Analysis of hydrofilm extrusion of three-dimensional shapes from round billets

A new method of die construction is proposed, which enables the exact geometrical control of die shape and ensures the initial sealing between billet and die. Using the modified method of die construction the internal metal deformation is analyzed with the aid of a special transformation combined with the upper-bound method. Based on a concept of equivalent friction factor the energy dissipation in fluid film is calculated approximately for three-dimensional hydrofilm extrusion. Computations are carried out for hydrofilm extrusion of various sections such as squares, rectangles, ellipses and clover shapes and various factors affecting the process are discussed. Experiments are performed for clover and square sections using the dies from NC manufacture based on the suggested theoretical design. A reliable sealing system is developed between punch and container. The experimental results are compared with the theoretical prediction and it is shown that the theory is in reasonable agreement with the experimental observation. Various aspects are discussed from the experiment.     

Round-to-channel section extrusion through linearly converging die: a three-dimensional analysis

Metal flow in the extrusion process is an important factor in controlling the mechanical properties of the extruded products. It is, however, difficult to predict the metal flow in three-dimensional extrusion of sections due to the involvement of re-entrant corners. The present work is an attempt to find an upper bound solution for the extrusion of channel section from round billet through the taper die. The rigid-perfectly plastic model of the material is assumed, and the spatial elementary rigid region (SERR) technique is presented for which the kinematically admissible velocity field is found out by minimizing the plastic dissipation of power. The presented analysis allows for specification of process control parameters and their relation to extrusion load, equivalent die angle, reduction ratios and friction factor.     

Asymptotic analysis of extrusion of porous metals

Plane strain extrusion of fully dense and porous metals is analysed using asymptotic techniques. The extrusion die is assumed to taper gradually down the extrusion axis. The asymptotic expansions are based on a small parameter ε which is defined as the ratio of the total reduction of the original cross-section to the length of the reduction region. Coulomb's law is used to model the frictional forces that develop along the metal-die interface and the coefficient of friction is assumed to be of order ε. Analytical solutions for the first two terms in the expansions are obtained. In the case of the fully dense metals, it is shown that the leading order [O(1)] solution involves “slab flow.” It is also shown that the next term in the expansion of the solution is O(ε²), and this provides a theoretical justification for the use of the so-called “slab methods” of analysis for dies of moderate slope. An asymptotic analysis of the extrusion of porous metals with dilute concentration of voids is also carried out. Gurson's plasticity model is used to describe the constitutive behavior of the material. The leading order solution is the same as that of the fully dense material and the effects of porosity enter as an O(ε) correction. In order to verify the asymptotic solutions developed, detailed finite element calculations are carried out for both the fully dense and the porous material. The asymptotic solutions agree well with the results of the finite element calculations.     

Friction at high normal pressures

Friction conditions between tool and workpiece in metal working are of the greatest importance to a number of factors such as force and mode of deformation, properties of the finished specimen and resulting surface roughness.It is shown, theoretically and experimentally, that the Amonton friction law expressed by τ = μq does not apply when normal pressure is higher than approximately the yield stress of the specimen; in this case it is necessary to consider the frictional stress as a function of normal pressure, surface topography, length of sliding, viscosity, and compressibility of the lubricant.The theoretical work was carried out by means of upper bound and slipline field analysis based on experiments with model surfaces in wax and metal. The theoretical model applied is one of multihole extrusion, the material beneath the valleys of the workpiece surface being extruded up towards the tool when the real area of contact exceeds a certain value. The effect of the trapped lubricant is to build up a back-pressure on the extrusion process.The experimental work was carried out with newly developed equipment enabling direct determination of the abovementioned function; construction and calibration of the equipment are described. The equipment allows determination of frictional stress on a surface with well-defined values of normal pressure, sliding length, and sliding velocity. The normal pressure can attain about 8 times the yield stress for commercially pure aluminium.The results obtained show reasonably good agreement between theory and experiment, and a dependence of the frictional stress on the sliding length, this dependence being a function of normal pressure.     

