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In the case of plane strain plastic compression, behavior of a viscous lubricating oil trapped in a small pit on a contact surface is calculated by a finite element method. The oil pressure is controlled by the yielding condition. When the oil pressure is constant over the surface, the oil does not flow and the pit is not flattened. When the lateral deformation of material is constrained and pressure gradient is produced, the oil in the pit flows out and the pit is flattened. Reduction in heigth required to flatten the pit is above several times of the pit depth. A decrease in the viscosity and an increase in the pit depth enhance the flattening. When the compression tool is slid with a high speed, a hydrodynamic effect of the oil causes a pressure change and the pit moves in the sliding direction.

The penetration of a viscous lubricant into a three dimensional surface crack under a rolling contact stress was calculated. The finite element method was applied to solve the Reynolds equation coupled with the elastic deformation of the crack. The process of penetration is roughly the same as the two dimensional model. The lubricant begin to flow into the crack when the contact pressure is passing the crack mouth. The lubricant enters to the crack tip and increases the stress intensity factor, when a nondimensional parameter β=ηυE2/(ap30)is small. The crack does not open when β is large, because the contact pressure has passed before the lubricant flows into the crack. The critical value of β was calculated. The penetration of the lubricant is not easy as compared with the two dimensional model.

The penetration of a viscous lubricant into a two dimensional surface crack under a rolling contact stress was calculated. The finite element method was applied to solve the Reynolds equation coupled with the elastic deformation of the crack. The lubricant begins to flow into the crack when the contact pressure is passing the crack mouth. The lubricant enters to the crack tip and increases the stress intensity factor, when a nondimensional parameter β=ηνE2/(ap30) is small. The crack does not open when β is large, because the contact pressure has passed before the lubricant flows into crack. The critical values of β were calculated. The penetration of the lubricant becomes easy when a frictional stress acts as the crack opening.

Initial movements of a lower first premolar were analyzed by a three dimensional elastic finite element method. When the elastic constants of the periodontal ligament were the following : Young's modulus Ep=0.2 MPa, Poisson's ratio νp=0.47, the calculated mobility values almost agreed with measured ones. In these case where the ratio of Young's modulus in alveolar bone Ep to Eb, Eb/Ep, became greater than 104, only the periodontal ligament was subjected elastic deformation whereas the tooth and the alveolar bone hardly deformed. Stress values calculated by the two dimensional plane strain model were about the half of the three dimensional case, because the stiffness of the alveolar socket decreases. Assuming that the tooth and the alveolar bone were rigid bodies, the initial movements and the stress distributions in the periodontal ligament were able to calculate simply. The results calculated by the simple method almost agreed with those by the finite element method.

A simple method for measuring contact pressure at a tool-workpiece interface is presented. The strain of the tool near the contact surface is measured using a pipe-type strain gage, and is converted into the pressure. The measured pressure distributions in plastic compression of rectangular blocks almost agreed with those estimated from the strain distribution. The pressure was distributed uniformly over the contact surface in the well-lubricated specimens regardless of the height-to-width ratio of the specimen, H0/L0 Friction hills were observed in the unlubricated specimens with H0/L0=0. 25 and 0. 5. A concave pressure distribution was obtained for the specimen with H0/L0=1, where the pressure increased from the center to the periphery of the contact surface. The present method can be applied to measure die pressure in practical metalworking processes.

A finite element method formulated by a total lagrangian method was used to calculate the nonlinear part of deformation. In the case of double beam load cells, when an off-center load is applied, axial forces of the beams produce a nonlinear bending strain. The nonlinear strain is proportional to the applied load and the off-center distance. The output of the nonlinear strain can be avoided by shifting strain gages to an appropriate position. The nonlinear strain distributions of load cells with thinned sections in beams are affected by the flexural rigidity along the beam. In the case of a center-beam load cell, the nonlinear strain is relatively small, but the deformation mode is more complicated compared to double-beam load cells.

