Papers in JOURNAL OF THE JAPAN SOCIETY FOR TECHNOLOGY OF PLASTICITY
(Vol.38 No.442 November 1997)
Concept and Equation of Finite Slab Method
- Proposal of Simple Analysis in Cold Forging -
Tadasu MURAKAMIC Keiou NISHIMURA and Keisuke IKEDA
(Received on November 28, 1996)
A finite slab method FSM is proposed as a simple technique for calculation of stress distribution and deformation in cold forging. The material to be forged is divided into various deformation regions, called units, as in the upper bound technique. Additionally, each unit is cut into n finite slabs. The stress boundary condition at the interface of units is given by the mean stress in the direction normal to the interface. The stress components are calculated by the use of the conditions of volume constancy and approximate relations such as the Levy-Mises flow rule and the Mises yield criterion. The results for a ring compression problem obtained by the present method agree well with those obtained by Hawkyard and Johnson. The method can be applied to three-dimensional problems.
Key words : numerical, cold forging, finite slab method, slab method, stress distribution, deformation
Extension of Finite Slab Method to 3-Dimensional Problem
- Proposal of Simple Analysis in Cold Forging II -
Tadasu MURAKAMIC Keiou NISHIMURAC Keisuke IKEDA and Ken-iti KANAI
(Received on November 28, 1996)
A finite slab method proposed in previous work is modified into a method of analysis for 3-dimensional forging problems. The method is applied to closed die forging of a square prism from a cylindrical billet. A 4-unit model involving two parameters, radius rn and velocity urCis proposed. ur is determined by the stress boundary condition. The curves denoting the relation between mean pressure and rn for each filling factor have points of minimum values or inflection. The relation between mean pressure at these points and filling factor is in comparative agreement of empirical law.
Key words : numerical, cold forging, finite slab method, slab method, stress distribution, deformation
The Effect of Planar Anisotropy on Fracture Limit
Strain in Sheet Metals
- Forming Limit Analysis in Sheet Metals by the Constitutive Law
Incorporating Stress Increment Dependence I -
Tohru YOSHIDA, Koichi ITO, Yukihisa KURIYAMA and Matsuo USUDA
(Received on December 10, 1996)
A forming limit diagram (FLD) is often used to decide the forming limits in finite element (FE) simulations of sheet metal forming processes. By improving the accuracy of formability prediction using FEM, theoretical FLD considering planar anisotropy is derived with reference to localized necking criteria. In the constitutive law incorporating stress increment dependence used in this analysis, the material parameter Kc is determined by a bi-axial stretching test. The effect of the angle alpha between the anisotropy axis and the principal stress axis on the forming limit strain was calculated. In addition, the forming limit height considering planar anisotropy was predicted using FE simulation of hemispherical punch stretching and compared with the experimental one.
Key words : sheet metal forming, planar anisotropy, forming limit diagram, localized necking, finite element method
Lubricities of Phosphorus-Type Oils and Workpiece
Precoating in Cold Forging
Kazuhiko KITAMURA and Toshihide OHMORI
(Recieved on December 26, 1996)
Combinations of phosphorus-type oils and workpiece precoating were evaluated in terms of friction and galling using a backward can extrusion test and a ring compression test. Iron phosphates of 0.2-2g/m2 were precoated to workpieces of 0.1C carbon steel using a phosphorus-type oil before the tests. A combination of a mineral oil with more than 1.3g/m2 of precoating was superior to that of a mineral oil with 4 and 11g/m2 of conventional phosphate coating. Oil containing acid phosphate with precoating was proved to reduce friction and prevent galling. Oil containing acid phosphate and phosphoric acid with precoating showed performance superior to those of mineral oil and only acid phosphate with precoating, and it was comparable with a conventional soap-phosphate coating in lubricity. The phosphorus distribution on the workpiece after the tests, detected by EPMA, showed that the phosphoric acid formed iron phosphate. This compensated for the decrease in the amount of precoated iron phosphate with an increase in extruded cup depth. The combination of the active phosphorus-type oil and the pre-coating was found to be effective under the severe frictional conditions of backward can extrusion.
Key words : cold forging, tribology, lubricants, seizure, ferrous metal, backward extrusion
Prediction of Thickness Distribution and Curvature in
Unsymmetrical Plate Rolling by Simulation
- Analysis of Unsymmetrical Rolling by Rigid-Plastic FEM I -
Hideaki FURUMOTO, Kanji HAYASHI, Jun-ichi NISHIZAKI,
Kazuo MORIMOTO and Kozo OSAKADA
(Received on January 14, 1997)
A method for analyzing the thickness difference in the transverse direction of a plate and the resulting curvature in unsymmetrical rolling is proposed on the basis of the rigid-plastic finite element method. To handle the boundary conditions of the rigid areas before entry and after delivery from the roll bite, a velocity field that permits rotation, as well as movement in rolling and width directions, is employed.
