A study on the analysis of O-ring under uniform squeeze rate and internal pressure by photoelastic experimental hybrid method

There are three kinds of loading conditions applied to the O-ring, The first loading condition is the case in which uniform squeeze rates are applied to the upper side and the lower side of the O-ring (the strain condition). The second loading condition is the case in which uniform squeeze rates are applied to the upper side and the lower side of the Oring and other squeeze rates are applied to the front side of the O-ring. The third loading condition is the case in which uniform squeeze rates are applied to the upper side and the lower side of the O-ring, other squeeze rates are applied to the front side of the O-ring, and internal pressures are applied to another front side of the O-ring(loading condition is the combination of stress condition and the strain condition). In this research, a new photoelastic experimental hybrid method under the third loading condition was developed and it was verified. The stresses of the O-ring under the third loading condition were analyzed by the new photoelastic experimental hybrid method developed in this research. The internal pressures applied to the O-ring were 0.98 MPa, 1.96 MPa, 2.94 MPa and 3.92 MPa. This paper was recommended for publication in revised form by Associate Editor Jooho Choi Jai-Sug Hawong received a B.S. degree in Mechanical Engineering from Yeungnam University in 1974. Then he received his M.S. degree and Ph.D. degree from Yeungnam University in Korea in 1976 and from Kanto Gakuin University in Japan in 1990, respectively. Prof. Hawong is currently a professor at the school of Mechanical Engineering at Yeungnam University, in Gyeongsan city, Korea. He is currently serving as an vise-president of Korea Society Mechanical Engineering. Prof. Hawong’s research interests are the areas of static and dynamic fracture mechanics, stress analysis, experimental mechanics for stress analysis and composite material etc.     

A study on the contact stresses of square ring under uniform squeeze rate and internal pressure by photoelastic experimental hybrid method

The square ring has over the past few years been used as an alternative sealing element to the O-ring, which has been used widely for a long time. The square ring geometry is believed to be especially suitable for axial static applications because its square form remains practically constant under high pressures, has a high resistance to extrusion, not sensitive to gap extrusion and high leak tightness. Some of these fundamental properties that are crucial in the design of a square ring can be justified by analysis of the stress distribution of the square ring under various loading conditions, especially under a combined loading of uniform squeeze and internal pressure. In order to justify these properties a stress frozen square ring under this combined loading condition of uniform squeeze rate and internal pressure was analyzed using the photoelastic experimental hybrid method to obtain the contact and internal stresses. This research confirmed that contrary to the established theory, the square ring extrudes at a lower pressure of 1.96 MPa. The photoelastic experimental hybrid method can adequately be used for stress analysis of square ring seals. Internal pressure plays a significant role in the design of the seals. As the internal pressure increases, the internal stresses also increase. Maximum internal stresses were observed in the region close to the extrusion gap at points 2 and 2??. The square ring experienced contact stress singularity on the upper end of the contact surface (point 2??) on the front side and at point 2 on the upper side. The upper region experienced the largest contact stresses as well as internal stresses and so the fracture criterion of maximum shear stress should be applied in this region.     

3-Dimensional stress analysis of O-ring under uniform squeeze rate and internal pressure by photoelastic experimental hybrid method

Until now, studies have shown that stresses on the plane (y-z plane) perpendicular to the circumferential direction (x-axis) of an O-ring do exist. Stresses on the planes (x-y plane and x-z plane) parallel to the circumferential direction of the O-ring have not been reported to exist. In this study however, it is demonstrated through a 3-dimensional stress analysis that stresses on the x-y plane and x-z plane of the O-ring under uniform squeeze rate and internal pressure do exist. Therefore, to study effectively 3-dimensional stress distributions of an O-ring under these loadings, stress distributions of every plane should be analyzed. This study develops a photoelastic experimental hybrid method to analyze 3-dimensional stress distributions of an O-ring under uniform squeeze rate and internal pressure, and uses it to determine the stress distributions in every plane, including the Von Mises equivalent stresses, at any arbitrary point of the O-ring under uniform squeeze rate and internal pressure.     

