, a method of identifying milling force coefficients is suggested based on the proposed model, which considered both the mean value and the amplitude of the milling force. Based on the proposed milling force prediction model, milling force probabilistic analysis while considering randomness of cutting parameters is performed. To improve computational efficiency, the function relationship between cutting parameters and the milling force is reconstructed by adaptive Kriging model. Furthermore, trained Kriging model is employed to analyze the probabilistic characteristics of the milling force. Both experimental and computational results indicate that the method proposed in this paper has high accuracy and efficiency.

Research on machining error prediction and compensation technology for a stone-carving robotic manipulator

Stone-carving robotic manipulators (SCRMs) have a broad range of applications due to their high efficiency, diverse processing capabilities, and strong flexibility. However, due to its weak rigidity, the milling accuracy of an SCRM is lower than that of a computer numerical control (CNC) machine for working stone into special shapes, making it difficult to meet the requirements of stone milling processing. To improve the milling accuracy of SCRMs, multi-iteration error compensation technology considering the coupling relationship between compensation and deformation is proposed in this paper. First, a global stiffness model of an SCRM in which the robot arm bars are regarded as flexible links is established, and the relationship between the milling force and milling depth is fitted based on a milling force prediction model. Then, the machining error and milling depth when processing a marble workpiece are predicted. Finally, a multi-iteration method is applied for calculation using an interval correction strategy to construct a discrete control system for error compensation in the SCRM. The feasibility and effectiveness of the proposed compensation technology are verified by an experiment using the KUKA-240-2900 SCRM system.

Milling Force Prediction Model for Five-Axis Machining of Freeform Surface Considering Mesoscopic Size Effect

Abstract The core parts with the characteristic of freeform surface are widely used in the major equipment of various fields. Cutting force is the most important physical quantity in the five-axis CNC machining process of core parts. Not only in micro-milling, but also in macro-milling, there is also an obvious size effect, especially in medium- and high-speed milling, which is frequently ignored. In this paper, the milling force prediction model for five-axis machining of a freeform surface with a ball-end mill considering the mesoscopic size effect is established. Based on the characteristics of cutting thickness in macro-milling, a new dislocation density correction form is proposed, and a new experiment is designed to identify the dislocation density correction coefficient. Therefore, the shear stress calculated in this paper not only reflects the cutting dynamic mechanical characteristics but also considers the mesoscopic size effect. A linear function is proposed to describe the relationship between friction coefficient and cutting speed, cutter rake angle, and cutting thickness. Considering cutter run-out, the micro-element cutting force in the shear zone and plough zone are analyzed. The cutting geometry contact between the freeform surface and the ball-end mill is analyzed analytically by the space limitation method. Finally, the total milling force is obtained by summing all the force vectors of cutting edge micro-elements within the in-cut cutting edge. In the five-axis machining experiment of freeform surface, the theoretically predicted results of milling forces are in good agreement with the measured results in trend and amplitude.

Construction of Milling Force Model of Cycloid Gear

The change of the milling force during the milling process will directly affect the machining accuracy of the cycloid gear. In this article, the milling force prediction model of the cycloidal gear is used to predict the milling force of the cycloid gear. The results show that when the spindle speed increases, the milling force gradually decreases; the milling force is also closely related to the feed speed, axis milling depth and radial milling width. With the increase of axial milling depth and radial milling width, the milling force gradually increases, but the magnitude of the increase is different.

Milling force prediction model development for CFRP multidirectional laminates and segmented specific cutting energy analysis

This paper presents a milling force model for carbon fiber-reinforced polymer (CFRP) multidirectional laminates based on segmented specific cutting energy. The proposed model simplifies the milling process of CFRP unidirectional laminates into multiple orthogonal cuttings. The CFRP specific cutting energy was determined by experimental segmentation. An empirical formula for the CFRP segmented specific cutting energy was established, and the milling force of the CFRP multidirectional laminates was predicted using the linear superposition principle. Experimental results confirmed the high accuracy of the milling force model. The specific cutting energy gradually decreased with increasing equivalent cutting thickness. With an increase in the fiber cutting angle θ, the specific cutting energy increased first and then decreased, peaking around θ = π/2.

An effective thread milling force prediction model considering instantaneous cutting thickness based on the cylindrical thread milling simplified to side milling process

An effective thread milling force prediction model considering instantaneous cutting thickness is presented based on the cylindrical thread milling simplified to the side milling process. Firstly, based on the thread milling process simplified to side milling, an effective calculation model of instantaneous cutting thickness and a milling force model of single-layer cutter teeth are established considering the specific geometric profile of the cutting edge, chip groove angle, and tooth profile angle of the threaded milling cutter. Then, according to the time-domain difference of each layer of cutter teeth, a simplified thread milling force prediction model corresponding to the number of layers can be obtained. Finally, comparing the predicted values of the proposed model with the experimental results of cylindrical thread milling forces, the results show that the average prediction accuracy of Fx, Fy, and Fz are 90.75%, 83.56%, and 78.79%, respectively. The established simplified cylindrical thread milling force prediction model is accurate and reliable.

