Edge Forces Research Articles

A PSO-based semi-analytical force prediction model for chamfered carbide tools considering different material flow state caused by edge geometry

The prediction of force in metal cutting is essential when estimating tool wear, surface quality and energy consumption. As a significant characteristic in tool design, edge geometry results in more challenges in force modeling especially under the condition of cutting with chamfered insert. In this paper, a semi-analytical model is proposed to describe the effect of chamfered edge on cutting force considering multiple material flow state. In orthogonal cutting, shear effect is calculated based on the unequal division shear-zone model and Johnson-Cook's material constitutive law. Two kinds of chip-tool contact patterns are considered to discuss the effect of tool edge, chip flows on both chamfered edge and rake face when chamfer length is close to Uncut Chip Thickness (UCT), or chip flows only on chamfered edge when chamfer length is much larger than UCT. Edge force coefficients of chamfered edge are modeled as linear functions with respect to shear stress, chamfer length and chamfer angle. The variation of edge force with respect to edge geometry is studied through Finite Element Method (FEM) simulations. The modified force prediction model is established by introducing a factor S to describe the trend of edge effect with respect to the ratio of chamfer length to UCT. Finally, a modified force prediction model is presented and the constants in the model can be calibrated through a Particle Swarm Optimization (PSO)-based algorithm. Experiments of orthogonal cutting AISI304 with different chamfered carbide inserts are performed to validate the correctness and feasibility of the proposed model. The experimental results show that this model is effective in predicting the cutting force components under the condition of different edge preparations and cutting parameters.

Study on Machining Accuracy Simulation of Deep Die Mold Cutting

In aim to shorten lead-time of die fabrication, electrical discharge machining is being replaced with cutting. However, when cutting with tools of long extrusion length, achieving necessary accuracy becomes difficult due to chatter and machining remains. Therefore, cutting and measurement are repeated until satisfactory cutting conditions are achieved. Concerning this problem, we have developed a technique that analyzes profile error and surface roughness before machining, by simulating dynamic vibration of the tool. In the simulation, cutting force is calculated through integration of cutting force and edge force. It has been confirmed that taking in account the area where ploughing takes place due to the tool shape, takes a large role especially in deep die mold cutting. Also through the developed time domain simulation, the normal chatter free cutting conditions at around 0 degrees phase shift between the cut, was found to have large profile error. On the other hand, it has been found that at around 180 degrees phase shift, there is a condition where both chatter and profile error are suppressed, enabling high speed machining of deep die mold, without the need to repeat the same process in production, to satisfy the necessary accuracy.

A systemic investigation of tool edge geometries and cutting parameters on cutting forces in turning of Inconel 718

In metal cutting process, size effects and edge effects have a significant influence on cutting forces and therefore on the machining performance. This paper facilitates those behaviors with different cutting tool geometry, i.e., round edge and chamfered edge, using analytical cutting force prediction models when turning Inconel 718 with round cutting inserts. Analytical methods used for different edge preparation are developed with the consideration of size effects and edge effects. Then, an attempt is made to analyze the cutting investigations of the influence of size effects and edge features. The cutting forces and edge forces are estimated with the modified Johnson–Cook constitute model considering the size effects and edge effects. Rounded edge coefficients and chamfered edge coefficients estimated with different analytical methods are used in calculating edge forces for rounded edged tools and chamfered edged tools, respectively. Simulations with finite element model (FEM) and cutting experiments are used to verify the proposed model. Finally, the detailed influences of size effects, edge geometries, and feed rate on the cutting forces are studied based on the proposed model and FEM simulations.

Dynamical Theory of X-Ray Diffraction in a Crystal with a Surface Grating of Another Material

A general theory is developed for dynamical X-ray diffraction in a crystal on the surface of which a lateral periodic structure of thin-film lines (strips) of another material is formed. On the basis of the model of edge forces, the fields of elastic lattice displacements in the substrate are calculated that arise as a result of formation of a lateral surface grating (SG). With the use of the formalism of diffraction of spatially restricted X-ray beams, solutions are obtained for the amplitudes of X-ray waves reflected from a crystal with an SG whose chemical composition differs from the composition of the substrate. A numerical simulation is carried out of X-ray diffraction in a silicon substrate with SGs of tungsten and SiO2 oxide. It is shown that the angular distributions of the scattering intensity by a silicon crystal with tungsten and oxide lines of identical size differ significantly, and the physical nature of such difference is established.

