Cutting Force Model Research Articles

Application of Grey Relational Analysis and Multiple Linear Regression to Establish the Cutting Force Model of Oil Peony Stalk

Oil peony is an important oil crop, which has high quality and oil content. In order to improve the cutting quality and harvest efficiency of oil peony, the cutting equipment of the pruning machine and harvester is a key component. Also, the accurate prediction of cutting force of oil peony stalk is one of the essential processes for the design of the cutting equipment. In this article, to accurately predicted the cutting force of the stalk, the physical property parameters and chemical components were considered as influencing factors, which were used to establish the model of mechanical property parameter of oil peony stalk. The physical property parameters of oil peony stalk included the stalk diameter, internode distance, fresh weight, dry weight, relative moisture content, volume, fresh density, and dry density. The chemical components of the stalk were cellulose, hemicellulose, and lignin. Besides, the modeling methods, which were the partial least squares regression (PLSR), principal component analysis (PCA) couple with multiple linear regression (MLR), and grey relational analysis (GRA) couple with MLR, were used to optimize the multiple parameters (physical property parameters and chemical components). The results showed that the internode distance and relative moisture content had significant effects on the cutting force of oil peony stalk. The R c 2 and R p 2 values of the GRA (0.5) + MLR method were 0.801 and 0.820, and RMSEC and RMSEP values were 2.862N and 4.715N, respectively. Consequently, the GRA + MLR method could be used to predict the cutting force of oil peony stalk, which was an important basis for the design of precision cutting equipment.

Reliability updating and parameter inversion of micro-milling

Accurate prediction of the force on the cutting tool and workpiece is of great significance for the micro-milling process safety. To improve the machining precision and the sustainability of micro-cutting tools, the uncertainty of parameters and the inaccuracy of measurement in actual manufacturing should be considered. In this work, an improved cutting force model is proposed, in which the tool runout and the size effect are involved, and a new method to calculate the cutting coefficient is presented. Adaptive Bayesian updating based on structural reliability analysis and adaptive-kriging method is developed to solve the actual distribution of parameters with uncertainty. The actual cutting force data is measured by the micro-milling experiment with workpiece material Al6061. The posterior parameter distribution characteristics are obtained and verified based on the experimental data, the proposed Bayesian method, and the established mechanical model. The reliability analysis is used to evaluate the influence of various parameters on the micro-milling system and explore its reasonable selection range. The results show that the calculation efficiency of the proposed Bayesian method is significantly improved, and the conclusion of reliability research can provide helpful guidance for complex practical machining.

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.

Effect of workpiece work hardening on machined surface topography generated in two-step milling process

The surface topography of the workpiece affects the performance of finished components. The finished component is usually machined with series of machining steps. However, the models had been developed to predict surface topography usually focused on in a single-step machining process. The effect of the previous machining step on the machined surface topography of the current cutting process was ignored. A novel prediction model for surface topography in two-step milling Inconel 718 considering the influence of the work-hardened layer generated in the previous machining process was proposed in this paper. Firstly, the cutting force model with variable force coefficients was developed. The workpiece in the depth direction was layered according to the degree of work hardening, and each layer of workpiece material corresponds to a set of force coefficients. The calculation results with the developed cutting force model were verified using two-step milling experiments. Then, the influence of the work-hardened layer generated in the previous milling process was converted into the cutting force effect on the actual cutting thickness. The actual cutting thickness was superimposed into the cutting edge motion trajectory. The prediction model of machined surface topography generated in the two-step milling process was established considering both effects of cutting edge motion trajectory in the current milling step and workpiece material work hardening due to the previous step of milling. The proposed model can accurately predict the surface topography, and the average relative error of the surface roughness (Sa) prediction was 12.44%. The experimental and simulation results of surface topography shown that the effect of work-hardened layer cannot be ignored in two-step milling Inconel 718, which is prone to work hardening.

