A universal slip-line model with non-unique solutions for machining with curled chip formation and a restricted contact tool

A universal slip-line model and the corresponding hodograph for two-dimensional machining which can account for chip curl and chip back-flow when machining with a restricted contact tool are presented in this paper. Six major slip-line models previously developed for machining are briefly reviewed. It is shown that all the six models are special cases of the universal slip-line model presented in this paper. Dewhurst and Collins's matrix technique for numerically solving slip-line problems is employed in the mathematical modeling of the universal slip-line field. A key equation is given to determine the shape of the initial slip-line. A non-unique solution for machining processes when using restricted contact tools is obtained. The influence of four major input parameters, i.e. (a) hydrostatic pressure (P_A) at a point on the intersection line of the shear plane and the work surface to be machined; (b) ratio of the frictional shear stress on the tool rake face to the material shear yield stress (τ/k); (c) ratio of the undeformed chip thickness to the length of the tool land (t₁/h); and (d) tool primary rake angle (γ₁), upon five major output parameters, i.e. (a) four slip-line field angles (θ, η₁, η₂, ψ); (b) non-dimensionalized cutting forces (F_c/kt₁w and F_t/kt₁w); (c) chip thickness (t₂); (d) chip up-curl radius (R_u); and (e) chip back-flow angle (η_b), is theoretically established. The issue of the “built-up-edge” produced under certain conditions in machining processes is also studied. It is hoped that the research work of this paper will help in the understanding of the nature and the basic characteristics of machining processes.     

A rate-dependent model for hot-rolling

A rate-dependent model for the plane-strain sheet-rolling problem is proposed. The governing equations are solved using an asymptotic scheme that assumes that the ratio δ of thickness of the sheet material at the entry to the roll-bite length is small. Both the relative-slip and no-slip sheet-roll interface conditions are considered. Depending on the magnitude of the friction, different regimes that correspond to different levels of shear deformation have been identified and asymptotic solutions are provided for each of these regimes. The effect of the reduction, the strain-rate hardening parameter and the magnitude of the friction on the field variables and the roll-speed is also studied. Further, it is shown that in the limit as the strain-rate hardening index n → ∞, the asymptotic solutions for the rate-dependent model are shown to approach those predicted by rigid perfectly-plastic theory. The theoretical predictions are compared with experimental results for a commercial purity aluminum. The comparisons indicate a reasonable agreement between theory and experiment.     

Welding wave on the contact spot of solids

In this paper the theoretical model of adhesion between clean solid surfaces is presented. Material behaviour is described by hydrodynamic equations for viscous liquid and by the Gruneisen equation of state. This approach is quite suitable for quantitative analysis of mechanical processes running under high pressures. The model states that growth of a bonded area can occur in a regime of self-propagating welding wave (WW). WW originates at any active point where initial bonding takes place and further moves at velocity U_wwγ/η (γ is surface energy and η is viscosity of material). According to the model presented surface energy plays the key role in adhesion.     

decentralized observation and control of nonlinear interconnected systems

In this paper, we investigate the problem of H_∞ decentralized tracking control design with a decentralized observer for interconnected nonlinear systems which are characterized by the interconnection of N subsystems. Each subsystem is modeled by a linear constant part perturbed by an additive nonlinearity which is illustrated by the interconnection terms.The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each subsystem, to maximize the nonlinearity domain, and to improve the performance of the model reference tracking control by using the H_∞ criterion despite the external disturbances.The proposed control approach is formulated in a minimization problem and derived in terms of linear matrix inequalities (LMIs) whose resolution yields the decentralized control and observation gain matrices.The effectiveness of the proposed control scheme is demonstrated through numerical simulations on a power system with three interconnected machines.     

The stability of a vertical cut

Coulomb's problem of the depth to which a trench can be dug in cohesive soil without the sides falling in is investigated. In the present paper the soil is assumed to be perfectly plastic with yield stress c in shear and unit weight γ; internal friction is ignored. Thus the problem will be treated as one of plane strain with the maximum shear stress criterion of failure. Coulomb's own expression for the depth of cut was the upper-bound value 4c/γ (actually 4(c/γ) cot ς, allowing for internal friction, where and ø is the angle of friction). The best upper bound in the literature is 3·83c/γ, given by a slip-circle analysis; the highest lower bound seems to be 2c/γ. Simple distributions of stress which satisfy both equilibrium and the yield condition for the whole field are shown to give a lower bound of 2√2(c/γ). A partial solution is established for 3·2c/γ.     

