Milling Force Model Research Articles

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.

Research on stability of robotic longitudinal-torsional ultrasonic milling with variable cutting force coefficient

With their successful applications in handling, spraying, arc welding and other processing fields, industrial robots are gradually replacing traditional CNC machine tools to complete machining tasks due to the wider working envelope and the higher flexibility. Aiming at the chatter problem, a robotic longitudinal-torsional ultrasonic milling method with variable force coefficient is proposed in this paper. Taking carbon fiber-reinforced plastics (CFRP) as the processing object, the influence of the fiber layup angle on the milling force is analyzed first; then, the robot milling force parameters are determined, and the robot milling kinematics model is established. Furthermore, the ultrasonic function angle is defined, and the cutting layer thickness model, the dynamic milling force model, and the dynamic differential equation under ultrasonic vibration are established to analyze the stability of robotic longitudinal-torsional ultrasonic milling of CFRP. Finally, the full discrete method is used to obtain stability lobe diagrams.

Cutting force and nonlinear chatter stability of ball-end milling cutter

Ball-end milling cutters are one of the most widely used cutters in the automotive, aerospace, die, and machine parts industries. Milling chatter reduced the surface quality and production efficiency, resulting in noise. It is particularly important to model the cutting force and analyze the flutter stability of ball-end milling cutters. In this study, a simplified milling force model of ball-end milling cutter with three degrees of freedom was established based on Merchant bevel cutting theory. The model simplified the milling force coefficient. The expressions of instantaneous milling area considering the vibration displacements in X, Y, and Z directions were derived. The nonlinear dynamic cutting force model of ball-end milling cutter with three degrees of freedom was proposed. The nonlinear chatter vibration mechanical model of ball-end milling cutter with three degrees of freedom was developed by introducing the time delay term, and the stability analysis is carried out by the stability lobe diagram. The proposed models were experimentally verified.

Force model of two-flute continuous milling based on tool deflection

Accurate modeling of the instantaneous uncut chip thickness is one of the key issues in milling mechanics. Although most current cutting force models take into account the effects of tool deflection and tool run-out, they only consider single-edge continuous milling processes and do not consider processes where multiple edges are simultaneously engaged in milling. Considering the tool runout and tool deflection that affect the end milling process, a novel uncut chip thickness algorithm based on two-flute continuous milling is proposed in this paper, and an analytical force model for actual milling is established. There is no need to use iterative methods, and the predictive power can be obtained by solving a linear system of equations, so the computational cost is greatly reduced. At the same time, stainless steel 316 was processed, and the experimental results showed that the predicted force was in good agreement with the measured force.

Modeling study of milling force considering tool runout at different types of radial cutting depth

Accurate force model during batch precision machining is the basis for optimizing milling parameters and maintaining process stability. Tool radial runout is inevitable and affects milling force, and milling parameters are also important factors affecting milling force. However, existing milling force models rarely consider the influence of tool runout under different types of radial cutting depth, resulting in unsatisfactory accuracy and limited practical application of the models. In this study, a model of the instantaneous undeformed chip thickness of tool considering the effect of tool radial runout is established in stages on the basis of the contact geometry of tool and workpiece. A prediction model for milling force at three types of radial cutting depth is obtained by combining the instantaneous stiffness model. In the model, the true tool radial runout value is calibrated by calculating milling force. The accuracy of the proposed model and the effects of milling parameters on milling force and true tool radial runout are investigated via milling experiments for three types of radial cutting depth. The experimental results show that the proposed milling force model has better accuracy than the models without considering tool runout and considering only tool static runout by comparing milling force curves, the values of R2, and the spectral characteristics of the three models. Milling parameters change the true tool radial runout. The results of this study can provide theoretical guidance for the selection of end milling parameters and theoretical support for maintaining the stability of milling forces in cutting operation.