Drilling force model for forced low frequency vibration assisted drilling of Ti-6Al-4V titanium alloy

Forced low frequency vibration assisted drilling (forced LFVAD) is an important machining method, in which the prediction of drilling thrust force and torque is necessary to optimize the drilling parameters. However, drilling force prediction remains a problem in forced LFVAD. This article presents a novel analytical model that predicts the drilling thrust force and torque, by incorporating the vibration amplitude and frequency correction, drill working angle, drilling forces within different cutting lip positions, and their transformation into thrust force and torque. In particular, the drilling forces investigated here include indentation force at chisel edge, chipping force, bouncing force, ploughing force in the ploughing area of the primary edge, and chipping and bouncing forces in the remaining part of the primary edge. Drill micro-displacement is also considered. Finally, the maximum, mean, and minimum values of the thrust force and torque predicted using this new model are verified as valid by performing a the drilling experiment of Ti–6Al–4V titanium alloy. The prediction error of maximum thrust force, maximum torque, mean thrust force and mean torque can reach 12%, 9%, 6.5%, and 10.1%, respectively. The effect of vibration amplitude on the cutting force at different positions along the drill lip is analyzed using the prediction model. Critical chip breaking amplitude is proposed and an optimization case of drilling parameters is presented.

Using a continuum model to decipher the mechanics of embryonic tissue spreading from time-lapse image sequences: An approximate Bayesian computation approach.

Advanced imaging techniques generate large datasets capable of describing the structure and kinematics of tissue spreading in embryonic development, wound healing, and the progression of many diseases. These datasets can be integrated with mathematical models to infer biomechanical properties of the system, typically identifying an optimal set of parameters for an individual experiment. However, these methods offer little information on the robustness of the fit and are generally ill-suited for statistical tests of multiple experiments. To overcome this limitation and enable efficient use of large datasets in a rigorous experimental design, we use the approximate Bayesian computation rejection algorithm to construct probability density distributions that estimate model parameters for a defined theoretical model and set of experimental data. Here, we demonstrate this method with a 2D Eulerian continuum mechanical model of spreading embryonic tissue. The model is tightly integrated with quantitative image analysis of different sized embryonic tissue explants spreading on extracellular matrix (ECM) and is regulated by a small set of parameters including forces on the free edge, tissue stiffness, strength of cell-ECM adhesions, and active cell shape changes. We find statistically significant trends in key parameters that vary with initial size of the explant, e.g., for larger explants cell-ECM adhesion forces are weaker and free edge forces are stronger. Furthermore, we demonstrate that estimated parameters for one explant can be used to predict the behavior of other similarly sized explants. These predictive methods can be used to guide further experiments to better understand how collective cell migration is regulated during development.

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.

3D elasticity solutions for stress field analysis of FGM circular plates subject to concentrated edge forces and couples

In this paper, the complex variable method is applied to study three-dimensional problems of transversely isotropic functionally graded circular plates subjected to concentrated edge forces and couples. To that end, the extended England–Spencer plate theory is adopted to obtain the general solutions of the governing equations in which four analytic functions $$\alpha (\zeta )$$ , $$\beta (\zeta )$$ , $$\phi (\zeta )$$ and $$\psi (\zeta )$$ are involved. The material properties can vary along the thickness direction in an arbitrary fashion. The cylindrical boundary of the plate is considered to be free which is well known as the first kind basic problem in plane elasticity. Four analytic functions can be determined by the Cauchy’s integral formula and conformal mapping technology. As a result, the 3D stress field is investigated for a transversely isotropic FGM circular plate whose cylindrical boundary is subjected to concentrated forces and couples. The proposed elasticity solutions can be used as benchmarks to validate solutions obtained based on various simplified plate theories or numerical methods.

