The mechanics of chip formation involves a complex interplay between surface plastic flow, material microstructure and tool-chip interface dynamics. At the continuum scale, this process has often been approximated as being one of pure shear along a very narrow zone — the shear plane. The primary assumption behind this approximation is that of steady or time-independent plastic flow. This approximation addresses the exception rather than the rule, since most metal cutting processes involve unsteady time-dependent plastic flows. In this work, we attempt to develop parallels with an analogous problem in fluid mechanics — flow past a rigid fixed body — to quantify the unsteady nature of plastic flow. Here the role of the body is played by the tool, and the flow field corresponds to the plastically deforming material. The prerequisite for fully exploiting this kinematic analogy is full-field material flow measurements. This is provided by digital image correlation (DIC), a family of techniques that use in situ imaging of the cutting process to obtain instantaneous full-field material displacements. Given this kinematic flow information, we show how one can describe the cutting process more accurately using the fluid flow analogy, and without having to resort to specific preconceived models. For steady flows, the analogy is more than merely cosmetic — the pathlines, streamlines and streaklines, all determined kinematically, coincide exactly. The analogy also allows consideration of time-dependent unsteady plastic flows that are usually beyond the purview of theoretical analyses. One can, for instance, ask the question of whether the transition from steady to unsteady plastic flow observed in metal cutting can be described by a dimensionless parameter, analogous to the Reynolds number for fluids. We show that in the case of unsteady flows, the actual deformation field is far removed from that described by conventional shear plane or slip line field models. Now the streaklines develop undulations or folds for the same boundary conditions as for the steady case (cutting velocity, depth of cut). Of the three flow lines, we attempt to extract information from streaklines, since they contain information about both spatial and temporal gradient. We present analyses of these streakline curvature features using simple geometric techniques that reflect both the spatial and temporal flow evolution. Our results shed light on the importance of considering unsteady flows in chip formation and machining. Borrowing ideas from fluids to describe these flows appears to hold significant promise for quantifying unsteady flows and their consequences for practical machining operations.

Grinding swarf is conventionally of secondary interest to the process engineer. However, it has long been recognized that it is a useful indicator of process performance — the exact particle morphologies occurring in the swarf contain a wealth of information about the abrasive-workpiece interaction mechanics. In this work, we study the generation of perfectly spherical particles when grinding two plain carbon steels and a grade of stainless steel with an alumina wheel. Similar particles have also been reported in the wear community and several possible formation mechanisms have been discussed including chip curl resulting from electronic charge distributions; melting due to local flash temperatures in the grinding zone; and repeated abrasive wear of the workpiece surface. We postulate that the particles are likely formed as a result of an oxidation-melting-solidification route with small grinding chips. We present spectroscopy and X-ray diffraction data in support of this hypothesis — significant oxygen content, in the form of Fe 3 O 4 was detected on the surface of the spheres. Electron micrographs also show remarkably robust dendrite-like structures on the surface of the particles, indicative of rapid solidification from the melt. Motivated by these results, we present model calculations to support our hypothesis. We first evaluate the initial temperature of chips exiting the grinding zone using a three-way heat partition model for dry grinding. An upper bound for the chip temperature is ∼ 600°C, well-below the melting point for the metal. Next, we show that the oxidation kinetics at this elevated temperature are such that the formation of a thin oxide layer (∼ 2 μ m) on the surface of an initially curled up chip, with size ∼ 50 μ m comparable to the observed spheres, is enough to melt the entire chip on a timescale of 10 −6 seconds. Surface tension then brings the molten chip into a perfectly spherical shape, followed by rapid solidification. We present a preliminary calculation of this solidification process, using a coupled heat conduction model along with a moving interphase interface. By making suitable approximations, we derive an ordinary differential equation describing the temporal evolution of the interface location. Coupling the interface velocity with a Mullins-Sekerka type instability analysis, we argue that solidification of these drops likely starts from a nucleated core in the drop interior, resulting in dendrite-type patterns on the outer surface. Our work is a preliminary attempt to put decades old observations of grinding swarf on a firm quantitative footing. The experimental evidence and related analysis presented here make a strong case for the oxidation-melting-solidification hypothesis for the formation of spherical particles in grinding swarf.