In order to investigate load position errors due to dimensional errors, the strain changes caused by infinitesimal shape altering are calculated by using the three-dimensional finite element method. The strain changes which result in load position errors take place not only in the region of the beam which has been altered, but in all regions where the strain gage has bonded. In the case where the horizontal bending forces rise from a transverse load position movement, being some dimensional errors in the vicinity of one of the strain gage elements, both the local shift of the neutral axis for the bending in that region, and the global deformation due to the asymmetry of beams give rise to error in measurement. From the results presented in this report, particular modes of dimensional error resulting in serious load position errors are charified, so that the accuracy of dimensions to avoid load position errors may be estimated.

Finite element methods are applied to calculate the squeeze effect of lubricant filling in semi-ellipitical surface cracks under unloading. The two-dimensional Reynolds equation for the lubricant and the three-dimensional elasticity equation for the surface crack specimen are solved simultaneously using an incremental iterative scheme. Although the external stress is zero, the crack opens due to the pressure rise caused by the squeeze effect. For shallow and deep semi-ellipitical surface cracks, the pressure distributions are roughly the same as in the case of a through crack in a thick plate. When the crack depth compared with the surface length is large, since the pressure of lubricant increases and the compliance of the crack opening displacement with the pressure decreases, the stress intensity factors due to the squeeze pressure are kept unchanged.

Using a specially designed die with a very slightly inclined face, the punch load is decreased to a lower level than that for the usual flat die. This is because the lubricant trapped on a slightly inclined die face enters on the die radius in the course of the punch stroke, so that friction on the die profile decreases. The punch penetration, at which point the decrease of the punch load starts, can be estimated by calculating the volume of lubricant initially trapped and the change in the intervening space between the die face and the deforming flange during the press. The increase in the limiting drawing ratio (LDR) is brought about by the decrease of maximum punch load, and it depends on the inclination of the die face. The experimental results show that the LDR is increased by about 0.15 at the optimum inclination.

The temperature variations of strain gages, caused by the power dissipated in the gage are calculated by the three-dimensional finite element method. When gages are bonded to materials with lower thermal diffusivities, such as plastic, the rise in the temperature of the gages depends not only upon the area of the grid of the gage, which is often used to characterize the heat-dissipation characteristics of a strain gage, but upon the length and the width of the filament, and the number of filaments. When gages are bonded to materials with higher thermal diffusivities such as steel or alumimum alloy, most of the temperature rise is produced in the base of the gage, so as to depend upon the heat flux per unit area of filament and the thickness of the base. Temperature variations of strain gages caused by ambient-temperature variations with time are also calculated using an axis-symmetrical model. In various conditions of a gage installation, the effective factors which govern temperature variation were clarified.

A new method is proposed to estimate the distribution of tooth root stress of a gear pair under partial and nonuniform contact by a three-dimensional finite element method. In the method, the usual finite element program can be used with no special changes. To check the accuracy of the present method, a contact problem of two circular disks is analyzed. Numerical results are obtained with good accuracy, comparing with the results by Hertz theory. A pair of spur gears with lead error which gives partial contact is analyzed by the present method, and the distributions of tooth root stress and tooth deflection are obtained. The results are compared with those given by the draft proposal of ISO and by the standard of AGMA.

深絞りダイスの平面部にわずかな傾斜を設けると、この部分に貯留された潤滑油がダイラジアス部分に流入し、摩擦抵抗を減少させる。このためパンチ荷重は、行程途中で傾斜のないダイスよりも低い値へと急減する。ダイスに貯留される初期潤滑湯量vtoおよびダイス・プランク間のすきま容積vsを求め、vs=vtoとなる行程Scで荷重の急減がおこると仮定したところ、各種条件によるScの変化をよく説明することができた。

A center crack specimen is assumed under plane strain condition to calculate the stress intensity factor. For the viscous lubricant filling in a crack, it is assumed that the pressure rise from the squeeze effect follows the Reynolds equation. In the same way as the infinitely long bearing and infinitely short bearing in the case of sliding bearings, the full Reynolds equation is approximated with a one-dimensional equation. As a result of the squeeze effect of the lubricant, the effective stress intensity factor is lower than the nominal one. In the case of the ratio of the specimen thickness and the crack length filled with lubricant where B/c is smaller than 1/2, the effective stress intensity factor Kγ can be calculated by using the infinitely short approximation. And, where B/c is greater than 2, the infinitely long approximation can be applied. In the region 1/2