Cutting force prediction considering force–deflection coupling in five-axis milling with fillet-end cutter

With the increasing demand for higher quality and performance of equipment and assembly in aerospace, shipbuilding, medical and other fields, the machining accuracy of parts is facing higher requirements. It is particularly important to predict the cutting force accurately, which is the main physical quantity in the machining process and basis of process inspection and quality control. In this paper, the cutting force model in five-axis milling with fillet-end cutter is proposed, which reveals the law of force–deflection coupling. Firstly, the initial cutter deflection model induced by the ideal cutting force ignoring the effect of deflection is built based on analysis of the geometric characteristics of fillet-end cutter. Then, the undeformed chip thickness model is educed considering the cutter posture and cutter deflection. Further, the iterative method is utilized to resolve the coupling relationship between cutter deflection and cutting force. Finally, the cutting force model under force–deflection coupling is established for achieving more accurate prediction. To verify the effectiveness of the proposed cutting force model, the milling experiment is carried out on a five-axis milling center. The measured cutting force values are utilized to inspect the accuracy of prediction models considering and not considering force–deflection coupling, respectively. The results show that the proposed method could improve the prediction accuracy of cutting force, which show the effectiveness of taking force–deflection coupling law into consideration clearly. The influence of cutter posture on cutting force is analyzed using the proposed cutting force model. The cutting force decreases with the increase in lead angle or tilt angle, and the influence of tilt angle is greater than that of lead angle under experimental conditions of five-axis milling using the set process parameters.

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.

Prediction of micro milling force and surface roughness considering size-dependent vibration of micro-end mill

When the characteristic structure size of the component is at the micron level, the internal crystal grains, grain boundaries, and pore defects of the component material with the same size at the micron level cannot be ignored, so the micro-sized component will show different physical properties from the macro-sized component, which is called size effect. Since the tool diameter of a micro-end mill is in the micron level, the micro-end mill will also show a significant size effect phenomenon. In addition, in the micro milling process, because the surface roughness that affects the performance and service life of micro parts is mainly influenced by the vibration of the micro-end mill, in order to enhance the machined surface quality, it is crucial to research the formation mechanism of surface topography in the micro milling process. In this paper, a comprehensive method is proposed to predict micro-end mill vibration, micro milling force, and surface roughness. At first, a size-dependent dynamic model of micro-end mill is presented based on the strain gradient elasticity theory (SGET). Secondly, considering the feedback of a micro-end mill vibration, the micro milling force model is presented and solved through the iterative method. Then the machined surface topography is simulated through the actual cutting edge trajectory considering the micro-end mill size-dependent vibration and material elastic recovery. The results show that the vibration of the micro-end mill will increase the micro milling force and surface roughness. In order to verify the accuracy and efficiency of the presented method, experiments are performed, and it is found that the predicted results are consistent with the experimental results.

Generalized modeling of milling dynamics for the 4DOF machining system with asymmetric flexibility

Asymmetric flexibility of the machining system exists widely in the practical milling process. In this paper, a generalized milling dynamics modeling method for an asymmetric flexible 4DOF cutter-workpiece system is proposed, which is further used to reveal how the asymmetric flexibility affects the milling dynamics characteristics. The regenerative milling force model is firstly established through the coupling coefficient matrix, in which the milling condition with non-parallel direction between the axis directions of coordinate system, the vibration directions of system DOF and the acting directions of milling force are well handled. Then, a generalized 4DOF milling dynamics model considering a new dimension, namely the cutter and workpiece feed direction angle combination ψ (ψc, ψw), is presented. The studies point out that the milling dynamics characteristics of the asymmetric flexible machining system, including the milling stability and surface location error (SLE), have a significant feed direction-dependent feature. Moreover, the generation mechanism of this kind of asymmetric milling dynamics has been successfully clarified. The proposed method has been experimentally validated by a series of milling tests in an asymmetric flexible machining system. Lastly, the influences of the asymmetry degree of the system flexibility, milling type and radial depth of cut on the milling dynamics are both analyzed by numerical simulation.

Modeling of cutting forces in 1-D and 2-D ultrasonic vibration-assisted milling of Ti-6Al-4V

To meet the modern demands for lightweight construction and energy efficiency, hard-to-machine materials such as ceramics, superalloys, and fiber-reinforced plastics are being used progressively. These materials can only be machined with great effort using conventional machining processes due to the high cutting forces, poor surface qualities, and the associated tool wear. Vibration-assisted machining has already proven to be an adequate solution in order to achieve extended tool lives, better surface qualities, and reduced cutting forces. This paper presents an analytical force model for longitudinal-torsional vibration-assisted milling (LT-VAM), which can predict cutting forces under intermittent and non-intermittent cutting conditions. Under intermittent cutting conditions, the relative contact ratio between the rake face and the sliding chip is utilized for modelling the shearing forces. Ploughing forces and shearing forces under non-intermittent cutting conditions are calculated by using an extended macroscopic friction reduction model, which can predict the reduced frictional forces under parallel and perpendicular vibration superimposition. The force model was implemented in MATLAB and can predict cutting forces without using any experimental vibration-assisted milling (VAM) data input.

