Instantaneous Undeformed Chip Thickness Research Articles

An Integrated Model Based Prediction of Machining Accuracy for Milling Machine

The accuracy of machining can be predicted during the design process of CNC machine tools, while the prediction accuracy depends on the prediction model. However, when establishing the prediction model, the coupling effect among the machine tool’s different components is always ignored for modeling efficiency, so this will lead to its reliability cannot be guaranteed. To address this problem, the model reduction theory and the lumped parameter method are used in this study to set the state-space equations of the essential structural parts. Moreover, the electro-mechanical coupling parameter equation of the servo system is transformed into a state-space equation. Then the state-space equations of the components and the servo system are coupled to establish the machine tool dynamic model. Furthermore, a theoretical model of instantaneous undeformed chip thickness is found, and according to the linear relationship between the micro-cutting force and the instantaneous undeformed chip thickness, the instantaneous cutting force model of the cylindrical milling cutter is established. Based on these, the integrated model, which considers the mechanical structure, control system and cutting force, is obtained and further used in Simulink to build the machining accuracy prediction platform, as well as the accuracy of the integrated prediction model is verified. Moreover, the prediction model established by the integrated modeling method can effectively simulate the actual machining conditions of the machine tool, and the superiority of prediction is confirmed by comparing the simulated and measured results in peripheral milling applications. The results show the error in the system response efficiency is 14.8%, while the error in position accuracy and delay characteristics is less than 10%, the error between the predicted size of the prediction model and the actual size is within 28 μm, a minimum prediction error is 7 μm.

Accurate modeling and controlling of weak stiffness grinding system dynamics with microstructured tools

The weak stiffness grinding system often produces uncontrollable vibration, which directly reduces the machining quality. In order to accurately predict and control the weak stiffness grinding system dynamics, an accurate dynamics modeling and the controlling method with microstructured tools are presented innovatively. Based on the real random abrasive grain model, an instantaneous undeformed chip thickness model considering the phase deviation, time accuracy and grinding wheel-workpiece separation caused by vibration is established. On this basis, the controlling principle of microstructured grinding wheel on chip formation mechanism and grinding forces is studied. Then, combined with the element division principle and dynamics parameters of grinding system, the dynamics model of weak stiffness grinding system is established. According to the grinding experimental results based on vibration monitoring, the error rate of the established dynamics model is less than 9.8 %. Compared with the non-structured grinding wheel, the microstructured grinding wheel can control the vibration amplitude, the vibration frequencies and the wheel deflection. Based on the workpiece surface machining results, the addition of microstructures suppresses the phenomena of overcutting and the wheel bounce, and the profile protrusion height caused by grinding vibration is decreased by 77 %. The established dynamics model is of great significance for understanding and control the dynamic behavior of weak stiffness grinding systems.

Investigation on surface quality in micro milling of additive manufactured Ti6Al4V titanium alloy

The additive manufactured technology is widely applied to produce titanium alloy parts with complex structures. The subsequent machining operations are necessary for additive manufactured parts to achieve the required machining quality. In this paper, the theoretical surface roughness model in micro milling was established. The model indicated the theoretical milled roughness mainly depends on the feed per tooth, tool nose radius and bottom edge inclination angle. Then, micro milling experiments are conducted on additive manufactured titanium alloy using PCD micro end mill. The surface roughness on milled surface was measured and investigated. At the middle position of micro milled surface, the distribution curves of surface roughness Ra and Sa show the same variation trend under different milling parameters. Moreover, the measured surface roughness results on different transverse positions of milled surface showed that the difference value between the actual and theoretical surface roughness of milled surface is mostly induced by the unstable cutting behaviors, which is also mainly responsible for the surface roughness size effect. The transverse distribution of surface roughness on milled surface exhibited a W shape because of the variation of the instantaneous undeformed chip thickness and material removal mode at different transverse positions.

Modeling and investigation of minimum chip thickness for silicon carbide during quasi-intermittent vibration–assisted swing cutting

In micromachining, the quasi-intermittent vibration—assisted swing cutting technology alleviates the residual height problem of elliptical vibration–assisted cutting (EVC) and inherits its intermittent machining characteristics. The minimum chip thickness has a significant impact on cutting forces, tool wear, and process stability when working with difficult-to-machine materials. This study thoroughly examines the impact of cutting parameters and tool parameters on the quality of the workpiece during machining in order to better understand the time-varying characteristics of the quasi-intermittent vibration–assisted swing cutting (QVASC) machining process and the size effect on micro-cutting of silicon carbide crystal. This paper created the minimum chip thickness prediction model suited to QVASC machining process. The effects of variables such as cutting velocity and tool inclination on the minimum chip thickness were discussed as well as the scribing tests that were conducted on such challenging materials as silicon carbide. The research findings shown that during the machining process, the critical undeformed chip thickness of silicon carbide decreased continuously as the cutting velocity sequentially increased (1.51 mm/min, 1.88 mm/min, 2.26 mm/min); under the down inclination angle (0–10°), the critical undeformed chip thickness also continuously decreased. These results confirm that cutting too fast reduces the instantaneous undeformed chip thickness, which is not conducive to ductile removal.