Brushes consist of a body with fixed highly flexible filaments and can be used for deburring and surface finishing operations. During the brushing process, axial and tangential deflections of the highly flexible filaments lead to an adaptation to the shape of the workpiece and interaction between the filaments. The described complex contact behavior has been insufficiently investigated so far. For a better understanding of the contact between a brush and the workpiece surface, this paper presents a model based on physical principles. The model describes the dynamic behavior of a brush in contact with different workpiece geometries and consists of separate physical descriptions for the filaments of the brush, the workpiece surface and the occurring contacts. A description of a single filament is given by a multi-body system of rigid links. The rigid links are connected by joints which approximate the material behavior of the filaments. To approximate different geometries, the workpiece surface is specified by a polynomial. Contact can occur between the filaments and the workpiece surface as well as between the filaments. For the description of the occurring contacts, Hertz’s theory of elastic contact and Coulomb’s law of friction are used. The aforementioned physical descriptions are included in the Lagrange’s equations to obtain a system of equations of motion that calculates the deflection of the filaments of the brush and the acting forces during the contact with the workpiece surface. A numerical solution to the system of equations of motion was calculated by using experimentally determined material and contact properties of the filament. A comparison of the calculated forces with experimentally determined values shows good correlations for different workpiece surfaces and process parameters. In this context, the developed model calculates the progression and the maximum value of the acting contact forces. The results show a shorter contact length of the filament l c for a circular surface compared to a plane surface, and a rise of the maximum normal force F n with the depth of cut a e . Furthermore, consideration of the filament interactions leads to a more accurate approximation of the brush-workpiece contact. Based on the findings, the developed model can be used to calculate predictions for different brushing processes which reduce the number of time-consuming preliminary tests for the process design.

Chatter identification is necessary in order to achieve stable machining conditions. However, the linear approximation in regenerative chatter vibration is problematic because of the rich nonlinear characteristics in machining. In this study, a novel method to detect chatter is proposed. Firstly, measured cutting force signals are decomposed into a set of intrinsic mode functions by using ensemble empirical mode decomposition. Hilbert transform is following to extract the instantaneous frequency. Fast Fourier transform is also utilized for each intrinsic mode function to determine the intrinsic mode function that contains rich chatter. Finally, the standard deviation and energy ratio in frequency domain of intrinsic mode functions are found as simply dimensionless chatter indicators. The effectively proposed approach is validated by analyzing the machined surface topography and also compared to the stability lobe diagram.

A limitation frequently encountered in additive manufacturing (AM) models is a lack of indication about their precision and accuracy. Often overlooked, information on model uncertainty is required for validation of AM models, qualification of AM-produced parts, and uncertainty management. This paper presents a discussion on the origin and propagation of uncertainty in Laser Powder Bed Fusion (L-PBF) models. Four sources of uncertainty are identified: modeling assumptions, unknown simulation parameters, numerical approximations, and measurement error in calibration data. Techniques to quantify uncertainty in each source are presented briefly, along with estimation algorithms to diminish prediction uncertainty with the incorporation of online measurements. The methods are illustrated with a case study based on a transient, stochastic thermal model designed for melt pool width predictions. Model uncertainty is quantified for single track experiments and the effect of online estimation in overhanging structures is studied via simulation. The application of these concepts to estimation and control of the L-PBF process is suggested.

Percutaneous medical procedures rely upon clinicians performing precise needle insertion in soft tissue. The utility of haptic simulation systems in training clinicians for these procedures is highly dependent upon the ability to render accurate insertion force feedback. This paper presents a piecewise mathematical model for insertion force that does not require tissue material properties, detailed mechanical approximations, or complex computations. With manipulation of model parameters, a wide variety of insertion tasks and clinical scenarios can be modeled. Through needle insertion experiments and parameter estimation, this model was demonstrated to replicate the insertion forces associated with a variety of needle and tissue types. In 11 of 12 needle and tissue combinations tested, the model replicated the insertion force with an average absolute mean error of less than 0.065 N.

It was proposed to estimate the accuracy of the hydro-cylinder cross-section shapes basing on the analysis of the circle diagram of their inner cylindrical surfaces, formed by the manufacturing operations, such as rough and semi-finishing boring and finishing paying-out, taking advantage of the method of deflection approximation from the circle by the Fourier’s trigonometric series in the gap [0, 2 π ]. Characteristics of the deflection dispersion of the radius-vector as the random value (average value, dispersion, amplitude spectrum) have been obtained for every circle diagram separately. It is proposed to present these characteristics as random values. Dependences for finding mathematic expectation and dispersion for the lot of parts, machined at every of the available manufacturing operation, have been obtained for certain number of samples and circle diagrams, taking advantage of the small sampling theory, the method of rectangular engagement in particular. The effectiveness of manufacturing operations has been estimated according to the Student and Fisher t-test. Availability of the advantageous or disadvantageous manufacturing heredity of the hydrocylinder cross-section shape has been found. As the result of carried out experimental investigations and processing of the obtained statistic data on the inner cylindrical surface of the truck hoist crane hydrocylinder KTA-25, produced by the company “Drogobych truck crane plant” (Ukraine), the need to improve the manufacturing operation of the semi-finishing boring has been analysed.

Unexpected disruptive events always interrupt normal production condition and cause production losses in the manufacturing system. A resilient system is capable of settling itself to the steady-state quickly after the disruption, and compensating for the lost production by using a relatively little overtime. In this paper, we define throughput settling time (TST) and overtime to recover (OTTR) as two resilience measures to analyze multi-stage serial-parallel systems with unreliable machines and finite intermediate buffers. We perform an exact analysis for a two-stage system and develop an approximation method for general multi-stage systems. Numerical case studies are conducted to investigate the system resilience under different configurations.