The thickness difference and curvature are calculated by considering the elastic deformation of the rolls. It is found that a linear relation exists between the roll gap difference and the thickness difference, and the printing ratio of the roll gap difference to the thickness difference increases as the plate width decreases. When the thickness difference per unit width is constant, the plate curvature decreases as the plate width decreases. The analyzed results of the thickness difference and of the plate curvature agree well with the experimental results.
Key words : rolling, numerical analysis, FEM, thickness difference, curvature
Simulation of Snaking in Unsymmetrical Rolling
- Analysis of Unsymmetrical Rolling by Rigid-Plastic FEM II -
Hideaki FURUMOTO, Kanji HAYASHI, Jun-ichi NISHIZAKI,
Kazuo MORIMOTO and Kozo OSAKADA
(Received on January 14, 1997)
A method for analyzing the thickness difference in the transverse direction of a plate in unsymmetrical rolling is proposed on the basis of the rigid-plastic FEM, and in addition the snaking phenomenon in rolling is predicted. The distributions of tensile forces before and after the roll bite, calculated with the Shohet model using elastic FEM, are used as the boundary conditions of the rigid-plastic FEM analysis. The calculated boundary velocities are, in turn, given to the elastic model and the calculation process is repeated until a convergence is obtained.
The thickness difference and the amount of off-center caused by snaking are predicted using the proposed method. It is found that the printing ratio of the roll gap difference to the thickness difference and the amount of off-center decreases as the tensile force increases, especially in the case of back tension. The printing ratio and the amount of off-center become significant when buckling of the plate occurs. The analytical results of the thickness difference and the amount of off-center agree well with the experimental results.
Key words : rolling, numerical analysis, FEM, thickness difference, amount of off-center, tension
Surface Finish of Aluminium Pipe by Ironing with Ultrasonic Vibration
- Trial Construction of Experimental Apparatus and Preliminary Experiments -
Teruie TAKEMASU, Tatsuo OZAKI, Ryoichi MATSUNAGA,
Susumu YAMASAKI, Masashi SAKAGUCHI and Kenji TOMITA
(Recieved on January 14, 1997)
Preliminary experiments of single-stage ironing with ultrasonic vibration are carried out using an apparatus constructed for these trials to reduce the number of ironing stages in the extruded and ironing process for photosensitive drums. The whole vibrating system is analyzed by Finite Element Method as an axisymmetric eigenvalue problem to examine the relationship between the natural frequencies and the natural modes of vibration. The frequency of the ultrasonic vibration is set at 20.0 kHz. A die vibrates axisymmetrically with about 5 micro meters amplitude in the axial direction and with about 0.5 micro meter amplitude in the radial direction under no load. The amplitudes in both directions are diminished by about half during ironing. The following facts are obtained by applying ultrasonic vibration. (1) The ironing load is markedly decreased by 35%`55%. (2) The surface roughness of the products is greater for lubricants with a high viscosity, but gradually reaches the same level as that of the products of conventional ironing as the viscosity of the lubricants decreases. (3) The roundness error of the products is reduced to below 10 micro meters.
Key words : sheet metal forming, ironing, surface finishing, surface roughness, lubricants, ultrasonic vibration, FEM, photosensitive drum, accuracy
Effects of Rolling Conditions on Crack Initiation in Elongating
Mill Rolling of 13%Cr Stainless Steel
Shuji YAMAMOTO, Kazushi MARUYAMA,
Teruaki BITOU and Tatsuo OZAKI
(Received on February 5, 1997)
In order to prevent inner defects in 13%Cr stainless steel seamless pipes, the behavior of inner defects during an elongator rolling mill process were investigated by means of experiments on a production mill and an experimental mill. First, it was found from suspended-rolling experiments on a production mill, that surface cracks are initiated before the inner surface touches the plug, remaining as origins of inner defects after the openings of the cracks are compressed by the plug. Second, influences of various rolling conditions on crack initiation were examined by means of experiments on an experimental mill and use of the elastic-plastic FEM. The results are as follows. (1) As the feed angle is decreased, cracks are initiated more easily even with a smaller diameter reduction Rd. (2) When inlet tubes with a large thickness-to-diameter ratio t/D are used, large cracks are easily initiated even with the same Rd. (3) The cracks are induced by successive application of tensile/compressive circumferential strain during the rolling deformation. These results have been used successfully to prevent inner defects in a production line.