CWE identification and cutting force prediction in ball-end milling process

Ball-end milling of sculptured surfaces is an efficient and cost effective manufacturing technique when compared with other methods. However, an accurate cutting force prediction is still challenging when the Cutter Workpiece Engagement (CWE) and Instantaneous Undeformed Chip Thickness (IUCT) vary simultaneously. In order to predict the milling force accurately, an algorithm is designed to obtain the CWE boundaries with the variable tool orientations. Inspired by the main idea of analytical CWE model, an improved Z-map method is developed, which is based on the classic Z-map method. The point cloud of tool envelope surface method is generated based on the classic Z-map and the points of the CWE are screened according to the chosen criteria. Afterwards, the IUCT is calculated numerically by the accurate cutting thickness model. In order to overcome the drawbacks of the IUCT method, a simplified IUCT model is proposed to eliminate the iterative calculation. Related milling experiments were carried out on Al7075 workpiece to validate the proposed models showing a good agreement with errors smaller than 12.5%. It can be concluded from simulation results that tool postures have a significant effect on the machining process. This contributes to in-depth understanding the material removal process and optimizing the process parameters of multi-axis machining processes.

An Alternative Approach to Compute Chip Thickness in Milling

Abstract The accurate evaluation of the instantaneous undeformed chip thickness (IUCT) plays a crucial role in the modeling of milling processes. However, the vibrations of the tool–workpiece system can make conventional IUCT models either inaccurate or not applicable. This paper introduces the concept of surface function to describe the milled surface, through which the IUCT can be readily computed. The evolution of this surface function is governed by a partial differential equation (PDE) in the form of a balance law, and the material removal process is characterized by discontinuous conditions at the cutters. A finite volume algorithm is adopted to solve the proposed PDE with discontinuous conditions at the cutters. Through a case study of the asymmetric cutting process, the surface function method demonstrates two main advantages over conventional methods: (i) a detailed description of IUCT evolution considering the influence of the initial shape of the workpiece and (ii) a general framework to accurately compute the IUCT. This method shows a promising potential for computing the IUCT in numerical simulations of chattering phenomenon in the milling process.

The Modelling and Analysis of Micro-Milling Forces for Fabricating Thin-Walled Micro-Parts Considering Machining Dynamics

In the fabrication process of thin-walled micro-parts, both micro-cutting tools and thin-walled micro-parts have the characteristics of small size and low stiffness. Therefore, the regenerative chatter during the machining process cannot be ignored. The influence of the tool runout error and actual trochoidal trajectories of the cutting edge on micro-milling forces should also be considered comprehensively. In this paper, the tool runout error in the micro-milling process is first analysed, and an instantaneous undeformed chip thickness model is established considering the runout error. On this basis, the dynamic deformation of the micro-cutting tool and thin-walled micro-part is studied, and an instantaneous, undeformed, chip-thickness model is proposed with the consideration of both the runout error and dynamic deformation. The dynamic parameters of the machining system are obtained using the receptance coupling method. Finally, thin-walled micro-part machining experiments are carried out, and the obtained results of micro-milling force simulation based on the proposed model are compared with the experimental results. The results indicate that the micro-milling force modelling, by taking the influence of machining dynamics into account, has better prediction accuracy, and the difference between the predicted resultant forces and the experimental results is less than 11%.

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 Modeling and Experimental Study for Ball-End Milling of Free-Form Surfaces

In order to improve the machining quality and efficiency and optimize NC machining programming, based on the existing cutting force models for ball-end, a cutting force prediction model of free-form surface for ball-end was established. By analyzing the force of the system during the cutting process, we obtained the expression equation of the instantaneous undeformed chip thickness during the milling process and then determined the rule of the influence of the lead angle and the tilt angle on the instantaneous undeformed chip thickness. It was judged whether the cutter edge microelement is involved in cutting, and the algorithm flow chart is given. After that, the cutting force prediction model of free-form surface for ball-end and pseudocodes for cutting force prediction were given. MATLAB was used to simulate the prediction force model. Finally, through the comparative analysis experiment of the measured cutting force and the simulated cutting force, the experimental results are basically consistent with the theoretical prediction results, which proves that the model established in this paper can accurately predict the change of the cutting force of the ball-end cutter in the process of milling free-form surface, and the error of the cutting force prediction model established in this paper is reduced by 15% compared with the traditional cutting force prediction model.