An Interfacial Friction Law for a Circular EHL Contact Under Free Sliding Oscillating Motion

The friction response of a lubricated interface under free sliding oscillating motion is investigated as a function of the contact pressure and the rheology of the lubricant in terms of viscosity and piezoviscosity. For loaded contacts, both velocity dependent friction, referred to as viscous damping, and friction independent of the instantaneous sliding velocity contribute to the energy dissipation. Viscous damping mainly corresponds to the dissipation in the lubricant meniscus surrounding the contact, while dissipation within the confined lubricated interface is mainly independent of the instantaneous sliding velocity. The friction coefficient independent of the instantaneous sliding velocity falls on a master curve for the wide range of tested operating conditions and lubricant rheological properties. The master curve is a logarithmic function of a dimensionless parameter corresponding to the ratio of the viscosity of the confined lubricant to the product of the pressure and a characteristic time. The physical meaning of this latter and the friction law are discussed considering the confined interface as a viscoelastic fluid or a non-Newtonian Eyring fluid.     

Calculating frictional force with considering material microstructure and potential on contact surfaces

A method based on the energy dissipation mechanism of an Independent Oscillator model is used to calculate the frictional force and the friction coefficient of interfacial friction. The friction work is calculated with considering the potential change of contact surfaces during sliding. The potential change can be gained by a universal adhesive energy function. The relationships between frictional force and parameters of a tribo-system, such as surface energy and microstructure of interfacial material, are set up. The calculation results of the known experimental data denote that the frictional force is nearly proportional to the surface energy of the material, nearly inversely proportional to the scaling length, and independent of the lattice constant. The results agree with that of adhesion friction equations. They also agree with the experimental results performed with an atomic-force microscope under the ultra high vacuum condition. __________ Translated from Tribology, 2006, 26(2): 159–162 [译自: 摩擦学学报]     

湿式离合器考虑纸基衬面孔隙弹性特性摩擦振动理论

本文提出考虑纸基摩擦材料界面间变形和其中造成润滑油流动的摩擦振动新理论,推荐了一摩擦振动模型,采用引入的粘性液体浸透多孔体,联合假定在切向和法向两个方向的振动导出一稳态准则,和实验相比较,确认所推荐的准则可预测该稳态极限比常规的更精确。它不考虑摩擦材料的变形,只与摩擦系数与滑动速度的斜率有关。基于本准则,讨论了材料特性摩擦振动对稳态的影响。     

Evaluation of interfacial friction condition by boss and rib test based on backward extrusion

Proper consideration of tribological problems at the contact interface between the tool and workpiece is crucial in metal forming, since interfacial friction condition plays an important role in metal forming by influencing the metal flow, forming load, die wear, etc. In order to quantitatively estimate such friction condition, a new friction testing method “Boss and Rib Test” based on the backward extrusion process is proposed in this work. In boss and rib test, a key design is to use a tube-shaped punch so that the boss and rib at the deforming workpiece along the inner and outer surfaces of the punch are formed during backward extrusion. It was experimentally and numerically revealed that the heights of the boss and rib vary according to the friction condition applied. It was also found that the height of the boss is higher than that of the rib when the friction condition at the contact interface is severe. From this finding, the shear friction factor can be evaluated according to lubricant characteristics assigned. In addition, simulation results revealed that calibration curve demonstrating deformation pattern of the workpiece is affected by strain-hardening exponent of the workpiece.     

湿式离合器考虑纸基衬面孔隙弹性特性摩擦振动理论(二)

本文提出考虑纸基摩擦材料界面间变形和其中造成润滑油流动的摩擦振动新理论,推荐了一摩擦振动模型,采用引入的粘性液体浸透多孔体,联合假定在切向和法向两个方向的振动导出一稳态准则,和实验相比较,确认所推荐的准则可预测该稳态极限比常规的更精确。它不考虑摩擦材料的变形,只与摩擦系数与滑动速度的斜率有关。基于本准则,讨论了材料特性摩擦振动对稳态的影响。     

基于虚拟仪器的滑动轴承摩擦试验系统的设计

通过改造MS-800A四球摩擦试验机的摩擦实验部分,引入虚拟仪器LabVIEW软件建立测试系统,对摩擦副之间摩擦系数和温度的变化进行采集、处理和实时检测,建立对滑动轴承的摩擦磨损试验系统,从而建立一套研究滑动轴承在不同工况条件（润滑介质、载荷和转速）下的摩擦磨损特性。     