Evaluating the stresses of a stepped unrounded D-ring under uniform squeeze rate and internal pressure by photoelastic experimental hybrid method

The stresses that develop in a stepped unrounded D-ring loaded with internal pressures at a 20% squeeze rate are analyzed using the photoelastic experimental hybrid method. The analysis demonstrated that the contact stresses on both the upper and front sides of the Dring increased as the applied internal pressure increased, with the magnitudes of ??_X/p_i and ??_Y/p_i being considerably higher than those of ??_XY/p_i. Moreover, as applied internal pressure increased, the semi-circular portion of the D-ring moved to fill the space ahead of the step before contacting the restraining wall of the front side. The order of magnitude of stresses in region 1 of the front side of the D-ring was lower than those in region 2. At an internal pressure of 3.92 MPa, the contact stresses on the upper side decreased before increasing again at points away from the region of extrusion. The study further showed that a sharp corner in the geometry of the D-ring does not contribute to the generation of detrimental stresses that may lead to failure of the D-ring before extrusion.     

Contact stress of O-ring under uniform squeeze rate by photoelastic experimental hybrid method

In this paper, photoelastic experimental hybrid methods using the external traction free boundary condition and that using the relative equation of two stress functions in contact problems are developed. The validities of these two methods are confirmed through experiments and discussions. Hertz’s contact theory and the two photoelastic experimental hybrid methods explained are applied to the analysis of the contact stress of an O-ring under 10% or 20% squeeze rate. The photoelastic experimental hybrid method using the relative equation of two stress functions in contact problems was found to be more effective. When the squeeze rates of an O-ring were 10% or 20%, the maximum of absolute σ _x was greater than the maximum of absolute σ _y , but was almost equal. Maximums of absolute τ _xy were 1/8 of absolute σ _x and 1/5 of absolute σ _x when the squeeze rates of the O-ring were 10% and 20%, respectively. This paper was recommended for publication in revised form by Associate Jai-Sug Hawong received a B.S. degree in Mechanical Engineering from Yeungnam Uni-versity in 1974. Then he received his M.S. degree and Ph.D. degree from Yeungnam University in Korea in 1976 and from Kanto Gakuin University in Japan in 1990, respectively. Prof. Hawong is currently a professor at the school of Mechanical Engineering at Yeungnam University, in Gyeongsan city, Korea. He is currently serving as an vise-president of Korea Society Mechanical Engineering. Prof. Hawong’s research interests are the areas of static and dynamic fracture mechanics, stress analysis, experimental mechanics for stress analysis and composite material etc.     

Contact behavior analysis of X-ring under internal pressure and uniform squeeze rate using photoelastic experimental hybrid method

X-rings were introduced as a result of the limitations of O-rings that twist, especially during dynamic applications. The X-ring design avoids twisting, and the presence of a groove between the lobes acts as a lubricant reservoir that improves the packing life of these seals. Because of the multiple seal points, less squeeze rate is required to provide an effective seal. In addition, friction and wear is decreased, which increases seal life and decreases maintenance costs. Therefore, a better understanding of the behavior and stress distribution of X-rings under a loading condition of uniform squeeze rate and internal pressure is necessary. However, most research to date has been done on the O-ring. We focused on analysis of contact length and contact stresses developed in X-rings under a uniform squeeze rate of 20% (which is suitable for static applications) using a photoelastic experimental hybrid method, and ascertained the packing ability of the X-ring. We show that sealing rings with the X geometry have considerably higher contact stresses than O-ring seals. Also, the contact stresses were higher than the internal stresses of the X-ring. Therefore, our analysis of the contact stresses is adequate in establishing the behavior of the X-ring.     

Internal stress analysis of a stepped rounded D-ring under a uniform squeeze rate and internal pressure using a photoelastic experimental hybrid method

Internal stresses occurring in a stepped rounded D-ring compressed to 20% squeeze and pressurized with internal pressures of 0, 0.98, 1.96, 2.94, 3.92 and 4.9 MPa are analyzed using a photoelastic experimental hybrid method. At a pressure of 0 MPa and 20% squeeze, the photoelastic isochromatic fringes of the stepped rounded D-ring were almost symmetrical. As the internal pressure increased, the isochromatics shifted and curved towards the extrusion gap. By supplying a radius of 0.33 mm at the corners of the stepped D-ring, the high stresses at the sharp corners were reduced by up to 25%. These results further indicate that extrusion of the stepped rounded D-ring occurred at an internal pressure of 4.9 MPa which was about 25% higher than the pressure at which the extrusion of the stepped unrounded D-ring occurred.     

