Uncut Chip Thickness Model Research Articles

The curved uncut chip thickness model: A general geometric model for mechanistic cutting force predictions

The curved uncut chip thickness model is introduced to predict the cutting forces for general uncut chip geometries using the mechanistic approach. Classical geometric models assume that the cutting force is distributed along straight elementary sections of the uncut chip area, which has limited physical validity, but makes mathematical treatments easier for simple cases. The new model assumes that the flow of the material on the contact area of the tool is given by a continuous vector field, according to which the curved uncut chip thickness is measured. The cutting force is distributed along these paths, which leads to a mathematically unique and consistent solution for regular and complex cutting edge geometries. These curved paths can be generated by basic mechanical models, which mimic the more realistic motion of the chip segments along the rake face, without the need of explicit time-consuming cutting simulations. The presented computational procedure generalizes cutting force prediction based on geometric parameters, orthogonal cutting data and the orthogonal to oblique transformations only. The effectiveness of the model for various cutting edge geometries (e.g., thread turning inserts) under extreme cutting conditions is presented in case studies, laboratory and industrial experiments.

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.

Prediction of Nonlinear Micro-Milling Force with a Novel Minimum Uncut Chip Thickness Model.

The minimum uncut chip thickness (MUCT), dividing the cutting zone into the shear region and the ploughing region, has a strong nonlinear effect on the cutting force of micro-milling. Determining the MUCT value is fundamental in order to predict the micro-milling force. In this study, based on the assumption that the normal shear force and the normal ploughing force are equivalent at the MUCT point, a novel analytical MUCT model considering the comprehensive effect of shear stress, friction angle, ploughing coefficient and cutting-edge radius is constructed to determine the MUCT. Nonlinear piecewise cutting force coefficient functions with the novel MUCT as the break point are constructed to represent the distribution of the shear/ploughing force under the effect of the minimum uncut chip thickness. By integrating the cutting force coefficient function, the nonlinear micro-milling force is predicted. Theoretical analysis shows that the nonlinear cutting force coefficient function embedded with the novel MUCT is absolutely integrable, making the micro-milling force model more stable and accurate than the conventional models. Moreover, by considering different factors in the MUCT model, the proposed micro-milling force model is more flexible than the traditional models. Micro-milling experiments under different cutting conditions have verified the efficiency and improvement of the proposed micro-milling force model.

An accurate instantaneous uncut chip thickness model combining runout effect in micro-milling using cutters with the non-uniform helix and pitch angles

As a key factor, the accuracy of the instantaneous undeformed thickness model determines the force-predicting precision and further affects workpiece machining precision in the micro-milling process. The runout with five parameters affects the machining process more significantly compared with macro-milling. Furthermore, modern industry uses cutters with non-uniform pitch and helix angles more and more common for their excellent properties. In this article, an instantaneous undeformed thickness model is presented regarding cutter runout, variable pitch, and helix angles in the micro-milling process. The cutter edge with the cutter runout effect is modeled. Then, the intersecting ellipse between the plane vertical to the spindle axis and the cutter surface which is a cylinder can be gained. Based on this, the points, which are used to remove the material, on the ellipse as well as cutter edges are calculated. The true trochoid trajectory for each cutting point along the tool path is built. Finally, the instantaneous undeformed thickness values are computed using a numerical algorithm. In addition, this article analyzes runout parameters’ effects on the instantaneous undeformed thickness values. After that, helix and pitch angles’ effects on the instantaneous undeformed thickness are studied. Ultimately, the last section verifies the correctness and validity of the instantaneous undeformed thickness model based on the experiment conducted in the literature.

Identification of optimal machining parameters in trochoidal milling of Inconel 718 for minimal force and tool wear and investigation of corresponding effects on machining affected zone depth

Increasing the productivity and efficiency of milling practices is of high importance with the rapidly changing global economy. To this end researchers have turned to alternative milling toolpaths, such as trochoidal milling, which has been shown to increase tool life with a corresponding reduction in machining time for some applications. To better understand the trochoidal milling process and optimize it for manufacturing scenarios, the modeling of cutting forces must be investigated; semi-mechanistic methods are the focus of this work. The basis for this type of force modeling lies in uncut chip thickness modeling combined with cutting force coefficients and edge force coefficients. With a novel uncut chip thickness model proposed by the authors in a previous work, this investigation looks to understand the dependence of the model coefficients as they relate to trochoidal path parameters along with machining outputs such as maximum cutting force and tool wear. Furthermore, the machining parameters are investigated as to how they relate to the improvement of tool life and cutting force utilizing the Taguchi method, where optimal parameters are found for minimum tool wear and cutting forces. The effects of the trochoidal path on the subsurface of the machined samples as they relate to the machining affected zone, are also investigated in both the radial and axial directions. It is found that tool wear increases the depth of the machining affected zone as does increasing chip thickness.