Milling force prediction model based on transfer learning and neural network

In recent years, the growing popularity of artificial neural networks has urged more and more researchers to try introduce these methods to the machining field, with some of them actually producing good results. The acquisition of cutting data often means higher cost and time, limiting the application of neural network in the machining sector, to a certain extent. In this paper, for the task of cutting force prediction, a “transfer network” was established, based on data obtained by simulation, combined with the theory and method in the field of transfer learning. Compared to “ordinary network”, that is, traditional back-propagation neural network based on experimental samples alone, transfer network exhibits obvious performance advantages. On one hand, this means that, using the same experimental samples, the prediction error of transfer network will be controlled; while on the other hand, when the same prediction error is achieved, the number of experimental samples required by the transfer network will be less.

Predicting milling force variation in time and space domain for multi-toothed face milling

Variations of milling force in time domain and space domain are the common behaviors of face milling for large-scale component with discontinuous multi-holed surface, which specifically generate surface variations along feed direction and circumferential direction. An accurate prediction model of local milling force is a key issue to reliable simulation of the milling force variations and the resultant machined surface variations. However, milling force variation modeling is still a significant challenge due to changing of instantaneous chip thickness in angular domain and the non-constant cutting coefficients under different milling conditions. Therefore, a general milling force model with cutting coefficients derived from average forces of milling experiments may loss the robustness when applied to different milling conditions. To address this issue, this paper attempts to provide a methodology to identify the unknown cutting coefficients in dual-mechanism local force model for face milling through the periodic averages integrated with multiple angular local forces which are measured at specific sampling angular positions in each single test. And each of the dual-mechanism cutting coefficients is modeled as multi-quadratic regression equation individually based on response surface methodology (RSM) via the design of experiments. The influence of feed per tooth, spindle speed, and cutting depth on the cutting coefficients are studied in order to build a model which can predict reliably the local milling force for different process parameter combinations. The proposed prediction model of milling force variations in time and space domains is verified by experimental measurements.

Cutting force prediction based on study of cutter-workpiece engagement in flexible ball-end milling of panel molds

In this paper, the flexible cutting force forms the basis for investigating the stability of the process involved in milling hardened steel mold with a curved surface. The cutter-workpiece engagement, which changes along the curved tool path, is inevitably affected by cutter deflection. An analysis of cutter-workpiece engagement therefore plays a critical role in predicting the flexible cutting force. First, the influence of the curved surface milling force on ball-end cutter deflection is analyzed, and the effect of tool load on the deflection of the cutting edge at different discrete positions is evaluated. A model of the uncut thickness of the milling surface is then constructed, based on the three-dimensional trochoidal trajectory of the milling process. The rules relating to the cutting process of the uncut thickness with the cutting edge at different discrete positions are analyzed. A milling force prediction model relating to the milling of the curved surface is constructed that considers cutter deflection as a part of the cutter-workpiece engagement. Finally, a hardened steel mold milling experiment is carried out. This confirms that the amplitude and trend predicted by the milling force model and the experimental results are consistent. The results validate the capacity of the proposed method to accurately predict the cutting force for different cutter teeth with tool deflection. Application of the method shows that the milling forces are relatively stable when the lead angle is between 6° and 12° or − 6° and − 12°. When the lead angle exceeds 12° or is less than − 12°, both the milling forces and cutter deflection increase rapidly.

Mechanics and dynamics research considering the tool radial runout effect in plunge milling

The tool radial runout effect in milling process has a significant impact on milling mechanics and dynamics, which increases the difficulty of accurate characterization of milling process. According to the cutter-workpiece contact relationship, the instantaneous chip thickness model considering the tool radial runout effect is established, and the prediction model of plunge milling force is obtained by combining the instant rigidity force model. The dynamical model with three degrees of freedom is established according to the characteristics of plunge milling and the time-varying delay effect caused by tool radial runout. The stability lobe diagram of the plunge milling process is obtained by the improved semi-discrete method. The simulation results are in good agreement with the experimental results, which verify the correctness of the model. The results show that the tool radial runout effect can improve the milling stability in a certain speed range. The effect of the tool radial runout on bifurcation frequency is also studied. It is found that the tool radial runout effect can produce period 1 bifurcation frequency in the milling non-stationary process and double the period 2 bifurcation and Hopf bifurcation frequency. The research results can provide theoretical support for accurate characterization and optimization of process parameters in plunge milling process.

Investigation on milling force of thin-walled workpiece considering dynamic characteristics of workpiece

The idea of integral calculus is used in traditional milling force prediction methods. In the traditional method, the milling cutter is divided into many micro-elements, the force of each micro-element is calculated, and then the integral summation process is applied to all the micro-elements. In traditional milling force prediction methods, both the workpiece and the tool are assumed to be rigid bodies. In this paper, the method is improved; the Fourier series expansion is used to approximate the periodic milling force and the workpiece is considered as a single degree of freedom spring-damping-vibration system. Through the forced vibration model of periodic force, the vibration displacement of the workpiece is obtained. Then, the radial cutting depth is corrected by the vibration displacement of the workpiece. Finally, the original milling force is corrected with the corrected radial cutting depth. The milling force prediction model based on thin-walled workpiece is obtained through the above process. The model is named as variable-radial-cutting-depth-algorithm (VRCDA). Finally, the accuracy of this model was verified through modal test and milling force acquisition experiments.