Instantaneous Uncut Chip Thickness Research Articles

A theoretical and experimental investigation on the surface formation mechanism in elliptical vibration cutting of single crystal magnesium fluoride

Manufacturing precise microstructures on magnesium fluoride surface remains challenging due to its brittleness and anisotropy. This study investigates the surface formation mechanism in ductile machining of single crystal magnesium fluoride and explores the feasibility of fabricating sophisticated microstructures on magnesium fluoride surfaces by applying elliptical vibration cutting technology. We conducted a systematic study on the ductile-brittle transition behavior, material removal mechanism, and fabrication performance of microstructures through theoretical analysis and cutting experiments. A theoretical model that takes into account the elliptical trajectory's orientation angle has been established to determine the evolution of instantaneous uncut chip thickness and the characteristic nominal depth of cut in one cycle during elliptical vibration cutting. By comprehensively examining the influence of the elliptical trajectory, determined by vibration amplitudes, orientation angle, and nominal cutting speed, on the dynamic behaviour of the ductile-brittle transition, we verified the proposed theoretical model with convincing experimental results. Larger critical depth of cut for ductile-brittle transition and smaller cutting forces achieved by EVC contribute to the improved ductile machinability of MgF2. With optimal vibration parameters, the critical depth of cut increases by 56 times compared to ordinary cutting. Theoretical findings regarding plastic deformation parameters and cleavage fracture parameters align well with experimental observations, providing a more comprehensive understanding of the anisotropy influence on damage evolution during the surface formation in elliptical vibration cutting of magnesium fluoride. Furthermore, leveraging our fundamental understanding of material removal and surface formation mechanisms, we successfully generated bi-sinusoidal arrays on magnesium fluoride surfaces with exceptional accuracy (machining error < 1.5%) and high efficiency (machining time < 121.5 min) by applying elliptical vibration cutting.

Investigation of the tool flank wear influence on cutter-workpiece engagement and cutting force in micro milling processes

Cutting force modeling is essential for comprehending the dynamic mechanics of the micro-milling process. Accurate calculation of the cutter-workpiece engagement is crucial for predicting cutting force accurately. This study proposes an accurate analytical model of cutter-workpiece engagement that comprehensively incorporates tool flank wear, tool edge radius, and tool runout for predicting cutting forces in the micro-milling process. Based on the actual tool radius model, which takes into account tool flank wear and tool edge radius, a fast real-time online method for accurately calculating the entry and exit angles is presented. This method involves the trochoidal trajectories of the current cutting edge and all passing cutting edges from the previous cycle under the influence of tool runout. Then the cutter-workpiece engagement is determined. Based on this, the cutting force is predicted combined with instantaneous uncut chip thickness and cutting force coefficients considering tool flank wear and tool runout. Through micro-end milling experiments, the validity of the cutting force model is confirmed. The statistical analysis of the predicted cutting forces further demonstrates the effectiveness of accounting for the impact of tool flank wear on the cutting forces throughout the entire micro-milling process. Through case analysis, it is concluded that tool flank wear leads to increased cutter-workpiece engagement and significantly affects the cutting forces in three directions. This work could offer a theoretical foundation and practical guidance for predicting tool life and controlling surface quality during the machining process.

Tooth-wise monitoring of the asymmetrical tool wear in micro-milling based on the chip thickness reconstruction and cutting force signal

Tooth-wise monitoring of the tool wear condition is of great importance for improving the machining quality and efficiency of micro-milling. However, the uncut chip thickness, cutting force, and tool wear condition of the multi-tooth evolve asymmetrically coupled due to the tool runout, and it is difficult to monitor the tool wear of each cutting tooth solely based on the cutting force signal. The reconstruction of chip thickness is the key to overcoming this challenge. With such consideration, this study proposes a tooth-wise monitoring method for estimating the asymmetrical micro-milling tool wear based on the chip thickness reconstruction and cutting force signal. The instantaneous uncut chip thickness of each tooth is reconstructed from the floor surface topography of the machined material with the guide of the proposed surface topography model considering the asymmetrical tool wear. The wear condition of each tooth is estimated by integrating the reconstructed chip thickness and the measured cutting force signal into the proposed asymmetrical micro-milling force model. Experimental results show that the asymmetrical models outperform the traditional symmetrical models in terms of modeling flexibility and accuracy. With the consideration of the asymmetrical tool wear, the prediction accuracy of the proposed topography and cutting force models increases by 11.4% and 5.3%. The relative monitoring error within 9% demonstrates that the proposed method can accurately estimate the tool wear condition of each cutting tooth in micro-milling.