Trochoidal milling: investigation of a new approach on uncut chip thickness modeling and cutting force simulation in an alternative path planning strategy

Trochoidal milling is an alternative tool path strategy which has been shown to increase productivity, improve tooling life, and reduce resultant cutting forces. While the advantages of trochoidal milling over conventional slot or shoulder milling were previously reported, the complexity of trochoid tool path makes developing an analytical force model highly complicated. In this work, a numerical algorithm to construct the uncut chip thickness model in trochoidal milling is introduced, which is based on the geometrical relation of self-intersection and cross-intersection points of the tool path curve. In addition, an extensive series of experiments is carried out in slot and trochoidal-milling operations in order to investigate the dependency of cutting pressure coefficients on tool path parameters and to develop a model to relate the two. Furthermore, the performance of the developed model for uncut chip thickness and the cutting pressure coefficients are evaluated in predicting cutting forces; it is shown that the model predicts the maximum cutting force in the feed direction and between all the testing sets with 8% total average error, while 17% total average error is observed in predicting maximum cutting force in the lateral direction. This demonstrates the potential of the proposed approach in offline simulation of the cutting forces which is a critical step in selecting proper tooling and process parameters to increase productivity of the cut.

The determination of instantaneous uncut chip thickness for non-uniform helix angle tools with complex tool path in ultrasonic milling process

Ultrasonic milling is used more and more common in fields such as aerospace, mould and so on. Whereas, there are few literatures studying the ultrasonic milling. In consequence, focus on one of important skills for the ultrasonic milling process, instantaneous uncut chip thickness (IUCT) model for the cutter with non-uniform helix angle and complex toolpaths, is built and then a calculation theory is introduced to compute the IUCT using a numerical method. Subsequently, two examples of the toolpath are taken to show the validity of the presented method, the first one is the line toolpath and the second one is circle. The results is shown that the method in this paper can compute the IUCT values for the complex tool path, also, the method in this paper can be used by the cutter with non-uniform helix angles. [Submitted 19 December 2016; Accepted 24 October 2017]

The determination of instantaneous uncut chip thickness for non-uniform helix angle tools with complex tool path in ultrasonic milling process

Ultrasonic milling is used more and more common in fields such as aerospace, mould and so on. Whereas, there are few literatures studying the ultrasonic milling. In consequence, focus on one of important skills for the ultrasonic milling process, instantaneous uncut chip thickness (IUCT) model for the cutter with non-uniform helix angle and complex toolpaths, is built and then a calculation theory is introduced to compute the IUCT using a numerical method. Subsequently, two examples of the toolpath are taken to show the validity of the presented method, the first one is the line toolpath and the second one is circle. The results is shown that the method in this paper can compute the IUCT values for the complex tool path, also, the method in this paper can be used by the cutter with non-uniform helix angles. [Submitted 19 December 2016; Accepted 24 October 2017]

General Modeling and Calibration Method for Cutting Force Prediction With Flat-End Cutter

A general calibration method of cutter runout and specific cutting force coefficients (SCFCs) for flat-end cutter is proposed in this paper, and a high accuracy of cutting force prediction during peripheral milling is established. In the paper, the cutter runout, the bottom-edge cutting effect, and the actual feedrate with limitation during large tool path curvature are concerned comprehensively. First, based on the trochoid motion, a tooth trajectory model is built up and an analytical instantaneous uncut chip thickness (IUCT) model is put forward for describing the cutter/workpiece engagement (CWE). Second, a noncontact identification method for cutter runout including offset and inclination is given, which constructs an objective function by using the cutting radius relative variation between adjacent teeth, and identifies through a numerical optimization method. Thirdly, with consideration of bottom-edge cutting effect, the paper details a three-step calibration procedure for SCFCs based on an enhanced thin-plate milling experiment. Finally, a series of milling tests are performed to verify the effectiveness of the proposed method. The results show that the approach is suitable for both constant and nonconstant pitch cutter, and the generalization has been proved. Moreover, the paper points out that the cutter runout has a strong spindle speed-dependent effect, the milling force in cutter axis direction exists a switch-direction phenomenon, and the actual feedrate will be limited by large tool path curvature. All of them should be considered for obtaining an accurate milling force prediction.