Surface contour error model of five-axis machining considering multifactor coupling effects

During five-axis flank milling procedure, the static deflection of workpiece and cutter creates surface errors that lead to defects in projects with strict requirements, especially in thin-walled parts industry. Focusing on the mentioned issues, the surface contour error is predicted in this paper considering the coupling between the deflection and cutting force. First, an efficient calculation method of the cutting force is presented in five-axis flank milling. This method accounts for the impact of cutter runout on cutter/workpiece engagement (CWE) and the instantaneous undeformed chip thickness (IUCT). Then, a cutter is modelled as a cantilever structure and thus an analytical solution for the deflection of the end mill can be obtained. Next, the flexible cutting force is distributed on a finite element (FE) model of workpiece, while the workpiece stiffness keeps varying with the material removal. Subsequently, a flexible iterative calculation method for achieving deflection prediction is established. Finally, the prediction model is proven by machining tests of an S-shaped specimen in which predicted values of the surface error match with the experimental results.

A general method for instantaneous undeformed chip thickness calculation in five-axis milling based on Boolean operations

A general method for instantaneous undeformed chip thickness calculation in five-axis milling based on Boolean operations

A Comprehensive Micro-Milling Force Model for a Low-Stiffness Machining System

Abstract Micro-milling is widely used in various crucial fields with the ability of machining micro- and meso-scaled functional structures on various materials efficiently. However, the micro-milling force model is not comprehensively developed yet when tool feature sizes continually decrease to under 200 µm in a low-stiffness system. This paper proposes an analytical force model considering the influence of tool radius, size effect, tool runout, tool deflection, and the actual trochoidal trajectories and the interaction of historical tool teeth trajectories (IHTTT). Different micro-milling status are recognized by analyzing the cutting process of different tool teeth. Conditions of single-tooth cutting status are determined by a proposed numerical algorithm, and entry angle and exit angle are analyzed under various cutting conditions for the low-stiffness system. Three micro-milling status, including single-tooth cutting status, are distinguished based on the instantaneous undeformed chip thickness resulting in three types of material removal mechanisms in predicting micro-milling force components. Discontinuous change rates of undeformed chip thickness are found in the low-stiffness micro-milling system. The proposed micro-milling force model is then verified through experiments of micro slot milling Elgiloy alloy with a 150-μm-diametrical two-teeth micro-end mill. The experimental results show a root-mean-square error (RSME) of 0.092 N in the predicted resultant force, accounting for approximately 5.12% of the measured force, by which the proposed theoretical model is verified to be of good prediction accuracy.

Feedrate scheduling method for constant peak cutting force in five-axis flank milling process

It is extremely important to select appropriate feedrates for the stable machining of parts with ruled surface in modern aviation industrial applications. However, the current studies take too much time to achieve this goal. Therefore, this paper presents an efficient feedrate optimization method for constant peak cutting force in five-axis flank milling process. The solution method of the instantaneous undeformed chip thickness (IUCT) is proposed using least squares theory with the cutter entry angle and feedrate as variables. Based on this method, an explicit analytical expression of the peak cutting force for each cutting point is established. Furthermore, a feedrate scheduling method is developed to quickly solve the appropriate feedrate under constant peak cutting force. To verify the proposed IUCT model, the fitting IUCT is compared with the accuracy data at different feedrates. Additionally, some experiments of five-axis flank milling are conducted to demonstrate the effectiveness of the peak force model and the feedrate scheduling method. And the surface roughness before and after feedrate scheduling is detected. The results show that the proposed feedrate scheduling method can quickly adjust the feedrate and ensure constant peak force during machining. At the same time, the surface quality is kept at a high level.

A cutting force model based on compensated chip thickness in five-axis flank milling

In the five-axis flank milling process, the instantaneous undeformed chip thickness (IUCT) and the entry/exit angles vary continuously because of the complex tool path and workpiece geometry. The changes result in time-varying cutting forces in consecutive cutting operations, which are difficult to predict. This paper comprehensively considers the effects of cutter runout on the IUCT and the influence of the curved tool path on the entry/exit angles in the calculation of cutting force. A simplified IUCT model is presented based on compensated chip thickness in five-axis flank milling. Compared with the existing IUCT model, it can achieve high precision and greatly improves the calculation efficiency. Subsequently, the entry angles of surface with varied curvature are verified. Five-axis flank milling experiment for a non-developable ruled surface was conducted to verify the proposed theory. The results show that the proposed cutting force model has the ability to predict the cutter forces with a high precision and can be used in simulations and optimizations of five-axis flank milling.