Inverse approach for estimating rheological characteristics of adsorption layer in thin film EHL contacts

A modified Reynolds equation is derived for thin film elastohydrodynamic lubrication (TFEHL) by means of the viscous adsorption theory. This TFEHL theory can be used to explain the deviation between the measured film thickness and that predicted from the convenient elastohydrodynamic lubrication (EHL) theory under very thin film conditions. Results show that the thinner the film, the greater the ratio of the adsorption layer to the total film thickness becomes, and the greater the value of the pressure–viscosity index (z′). An inverse approach is proposed to estimate the pressure distribution based upon the film thickness measurement and to determine the pressure–viscosity index of oil film, and the thickness (δ) and the viscosity ratio (η^*) of the adsorption layer in TFEHL circular contacts. Based on TFEHL theory, the inverse approach can reduce z′ error, and provides a reasonably smooth curve of pressure profile by implementing the measurement error in the film thickness. This algorithm not only estimates the pressure, but also calibrates the film shape. Consequently, it predicts z′, η^*, and δ with very good accuracy. It can also be used to evaluate the lubrication performance from a film thickness map obtained from an optical EHL tester. Results show that the estimated value of z′ is in very good agreement with the experimental data.     

A new method for determining the mechanical stability of lubricating greases

Mechanical stability is of central importance when dealing with the long-term service-length of grease-lubricated roller bearings. Poor stability will lead to consistency degradation of the grease, because of mechanical forces between the rolling parts of the bearing. The result can be leakage of grease through seals, or at worst a total failure of the bearing. The present investigation was initiated because present-day methods for prediction of mechanical stability show weak correlation with real service-length. The aim of the project was to develop a useful alternative. In order to fulfil this, both field tests and laboratory tests were carried out. In the field tests, nine different commercial greases were examined in the wheel bearings of five ore waggons, used for transporting ore by railroad from the Kiruna Mine in northern Sweden to Narvik in northern Norway for shipping to foreign markets. The test ore waggons travelled a distance of about 300,000 km during a period of 3 years. Small samples of greases were taken, on eight different occasions, for consistency testing. After the end of the test period, the damage on the bearings was also studied. In the laboratory tests, new undestroyed greases of the same brand as in the field tests were examined using conventional methods, such as the V2F, the Roll Stability Test and the Grease Worker. Comparisons between the field tests and these laboratory tests indicate poor correlation. In addition to these conventional methods, the relevance of the shear strength of the greases to the prediction of the mechanical stability was also tested. The shear stress τ_L depends on the applied pressure p, thus τ_L=τ₀+γ·p where τ₀ is the shear stress at atmospheric pressure. γ is a property of the lubricant in the same way as viscosity or density. It was found that γ correlates well with the mechanical stability in service. Increased γ values lead to a decrease in the mechanical stability. One reasonable explanation is that high γ values correspond to high shear stresses in the grease, and thus severe conditions for the thickener.     

Frictionally excited thermoelastic instability in viscoelastic and poroelastic media