Cutting force modeling for non-uniform helix tools based on compensated chip thickness in five-axis flank milling process

Cutters with non-uniform helix and pitch angles are increasingly used in modern industries. However, few works have studied the cutting forces of this type of tool. Therefore, this study presents a compensated-chip thickness-based cutting force model for non-uniform helix tools in the five-axis milling process. First, the geometry of this special cutter is mathematically expressed. Based on this, the instantaneous uncut chip thickness (IUCT) model is established using error compensation theory combined with real trajectories of cutter edges. This model can overcome the disadvantages of numerical methods Subsequently, the cutting force coefficients are computed using the average IUCT. The engagement between the cutter and the workpiece is discussed. Finally, for verifying the validity and accuracy of the force model, the proposed IUCT, classical, vector-form and true models are compared for a traditional cutter and a cutter with variable helix and pitch angle. Two toolpaths including a line and a circle are selected to predict the IUCT values. The results show that the presented IUCT model exhibits the highest accuracy among the first three models. Additionally, some experiments are conducted. For the three-axis machining process, the toolpaths including a line and a circle are selected. The results show that the cutter with the variable helix angles can predict cutting forces with variable toolpaths. Using the same tool and for the five-axis machining process, a conical surface is selected as toolpath surface. The results show the validity of the cutting force model.

Surface texture formation in precision machining of direct laser deposited tungsten carbide

This paper focuses on an analysis of the surface texture formed during precision machining of tungsten carbide. The work material was fabricated using direct laser deposition (DLD) technology. The experiment included precision milling of tungsten carbide samples with a monolithic torus cubic boron nitride tool and grinding with diamond and alumina cup wheels. An optical surface profiler was applied to the measurements of surface textures and roughness profiles. In addition, the micro-geometry of the milling cutter was measured with the application of an optical device. The surface roughness height was also estimated with the application of a model, which included kinematic-geometric parameters and minimum uncut chip thickness. The research revealed the occurrence of micro-grooves on the machined surface. The surface roughness height calculated on the basis of the traditional kinematic-geometric model was incompatible with the measurements. However, better agreement between the theoretical and experimental values was observed for the minimum uncut chip thickness model.

A non-contact calibration method for cutter runout with spindle speed dependent effect and analysis of its influence on milling process

The Cutter runout in traditional studies about milling mechanics and dynamics are always assumed as a constant value. Actually, the dynamic characteristics and vibration response of spindle system will change under different spindle speeds, which would result in a spindle speed dependent effect for cutter runout. A non-contact calibration method for cutter runout with consideration of spindle speed dependent effect is proposed in the paper, and the influence of cutter runout on milling mechanics and dynamics is further analyzed. Based on the measured relative variation of tooth by the eddy current sensor measurement system, a numerical optimization method for identifying cutter runout parameters is presented. The main advantage of the method is simple and convenient, especially for studying the cutter runout under different spindle speeds. Then, the paper gives out an instantaneous uncut chip thickness model during cutter/workpiece engagement with runout effect, and puts forward an enhanced SDM for milling stability prediction. Theoretical and experimental results show that milling force, stability and SLE prediction considering the cutter runout with spindle speed dependent effect have a higher prediction accuracy compared with other previous methods. Lastly, the studies analyze the influence of cutter runout on milling force, milling stability and SLE, and the results indicate that cutter runout can improve the milling stability, but deteriorate the milling force excitation characteristics and SLE.

An improved cutting force model for micro milling considering machining dynamics

Micro milling, as a versatile micro machining process, is kinematically similar to conventional milling; however, it is significantly different from conventional milling with respect to chip formation mechanisms and uncut chip thickness modelling, due to the comparable size of the edge radius to the chip thickness, and the small per-tooth feeding. Considering tool runout and dynamic displacement between the tool and the workpiece, the contour of the workpiece left by previous tool paths is typically in a wavy form, and the wavy surface provides a feedback mechanism to cutting force generation because the instantaneous uncut chip thickness changes with both the vibration during the current tool path and the surface left by the previous tool paths. In this study, a more accurate uncut chip thickness model was established including the precise trochoidal trajectory of the cutting edge, tool runout and dynamic modulation caused by the machine tool system vibration. The dynamic regenerative effect is taken into account by considering the influence of all the previous cutting trajectories using numerical iteration; thus, the multiple time delays (MTD) are considered in this model. It is found that transient separation of the tool-workpiece occurring at a low feed per tooth, caused by MTD and the existing cutting force models, is no longer applicable when transient tool-workpiece separation occurs. Based on the proposed uncut chip thickness model, an improved cutting force model of micro milling is developed by full consideration of the ploughing effect and elastic recovery of the workpiece material. The proposed cutting force model is verified by micro end milling experiments, and the results show that the proposed model is capable of producing more accurate cutting force prediction than other existing models, particularly at small feed per tooth.