Design method of a multi-blade skiving tool for gear skiving

Power skiving is one of the most effective methods for manufacturing high-accuracy gears, especially internal gears. However, the shortened tool life inhibits the large-scale industrialization of the promising technology. The study proposes a novel multi-blade skiving tool consisting of one finishing blade and several roughing blades, which can achieve a higher productivity and a longer tool life. The barrel-shaped cutter is derived based on the analysis of the conjugated surface of the tool for cylindrical gear skiving. By establishing a cutting force model that can accurately predict undeformed chips, the influence of the cutter blade outer diameter on cutting force and the influence of cutting blade crossed angle on chips and tool wear are analysed. The feasibility of the tool is verified by cutting experiments. The proposed multi-blade skiving tool is a promising approach to improve productivity and tool life. It can be applied in gear skiving applications such as the design of skiving tools.

Milling force coefficients-based tool wear monitoring for variable parameter milling

Tool wear is an important factor that affects the quality and machining accuracy of aeronautical structural parts in the milling process. It is essential to monitor the tool wear in titanium alloy machining. The traditional tool wear features such as root mean square (RMS), kurtosis, and wavelet packet energy spectrum are related to not only the tool wear status but also to the milling parameters, thus monitoring the tool wear status only under fixed milling parameters. This paper proposes a new method of online monitoring of tool wear using milling force coefficients. The instantaneous cutting force model is used to extract the milling force coefficients which are independent of milling parameters. The principal component analysis (PCA) algorithm is used to fuse the milling force coefficients. Furthermore, support vector machine (SVM) model is used to monitor tool wear states. Experiments with different machining parameters were conducted to verify the effectiveness of this method used for tool wear monitoring. The results show that compared to traditional features, the milling force coefficients are not dependent on the milling parameters, and using milling force coefficients can effectively monitor the transition point of cutters from normal wear to severe wear (tool failure).

Z-map based cutting force prediction for elliptical ultrasonic vibration-assisted milling process

Elliptical ultrasonic vibration-assisted milling (EUVAM) adds high-frequency vibration to conventional milling (CM) to realize high-frequency intermittent milling. It has broad application prospects in the processing of difficult-to-cut materials such as titanium alloys, superalloys, and hard and brittle materials. To reveal the mechanism of the highly intermittent cutting nature in EUVAM, according to the motion relationship between the cutting edge and the workpiece and the Z-map representation of the workpiece, a method and its algorithm for calculating the undeformed cutting thickness and thus the cutting force in EUVAM are proposed. The simulation results show that EUVAM can improve the actual cutting speed when compared with CM, and the proportion of idle cutting time will directly determine the intermittent degree of the milling process. The experiment of EUVAM is performed to verify the correctness of the proposed cutting force model, and the impact of spindle speed on the cutting force in EUVAM is also analyzed. It is shown that UEVAM can reduce the cutting force by up to 50% under appropriate cutting conditions.

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.

An analytical cutting force model of quasi-intermittent vibration assisted swing cutting based on predictive machining theory

Quasi-intermittent vibration assisted swing (QVASC) method was aimed to improve the cutting machinability of difficult-to-machine materials. Inherited the intermittent cutting characteristics of the elliptical vibration cutting (EVC) technology, this method reduces the impact of residual height on the machined surface quality. But there is still a lack of in-depth research on cutting force modeling of QVASC. Based on the conventional cutting force model, a cutting force prediction model in QVASC processing, which considers the time-variable characteristics of QVASC, adopts the non-equidistant shear zone model and regards the workpiece material properties, tool geometry, and cutting conditions as the input data are proposed in this paper. Using the micro-element method, the proposed model decomposed the cutting edge to calculate the cutting force and the cutting force value by superimposing them. It finally predicts the chip flow angle. Experimental results show that when the cutting velocity increases, the average cutting force and the Z -direction increases by 20%, the average cutting force and the Y direction decreases by 17%. The average cutting force along X direction remains unchanged; the depth of cutting became larger. Besides, the average cutting force X decreased by 18%, Y decreased 21%, and Z increased by 13%. As the feed rate increases, the X direction is increased by 26%, and the Z direction is reduced by 22%, while the cutting force in the Y direction is unchanged. After comparing and verifying the measured value and the predicted value, the minimum error of the prediction model reaches 4.01%, which validates the force model of QVACS.