Altering of optical and mechanical properties in high-translucent CAD-CAM resin composites during aging

ObjectivesThis study was aimed to monitor the alteration of the optical and mechanical properties of high-translucent CAD-CAM resin composites (HTRCs) during aging. Corrections for the measured transmitted irradiance are proposed. MethodsIndividual sets (n = 6) of plane-parallel test specimens (0.5-, 2- and 4-mm) of seven HTRCs were prepared. The optical properties (absorbance, transmittance, reflectance, linear absorption coefficient, and transmitted irradiance) were assessed by regular spectrometric testing methodologies and were corrected to account for light reflection. Several edge chipping resistance parameters (edge force at different edge distances, edge chip resistance), as well as mechanical parameters obtained from depth-sensing indentation (Vickers hardness, indentation modulus, creep, elastic and plastic indentation work), were considered. Aging involved storage for two weeks in artificial saliva at 37 °C, followed by thermal aging (10,000 thermocycles, 5 °C–55 °C) and storage in alcohol/water solution, employing non-aged specimens as a reference. Filler size and shape were analyzed by scanning electron microscopy. ResultsReflectance varied from 11% to 27% and was altered during aging. Linear absorption coefficients of 0.281 mm−1 to 0.369 mm−1 were obtained for non-aged specimens, with very low changes during aging. A difference between the true and measured irradiance was identified to decrease exponentially with the specimen’s thickness. The impact of HTRC was stronger than the impact of aging. ConclusionsReflectance determined by spectrometric analysis was identified as a possible criterion to estimate surface degradation during aging. Corrections for thin and translucent specimens are needed when determining transmitted irradiance through restorations. Depth-sensing indentation was evidenced as the most discriminatory testing methodology for aging, but the results do not correlate with the edge chipping resistance parameters.

Optimization of a finite element mesh for plates subjected to in-plane patch loading

In designing in-plane stressed thin plates, the loading condition where the uniform distributed edge forces are locally applied along one or more of the plate’s boundaries is often encountered. We investigated the optimal grid pattern that can be used in the analysis of the displacement and stress fields of a simply supported thin plate partially compressed. The plate modelling was created by means of an isoparametric rectangular element. This grid pattern was designed to satisfy good accuracy with low density. A convergence analysis was performed through different sets of meshes locally refined in a judicious way. For each focused field, the critical plate area was searched. Displacement and max stress values were recorded in the respective searched critical zone. Good results were obtained in seeking stress and displacement fields using, respectively, a small and a more expanded local refinement.

Effect of axial vibrations on regenerative chatter in robotic milling

The highly flexible structure of industrial robots introduces new challenges to modeling vibrations during robotic milling processes. This paper studies the contribution of the axial vibrations of the milling end-effector to regenerative chatter in robotic milling. While axial vibrations of the tool are usually neglected in standard CNC machines, in industrial robots, they may significantly affect the stability of the process. The numerical case studies in this work show that the modulation of the nominal depth of cut due to axial vibrations may cause nonlinearities in the cutting forces. In addition, it is also shown that axial vibrations may cause the feed-generated and edge forces to affect the stability of regenerative vibrations in robotic milling.

Modeling of Cutting Forces with a Serrated End Mill

The paper presents a mechanistic cutting force model of serrated end mill to predict cutting forces. Geometric model of serrated end mill is established, which covers variable helix end mill geometries. In this model, the serration of helical cutting flutes is expressed spatially and the wave of serration is defined to be a sine wave. The spatial vector is applied to define chip thickness so as to enhance the spatial expressiveness of the model, which is perpendicular to the curvature of each flute. Each helical flute is scatted into a series of infinitesimal cutting edges. The infinitesimal cutting forces depend on three cutting force coefficients and three edge force coefficients in the tangential, radial, and axial directions at every cutting element. By integrating the infinitesimal cutting forces along each cutting edge, the milling forces with serrated end mill can be predicted. The model feasibility of the serrated end mill is verified by comparing the predicted and measured cutting forces. Moreover, the model is also verified such that it can also predict cutting forces with other types of end mills, such as variable helix serrated end mill, variable helix end mill, and regular end mill.

Modeling of cutting force coefficients in cylindrical turning process based on power measurement

The cutting force is an important physical quantity in metal cutting, and the cutting force coefficients are the basis for establishing the cutting force model. In this paper, the relation between the cutting power and the cutting force coefficients is established. A cutting power model was established with a linear relationship between the spindle power and material removal rate (MRR). The power-based model of the main cutting force coefficients is proposed by extracting the linear equation coefficients of the power-MRR function. The power-based model of feed force coefficients is established as a quadratic polynomial equation between the motor power of the feed axis and feed rate. And the cutting force coefficients and the edge force coefficients of feed force are expressed respectively by the two orders of coefficients of the equation. The thrust force coefficients are indirectly calculated from the relation between tangential cutting force and thrust force with friction angle of tool-chip. The power-based models were verified by a series of cutting tests regarding material properties, cutting parameters, and axial directions. The results show that the cutting force coefficients obtained by measuring the cutting power have good correspondence with that identified by dynamometer.