Friction materials commonly used in sliding applications, such as clutches and brakes, can be poroelastic and exhibit a viscoelastic behaviour. To the author's knowledge, there are no comprehensive analysis of the influence of poroelastic and viscoelastic material properties on the onset of the phenomenon of frictionally excited thermoelastic instability in sliding systems. This issue is here analysed in some details. Firstly, a linear standard model for the friction material is adopted, introducing an effective complex dynamic modulus E=|E|e^jδ and individuating three independent parameters, E₁, E₂/E₁ and c₂/E₁, that fully describe its viscoelastic behaviour. Subsequently, a similarity between viscoelastic and poroelastic formulation is presented and the three independent parameters introduced are related to the viscosity of the fluid μ_f, the permeability k_p and elastic properties M, α_B of the porous material.The linear elastic formulation proposed by Decuzzi et al. (ASME J. Tribiol. 2001;123:865) has been modified in order to take account of the new constitutive model and the variation of the critical sliding speed with the wave parameter, and viscoelastic/poroelastic properties of the material are examined.It has been found that the susceptibility towards thermoelastic instability increases by increasing both the elastic E₂/E₁ and viscoelastic c₂/E₁ parameters, or by increasing the Biot modulus M and effective stress coefficient α_B, the viscosity μ_f of the fluid, and by reducing the permeability k_p of the porous skeleton. It has been shown that for porous friction materials employed in wet clutches which are weakly viscoelastic, the neglect of its poroelastic behaviour leads to an overestimation of the critical speed smaller than 10%. However, much larger variations are predicted for elastomeric and porous materials with more pronounced viscoelastic behaviour.     

Predictive model to estimate the stress–strain curves of bulk metals using nanoindentation

Many studies have shown that finite element modeling (FEM) can be used to fit experimental load–displacement data from nanoindentation tests. Most of the experimental data are obtained with sharp indenters. Compared to the spherical case, sharp tips do not directly allow the behavior of tested materials to be deduced because these produce a nominally-constant plastic strain impression. The aim of this work is to construct with FEM an equivalent stress–strain response of a material from a nanoindentation test, done with a pyramidal indenter. The procedure is based on two equations which link the parameters extracted from the experimental load–displacement curve with material parameters, such as Young's modulus E, yield stress Y₀ and tangent modulus E_T. We have already tested successfully the relations on well-known pure metallic surfaces. However, the load–displacement curve obtained using conical or pyramidal indenters cannot uniquely determine the stress–strain relationship of the indented material. The non-uniqueness of the solution is due to the existence of a characteristic point (ε_c, σ_c); for a given elastic modulus, all bilinear stress–strain curves that exhibit the same true stress σ_c at the specific true strain ε_C lead to the same loading and unloading indentation curve. We show that the true strain ε_c is constant for all tested materials (Fe, Zn, Cu, Ni), with an average value of 4.7% for a conical indenter with a half-included angle θ=70.3°. The ratio σ_c/ε_c is directly related to the elastic modulus of the indented material and the tip geometry.     

Onset of matrix cracking in angle-ply ceramic matrix composites

The problem of initial damage in angle-ply [−θ_m/0_n/θ_m] and [−θ/θ] ceramic matrix composites subjected to axial tension is considered in this paper. The damage is in the form of matrix cracks that may appear in either inclined (−θ and θ lamination angle) or longitudinal layers. As follows from the analysis, if the lamination angle of the inclined layers is small, the initial failure occurs in the 0-layers of [−θ_m/0_n/θ_m] composites or in [−θ/θ] composites in the form of bridging cracks. However, if the inclined layers form a larger angle with the load direction, they fail due to tunneling cracks. It is shown that the boundary between two different modes of failure in a representative SiC/CAS composite corresponds to a lamination angle equal to 35° in the case of [−θ_m/0_n/θ_m] composites. In the case of [−θ/θ] laminates, the boundary value of the lamination angle is equal to 45°, i.e. bridging cracks form if θ<45° and tunneling cracks appear if θ>45°.     

A new methodology for determining the stress state of the plastic region in machining with restricted contact tools

In rigid-plastic slip-line theory, once the geometry of the slip-line field is established, the stress state of the plastic region (including the primary and secondary deformation zones) in restricted contact machining is governed by the hydrostatic pressure P_A (at a point on the intersection line of the shear plane and the work surface to be machined) and the frictional shear stress τ on the tool rake face. Based on the recently established universal slip-line model and a detailed study of six representative machining cases, a new methodology for determining the stress state of the plastic region, i.e. maximum value principle, is presented in this paper. According to this principle, the stress state of the plastic region can be determined by giving both P_A and τ their theoretical maximum permissible values. The theoretical maximum permissible values of P_A and τ can be found by satisfying four mechanical and geometrical constraint conditions under which the universal slip-line model applies. A comprehensive assessment factor is introduced in this paper. It is shown that the three machining parameters investigated in this present study, i.e. cutting force ratio, chip thickness ratio, and chip back-flow angle can be simultaneously considered to form a comprehensive criterion to compare predicted and experimental results. The applicable range of the maximum value principle is also discussed.     