BOOLEAN OPERATION-BASED FAST CALCULATION OF CUTTER-WORKPIECE ENGAGEMENT DURING PERIPHERAL MILLING

The cutter-workpiece engagement (CWE) is an important basis for accurately predicting milling force and vibration of machining system, which can be dramatically affected by the complex tool path, variable part allowance and various tool profiles. The paper presents a fast calculation method of CWE during peripheral milling process based on the Boolean operation. A second-developed simulation environment embedded the kernel program with the aid of commercial CAM is established. In the computing model, the locally past-cut material entity of the workpiece is replaced by a set of neighboring tools, and the geometric entity of CWE is quickly obtained through the Boolean operation between the tool, workpiece blank, and past-cut entities. The instantaneous uncut chip thickness (IUCT) is further obtained after extracting the tooth start and end cutting angles. Thanks to the first-order computation time complexity, the method has a significant advantage of fast computing speed when compared to the traditional method with a globally updated workpiece. In the milling case of S-shaped workpiece, the results indicate that the method can effectively calculate the CWE status along the entire tool path, and achieve the fast prediction of milling force under a long-time machining condition.

Investigation on the machinability of copper-coated monocrystalline silicon by applying elliptical vibration diamond cutting

Although monocrystalline silicon exhibits promising microstructural properties for enhancing the performance of optical systems, precise and efficient silicon fabrication is still challenging due to its brittleness. In the present work, we demonstrate the ductile machinability of copper-coated silicon by applying elliptical vibration diamond cutting. Firstly, the influence of the copper coating on the ductile machinability of silicon was experimentally investigated by applying ordinary diamond cutting, showing that the critical depth of cut (DOC) for the ductile-to-brittle transition increased from 118 to 418 nm due to the advantages of the copper coating. This provided hydrostatic pressure in the microcutting regime and the compressive force on the subsurface defects to prevent crack propagation. Subsequently, grooving tests on coated and uncoated silicon were performed by applying elliptical vibration cutting (EVC). Due to the small instantaneous uncut chip thickness in each vibration cycle, the critical DOC by EVC for uncoated silicon increased to 459 nm. Applying the favorable copper coating process, the critical DOC by EVC for coated silicon increased to about 988 nm. The ductile machinability of silicon was efficiently improved by combining EVC and the coating process. Furthermore, the influence of vibration amplitude and cutting speed on the ductile machinability of silicon was explored in detail, leading to the optimized machining conditions for the ductile machining of silicon. Finally, based on these fundamental results, ultra-precision microlenses on silicon were efficiently fabricated, which is appropriate for further industrial applications.

Investigation of the cutting-edge radius size effect on dynamic forces in micro end milling of brass260

Rapid increases in the number of industries that need a sub-micron surface finish on 3D micro/meso technological innovation parts are being seen. Due to the high rotating speeds of activities, chatter behaviour also occurs during micro-cutting. Changes in bearing stiffness, gyroscopic effects, and misalignment are only some of the factors that need to be considered while studying the spindle's dynamics. By regulating the movement of the cutting edge, the cutting action may be made more consistent. The structure of the tools also affects the machine's dynamics. Since the modes of different machine-tool components interact with one another, the dynamics of the tool tip are affected. In this research, we consider a model of a micro spindle system to enhance machining accuracy. Timoshenko beam theory is used to account for shear deformation and rotational inertia effects due to the short and thick beam-type designs of each component of the micro tool. A detailed dynamical model of the moving micro end mill is created using an extended form of Hamilton's Principle. A two-degree-of-freedom model of the micro-milling process considers the modal dynamic properties of the tool-holder-spindle assembly and the micro-milling cutting forces. A three-dimensional finite element model of the system is built, and its dynamic response is gathered, to validate the full order finite element approach. Cutting force coefficients are then modelled as a function of instantaneous uncut chip thickness, which is principally affected by the tool edge radius and feed per tooth at different radial immersion depths.