Effect of tool size on the cutting of aluminum film with micrometer-level thickness

Cutting aluminum films with micrometer-level thickness requires a full understanding of the mixed effect due to bending, buckling, and fracture. These three deformation patterns have a strong relationship with the tool size. In this study, we present experimental, numerical, and theoretical studies of the tool size effect on a fracture. Using the energy analysis during a cut, we first build up a cutting force model that takes both the tool size and film thickness into account. The proposed model differs from previous models that used the ratio of size to thickness as the only factor. Our results first show that tool size affects fracture morphology. Films cut with large tools fail in the form of sequenced concertina tears, while films cut with small tools fail in the form of curling flaps. Furthermore, the transition of the two failure modes is theoretically presented with the critical value being obtained by the cutting force model proposed. Additionally, we find that when predicting the cutting force of aluminum films with micrometer-level thickness, the effect of fracture energy cannot be neglected. Increasing film thickness will decrease the effect of fracture energy on cutting force.

An Explicit Coupling Model for Accurate Prediction of Force-Induced Deflection in Thin-Walled Workpiece Milling

Abstract Cutting force-induced vibrations in thin-walled parts milling may cause violation of dimensional tolerance while accurate modeling of the milling error distribution is still a challenging work because of the coupling effect between the dynamic cutting forces and the resulting steady-state vibrations. It greatly increases the computational complexity to capture the true cutter–workpiece engagement with classic time domain or iteration method. This paper proposes a novel explicit model to predict the error distribution considering this coupling relationship without iterative calculation. A new cutting force model with variable coefficients with respect to the deflections is developed to describe the dynamic cutting forces. The effectiveness of the force model is verified by a group of calibration experiments. The analytical solution of the dynamic model is discussed and a semi-analytical method is constructed to predict the error distribution directly. Machined surface as well as the deformation errors are derived and thin-walled workpiece milling experiments for verification are conducted. Comparisons between simulations and experiments show that the proposed method is accurate and efficient.

Microstructured surface generation and cutting force prediction of pure titanium TA2

Titanium and its alloys have widespread applications in aerospace and medical fields due to their outstanding mechanical properties and corrosion resistance. However, very limited attention has been focused on machining the microstructure on their surface and the cutting force prediction during machining. Motivated by this, this study used the ultraprecision diamond surface texturing (UDST) process to generate microstructure on the commercially pure titanium TA2 and established a cutting force prediction model. Firstly, the two special characteristics of UDST are systematically investigated by the finite element simulation and the vibration trajectory analysis. And as a core component of the UDST process, a two-degree-of-freedom vibration generator is presented. Considering the periodical vibration motion, tool geometry, and material properties, a practicable cutting force model is next developed for predicting the dynamic cutting force. Finally, two types of unique microstructures are successfully fabricated on the TA2 surface. Experimental results show that the proposed cutting force model agrees well with the measured results, validating its effectiveness.

An improved cutting force model in micro-milling considering the comprehensive effect of tool runout, size effect, and tool wear

Tool runout, cutting edge radius-size effect, and tool wear have significant impacts on the cutting force of micro-milling. In order to predict the micro-milling force and the related cutting performance, it is necessary to establish a cutting force model including tool runout, cutting edge radius, and tool wear. In this study, an instantaneous uncut chip thickness (IUCT) model considering tool runout, a nonlinear shear/ploughing coefficient model including cutting-edge radius, and a friction force coefficient model embedded with flank wear width are respectively constructed. By integrating the IUCT, the nonlinear shear/ploughing coefficient and the friction force coefficient, a comprehensive micro-milling force model including tool runout, cutting edge radius, and tool wear is derived. Experiment results show that the proposed comprehensive model is efficient to predict the nonlinear cutting force of micro-milling with variable tool runout, cutting edge radius, and tool wear.