Identification of yield stress and plastic hardening parameters from a spherical indentation test

Assuming plastic hardening of metals are specified by the stress–strain curve in the form , the material parameters σ₀, k and m are identified from spherical indentation tests by measuring compliance moduli in loading and unloading of the load–penetration curve. The curve P(h_p) is analytically described by a two term expression, each with different exponents. Here, ε_p and h_p denote the plastic strain and permanent penetration. The proposed identification method is illustrated by specific examples including numerical and physical identification tests.     

Theoretical method for estimation of mean pressure on contact area between rolling tools and workpiece in cross wedge rolling processes

The paper gives a new method no determine the mean unit contact pressures on a material—tool contact surface in cross wedge rolling processes (CWR). The dependencies worked out on the basis of the energy and the upper bound methods permits rolling forces to be determined which are comparable to experimentally measured ones. The analysis provides equations which relate the mean contact pressure q_m to the basic process parameters, namely the forming angle α, the spreading angle β, the relative reduction of a portion δ and the shear friction factors m and m_k.     

Strengthening caused by power law creep deformation of dispersed particles in an elastic matrix

The interaction energy is approximated between an edge dislocation and a particle deformable by power law creep in an elastic matrix. The stress required to overcome the interaction energy barrier is found to be greater than the Orowan stress, and the dislocation bulges to escape the particle. If the ratio of the shear modulus of the matrix to the viscosity of the particle (μt^m/σ₀) is large, the stress required to climb over the particle is larger than the Orowan stress and the dilocation bulges before it climbs. It is concluded that even if the particle is soft enough to exhibit creep, the strengthening of alloys can be achieved by an Orowan mechanism. The critical resolved shear stress (CRSS) of Cu-B₂O₃, obtained experimentally by Onaka et al. [11], agrees closely with that obtained in our analysis. This supports our analysis that the strength of Cu-B₂O₃ alloy at high temperature may be accounted for by the Orowan mechanism and the attraction between a dislocation and viscous particles. The energy and the force to overcome the energy barrier increases significantly with decrease of m, the strain rate exponent associated with the power law creep particle. It is found through analysis that for m < 1.0 and for certain values of μt^m/σ₀ > 1, the particle repulses the dislocation, while for m = 1.0 and for all values of μt^m/σ₀ > 1, the particle attracts the dislocation, which is the expected interaction between an elastic particle and a dislocation in an elastic matrix.     

A dual-purpose positioner-fixture for precision six-axis positioning and precision fixturing: Part II. Characterization and calibration

The kinematics, stiffness, and repeatability of a moving groove, dual-purpose positioner-fixture were determined experimentally. A dual-purpose positioner-fixture is an alignment device that may be operated in a fixture mode or a six-axis nanopositioning mode. When operated in fixture mode, experiments show standard deviation in repeatability of 11, 11, and 38 nm in x, y, and z; and 0.7, 0.3, and 0.3 μrad in θ_x, θ_y, and θ_z. The stiffness characteristics were shown to match predictions within 5%. When operated in nanopositioner mode, the device demonstrated 4 nm resolution and a range, of 40 μm × 40 μm × 80 μm in translation and 800 μrad × 800 μrad × 400 μrad in rotation. The fixture possesses a load capacity of 450 N and a natural frequency of 200 Hz when the fixture is preloaded to 225 N.     

Tribological characterization of environmentally adapted ester based fluids

Fundamental properties of six synthetic ester base fluids, suitable for the formulation of environmentally adapted lubricants, have been investigated. High pressure viscosity data for the test fluids were obtained through experimental measurements with a high pressure Couette rheometer. The temperature, pressure and viscosity data η(p, T) were parameterized against the Roelands pressure–viscosity equation. Thermal conductivity and specific heat capacity data were obtained using a transient hotwire method, and the EHD friction coefficient, γ, was obtained experimentally as well. The results from these measurements are reported, and the correlation between thermal properties, molecular structure, and the fluid rheology parameters, of the test fluids are discussed.     