Instantaneous uncut chip thickness modeling for micro-end milling process

ABSTRACTThe prediction model of instantaneous uncut chip thickness is critical for micro-end milling process, which can directly affect the cutting forces, surface accuracy, and process stability of the micro-end milling process. This paper presents an instantaneous uncut chip thickness model systematically based on the actual trochoidal trajectory of tooth and the tool run-out in micro-end milling process. The variable entry and exit angles of tool, which are affected by the tool run-out, are concerned in the model. The related instantaneous uncut chip thickness is evaluated by considering the theoretical instantaneous uncut chip thickness and the minimum uncut chip thickness, which is formulated by two types of material removal mechanisms, in the elastic-plastic deformation region and the complete chip formation region, respectively. In comparison with the instantaneous chip thickness obtained from the conventional model, the feasibility of the proposed model can be proved by the related simulation results with variable process parameters including feed per tooth, radial depth of cut, and tool run-out. In addition, the predicted and measured cutting forces are compared with validate the accuracy of the proposed instantaneous uncut chip thickness model for the micro-end milling process.

A novel instantaneous uncut chip thickness model for mechanistic cutting force model in micro-end-milling

Modeling of cutting force plays a vital role in characterizing the micro-end-milling processes, including tool wear and surface quality as well as machining stability. It is well recognized that precise determination of instantaneous uncut chip thickness (IUCT) is essential for cutting force prediction, while the presence of tool run-out and material elastic recovery have an equally important influence. On the basis of the IUCT model considering run-out, elastic recovery is innovatively integrated into the surfaces generated by the previously passing tool tips to improve the accuracy of IUCT model. Subsequently, a novel IUCT model is proposed in this paper that considers trochoidal trajectory of tool tip, run-out, minimum chip thickness, elastic recovery, and variety in entry/exit angles. Also, it can be found that the elastic recovery has a significant effect upon IUCT (especially at small feed rate) based on the numerical analysis of the IUCT model, and meanwhile the role of elastic recovery is mainly affected by run-out, minimum chip thickness and elastic recovery rate. Furthermore, it is worth noting that entry/exit angles may change at small feed rate when taking into account elastic recovery. Then, the IUCT model and non-linear cutting force coefficients are integrated into the mechanistic cutting force model and used to predict cutting force. The predicted cutting force is found to be well in harmony with the experimental results; as a result, the developed theoretical cutting force model in this work can be used in real-time machining process monitoring as well as adaptive control of machining process.

A New Uncut Chip Thickness Model for Tilted Helical End Mills through Direct Correspondence with Local Oblique Cutting Geometry

Machining optimization algorithms in end-milling with helical cutters require an efficient and accurate model of the uncut chip thickness (UCT) at every location along the cutting flutes. Past work has either ignored the effects of tool tilt and orientation or treated them with simple assumptions about their coupling with tool shape. The current paper treats the problem with considerably greater generality using an arc-length parameterization of the axis-symmetric tool profile. Each discrete tool move was considered a 3-axis motion. Ignoring tool run-out, UCT was calculated in the direction of direct correspondence to local oblique cutting geometry, i.e., perpendicular to the local cutting edge and cutting velocity. The flute curves were intersected with the engagement contour corresponding to the instantaneous tool-work contact and the UCT inspected within. For a candidate taper ball end mill, the UCT results of the new model were compared with the standard Martellotti model. The new model agrees closely with the Martellotti model in the flank region and predicts a more realistic variation in the ball region.