Key words : tube rolling, elongating mill, 13%Cr stainless steel, crack, feed angle, FEM, elastic-plastic analysis
Thinning in the Cylindrical Cup Wall Thickness by
Ironing with Redrawing
Keiichi SHIMIZU and Tomoyuki WADA
(Received on February 19, 1997)
During fabrication on a cylindrical thin wall cup from a laminated steel sheet, the plastic film surface is damaged when ironing occurs after deep drawing. The damage can be avoided if during ironing, the force of redrawing is applied as a back tension in the region being ironed. In this paper, the limit of thinning of the cup wall thickness and the stress conditions of the cup wall are described when a cup wall is ironed with redrawing.
Key words : redrawing, stretch bending, ironing, laminated steel, back tension, material property, forming limit, can, cylindrical cup
Elementary Theoretical Analysis of Floating Expanding
Plug Pipe Bending Method
Kiyotaka HAYASHI, Masao NAKAMURA,
Seijiro MAKI and Yasunori HARADA
(Resceived on February 26, 1997j
In order to investigate characteristics of the pipe bending method via a floating expanding plug, an elementary theoretical analysis using the slab method is proposed. We consider an equilibrium for forces with an infinitely small volume, and material comforms to Hill's anisotropic yield, anisotropic flow criterion and n power hardening, and it is assumed that the pipe is deformed only when it is expanded. (1) Theoretical bending moment agrees well with the experimental results, but the calculated value is very large when no expansion occurs. (2) Close agreement between the experimental and calculated values is obtained at the strain distribution; consequently the deformed condition is understood. (3) Both expanding pipe and plug movements work effectively to enable the bending of a pipe with a good shape and small bending radius. (4) Small wall thickness difference and bending radius are obtained for a small n-value pipe. (5) Such a pipe that has a decreased circumferential anisotropy and/or increased longitudinal anisotropy can be bent into a good shape, however, a large bending moment is necessary and the bending radius limit is large.
Key words : tube forming, bending, expanding, new forming process, slab method
High-Temperature Shock Consolidation of High-Speed Steel Powders
Using Converging Underwater Shock Wave
Kazuyuki HOKAMOTO, Seiichiro TANAKA, Masahiro FUJITA,
Shigeru ITOH, Marc A. MEYERS, Hsi-Ching CHEN and Ryuichi TOMOSHIGE
(Received on March 10, 1997)
We attempted to consolidate high-speed steel powders with a high-temperature shock compression apparatus using converging underwater shock waves. The effects of experimental temperature and particle size were verified through a series of experiments, and the melting ratio generated due to heating by plastic deformation of particle surfaces was investigated. Normally, the melting ratio was increased by increasing the experimental temperature and particle size, which was explained by the consideration of how much energy from the shock waves was absorbed by melting the particle surfaces. High temperature experiments above 800 Celsius showed decreases in the melting ratio, which was due to a softening of the high-speed steel powders at high temperatures. A decrease in thermal residual stress and an increase in ductility of the powders caused a number of cracks generated in the consolidated sample to disappear upon heating of the powders.
Key words : powder metallurgy, shock consolidation of powders, high-speed steel powders, underwater shock wave, high-temperature shock compression
Shape Control Characteristics of Multicrown Roll (MC Roll)
Shoichi HASHIMOTO, Tetsuo KAJIHARA,
Eiichi YANAGISAWA and Yutaka MATSUDA
(Received on March 18, 1997)
To meet the recent strong demand for an improvement in the shape of rolled thin strips, shape control characteristics of a multicrown roll, called MC Roll, which consists of an arbor, roller bearings and a sleeve, have been investigated. In the MC Roll, each bearing is fixed to an arbor eccentrically, and symmetrically about the center of the roll, so a multicrown mode is created by changing the phase of the arbor. The shape of a strip rolled by a model mill was changed from edge wave to center buckle with a change of the crown mode of the MC Roll, and calculated results using the present model agreed with these data. Furthermore, it was predicted by calculations that the MC Roll has a great ability to control strip shape by combining work roll bending force with the multicrown mode. Thus it is concluded that the MC Roll is useful as a shape control device in commercial mills.
Key words : cold rolling, shape, arbor, roller bearing, sleeve, backup roll