Study on the energy dissipation mechanism of atomic-scale friction with composite oscillator model

A model called composite oscillator model is proposed for studying energy dissipation mechanism of atomic-scale wearless friction. The model consists of the whole macroscopic oscillator and the micro oscillators of interfacial atoms. The different influences of the two oscillators on the energy dissipation process of friction are discussed. It is found that the frequency of the interfacial exciting force is the key factor to energy conversion in the friction process by analyzing the dynamics characteristic of interfacial atoms. In the equilibrium stage, the interfacial force acts integrally and uniformly on each atom because its frequency is near zero. In the non-equilibrium stage, however, the distribution of energy received by the interfacial atoms is non-uniform because the frequency of the interfacial acting force is very high. Therefore, the extra energy may be easily transferred to the adjacent atoms to have the energy dissipated. Then, the formulas are derived to calculate a frictional force. The calculated force is found to be close to the experimental one. The comparisons show that the composite oscillator model can explain energy dissipation mechanism in a frictional process and it can be used to control friction as well.     

Analysis of hydrofilm extrusion of elliptic shapes using perturbation method

An approximate method of solution is proposed for the hydrofilm extrusion of elliptic shapes from round billets through optimized curved dies. A modified upper-bound theorem and hydrodynamic lubrication theory are used in combination, in order to analyze metal deformation and fluid flow respectively. The fluid analysis in hydrodynamic lubrication theory is simplified by use of elliptic transformation and perturbation technique. Strain-hardening effect of billet material and viscosity variation of fluid due to pressure are taken into consideration.For several reductions of area, experiments are carried out at room temperature by using mild steel specimens and caster oil as the lubricant.The experimental extrusion pressures are in good agreement with the theoretical predictions.     

Simulation and experimentation on the contact width and pressure distribution of lip seals

The relative motion between two mated parts of machinery always generates heat from friction. The lubricant serves as a medium not only to reduce the friction but also to enhance heat dissipation. In order to contain the lubrication oil, lip seal is a most frequent sealing part used in these applications. This paper aims to study the contact width and contact pressure of the seal lip under the various interference fits between the shaft and seal. The contact force associated with the pressure was used to estimate the generated heat due to friction. Thereby, this frictional heat flux was employed to analyze the temperature distribution within the rubber seal. According to the temperature distribution, the thermal deformation of the seal and the concern of material ageing can be examined. Since the use of a seal with a shaft under allowable dimension tolerance is foreseeable, the fit with different degree of interference was investigated. On the other hand, a simple apparatus to measure the width and pressure on the contact lip zone under different diameters of shaft was designed and fabricated. The contact width and contact pressure were distilled from the press mark of a pressure-sensitive film. The measurements were used to demonstrate the feasibility and accuracy of the proposed set up.     

Microscopic Frictional Response of Sodium Oleate Self-Assembled on Steel

The article peruses the frictional response of an important metal working lubricant additive, sodium oleate. Frictional force microscopy is used to track the response of molecules self-assembled on a steel substrate of 3–4 nm roughness at 0% relative humidity. The friction-normal load characteristic emerges as bell-shaped, where the peak friction and normal load at peak friction are both sensitive to substrate roughness. The frictional response at loads lower than that associated with the peak friction is path reversible while at higher loads the loading and unloading paths are different. We suggest that a new low-friction interface material is created when the normal loads are high.     

A Mixed Lubrication Model for Computer Simulation of Extrusion Processes

A mixed lubrication/friction model for extrusion process is developed in the present research. The model combines a rigid-plasticity finite element code to simulate the interface condition between the tooling and workpiece in the extrusion operation. The influence of surface roughness on lubricant flow is treated by using the average Reynolds equation. The active lubrication regime and appropriate friction factor were determined from the current local values of interface variables such as mean lubricant film thickness and workpiece and tooling roughness, in addition to the more traditional external variables such as interface pressure, node sliding velocity and strain rate of the workpiece. Numerical results using the coupled code include friction stress and normal pressure under different lubrication conditions are compared with experimental investigation. The discrepancy is very small and the proposed model proved to be very efficient in predicting interface friction condition in the extrusion processes.     