A comprehensive investigation of plowing and grain-workpiece micro interactions on 3D ground surface topography

The accumulation of plowing effect in the grinding process which is ignored in previous researches has an essential influence on the surface topography of the workpiece. In this study, a new grinding surface topography modeling method considering the plowing effect is proposed. The modeling method of the grinding wheel based on the replicated method is given to obtain the real and accurate wheel surface topography. According to the cutting path of abrasive particles extracted from the wheel topography, the instantaneous undeformed chip thickness is calculated to determine the contact stages of rubbing, plowing and cutting. The influence of material accumulation caused by the plowing effect on the microstructure is discussed, and the mechanism of complex changes in the surface topography resulting from the interference between the grains is analyzed to generate the grinding surface topography. Based on the proposed model, the effects of plowing effect and grain-workpiece micro interactions on 3D ground surface topography have been studied. And topography parameters (Sa, Sp, Sv, Sku) are utilized to evaluate the difference between the simulated result and experimental result. It has been found that the experimental result is in good agreement with the surface topography model and plowing effect could not be ignored. The modeling method of grinding surface topography considering the influence of the plowing stacking effect in this study may serve as a novel and more practical way to predict the grinding surface topography.

An approach to modeling the chip thickness and cutter workpiece engagement region in 3 and 5 axis ball end milling

The determination of the chip thickness in 5-axis ball end milling is most fundamental to calculate the cutting force which affects the machining stability and surface quality. In the 5-axis ball end milling, adding to the parameters of the 3-axis milling we have two important parameters which are the tilt and the lead angles. They affect the engagement region and the chip thickness and modify the cutting forces. Based on the true tooth trajectory and the machining surface geometries, this paper presents a new analytical model of the cutter workpiece engagement (CWE) region and the instantaneous undeformed chip thickness in three and five axis ball end milling. To validate the model a mechanistic force model was used, the simulation was compared to the measured one and a good agreement between them was proved.

Quantitative impacts of regenerative vibration and abrasive wheel eccentricity on surface grinding dynamic performance

In grinding, regenerative vibration and forced vibration due to grinding wheel eccentric rotation are main excited-vibration sources that interact with grinding material removal mechanism. In the paper, instantaneous undeformed chip thickness in down-grinding cutting phase may consist of two components, i.e. linear kinetic thickness and nonlinear dynamic thickness. Considering abrasive grit-workpiece interaction in the grinding contact zone, the grinding vibration system is presented by a new set of differential equations of two degrees of freedom (DOF) with a close-loop feedback control system models. Conventional grinding control parameters, including wheel spindle speed, work-speed in feed direction and radial cutting depth, are often regarded as linear constants in many existing simplified models. When considering time delay, they can be transferred to nonlinear variables, so the capability of prediction and the accuracy of solution of the grit-workpiece dynamic performance are improved. Based on quantitative comparison of force and vibration magnitudes, the influence of the eccentric rotation of abrasive wheel and the negative rake angle of working grit cutting edges on grinding performance are demonstrated in the paper.

Model of the instantaneous undeformed chip thickness in micro-milling based on tooth trajectory

Instantaneous undeformed chip thickness is one of the key parameters in modeling of micro-milling process. Most of the existing instantaneous undeformed chip thickness models in meso-scale cutting process are based on the trochoidal trajectory of the cutting edge, which neglect the influences of cutter installation errors, cutter-holder manufacturing errors, radial runout of the spindle and so forth on the instantaneous undeformed chip thickness. This article investigates the tooth trajectory in micro-milling process. A prediction model of radial runout of cutting edge is built, with consideration of the effects of the extended length of micro-milling cutter and the spindle speed. Considering the effects of cutting-edge trochoidal trajectory, radial runout of cutting edge and the minimum cutting thickness, a novel instantaneous undeformed chip thickness model is proposed, and the phenomenon of single-tooth cutting in micro-milling process is analyzed. Comparisons of cutting forces under different chip thickness models and experimental data indicate that this new model can be used to predict cutting forces.

A generic instantaneous undeformed chip thickness model for the cutting force modeling in micromilling

The precise modeling of the instantaneous undeformed chip thickness is one of the key issues in the mechanics of micromilling. While most current models noticed the influences of the tool tip trochoidal trajectory and tool runout, they took account only the workpiece removed by immediate passing tooth but not more preceded teeth. These lead to inaccuracy when the single edge cutting occurred, which has been identified to be a prevalent phenomenon in micromilling operation. In this paper, the actual cutting area in micromilling is derived, and then a generic instantaneous undeformed chip thickness model is proposed by considering the cutting trajectory of all passing teeth in one cycle. Additionally, this study derives a criterion that could determine the single-edge-cutting phenomenon in multi-tooth micromilling from the geometric relations. The accuracy of the model is verified by the real experimental data and the result are shown superior to known models.

New Mathematic Method of Calculating Instantaneous Un-deformed Chip Thickness with Tool Run-out in Micro-end-milling

New Mathematic Method of Calculating Instantaneous Un-deformed Chip Thickness with Tool Run-out in Micro-end-milling