In this paper, the authors present a platform for the modeling of mold filling and solidification of binary alloys with properties similar to Mg alloys. A volume-of-fluid (VOF) based method is used to capture the interface between solid and liquid in binary alloys solidification process on a fixed non-uniform grid, developed for implementation in a colocated finite volume framework. Contrary to other works, to update the volume fraction (of fluid) in the field, a link between source-based type of energy equation and VOF reconstruction algorithm is described and implemented. A new approximation to the pressure gradient is presented to remove all ‘Spurious Currents’ [1] resulting from pressure jumps in the vicinity of the interface. Based upon the work presented, it is concluded that the present combination of the equations are not only computationally straightforward to implement and upgrade to a 3D problem, but also provides an excellent platform to capture the interface between constituents in a die-casting process including solidification and mold filling process. The current framework will be used in future works to characterize the local mechanical properties of Mg alloys by using information from simulation at the dendritic level.

Laser hardening is a laser assisted process devoted to the surface hardening of the mechanical components. This process is highly suitable for medium carbon steels with carbon content comprised between 0.2 – 0.6% or for low alloy steels which are usually surface hardened during their manufacturing process. Laser hardening technology is gaining a great industrial interest in the last years in fact, the possibility of integrating the heating source directly on the production line, together with the absence of the quenching medium, meets the production needs of modern industries. Laser hardening optimization could be complex especially when tempering due to multiple passes effects must be considered. Many research studies have been proposed in the last years aimed at predicting the optimal laser process parameters such as beam power density, beam velocity and scanning strategies. Many Authors agree with the assumption that the whole austenite resulting from the heating is transformed into martensite during the quenching. This is a valid approximation for single pass but could be a rough hypothesis in multiple-passes when the cooling rate could be not so high. Moreover hysteresis phenomena, due to the severe heat cycle occurring in laser hardening, should be taken into account for pearlite to austenite and martensite to austenite transformations during heating and for martensite tempering during multiple passes. In this paper the crucial problems to be faced regarding laser surface hardening modeling are discussed with respect to current literature. In particular, partial austenitization of the pearlite is suggested as a solution of the hardness prediction of the profile depth. Then three transformation parameters are proposed in order to take into account the hysteresis phenomena in martensite and pearlite transformations into austenite and in martensite tempering. Finally several experimental examples are proposed in order to validate the mentioned assumptions.

Even though many models for machining exist, most of them are for low-speed machining, where momentum is negligible and material behavior is well approximated by quasi-static plastic constitutive laws. In machining at high speeds, momentum can be important and the strain rate can be exceedingly high. For these reasons, a fluid mechanics approach to understanding high-speed, very high-speed, and ultra-high-speed machining is attempted here. Namely, a potential flow solution is used to model the behavior of the material around a sharp tool tip during machining at high speeds. It is carefully argued that the potential flow solution is relevant and can be used as a first approximation to model the behavior of a metal during high-speed, very high-speed, or ultra-high-speed machining events; and at a minimum, the potential flow solution is qualitatively useful in understanding mechanics of machining at high speeds and above. Interestingly, the flow solution predicts that there is a stagnation point on the rake face, not at the tool tip as is usually assumed. Because the stagnation point is not at the tool tip, the flow solution predicts a significant amount of deformation in the workpiece resulting in large residual strains that may lead to a temperature rise on the finished surface.

Tolerance synthesis for complex assemblies is formulated as a probabilistic optimization problem. A main challenge in statistical tolerance synthesis for complex assembly system design is the computation intensity in estimating the conformity probability of Key Product Characteristics (KPCs) or yield of assembled products. In assemblies with multiple KPCs, the yield can only be obtained numerically through simulation techniques such as Monte Carlo (MC) algorithm. The existing tolerance synthesis methods require a large number of yield assessments in optimization. A new approach is developed for yield model approximation based on computer experiment, multivariate distribution transformation (MDT) and regression analysis. An explicit yield function can thus be approximated. Therefore, the widely used gradient-based approaches (such as Sequential Quadratic Programming) can be applied and the intensive computation in direct optimization can be avoided. An industrial case study is presented to illustrate and validate the proposed methodology and compared with the existed tolerance synthesis methods.

Extensive research on G 1 biarcs fitting to free-form curves (i.e., Bezier, B-spline, and NURBS curves) has been conducted in the past decades for various purposes, including CNC contouring to make smooth, accurate profile features such as pockets, islands, and sides. However, all the proposed approaches only focused on the approximation errors and the biarc number, not on the radius of the individual fitting arc; so it could be smaller than the cutting tool, which would cause gouging during machining. This work, based on the tool radius pre-determined by the minimum size of the concavities of the design profile, proposes a new approach to approximating the profile with a G 1 biarc curve in order to make smooth, accurate, and non-gouged profile features using CNC contouring. The significant new contribution of this work is a new mechanism that ensures all the concave arcs of the fitting curve are larger than the pre-determined tool and the fitting errors meet the specified tolerance. This approach can promote the use of G 1 biarc tool paths in the manufacturing industry to make high precision profile features.