Thermal Analysis of Metal Flow at the Chip-Tool Interface in Metal Cutting

1967 ◽  
Vol 89 (3) ◽  
pp. 539-542 ◽  
Author(s):  
R. F. Scrutton
Keyword(s):  
Thermal Analysis ◽  
Shear Stress ◽  
Equation Of State ◽  
Boundary Layers ◽  
Metal Cutting ◽  
Metal Flow ◽  
Plastic Layer ◽  
Mechanical Equation ◽  
Thin Plastic ◽  
Viscous Boundary

The plastic flow of metal adjacent to the chip-tool interface is analyzed using a mechanical equation of state, which relates the variables stress, strain, strain rate, and temperature. Expressions are derived for the temperature at points within the thin plastic layer. The assumptions, which are similar to those used in the theory of viscous boundary layers, include the hypothesis that the shear stress is constant throughout the layer.

The Plastic Flow of Surface Metal Layers

1971 ◽  
Vol 38 (4) ◽  
pp. 861-864
Author(s):  
J. H. L. The´ ◽  
R. F. Scrutton
Keyword(s):  
Plastic Deformation ◽  
Plastic Flow ◽  
Thermal Conduction ◽  
Metal Cutting ◽  
Plastic Layer ◽  
Approximate Analysis ◽  
Cold Surface ◽  
Surface Metal ◽  
Thin Plastic ◽  
Metal Layers

Various aspects of the plastic deformation of metals adjacent to the surfaces of tools or dies are discussed. The influence of thermal conduction between the thin plastic layer and the hot or cold surface of the tool or die is considered, while an approximate analysis is presented of the variation in the overall thickness of the layer at the chip-tool interface in metal cutting.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 2—Fluctuation Quantities

1996 ◽  
Vol 118 (4) ◽  
pp. 728-736 ◽  
Author(s):  
S. P. Mislevy ◽  
T. Wang
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Transition Region ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Turbulent Shear ◽  
Wall Region ◽  
Pressure Gradients ◽  
Baseline Case ◽  
Near Wall

The effects of adverse pressure gradients on the thermal and momentum characteristics of a heated transitional boundary layer were investigated with free-stream turbulence ranging from 0.3 to 0.6 percent. Boundary layer measurements were conducted for two constant-K cases, K1 = −0.51 × 10−6 and K2 = −1.05 × 10−6. The fluctuation quantities, u′, ν′, t′, the Reynolds shear stress (uν), and the Reynolds heat fluxes (νt and ut) were measured. In general, u′/U∞, ν′/U∞, and νt have higher values across the boundary layer for the adverse pressure-gradient cases than they do for the baseline case (K = 0). The development of ν′ for the adverse pressure gradients was more actively involved than that of the baseline. In the early transition region, the Reynolds shear stress distribution for the K2 case showed a near-wall region of high-turbulent shear generated at Y+ = 7. At stations farther downstream, this near-wall shear reduced in magnitude, while a second region of high-turbulent shear developed at Y+ = 70. For the baseline case, however, the maximum turbulent shear in the transition region was generated at Y+ = 70, and no near-wall high-shear region was seen. Stronger adverse pressure gradients appear to produce more uniform and higher t′ in the near-wall region (Y+ < 20) in both transitional and turbulent boundary layers. The instantaneous velocity signals did not show any clear turbulent/nonturbulent demarcations in the transition region. Increasingly stronger adverse pressure gradients seemed to produce large non turbulent unsteadiness (or instability waves) at a similar magnitude as the turbulent fluctuations such that the production of turbulent spots was obscured. The turbulent spots could not be identified visually or through conventional conditional-sampling schemes. In addition, the streamwise evolution of eddy viscosity, turbulent thermal diffusivity, and Prt, are also presented.

The Quantum‐Mechanical Equation of State

1950 ◽  
Vol 18 (10) ◽  
pp. 1412-1413 ◽  
Author(s):  
Robert W. Zwanzig
Keyword(s):  
Equation Of State ◽  
Quantum Mechanical ◽  
Mechanical Equation

scholarly journals Viscous coupling of shear-free turbulence across nearly flat fluid interfaces

2011 ◽  
Vol 671 ◽  
pp. 96-120 ◽  
Author(s):  
J. C. R. HUNT ◽  
D. D. STRETCH ◽  
S. E. BELCHER
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Lower Layer ◽  
Coupling Mechanism ◽  
Viscous Layer ◽  
Viscous Coupling ◽  
Viscous Effects ◽  
Horizontal Structure ◽  
Velocity Fluctuations ◽  
Viscous Boundary