Analytical Modeling and Experimental Validation of Cutting Forces Considering Edge Effects and Size Effects With Round Chamfered Ceramic Tools

The cutting force is one of the key factors for planning and optimizing the machining operation in material removal processes. An analytical cutting force prediction model that takes into consideration both edge effects and size effects based on the oblique cutting theory is developed and analyzed in this study. A detailed analysis of the cutting geometry is presented based on the coordinate system transformation and uncut chip thickness (UCT), which is evaluated on the rake plane instead of the reference plane. Then, the developed Johnson–Cook constitutive model of the workpiece that takes into consideration the size effects is then applied to the prediction of edge forces coefficients and cutting forces coefficients. The edge forces are predicted using the edge coefficients prediction model with the regularity found in the orthogonal simulations, which reflect the influences of chamfered length and chamfered angle. The developed model is validated using the turning operations of super alloys with round chamfered inserts. Finally, the effects of the cutter edge, cutting parameters, and UCT on the cutting forces are investigated using the developed model. The reasonableness and effectiveness of the proposed model is demonstrated through the comparison of the measured and predicted cutting forces for various chamfer characteristics.

Modelling time-domain vibratory deflection response of thin-walled cantilever workpieces during flank milling

While machining thin-walled workpieces, the chatter and corresponding damage to the machined surface can be avoided if that is predicted well in advance. Currently, investigations of machining vibrations mainly rely on experiments, which are costly and difficult to perform and FEM simulation methods that are many times computationally cumbersome. This work presents a mathematical model to obtain time domain forced vibration deflection response of a thin rectangular cantilever plate for any time and space varying external loads. The model is adapted for a milling process to obtain machining vibration response of a thin impeller blade by simplifying its geometry as a thin rectangular cantilever plate. The developed model was verified by checking the natural frequencies and mode shapes obtained by the model with the Finite Element simulation results for a thin cantilever plate. Peripheral milling experiments were performed to machine a thin rectangular cantilever plate of Ti-6Al-4V alloy on a vertical 3-axis CNC milling machine. Milling forces and workpiece acceleration were acquired during machining. Workpiece material properties and moving machining forces obtained by Linear Edge Force Model are input to the model. The model was validated by comparing vibratory deflection of thin cantilever plate obtained by the model and by the acquired experimental data. In general, the developed model can be used to obtain time-domain forced vibration response of thin rectangular cantilever plate workpieces.

Edge strength of CAD/CAM materials

ObjectivesTo investigate the edge force of CAD/CAM materials as a function of (a) material, (b) thickness, and (c) distance from the margin. MethodsMaterials intended for processing with CAD/CAM were investigated: eight resin composites, one resin-infiltrated ceramic, and a clinically proven lithiumdisilicate ceramic (reference). To measure edge force (that is, load to failure/crack), plates (d = 1 mm) were fixed and loaded with a Vickers diamond indenter (1 mm/min, Zwick 1446) at a distance of 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 mm from the edge. Edge force was defined as a loading force at a distance of 0.5 mm. The type of failure was determined. To investigate the influence of the thickness, all data were determined on 1-mm and 2-mm plates. To test the influence of bonding and an underlying dentin, individual 1-mm plates were bonded to a 1-mm-thick dentin-like (concerning modulus of elasticity) resin composite. ResultsFor the 1-mm plates, edge force varied between 64.4 ± 24.2 N (Shofu Block HC) and 183.2 ± 63.3 N (ceramic reference), with significant (p ≤ 0.001) differences between the materials. For the 2-mm plates, values between 129.2 ± 32.5 N (Lava Ultimate) and 230.3 ± 67.5 N (Cerasmart) were found. Statistical comparison revealed no significant differences (p > 0.109) between the materials. Brilliant Crios (p = 0.023), Enamic (p = 0.000), Shofu Blocks HC (p = 0.009), and Grandio Bloc (p = 0.002) showed significantly different edge force between the 1-mm- and 2-mm-thick plates. The failure pattern was either cracking, (severe) chipping, or fracture. ConclusionsMaterial, material thickness, and distance from the edge impact the edge force of CAD/CAM materials. Clinical significanceCAD/CAM materials should be carefully selected on the basis of their individual edge force and performance during milling.