Pressure-dependence of dielectric relaxation time in poly(propylene glycol) and its application to high-pressure viscosity estimation

Dielectric permittivity and loss of poly(propylene glycol) with different molecular weights (400–3000) and terminal groups (OH and CH₃) have been measured in the frequency range of 100 Hz to 1.5 MHz. Measurements were conducted over the temperature range 202–293 K under atmospheric pressure and 283–320 K under pressure up to 600 MPa. Two relaxation processes, one with strong absorption in the high-frequency region (α-relaxation) and the other a weak process in the low-frequency region (α′-relaxation), were observed for the OH-terminated samples having molecular weights above 2000 and for all the CH₃-terminated samples. Most of the experimental data under high pressure showed a nonlinear decrease in the logarithm of the frequency of maximum dielectric loss with increasing pressure. The pressure-dependence of the dielectric relaxation time of the α-process was analyzed by several models based on the free-volume concept. The regression results of dielectric relaxation time as a function of pressure were applied to the estimation of high-pressure viscosity. The predicted viscosity showed relatively good agreement with viscosity data obtained from a falling-sphere viscometer.     

Plastic flow localization in mechanism-based strain gradient plasticity

The theory of mechanism-based strain gradient (MSG) plasticity is used to study plastic flow localization in ductile materials. Unlike classical plasticity, the thickness of the shear band in MSG plasticity can be determined analytically from a bifurcation analysis, and the shear band thickness is directly proportional to the intrinsic material length, (μ/σ_Y)²b associated with strain gradients, where μ is the shear modulus, σ_Y is the yield stress, and b is the Burgers vector. The shear band thickness also depends on the softening behavior of the material. The analytical solution of the shear strain rate yields that the maximum shear strain rate inside the shear band is two orders of magnitude higher than that outside, which is a clear indication of plastic flow localization. The limitation of the present model is also discussed.     

Non-newtonian thermal analysis of an EHD contact lubricated with MIL-L-23699 oil

A thermal and non-Newtonian fluid model under elastohydrodynamic lubrication conditions is proposed, integrating some particularities, such as the separation between hydrodynamic and dissipative phenomena inside the contact. The concept of apparent viscosity is used to introduce the non-Newtonian behaviour of the lubricant and the thermal behaviour of the contact into the Reynolds equation, acting as a link element between the hydrodynamic and dissipative components of the EHD film, independently of the rheological and thermal models considered. The apparent viscosity enables the application of the rheological model better adapted to each lubricant, without appealing to special formulations of the EHD problem.The Newton–Raphson technique is used to obtain the lubricant film geometry and the pressure distribution inside the EHD contact. The shear stresses developed in the fluid film are evaluated assuming the non-linear Maxwell rheological model. The surfaces and lubricant temperature distributions are determined using the simplified Houpert's method, applied to the inlet contact zone, and the thermal method proposed by Tevaarwerk is applied in the high pressure contact zone.The non-Newtonian thermal EHD model is applied to the analysis of a contact lubricated with MIL-L-23699 oil. Significant results are obtained for the centre and minimum film thickness, for the inlet shear heating and film thickness reduction factor (φ_T), for the temperature rise of the lubricant and of the surfaces and for the friction coefficient inside the contact, considering wide ranges of the operating conditions (maximum Hertzian pressure, inlet oil temperature, rolling speed and slide-to-roll ratio).Finally, the numerical traction curves determined are compared with the corresponding experimental results, showing very good correlation.     

Twin shear stress yield criterion

A twin shear stress yield criterion is described. This criterion was proposed by the author in 1961[1]. It assumes that yielding begins when the sum of the two larger principal shear stresses reaches a magnitude C. Thus the initial yield function is f = τ₁₃ + τ₁₂ = σ₁ − 1/2(σ₂ + σ₃) = c[(τ₁₃ + τ₁₂) ± c][τ₂₃ + τ₂₁) ± c][τ₃₁ + τ₃₂) ± c] = 0.