The interactions between shear-free turbulence in two regions (denoted as + and − on either side of a nearly flat horizontal interface are shown here to be controlled by several mechanisms, which depend on the magnitudes of the ratios of the densities, ρ+/ρ−, and kinematic viscosities of the fluids, μ+/μ−, and the root mean square (r.m.s.) velocities of the turbulence, u0+/u0−, above and below the interface. This study focuses on gas–liquid interfaces so that ρ+/ρ− ≪ 1 and also on where turbulence is generated either above or below the interface so that u0+/u0− is either very large or very small. It is assumed that vertical buoyancy forces across the interface are much larger than internal forces so that the interface is nearly flat, and coupling between turbulence on either side of the interface is determined by viscous stresses. A formal linearized rapid-distortion analysis with viscous effects is developed by extending the previous study by Hunt & Graham (J. Fluid Mech., vol. 84, 1978, pp. 209–235) of shear-free turbulence near rigid plane boundaries. The physical processes accounted for in our model include both the blocking effect of the interface on normal components of the turbulence and the viscous coupling of the horizontal field across thin interfacial viscous boundary layers. The horizontal divergence in the perturbation velocity field in the viscous layer drives weak inviscid irrotational velocity fluctuations outside the viscous boundary layers in a mechanism analogous to Ekman pumping. The analysis shows the following. (i) The blocking effects are similar to those near rigid boundaries on each side of the interface, but through the action of the thin viscous layers above and below the interface, the horizontal and vertical velocity components differ from those near a rigid surface and are correlated or anti-correlated respectively. (ii) Because of the growth of the viscous layers on either side of the interface, the ratio uI/u0, where uI is the r.m.s. of the interfacial velocity fluctuations and u0 the r.m.s. of the homogeneous turbulence far from the interface, does not vary with time. If the turbulence is driven in the lower layer with ρ+/ρ− ≪ 1 and u0+/u0− ≪ 1, then uI/u0− ~ 1 when Re (=u0−L−/ν−) ≫ 1 and R = (ρ−/ρ+)(v−/v+)1/2 ≫ 1. If the turbulence is driven in the upper layer with ρ+/ρ− ≪ 1 and u0+/u0− ≫ 1, then uI/u0+ ~ 1/(1 + R). (iii) Nonlinear effects become significant over periods greater than Lagrangian time scales. When turbulence is generated in the lower layer, and the Reynolds number is high enough, motions in the upper viscous layer are turbulent. The horizontal vorticity tends to decrease, and the vertical vorticity of the eddies dominates their asymptotic structure. When turbulence is generated in the upper layer, and the Reynolds number is less than about 106–107, the fluctuations in the viscous layer do not become turbulent. Nonlinear processes at the interface increase the ratio uI/u0+ for sheared or shear-free turbulence in the gas above its linear value of uI/u0+ ~ 1/(1 + R) to (ρ+/ρ−)1/2 ~ 1/30 for air–water interfaces. This estimate agrees with the direct numerical simulation results from Lombardi, De Angelis & Bannerjee (Phys. Fluids, vol. 8, no. 6, 1996, pp. 1643–1665). Because the linear viscous–inertial coupling mechanism is still significant, the eddy motions on either side of the interface have a similar horizontal structure, although their vertical structure differs.

scholarly journals The Effect of LFC Process Variables on Solidification and Thermal Response of AZ91E Magnesium Alloy Castings

2021 ◽  
Author(s):  
Lukas Bichler
Keyword(s):  
Thermal Analysis ◽  
Magnesium Alloy ◽  
Magnesium Alloys ◽  
Metal Flow ◽  
Mold Filling ◽  
Second Phase ◽  
Process Variables ◽  
Pyrolysis Products ◽  
Alloy Castings ◽  
Non Equilibrium

Magnesium alloys are gaining in popularity as materials of choice for automotive and aerospace applications. Magnesium alloys have the lowest density of all structural metals, effectively making their specific properties highly attractive. Lost Foam Casting (LFC) is a novel near-net-shape manufacturing process utilizing expanded polystyrene (EPS) as a mold filler. Presence of the EPS in the casting cavity promotes formation of unique casting defects.These include misruns, folds, entrapped polystyrene pyrolysis products and potentially increased levels of gas porosity. There is very little published literature on the feasibility of casting magnesium alloys by the LFC process. This research was an attempt to evaluate the effect of selected LFC process variables on AZ91R magnesium alloy castings produced by the LFC process. In this work, the effect of melt superheat, casting section thickness, EPS foam properties and the application of vacuum during mold filling were investigated and correlated to the casting quality and molten flow behavior. Further, detailed thermal analysis was carried out to determine the solidification history of the castings. The results of the thermal analysis were used to determine the effect of the cooling rate on the development of the casting microstructure. Moreover, the morphology and the mode of second phase (Mg17Al12) precipitation were studied and quantified. The results suggest that application of vacuum during the mold filling process increased the metal flow lengths. However, the casting soundness deteriorated due to the applied vacuum. Variations in the density of the vacuum cast horizontal bars were explained through the presence of partially solidified metal. The molten metal flow was further influenced by the foam density and bead fusion. Greater flow lengths were observed in the high density 1.6 pcf foam castings. in the low density 1.3 pcf foam castings, numerous casting defects were associated with the presence of the liquid-EPS pyrolysis products. In general, the thermal analysis suggested that non-equilibrium alloy solidification promoted the formation of the lamellar non-equilibrium Mg17Al12 precipitate, and this was confirmed by optical microscopy.

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