Development and experimental validation of a mechanistic model of cutting forces in micro- ball end milling of full slots

ABSTRACTIn the present work, a mechanistic model of cutting forces is developed with a novel approach to arrive at the cutting edge geometry as well as the cutting mechanics. The geometry of cutting elements derived and verified using a virtual tool generated in CAD environment is considered. The cutting and edge force coefficients at every discrete point on the cutting edge of micro-ball end mill are established in a novel way from the basic metal cutting principles and fundamental properties of materials, considering edge radius and material strengthening effects. Further, measured edge radius is used in the model. Full slot micro-ball end milling experiments are conducted on a high-precision high-speed machining center using a 0.4 mm diameter tungsten carbide tool and cutting forces are measured using a high-sensitive piezo-electric dynamometer. It is established that the predicted as well as experimental cutting forces are higher at very low uncut chip thickness in comparison with the cutting edge radius in micro-ball end milling also. Amplitudes of cutting forces and instantaneous values with incremental rotation of the tool are compared with predicted values over two revolutions for validation of proposed model.

The role of Minkowski functionals in the thermodynamics of two-phase systems

Within this work quite old concepts from integral geometry are applied to classical equilibrium thermodynamics of two-phase systems. In addition to the area as basic interfacial quantity the full geometric characterization of the interface is used, which includes the two remaining Minkowski functionals, the mean curvature integral and the Euler Poincaré characteristic. The basic energetic characteristic of the interface (i.e. the interfacial tension) is extended by two additional properties: edge force as (up to a factor 4/π) the work necessary to form a right-angled edge of unit length, and item energy as the work to form an additional item in the phase morphology. Both quantities are of increasing importance, when going to micro- and nano-scales. They are subsequently used for interfaces of arbitrary shape to derive a relationship extending the classical Young-Laplace equation. The supplementary contribution is proportional to the Gaussian curvature, with the edge force as proportionality constant. Furthermore, both edge force and item energy are shown to be applicable to the description of crystal nucleation in liquids (extending the classical Becker Döring theory). It turns out, that even above the thermodynamic melting temperature stable nuclei can be present in the liquid phase. They immediately are able to grow when quenched to a temperature below a characteristic temperature. This temperature of spontaneous homogeneous nucleation is simply connected to the edge force, whereas the number of stable clusters per unit volume is dominated by the item energy. Finally, the additional energetic interfacial properties are used in a similar way to characterize the stability of emulsions.

An optimization methodology for material databases to improve cutting force predictions when milling martensitic stainless steel JETHETE-M152

A material database for JETHETE-M152 was developed applying a novel methodology for improving the precision of cutting forces. This approach defines a variable specific edge force depending on the feed rate and cutting edge geometry. Applying this methodology, accurate predictions could be obtained when using complex shape inserts with different micro-geometries or with feed rates lower than the cutting edge radius. These predictions showed an improvement compared to those of the strategy of keeping constant the specific edge coefficient.Furthermore, an orthogonal to oblique transformation technique was applied to predict the cutting forces in face and side milling. The results showed good agreement with experimental results.

Mechanical effects of negative pressure wound therapy on abdominal wounds - effects of different pressures and wound fillers.

The mechanical deformation of the wound edge resulting from negative pressure wound therapy (NPWT) at the standard setting of around -120 mmHg has positive effects in promoting wound healing. However, it may cause pain to the patient during treatment. It is therefore important to study the mechanical effects of the wound edges using lower pressure and different wound fillers. Abdominal wounds were created on eight pigs. The wounds were sealed for NPWT using foam or gauze. Negative pressures between -20 and -160 mmHg were applied, and the decrease in wound diameter and the force with which the edges of the wound were drawn together (wound edge force) were measured. Increasing levels of negative pressure resulted in a gradual decrease in wound diameter and increase in wound edge force and reached a maximum at -120 mmHg, which is the pressure commonly used in clinical practice. Both the decrease in wound diameter and the increase in wound edge force was greater with foam than with gauze. A pressure of -80 mmHg has only 15% less effect than -120 mmHg, while a lower pressure (-40 mmHg) diminished the effects on diameter and force markedly. The NPWT-induced decrease in wound diameter and increase in wound edge force are greater at higher levels of negative pressure and when using foam than when using gauze as a wound filler. It may be possible to tailor the type of wound filler and level of negative pressure to obtain the best balance between wound healing and patient comfort.