An approach for analyzing and controlling residual stress generation during high-speed circular milling

In the rapid development of the modern high-speed milling industry, particularly in the aerospace field, machined residual stress is an important evaluation indicator of the quality, and whether it can be controlled or not is critical. In this article, experimental data of residual stress in feed direction and vertical feed direction validated with finite element (FE) simulation, which resulted in the finding that residual stress distribution is nonuniform in varied machined circular areas. The maximum residual tensile stress in different directions changes with coordinates. It is well known that uncut chip thickness (UCT) will influence the cutting force and temperature, but the relation between UCT and residual stress is still difficult to understand and explicate. Traditional measurement of residual stresses in the feed and vertical feed direction is difficult to explain. Based on the UCT model which is a function of feed rate and tool diameter, by measuring residual tangential and radial stress, it is observed that residual tangential stress is influenced by the UCT. Moreover, residual radial stress, under high feed rate, is distributed with wave change, and residual radial stress under smaller feed rate is still affected by the UCT. These results indicate that it is possible to optimize the residual stress distribution by controlling UCT (feed rate and tool diameter) with high-speed milling.

Chatter modelling in micro-milling by considering process nonlinearities

This paper presents a new approach for chatter modelling in micro-milling. The model takes into account: the nonlinearity of the uncut chip thickness including the run-out effect; velocity dependent micro-milling cutting forces; the dynamics of the tool-holder-spindle assembly. The uncut chip thickness is determined after considering the full kinematics of the cutting tool including the run-out effect. The micro-milling cutting forces are determined by: (i) a finite element (FE) prediction of the cutting forces in orthogonal cutting at different cutting velocities and uncut chip thicknesses; (ii) describing the relationship between cutting forces, cutting velocities and uncut chip thicknesses into a nonlinear equation; (iii) incorporating the uncut chip thickness model into the relationship of the cutting forces as function of the cutting velocity and the uncut chip thickness. The modal dynamic parameters at the cutting tool tip are determined for the tool-holder-spindle assembly and used for solving the equation of motion. The micro-milling process is modelled as two degrees of freedom system where the modal dynamic parameters for the tool-holder-spindle assembly and the micro-milling cutting forces are considered. Due to nonlinearities in the micro-milling cutting forces, the equation of motion is integrated numerically in the time domain using the Runge–Kutta fourth order method. The displacements in the x and y directions are obtained for one revolution-per-tool. Statistical variances are then employed as a chatter detection criterion in the time-domain solution. Scanning electron microscope (SEM) inspection is carried out to observe potential chatter marks on the micro-milled AISI 4340 steel surfaces at different spindle speeds and depths of cut. The predicted stability lobes and the experimentally obtained stability limits resulted in satisfactory agreement. The influence of the run-out effect on the stability lobes at different feed rates was investigated, which demonstrated the capability of the developed chatter model to consider quantitatively the run-out phenomenon. The results showed that the stability limits decrease by increasing the run-out length.

Prediction of chatter in NC machining based on a dynamic cutting force model for ball end milling

Ball end milling is one of the most widely used cutting processes in the automotive, aerospace, die/mold, and machine parts industries, and the chatter generated under unsuitable cutting conditions is an extremely serious problem as it causes excessive tool wear, noise, tool breakage, and deterioration of the surface quality. Due to the critical nature of detecting and preventing chatter, we propose a dynamic cutting force model for ball end milling that can precisely predict the cutting force for both stable and unstable cutting states because our uncut chip thickness model considers the back-side cutting effect in unstable cutting states. Furthermore, the dynamic cutting force model considers both tool runout and the penetration effect to improve the accuracy of its predictions. We developed software for calculating the cutting configuration and predicting the dynamic cutting force in general NC machining as well as single-path cutting. The chatter in ball end milling can be detected from the calculated cutting forces and their frequency spectra. A comparison of the predicted and measured cutting forces demonstrated that the proposed method provides accurate results.

3D Ball-End Milling Force Model Using Instantaneous Cutting Force Coefficients

Application of a ball-end milling process model to a CAD/CAM or CAPP system requires a generalized methodology to determine the cutting force coefficients for different cutting conditions. In this paper, we propose a mechanistic cutting force model for 3D ball-end milling using instantaneous cutting force coefficients that are independent of the cutting conditions. The uncut chip thickness model for three-dimensional machining considers cutter deflection and runout. An in-depth analysis of the characteristics of these cutting force coefficients, which can be determined from only a few test cuts, is provided. For more accurate cutting force predictions, the size effect is also modeled using the cutter edge length of the ball-end mill and is incorporated into the cutting force model. This method of estimating the 3D ball-end milling force coefficients has been tested experimentally for various cutting conditions.