应用光弹实验研究等距型面联接接触应力分布

两弹性体的接触应力通常采用Hertz公式计算,但工程上有时不能完全满足Hertz公式成立的条件,这必然导致与实际情况的偏差。针对等距型面做无键联接传动时,其接触应力不宜用Hertz公式计算的情况,采用光弹实验的方法求其接触应力。     

受均匀内压作用涡旋齿根等效应力简化计算

提出受均匀内压作用的涡旋齿根等效应力的简化计算方案,对所建立的72个涡旋体有限元模型施加端面固定约束和不同内压进行模拟,由模拟结果分析,并经规划得到了简化计算公式.研究表明:不同参数的涡旋齿根等效应力分布规律基本相同,随展角呈指数分布,与涡旋齿高和内压呈线性关系.涡旋齿末段对应展角大约为π/2的部分与其余部分应力分布差别明显,与末段大约涡旋齿理论初始展角α对应的部分应力变化急剧.在不考虑涡旋齿根部应力集中的情况下,涡旋齿根等效应力可进行分段简化计算.大量实例证明:除末段α部分外,简化计算的结果与有限元模拟结果误差较小,最大误差不超过5%.     

A study of the development of the stress optic law of photoelastic experiment considering residual stress

Photoelastic experiment has two significant problems. The first problem is manufacturing a model specimen for complicated shapes of structures. The second problem is residual stress contained in the photoelastic model material. In this paper, the stress optic law that can be effecitvely used on photoelastic model materials with residual stress is developed. By using the stress optic law as developed in this research, we can obtain good results in photoelastic experiments using model material in which residual stress is contained. It is assured that the stress optic law developed in this research is useful. Therefore, it is suggested that the stress optic law considering residual stress can be applied to the photoelastic experiment for the stress analysis of the composite materials or bi-materials in which the residual stress is easily contained.     

Reference stresses and temperatures for cylinders and spheres under internal pressure with a steady heat flow in the radial direction

The paper examines the creep behavior of thick cylinders and spheres subjected to internal pressure and a negative temperature gradient in the radial direction. It is found that at stationary state the rate of radial displacement of the vessel wall is simply proportional to the material creep behavior associated with a single stress and temperature. Such “reference stresses” and “reference temperatures” are defined for spheres and cylinders of varying wall thicknesses. These reference stresses and reference temperatures are valid for any creep problem where the material behavior may be characterized by a function of the form exp (γT)σ^m. The extension of these results to variable pressure and temperature loading cases is discussed.     

Experiments on the buckling under internal pressure of thin torispherical ends of cylindrical pressure vessels

Ten cylindrical pressure vessels with torispherical ends, all of the same constant nominal thickness, were tested under internal pressure to observe the buckling behaviour of the toroidal knuckle. All specimens were of constant internal cylinder diameter to thickness ratio of 531·5. The sphere radius was equal to the cylinder diameter and only the torus radius was varied. Buckling was detected by rotating probes at the sphere/torus junction and at the mid-point of the torus. The buckling pressure increased with increasing torus radius and the two specimens with the largest torus radii did not buckle.For all specimens, the change of meridional shape with increase in pressure was measured. For one specimen, strain gauges were used to study the variation of circumferential strain on the inside and outside surface at the sphere/torus junction due to variation in thickness round the circumference.A simple theoretical expression for the buckling pressure, similar to the Rankine formula for a strut, is suggested.     

Effect of hole perpendicularity error and squeeze force on the mechanical behaviors of riveted joints

In the automatic drilling and riveting process, the perpendicular error of the hole is inevitable, which has a great influence on the assembly quality. In the current research, the shear and pull-out behaviors of riveted joints under different perpendicularity errors and squeeze forces were investigated and compared by the quasi-static tests. The fracture of the failed samples was characterized by a scanning electron microscope and the formation process of fracture was discussed. The failure mechanisms of riveted joints were analyzed in detail to guide engineering applications. The test results demonstrated that the shear load and pull-out load of riveted joints increased slightly with the increase of the tilt angle from 0° to 4°. The perpendicularity error did not affect the shear and pull-out failure modes of the riveted joints. However, the squeeze force had a significant effect on the failure modes of the pull-out samples. Fracture analysis showed that the failure of all shear samples occurred at the rivet shaft. Besides, when the squeeze force increased from 15 kN to 23 kN, the failure modes of the pull-out samples changed from the sheet to the rivet itself.     

A study on the effects of system pressure on heat and mass transfer rates of an air cooler

In the present paper, the effects of inlet pressure on the heat and mass transfer rates of an air cooler are numerically predicted by a local analysis method. The pressures of the moist air vary from 2 to 4 bars. The psychrometric properties such as dew point temperature, relative humidity and humidity ratio are employed to treat the condensing water vapor in the moist air when the surface temperatures are dropped below the dew point. The effects of the inlet pressures on the heat transfer rate, the dew point temperature, the rate of condensed water, the outlet temperature of air and cooling water are calculated. The condensation process of water vapor is discussed in detail. The results of present calculations are compared with the test data and shows good agreements.     