Investigation of tool-workpiece contact rate and milling force in elliptical ultrasonic vibration-assisted milling

Elliptical ultrasonic vibration-assisted milling (EUVAM) is widely used as an efficient processing method for hard-to-machining materials such as titanium alloy, superalloy, and hard-brittle materials. To uncover the mechanism of the intermittent cutting characteristics in EUVAM, the tool-workpiece contact rate model is developed by combining with the kinematic relationship between the tool edge and the workpiece in the process. According to the analysis of the contact rate model, the phenomenon that the contact rate increases rapidly with the time-varying tooth position angle in one-dimensional ultrasonic vibration assisted milling can be improved in EUVAM. In addition, considering the variation of window function and undeformed cutting thickness, a force model is established. And the experiment of EUVAM is performed to verify the model of ultrasonic milling force, and the influence of process parameters (amplitude, cutting speed, feed rate and cutting depth) on ultrasonic milling force is also analyzed.

Research on breakage characteristics in side milling of titanium alloy with cemented carbide end mill

Titanium alloy Ti6Al4V has the advantages of high specific strength, good heat resistance, and strong corrosion resistance, which is widely used in the manufacturing of aerospace industrial parts. However, in the side milling of titanium alloy, the temperature of the cutting area is high, and the cutting edge position is prone to breakage, which affects the surface quality of the workpiece. In order to reveal the tool damage failure mechanism in the milling process of titanium alloy, firstly, the impact force model when the tool cuts into the workpiece from the empty stroke and the milling force model during milling are established to obtain the cyclic load characteristics and impact effect of the tool. Then, based on the fatigue crack propagation theory and the energy balance equation of sliding crack, the elastic modulus and crack propagation law of tool material under different cutting impacts are analyzed. The interval method is used to recalculate the initial and critical damage value of tool material fracture in the maximum range. Finally, the limit conditions of the edge impact fracture of the end mill are established, and the safe cutting area of tool breakage is redefined. Through the milling test of titanium alloy, the impact damage morphology of tool in different states is redefined. The obtained redefined tool safety area provides a theoretical basis for high-speed and high-efficiency milling of titanium alloy, tool breakage, and tool life.

A force model of high-speed dry milling CF/PEEK considering fiber distribution characteristics

Carbon fiber reinforced polyetheretherketone (CF/PEEK) is an emerging material that is widely used in the automotive and aviation industry due to its high shock resistance, thermostability, and recyclability. However, its dry-machining requirement with an unclear dynamic material removal process limits the machining efficiency and surface quality. To this end, we firstly established a two-dimensional joint probability distribution model of cutting carbon fibers based on the microstructure of CF/PEEK. Compared with previous brittle models, the plastic model is verified to be more consistent with experimental results. A high-speed dry (HSD) milling force model considering carbon fiber distribution is then developed and is proofed with a high prediction accuracy of about 92.6%. With the proposed model, the milling force can be separated into forces of cutting carbon fibers and PEEK matrix, by which the influences of high-speed dry milling process on carbon fibers and PEEK matrix can be analyzed. The results show that carbon fiber distribution exhibits a significant impact on milling force and is more easily affected by milling parameters compared with the PEEK matrix. It is also verified feasible to HSD milling CF/PEEK, and the work gives the guidance of breaking the low-speed machining limits by improving the machining process.

Comparison on Milling Force Model Prediction of New Cold Saw Blade Milling Cutter Based on Deep Neural Network and Regression Analysis

A four factors and three levels orthogonal milling force (MF) test is designed, which qualitatively obtains the influence of four factors, namely workpiece material, workpiece diameter, milling speed and feed per tooth, on MF of the new cold saw blade milling cutter (NCSBMC), then further verifies the reliability of test data with simulation analysis of MF. The multiple linear regression analysis and deep neural network (DNN) are used to accurately fit and predict the magnitude of MF in three directions of NCSBMC, taking into account the influence of workpiece material factors on MF. Compared with the results of empirical formula, DNN has higher prediction accuracy. The research results provide theoretical guidance for the optimization of milling parameters in actual machining process.