Generic Cutting Force Modeling with Comprehensively Considering Tool Edge Radius, Tool Flank Wear and Tool Runout in Micro-End Milling.

Accurate cutting force prediction is crucial in improving machining precision and surface quality in the micro-milling process, in which tool wear and runout are essential factors. A generic analytic cutting force model considering the effect of tool edge radius on tool flank wear and tool runout in the micro-end milling process is proposed. Based on the analytic modeling of the cutting part of the cutting edge in the end face of the micro-end mill bottom, the actual radius model of the worn tool is established, considering the tool edge radius and tool flank wear. The tool edge radius, tool wear, tool runout, trochoidal trajectories of the current cutting edge, and all cutting edges in the previous cycle are comprehensively considered in the instantaneous uncut chip thickness calculation and the cutter-workpiece engagement determination. The cutting force coefficient model including tool wear is established. A series of milling experiments are performed to verify the accuracy and effectiveness of the proposed cutting force model. The results show that the predicted cutting forces are in good agreement with the experimental cutting forces, and it is necessary to consider tool wear in the micro-milling force modeling. The results indicate that tool wear has a significant influence on the cutting forces and cutting force coefficients in the three directions, and the influences of tool wear on the axial cutting force and axial force coefficient are the largest, respectively. The proposed cutting force model can contribute to real-time machining process monitoring, cutting parameters optimization and ensuring machining quality.

Investigation on dynamic tool deflection and runout-dependent analysis of the micro-milling process

Micro-milling is essential for manufacturing miniature precision components. The process involves free/restricted tool overhang length, runout, deflection, force and stability. In comparison to a macro-milling process, it is very difficult to determine the micro-milling force and stability in such a small machining scale due to higher spindle speeds, runout and deflection of the tool point. In this paper, we have proposed a complete and practical model for micro-milling process, which includes dynamic tool deflection and establishment of a stability lobe diagram (SLD) with runout-dependent effect. First, a multi-sections discretization method combined with dynamic tests was employed to the tool holder and tool dummy so that the frequency response function (FRF) at tool point was identified. Two runout models were introduced with the corresponding parameters, and the instantaneous uncut chip thickness (IUCT) was obtained by numerical solution. Then the dynamic tool deflection was developed by the product of force decomposition and FRF at tool point. Finally, the interaction between feed per tooth, runout and dynamic tool deflection was studied, which led to the proposed SLD. The experiments demonstrated that tool deflection as well as runout affected the IUCT, and runout enabled the cutter pitch angle acting on the workpiece to change, which enhanced stability limits despite reducing machining accuracy. In addition, the increase of feed per tooth also contributed to the improvement of stability boundary.

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 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.

A novel run-out model based on spatial tool position for micro-milling force prediction

The tool run-out significantly affects prediction of milling force, which is crucial for monitoring the micro-end-milling processes. For accurately predicting milling force, a novel tool run-out model is presented, which is based on spatial tool position to reflect a more realistic clamping situation. In the established model, the direction vector s ⃑ of the tool axis replacing the location angle ψ and tilt angle τ is firstly proposed to describe the tool position in space to simplify the calculation. The mechanistic cutting force model, which is relevant to instantaneous uncut chip thickness (IUCT), is adopted to predict milling force. An accurate IUCT at different axial positions is calculated by incorporating the proposed run out model on spatial tool position. The predicted cutting forces show a close agreement with the experimental cutting force. The proposed run-out model can be employed to identify the tool state as well as predict cutting force, thereof monitor the machining process. • A novel tool run-out model based on spatial tool position is presented to reflect a more realistic clamping situation. • An accurate IUCT at different axial positions is calculated by incorporating the proposed run out model. • An improved model is presented to rectify the effect of cutting parameters on tool runout and thereof on the cutting force. • The proposed run-out model can be employed to identify the tool state as well as predict cutting force.

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

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

Cutting Forces in Peripheral Up-Milling of Particleboard.

