Existing researches for studying the influences of mill's helix angle on peak cutting force were mainly carried out by using simulation or experimental means. Thus, the obtained conclusions were just ...empirical judgments or qualitative observations, which cannot be further used for optimally designing the helix angle of mills. This paper presents a theoretical method for the first time to reveal the working mechanism of peripheral milling tool's helix angle on peak cutting force through strict analytical formulation. To facilitate well understanding the effect of helix angle, variation tendency of peak cutting force versus helix angle is comprehensively studied by analyzing the formation principle of peak cutting force from the point view of both geometrical explanation and theoretical proof. Both infinitesimal element method and differential theory are used in the investigation procedure. It is proved that the peak value of cutting forces decreases with the increase of helix angle for a single engaged cutting edge. Combining this conclusion with the overlapping effect of multiple engaged cutting edges, optimal helix angle corresponding to the minimum of peak cutting forces is analytically derived to be the function of axial depth of cut, number of flutes and cutter diameter. Experimental verifications have been carried out to validate the proposed theory.
This work focuses on the analysis of the edge forces generated in ball end milling of hardened alloy 55NiCrMoV6 steel. The investigated forces consider the effects of friction, rubbing and ploughing ...mechanisms between the work piece and tool flank face during machining process. The primary objective of the paper concentrates on the determination of edge forces in the range of variable surface inclination angles and increasing tool wear. The proposed approach involves the measurements of instant cutting forces in machine coordinates (Fz, Fy, Fz). Subsequently, the measured forces are converted to the forces in the tool coordinates (Ft_av, Fr_av, Fa_av). In the next step, the Ft_av, Fr_av, Fa_av forces are expressed in function of average uncut chip thickness. In order to obtain the edge forces values, the extrapolation of forces in the tool coordinates to the zero uncut chip thickness is made. The investigations reveal that edge forces are strongly affected by surface inclination angle and progressing tool wear. The growth of the tool wear induced the monotonic increase in edge forces values. Nevertheless, in case of surface inclination angles α≥15° the influence of this factor on edge forces was low. It was also shown that cutting force estimation with the consideration of the variable edge forces is characterized by a higher accuracy than one based on constant edge forces. Therefore, the proposed method can be employed in the reliable calibration of specific force coefficients contained in mechanistic cutting force models dedicated to the finish ball end milling of sculptured surfaces.
•Edge forces were determined based on measured extreme forces in machine coordinates;•Influence of surface inclination angle on edge forces’ values was presented;•Monotonic growth of edge forces together with progressing tool wear was observed;•Cutting force model including variable edge forces has high accuracy.
Accurate modeling and prediction of cutting forces are important for process planning and optimization in micro end-milling process. In order to exactly predict the cutting forces, an innovative ...uncut chip thickness algorithm is proposed by considering the combination of the exact trochoidal trajectory of the tool tip and the cutting trajectory of all previously passing teeth, tool run-out, minimum chip thickness and the material’s elastic recovery. The proposed uncut chip thickness algorithm also considers the variation of the entry and exit angles caused by tool run-out. To determine the cutting force coefficients, a finite element model (FEM) of orthogonal micro-cutting that considers strain hardening, strain rate sensitivity, thermal softening behavior, and temperature-dependent flow has been established. Based on the results from FEM analysis, the cutting force coefficients are identified and represented by a nonlinear equation of the uncut chip thickness, cutting edge radius and cutting velocity. The identified cutting force coefficients are integrated into a mechanistic cutting force model and used to simulate micro end-milling forces. The simulation results show a very satisfactory agreement with the experimental results.
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•End milling of hybrid magnesium MMC (Mg + E-Waste CRT + BN).•Cutting forces, temperature and surface roughness were measured.•Effect of reinforcement, tool and machining factors in ...milling is explained.•Multi objective optimization through GRA and TOPSIS.•Amount of reinforcement and its size have noteworthy effect in MMC machining.
Present study investigates the effect of material and machining parameters on cutting force, surface roughness and temperature in end milling of Magnesium (Mg) Metal Matrix Composite (MMC) using carbide tool. Mg hybrid composite was fabricated by reinforcing Cathode Ray Tube (CRT) panel glass, an intensifying E-waste and Boron Nitride (BN) particles through powder metallurgy method. The milling experiments were conducted based on L27 orthogonal array designed by considering CRT glass particle size and weight percentage, tool diameter, speed, feed and depth of cut as input process parameters. Multi objective optimization was done through Grey Relational Analysis (GRA) and Techniques for Order Preferences by Similarity to Ideal Solution (TOPSIS). Both of the techniques provided a similar optimum parameter condition i.e. 10 µm particle size, 5% reinforcement, 8 mm diameter tool, 710 rpm speed, 20 mm/min feed and 0.5 mm depth of cut that outcomes in 139.48 N in-feed force, 63.92 N cross-feed force, 42.6 N thrust force, 68.96 °C temperature and 0.198 µm surface roughness. ANOVA is performed to identify significance and also the effect of each process variables on response parameters. Though all the parameters were found to be significant, reinforcement weight% and particle size affects the response parameters as that of machining parameters whereas speed turned to be the least significant factor.