Milling force model for asymmetric end-mills during high-feed milling on AISI-P20

ABSTRACT Manufacturing molds for plastic parts injection are a particular machining domain, where challenging materials, like AISI P20 steel, are forced to satisfy the highest surface quality requirements. Before mirror polishing, milling operation is a common and challenging task due to drilling and milling with the same tool. Thus, special cutting tools, like asymmetric indexable type, are often used. This tool presents two geometrically equal positive inserts – one placed horizontally and the other vertically – for the flexible machining of holes, cavities, floors, and walls. Rough-medium milling operations lead to a complicated relationship between cutting conditions and geometrical tool parameters, making it challenging to balance the tool life of both inserts. The novelty of this work is to propose a model for cutting force prediction with an asymmetric tool to explain the separated behavior of both inserts and determine a better compromise between cutting conditions and tool life. The experimental tests were done for model validation and then wear cutting tests for testing improved cutting conditions. The results predicted by the model proved that by changing the depth of cut from 0.3 mm to 0.8 mm, the wear in both inserts was more balanced, increasing chip volume up to 1.7 times.

Milling force modeling for disc milling cutter of indexable three-sided inserts considering tool runout

Cutting force is essential for studying cutting mechanism and improving cutting process. In order to predict cutting force, the cutting force was measured by experiments; cutter runout was measured by dial indicator; the actual undeformed cutting thickness was obtained in presence of cutter runout. Then a mechanical cutting force model was established. Three kinds of cutting force coefficients, linear, exponential, and polynomial coefficients, are solved and compared. The results show that the exponential model has the highest generality and accuracy. The validation experiment illustrates deviation rates between the predicted values and measured values are mostly <30%, and the deviation rates of the middle inserts are greater than that of the left and right inserts. The mechanical model in this paper can predict the cutting force quickly, which is helpful to select the reasonable cutting parameters and lays a foundation for the research of multi tooth cutting force.

Milling force model prediction considering tool runout with three-teeth alternating disc cutter

Disc cutter has a large diameter and more teeth, and obvious tool runout (δi) is produced during disc milling process, so the irregular distribution of cutting force is generated due to uneven distribution of cutting output per tooth (hi*) caused by tool runout. Therefore, the tool runout (δi) must be considered when milling force model of disc milling is established. In the paper, first, milling force model of disc milling is built with a three-teeth alternating disc cutter considering the tool runout (δi). Second, tool runout (δi) is measured by the dial gauge when the revolving speed of disc cutter is 1 r/min, then cutting output per tooth considering tool runout (hi*) is obtained by the formula between cutting output of each tooth (hi) without considering tool runout (δi) and tool runout (δi). Third, the parameters of frictional angle (βn), normal shear angle (ϕn), and shear yield strength (τs) in model coefficients are calibrated by orthogonal cutting experimental. Then, the predictive model of milling force is obtained. Last, the reliability verification experiment of model is conducted. The experiment results show that the model is with high efficiency and precision and the measured force and predictive force is in good agreement in amplitude and trend, which can be used in the study of milling force of disc milling.

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.

Generalized cutting force model for peripheral milling of wood, based on the effect of density, uncut chip cross section, grain orientation and tool helix angle

The influence of the grain angle on the cutting force when milling wood is not yet detailed, apart from particular cases (end-grain, parallel to the grain, or in some rare cases 45°-cut). Thus, setting-up wood machining operations with complex paths still relies mainly on the experience of the operators because of the lack of scientific knowledge easily transferable to the industry. The aim of the present work is to propose an empirical model based on specific cutting coefficients for the assessment of cutting force when peripheral milling of wood based on the following input: uncut chip thickness and width, grain angle (angle between the tool velocity vector and the grain direction of the wood), density and tool helix angle. The specific cutting coefficients were determined by peripheral milling with different depths of cut wood disks issued from different wood species on a dynamometric platform to record the forces. Milling a sample into a round shape (a disk) allows to measure the cutting forces toward every grain angle into a sole basic diameter reduction operation. Force signals are then post-processed to carefully clean the natural vibrations of the system without impacting their magnitudes. The experiment is repeated on five species with a large range of densities, machining two disks per species for five depths of cut in up- and down milling conditions for three different tool helix angles. Finally, a simple cutting force model, based on the previously cited parameters, is proposed, and its robustness analysed.

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.