An analysis of forces acting in the peripheral up-milling of particleboard is presented. First, a novel method of high-frequency piezoelectric force signal treatment is proposed and used to separate the original force signal from the vibrations of the previous cutting iteration. This allows for the analysis of single chip cutting force courses during industrial CNC (Computer Numerical Control) milling. The acting forces are compared with the theoretical, instantaneous, uncut chip thickness. The results show that, for a range of 40–60 m/s, the higher the cutting speed used, the higher the resultant and principal cutting forces. The method of cutting thrust force used was similar to that observed in solid wood milling, i.e., first using a pushing action, followed by a pulling action. The obtained average specific principal cutting forces for particleboard peripheral up-milling are equal to 32.0 N/mm2 for slow and 37.6 N/mm2 for fast milling. The specific cutting thrust force decreases with the increase in instantaneous uncut chip thickness.

Cutting force prediction considering tool path curvature and torsion based on screw theory

There are common features such as the tool path curvature and torsion, and cutter-orientation change in sculptured surface machining, which bring new challenges to the accurate prediction of cutting force. Aiming at the tool path curvature and torsion, and cutter-orientation change, a cutting force prediction method based on the screw theory is proposed in this paper. For the first time, the screw theory is used to describe the cutter spatial motion, which includes the feed motion considering the tool path curvature and torsion, and cutter-orientation change. Combining with Frenet frame, the analytical formula of the screw of cutting edge elements is derived through the homogeneous coordinate transformation. Then, the instantaneous uncut chip thickness (IUCT) of each cutting edge element is calculated by the vector projection method. And the cutting state of the cutting edge element is determined by its IUCT and position relative to the workpiece surface, which is updated by the cutter envelope surface along the machined tool path derived with the screw. To verify the effectiveness of the proposed cutting force prediction method, a milling experiment is conducted on a conical surface workpiece along a tool path with curvature and torsion characteristics, and changing cutter-orientations. Then, the effects of the tool path curvature and torsion, and cutter-orientation change on the cutting force are simulated and analyzed. The results show that the proposed cutting force model based on the screw theory has higher prediction accuracy for the sculpture surface machining with curving and torsional tool paths and changing cutter-orientations.

Analysis of the Effect of Tool Posture on Stability Considering the Nonlinear Dynamic Cutting Force Coefficient

Abstract In aviation and navigation, complicated parts are milled with high-speed low-feed-per-tooth milling to decrease tool vibration for high quality. Because the nonlinearity of the cutting force coefficient (CFC) is more evident with the relatively smaller instantaneous uncut chip thickness, the stable critical cutting depth and its distribution against different tool postures are affected. Considering the nonlinearity, a nonlinear dynamic CFC model that reveals the effect of the dynamic instantaneous uncut chip thickness on the dynamic cutting force is derived based on the Taylor expansion. A five-axis bull-nose end milling dynamics model is established with the nonlinear dynamic CFC model. The stable critical cutting depth distribution with respect to tool posture is analyzed. The stability results predicted with the dynamic CFC model are compared with those from the static CFC model and the constant CFC model. The effects of tool posture and feed per tooth on stable critical cutting depth were also analyzed, and the proposed model was validated by cutting experiments. The maximal stable critical cutting depths that can be achieved under different tool postures by feed per tooth adjustment were calculated, and corresponding distribution diagrams are proposed for milling parameter optimization.

Machinability of single crystal calcium fluoride by applying elliptical vibration diamond cutting

Functional micro/nano structures are promising for enhancing the performance of CaF2-based devices. However, it is still a challenge to precisely manufacture CaF2 micro/nano structures due to their brittleness. In the present work, we demonstrated the machinability of ductile-mode diamond cutting of CaF2 and the ability to sculpture sophisticated micro/nano structures on CaF2 by applying elliptical vibration cutting. Firstly, the nanoindentation of CaF2 reveals the crystal orientation-dependent interaction between dislocation slip and crack propagation, thus obtaining the optimal crystal orientation for plasticity. Subsequently, the grooving tests were conducted along the crystal orientation of (111)[1‾21‾]. With elliptical vibration cutting, the critical depth of cut from ductile-to-brittle transition is increased by 42 times as compared with ordinary cutting. Furthermore, considering the instantaneous uncut chip thickness in each vibration cycle, the influence of vibration amplitude on the ductile machinability of CaF2 is discussed in detail. Finally, based on these fundamental results, ultra-precision hexagonal microlenses were successfully sculptured on CaF2 by applying the amplitude-controlled sculpturing method in elliptical vibration cutting.