An analytical solution for the spread extrusion of shaped sections

Spread extrusion could be used for manufacturing of wide profiles in the extrusion industry. In this paper a new method of design and analysis has been presented for such a problem. Special dies were designed for profiled sections such as square, rectangular, elliptical and cross shapes. These dies force the material to flow sideways and spread so as to extrude sections with wider dimensions than the initial billet or the maximum container diameter. The geometry of the deforming zone in the die was formulated and based upon that, a kinematically admissible velocity field was derived. Using this velocity, we estimated the field upper bound on extrusion power. Profile sections with different aspect ratios were investigated and the influence of other process parameters such as friction and reduction of area on the extrusion pressure were studied. Optimum die lengths for each die were calculated so as to minimize the extrusion pressure. Finite element analysis for the numerical simulation of the process was also carried out. The finite element results were also used as an aid to the design process of the extrusion dies. Dies were manufactured for different sections such as square, rectangle, and ellipse and cross shapes. Experiments were carried out to obtain data to verify the theory. Comparison of the results showed good agreement between the theoretical, numerical and experimental data. It was concluded the present method could be used to design dies for the spread extrusion of different shaped dies.     

Analysis of three-dimensional extrusion of sections through curved dies by conformal transformation

A new method of analysis is proposed for the extrusion of arbitrarily shaped sections through curved die profiles. A kinematically admissible velocity field is found by deriving the equation of a stream line. Conformal transformation of a unit circle onto a section is utilized in the derivation. The upper-bound method is then applied to determine the extrusion pressure for the rigid-perfectly plastic material. The redundant work relating to the velocity discontinuities at the entrance and the exit is included in the formulation. The general formulation for an arbitrary cross section is obtained by use of conformal transformation. The upper-bound pressure for extrusion through curved die profiles is computed for a complex section with a curved boundary. Two curved die profiles widely used are chosen to compare the effects of die profiles. From the derived velocity field, the upper-bound extrusion pressures are also computed for the extrusion of regular polygons and rectangles of various aspect ratios. The effects of sectional shape, die profile and interfacial friction at the die surface are discussed.     

Analysis of hydrofilm extrusion through optimized curved dies

A new analysis of the hydrofilm extrusion process which includes strain-hardening effects and viscosity variation in the fluid due to pressure is developed. The upper-bound method and hydrodynamic lubrication theory are adopted for the analysis of metal forming and fluid flow respectively.Experiments were carried out at room temperature, for several reductions of area, using axisymmetric curved dies. The theoretical prediction of extrusion pressure shows good agreement with experimental measurements for mild steel using castor oil as the lubricant.     

On the optimal die curvature in deep drawing processes

The paper presents an attempt to increase the limit drawing ratio of deep drawing processes by searching an optimal die curvature, which minimizes the drawing load. The search done here for an optimal die curvature is based on experimental observations and followed by a detailed upper bound analysis. The analysis takes into account the non-steady character of the process (from a 2D circular plane blank into a 3D axisymmetric cup). The plastic flow along the die curvature is expressed in a toroidal coordinate system which seemingly describes more naturally a smooth velocity field along the real toroidal profile of the die. The outcome provides more closely the relationship between the energy dissipation rate and the die curvature so that a preferred die curvature is obtainable by energy minimization.Circular sheet blanks, made from aluminum and copper, were drawn through dies with different radii of curvature (with at least five repetitions at each radius) to capture the features of the optimal dies whenever exists.The main result is that under certain circumstances an optimal die curvature does exist. It depends largely on the drawing ratio and the blank/die interfacial friction, m, but appears quite insensitive to the initial thickness of the blanks. The optimal die curvature is pronounced in the cases where the frictional resistance is relatively low, otherwise it is indistinctable and remains practically undeterminable by designers.     

Chemical Control of Friction: Mixed Lubricant Monolayers

Controlling frictional behavior in nanoscale sheared systems can be made possible when the relationship between the macroscopic frictional response and the microscopic properties of the sheared systems is established. Here, a new approach is proposed for tuning the frictional response and obtaining desirable frictional properties. This tuning is achieved through shear-induced phase transitions in a mixed lubricant monolayer consisting of a base solvent and an additive. The interaction between the solvent and additive molecules and their relative concentrations are shown to be the major parameters in determining the magnitude of the friction force and the nature of the response (stick–slip or sliding).