Accurate cutting-force measurements appear to be the key information in most of the machining related studies as they are fundamental in understanding the cutting processes, optimizing the cutting ...operations and evaluating the presence of instabilities that could affect the effectiveness of cutting processes. A variety of specifically designed transducers are commercially available nowadays and many different approaches in measuring cutting forces are presented in literature. The available transducers, though, express some limitations since they are conditioned by the vibration of the surrounding system and by the transducer׳s natural frequency. These parameters can drastically affect the measurement accuracy in some cases; hence an effective and accurate tool is required to compensate those dynamically induced errors in cutting force measurements. This work is aimed at developing and testing a compensation technique based on Kalman filter estimator. Two different approaches named “band-fitting” and “parallel elaboration” methods, have been developed to extend applications of this compensation technique, especially for milling purpose. The compensation filter has been designed upon the experimentally identified system׳s dynamic and its accuracy and effectiveness has been evaluated by numerical and experimental tests. Finally its specific application in cutting force measurements compensation is described.
•Cutting force measurements can be drastically affected by machine tool dynamics.•Dynamic compensation can extend the bandwidth of commercial dynamometers.•Two different approaches suitable for milling applications have been developed.•The effectiveness of the proposed approaches has been experimentally evaluated.•Examples in cutting force measurements compensation are shown.
•An exactly mechanics cutting force model is established in micro end-milling.•Tool trajectory, tool runout, the minimum chip thickness and the material's elastic recovery are considered in the ...determination of IUCT.•A new model to rectify the issue of tool runout effect on the cutting force.•Force coefficients as nonlinear function of the IUCT are extracted by FE simulation of micro orthogonal cutting.
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.
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The majority of cutting force models applied for the ball end milling process includes only the influence of cutting parameters (e.g. feedrate, depth of cut, cutting speed) and estimates forces on ...the basis of coefficients calibrated during slot milling. Furthermore, the radial run out phenomenon is predominantly not considered in these models. However this approach can induce excessive force estimation errors, especially during finishing ball end milling of sculptured surfaces. In addition, most of cutting force models is formulated for the ball end milling process with axial depths of cut exceeding 0.5mm and thus, they are not oriented directly to the finishing processes. Therefore, this paper proposes an accurate cutting force model applied for the finishing ball end milling, which includes also the influence of surface inclination and cutter's run out. As part of this work the new method of specific force coefficients calibration has been also developed. This approach is based on the calibration during ball end milling with various surface inclinations and the application of instantaneous force signals as an input data. Furthermore, the analysis of specific force coefficients in function of feed per tooth, cutting speed and surface inclination angle was also presented. In order to determine geometrical elements of cut precisely, the radial run out was considered in equations applied for the calculation of sectional area of cut and active length of cutting edge. Research revealed that cutter's run out and surface inclination angle have significant influence on the cutting forces, both in the quantitative and qualitative aspect. The formulated model enables cutting force estimation in the wide range of cutting parameters, assuring relative error's values below 16%. Furthermore, the consideration of cutter's radial run out phenomenon in the developed model enables the reduction of model's relative error by the 7% in relation to the model excluding radial run out.
•Cutting force model applied for the finishing ball end milling is proposed.•Run out is included also in expression of active length of cutting edge.•Surface inclination has quantitative and qualitative influence on cutting forces.•Small run out's value (3μm) can cause influential cutting force variations (~30%).•Proposed force model enables the obtainment of global estimation errors below 16%.
In order to characterize cutting mechanics during high-speed milling and micromilling applications, high-end piezoelectric dynamometers with a wide frequency bandwidth are necessary. Nevertheless, ...when installed into the machine tool their signal bandwidth is limited by the dynamic behaviour of the machining system. Thus, special filters have to be adopted for dynamics compensation. State of the art filters are based on a simplistic 3 × 3 dynamic model of device transmissibility without taking into account the influence of input force location with respect to the centre of the sensing platform. The Upgraded Augmented Kalman Filter has been recently proposed for solving this problem. Although it outperformed the other state of the art filters, it was based on the preliminary identification of a parametric mathematical model that is generally a difficult and non-automatic task. Here a novel non-parametric filter is introduced, that was based on a more general and abstract model of dynamometer dynamics considering both input force direction and location. By so doing, impressive results were found both from modal analysis and from real cutting tests, showing the potential of the new method for an effective and almost completely automatic cutting force dynamic compensation.
•Upgraded deconvolution is conceived for effective cutting force filtering in milling.•The method is completely non-parametric: no complex identification is required.•The influence of both force direction and location are incorporated in the filter.•Successful experimental validation through modal analysis and cutting tests.•The method outperformed state of the art filters used in this field.
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.
•The cutting width spreading and piling up effects are observed and theoretically modelled.•The influence of the piling up effect on cutting force is studied in detail.•The simulated and predicted spread width and piling up height have good agreements.•The proposed method can achieve better force prediction accuracy for small feed.
•Reduction of forces and improvement of efficiency during finish ball end milling.•Multi-criteria optimisation in terms of cutting forces and efficiency.•Relations between ball end milling process ...efficiency and surface inclination angle.•Optimised forces and process efficiency achieved for vc=375m/min and α=15°.
This paper proposes a method for the reduction of forces and the improvement of efficiency during finish ball end milling of hardened 55NiCrMoV6 steel. The primary objective of this work concentrates on the optimal selection of milling parameters (cutting speed – vc, surface inclination angle α), which enables the simultaneous minimisation of cutting force values and increased process efficiency. The research includes the measurement of cutting forces (Fx, Fy, Fz) during milling tests with variable input parameters and calculation of process efficiency accounting for cutting parameters and surface inclination. The paper then focuses on the multi-criteria optimisation of the ball end milling process in terms of cutting forces and efficiency. This procedure is carried out with the application of the response surface method, based on the minimisation of a total utility function. The work shows that surface inclination angle has a significant influence on the cutting force values. Minimal cutting forces and relative high efficiency can be achieved with cutting speed vc=375m/min and surface inclination angle α=15°.
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