Temperature prediction of ultrasonic vibration-assisted milling

Machining temperature is a key factor in ultrasonic vibration-assisted milling as it can significantly influence tool wear rate and residual thermal stresses. In current study, a physics-based analytical predictive model on machining temperature in ultrasonic vibration-assisted milling is proposed, without resorting to iterative numerical simulations. As the tool periodically loses contact with the workpiece under vibration, three types of tool-workpiece separation criteria are first examined based on the tool trajectory under ultrasonic vibration. Type I criterion examines whether the relative velocity between tool and workpiece in cutting direction is opposite to the tool rotation direction. Type II criterion examines whether the instantaneous vibration displacement in radial direction is larger than instantaneous uncut chip thickness. Type III criterion examines whether there is overlap between current and previous tool paths due to vibration. If no contact, the instantaneous temperature rise is zero. Otherwise, the temperature rise is predicted under shearing heat source in shear zone and secondary rubbing heat source along machined surface. A mirror heat source method is applied to predict temperature rise, considering oblique band heat sources moving in a semi-infinite medium. The proposed predictive temperature model in ultrasonic vibration-assisted milling is validated through comparison to experimental measurements on Al 6063 alloy. The proposed predictive model is able to match the measured temperature with high accuracy of 1.85% average error and 5.22% largest error among all cases. Sensitivity analysis is also conducted to study the influences of cutting and vibration parameters on temperature. The proposed model is valuable in terms of providing an accurate and reliable reference for the prediction of temperature in ultrasonic vibration-assisted milling.

Analytical model of milling forces prediction in five-axis milling process

In the process of the five-axis milling process, due to the changing of the cutter-workpiece engagement area and instantaneous uncut chip thickness, five-axis milling forces prediction is difficult compared with three-axis forces prediction. This study proposed a new analytical method to predict milling force in five-axis milling. Compared with the mechanistic calibration method and experiment method, this method predicts the cutting force accurately, does not need experiments, and only needs to know the input parameters, such as tool parameters, workpiece parameters, and cutting conditions. The effect of lead angle and tilt angle is analyzed by theoretical simulation. The correctness of the prediction model is verified by experiments under different conditions.

Modelling and experimental analysis of the effects of run out, minimum chip thickness and elastic recovery on the cutting force in micro-end-milling

Prediction of cutting force has great significance for controlling the micro-end-milling processes. In this study, a mechanics model for exactly prediction cutting force is comprehensively established by considering the variety of entry and exit angles for each engaged cutting edge and an accurate instantaneous uncut chip thickness (IUCT). The determination of IUCT has considered the combination of the minimum chip thickness, tool run-out, and the material's elastic recovery, which is embedded in the cutting force model. Further, cutting force coefficients as function of uncut chip thickness have been calculated by using finite element method (FEM). To verify the reliability of the presented cutting force model, a series of experiments for cutting force are conducted and experimental results are compared to cutting force predicted. The results demonstrate that the cutting force predicted is well in agreement with that of measured. The effects of elastic recovery and tool run-out on cutting force also are investigated. Some conclusion can be drawn that elastic recovery can more obviously affect the cutting force predicted with smaller the feed per tooth, the errors of experimental and predicted is getting smaller with increasing the cutting depth, the slight change of tool run-out will lead to a great variation in cutting force.

Generic instantaneous force modeling and comprehensive real engagement identification in micro-milling

Cutting force modelling has been one of the most important tools for understanding the dynamics and for process control of micro milling. While current studies have widely investigated the uncut chip thickness and tool runout mechanics, they mostly took account a specific case and a general tool engagement determination is yet to be established. These lead to low adaptability and bring difficulties for process modeling and online control. In this study, a new and generic instantaneous force model is developed, in which the size effect is reflected in the force coefficients, and the tool runout effect is included in the instantaneous uncut chip thickness. In the model the real engagement is comprehensively identified under the tool run out effect, with the actual entry and exit angles at the critical position explicitly determined. The average uncut chip thickness (AUCT), actual cutting depth, center position and geometrical relations are analytically established. The proposed force model can be obtained conveniently and fast by only once calculation of the AUCT with inclusion of tool run out effect. With the main influencing factors considered, the force models are computational efficient, good in adaptability and could conveniently be generalized to universal model. Compared to the experimental measurements, the maximum peak errors of the forces are all less than 0.6%, which validates the efficiency and accuracy of the proposed model.