Analysis of thick-walled cylindrical pressure vessels under the effect of cyclic internal pressure and cyclic temperature

A problem common to the pressure vessels' designer is the evaluation of stresses due to the effect of both cyclic temperature and pressure. This paper presents a complete analysis of stresses within the wall of a cylindrical pressure vessel subjected to cyclic internal pressure and temperature. The time-dependent stress distribution is obtained using a numerical model on the basis of the forward finite difference technique. The influence of the working parameters, such as mean pressure and mean temperature, pressure and temperature amplitudes, diameter ratio, etc. on the effective stress is studied. The relation between the mean stress and stress amplitude is obtained for different working conditions. The relation between the working parameters according to Soderberg criteria is presented. An approximate expression for the relation between the working parameters is introduced in a simple and direct form. The results of the approximate solution are found to fit well with the numerical findings.     

Diagnostics of the technical condition of pressure vessels operating under internal pressure by a thermal (thermal imaging) method

Cylindrical reservoirs made of polymer composite materials (PCMs) operating under high internal pressures are presently used in the gas, petrochemical, aerospace, and other industries. Thermal imaging is used for testing of micro- and macroflaws in vessels during pressurizing. Experiments and theoretical studies have shown that, beginning at 5–10% of the maximum acceptable pressure, thermal testing ensures reliable detection and identification of flaws with an accuracy no worse than 15%. This ensures a lower damage hazard to articles without decreased reliability of tests and leads to significant savings due to a decrease in energy consumption and working hours during testing. In addition, a lower damage hazard allows the number of repeatedly occurring flaws to be decreased.     

Analytic description and explicit parametrisation of the equilibrium shapes of elastic rings and tubes under uniform hydrostatic pressure

The parametric equations of the plane curves determining the equilibrium shapes that a uniform inextensible elastic ring or tube could take subject to a uniform hydrostatic pressure are presented in an explicit analytic form. The determination of the equilibrium shape of such a structure corresponding to a given pressure is reduced to the solution of two transcendental equations. The shapes with points of contact and the corresponding (contact) pressures are determined by the solutions of three transcendental equations. The analytic results presented here confirm many of the previous numerical results on this subject but the results concerning the shapes with lines of contact reported up to now are revised.     

A study on the pressure ripple characteristics in a bent-axis type oil hydraulic piston pump

To improve the performance of a bent-axis type axial piston pump driven by tapered pistons, it is necessary to know the pressure ripple characteristics. The purpose of this paper is to understand the effect on the pressure ripple characteristics, and to predict by comparing experimental and theoretical analysis results. The simulation model of a bent-axis type axial piston pump is developed in the AMESim environment using the geometrical dimension, and the driving mechanism of the piston pump, such as the stroke of pump, the velocity of piston, the instantaneous volumetric flow, the overlap area of valve plate opening to cylinder bore, the angle of notch, and so on. The results show that theoretical analysis results of the bent-axis type axial piston pump by using the AMESim approximate the pressure ripple characteristic of the test pump, and through this, simulations can be obtained that predict the performance characteristics of a bentaxis type axial piston pump.     

A study on the development of photoelastic experimental hybrid method for colour isochromatics (I)

Isochromatics obtained from photoelastic experiment shows the stress distributions of the full field of a structure under load. Therefore, stress distributions of the structure can be read at a glance through isochromatics. Many experimental data can be obtained from isochromatics which are then used in various photoelastic experimental hybrid methods for stress analysis. Monochromatic light has however, until now been used in the photoelastic experimental hybrid method to produce black and white isochromatics. The use of black and white isochromatics in photoelastic experimental hybrid method for black and white isochromatics requires high fringe orders in order to obtain sufficient experimental data for photoelastic hybrid techniques. Accordingly, this paper develops the photoelastic experimental hybrid method for color isochromatics in which a fringe order of 1 is enough to gather the experimental data of the photoelastic experimental hybrid method. The method was applied to validate stress concentration problems. Experimental results from this study indicated that the photoelastic experimental hybrid method for color isochromatics is more precise than the photoelastic experimental hybrid method for black and white isochromatics. The use of few fringe orders in photoelastic experimental hybrid method for color isochromatics can offer significant advantages in stress analysis of real components using reflective-type photoelastic experimental method.