Material piling up and spreading effects in the cutting processes with small feed rates

Previous studies only reported that the material piling up effect will occur in the cutting processes with relatively small feed rates, and even in this case, there is no further theoretical report to touch its generation mechanism. In this work, it is the first time to experimentally report that obvious material spreading phenomenon together with the material piling up effect appears in the cutting process, whose uncut chip thickness is less than the minimum uncut chip thickness (MUCT). It is found that one part of the material to be cut will be piled up in front of the cutter’s rake face. Meanwhile, the remained part flows into the cutter’s clearance face, followed by further compression. As a result, the cutting tooth actually does not remove the material, but rolls the material by its rounded edge. Just because of this rolling effect, the flowed material is deformed and spread along the width direction of the workpiece surface, and this spreading behaviour leads to that the width of the machined workpiece is larger than its initial value. The spread width of the workpiece is quantitatively characterized by using Tselikov’s theory, which is widely used to capture the rolling behaviour. The volume of the material piled up in front of the cutter’s rake surface is calculated by subtracting the volume of the spread material, which is calculated based on the spread width, from the volume of the initial material to be cut according to the volume invariance principle. Subsequently, the height of the piled up material is calculated by geometrically modelling the piling up area as a triangle region. Based on the above analyses, the material spreading and piling up mechanisms in cutting are theoretically explored. The validity of the theoretically calculated spread width and piling up height is verified by the numerical results obtained from finite element simulations. Finally, a cutting force model that can characterize the influences of spreading and piling up effects is established. Several cutting experiments, including both the micro and conventional milling tests, confirm that the proposed methods can give better prediction accuracy of the cutting forces, especially when the ratio of feed rate to the radius of the rounded cutting edge is small.

Investigations on the micro-interactions of grit-workpiece and forces prediction in ultrasonic vibration side grinding of optical glass

The cutting force in ultrasonic vibration side grinding (UVSG) of brittle materials is of significance for the machined quality. However, the micro-interaction mechanism between abrasive grits and workpiece remains a significant issue in terms of the research on cutting forces in the brittle material grinding due to the stochastic distribution nature of the grits. Meanwhile, these micro-interactions are further affected by ultrasonic vibration in UVSG process. Considering these issues, this paper aims at modeling the cutting force affected by the stochastically distributed grits and ultrasonic vibration to reveal the multi-scale grinding mechanics in UVSG of optical glass. Through modeling the stochastic grinding wheel surface and analyzing the kinematics of multi-grits, the unified motion trajectory and the instantaneous chip thickness in UVSG were enabled to derived to determine the different grit-workpiece interaction stages. With consideration of the ultrasonic vibration effects on the micro-interactions, a novel theoretical cutting force model was developed based on the analysis of force generated at three interaction stages, i.e., rubbing, plowing, and cutting stages. The numerical simulations of this model could provide the time-domain variation features of cutting forces to evaluate the fluctuations and trends of the cutting forces from multi-scales. Experimental verifications indicated that the cutting force and its fluctuations are within the acceptable error margin. Furthermore, a thorough analysis of force fluctuating situations at different ultrasonic vibration amplitudes was conducted. The analytical results indicated that an increase in ultrasonic vibration amplitude was not only beneficial to restrain the force fluctuation, but helpful to reduce the brittle fracture damages of optical glass. The evolution trend of cutting force in different grinding conditions and wheel specifications were discussed in detail to reveal the influence mechanisms of machining parameters on the cutting forces. Afterwards, the detection results of ground workpieces demonstrate that the introduction of ultrasonic vibration would improve the machined quality of optical glass in UVSG process.

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.

Preparation and characterization of ultra-thin dicing blades with different bonding properties

Ultra-thin dicing blade is usually used to achieve a high precision cutting in semiconductor back-end packaging and assembly. Lots of interactional parameters involving in dicing blade preparation and cutting process bring difficulties to high cutting qualities and good working life of dicing blade. In order to address these problems, this study prepared three kinds of dicing blades and characterized the cutting properties of three dicing blades. It first proposed the abrasive exposure coefficient and the tool deviation coefficient to provide parameters for the cutting force model. Then, the experimental apparatus was set up to verify the proposed cutting force model. And a series of parameters including feed rate, spindle current, edge chipping coefficient, tool wear amount, and grinding performance are used to characterize the comprehensive performance of prepared dicing blades. Finally, the edge morphology was observed under 3D microscope to analysis the hardness of different dicing blades. The theoretical and experimental results indicate that the proposed cutting force model can reflect actual cutting process. There is an inverse proportional function between the shedding of abrasive particles from matrix and the hardness of the matrix. The cutting performance of dicing blades is very dependent on the material of workpiece. C-dicing blades presents outstanding comprehensive effects with small chips and good self-sharpening properties.

Study on tool deflection compensation method based on cutting force observer for orbital drilling of CFRP/Ti stacks

Orbital drilling is an alternative hole-making machining process that combines drilling and milling, usually performed with specific devices and industrial robots to make holes in aircraft composite structures. In order to eliminate the adverse effects on the diameter precision of the tool deflection in the orbital drilling process of CFRP/Ti stacks, a novel method that fuses cutting force model prediction and feed-axis disturbance observation is proposed to estimate the radial cutting force. The tool deflection caused by the radial cutting force is calculated based on the equivalent diameter cantilever beam model. Then the tool path is corrected to compensate for the tool deflection and prevent borehole diameter deviation by adjusting the tool eccentricity in real-time. The orbital drilling experiments demonstrate that the geometrical error of the hole was reduced by 50%, and the manufacturing precision requirements of IT9 level can be satisfied after one single shot even the cutting force was increased to twice the initial value caused by tool wear, the proposed method effectively improved the hole-making precision of CFRP/Ti stacks.

Analytical modeling of micro-milling operations on biocompatible Ti6Al4V titanium alloy

Among the biocompatible materials, Ti6Al4V titanium alloy is widely spread due to its properties, such as corrosion and fatigue resistance combined with low density. Ti6Al4V can be processed by Additive Manufacturing technologies, such as Power Bed Fusion (PBF). The biomedical applications require good surface finishing to ensure biocompatibility with tissues and organs. Machining is an adequate process to ensure low final roughness of components. The necessity to realize miniaturized features implicates the usage of micro mills with diameter lower than one millimeter. It implicates several issues, such as size effects, higher than expected cutting forces, rapid tool wear which can be addressed by experimental tests and process modeling. This work reports the results of micro-milling performed on additively manufactured samples in Ti6Al4V. PBF process was utilized to manufacture the samples by employing laser source (PBF-LB). The machining center was equipped with a loadcell to acquire cutting force signal. An analytical cutting force model was calibrated on the experimental data with the purpose of predicting loads on the tool by considering ploughing- and shearing- regimes. Specific machining tests were performed to calculate the Minimum Uncut Chip Thickness (MUCT) and to calibrate the unknow parameters of the model, while further tests allowed to verify the reliability of the model about the cutting force prediction. The elaboration of the cutting force data was performed by an iterative methodology based on the Particle Swarm Optimization (PSO) algorithm.

Online Parameterization of a Milling Force Model using an Intelligent System Architecture and Bayesian Optimization

This paper presents an efficient and industry-ready system architecture that enables both the control of machining operations and the high-frequency acquisition of controller data and external sensor signals. Using the recorded data, a dexel-based mechanistic cutting force model, which enables the estimation of cutting forces for complex tool geometries in arbitrary machining operations, is parameterized via an instantaneous cutting force identification method. In the introduced identification method, Bayesian Optimization and Dynamic Time Warping are combined to avoid time-consuming and error-prone synchronization of measurement and simulation. The suitability of this approach was demonstrated by performing cutting experiments at various radial depths of cut and feed rates per tooth. Thereby, a good agreement between simulation and measurement could be observed.