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.     

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.     

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.     

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.     

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.     

A study on the behaviors and stresses of O-ring under uniform squeeze rates and internal pressure by transparent type photoelastic experiment

The behaviors and stresses of an O-ring under uniform squeeze rates and internal pressure change with real time. Therefore, the behaviors and stresses of O-rings under uniform squeeze rates and internal pressures should be studied with real time. To achieve this, a loading device for a transparent type photoelastic experiment, through which various internal pressures and uniform squeeze rates are applied, was developed. The validity of the loading device in analyzing the behaviors and stresses of the O-ring under uniform squeeze rates and internal pressures with real time was verified. It was observed that the filling phenomenon of the O-ring into the space between the lower and front side occurred after forcing out continued for a duration of time. The study also indicated that maximum shear stress would be more effective as a fracture parameter than the maximum normal stress fracture criterion for an O-ring made from rubber.     

Stress and fracture analysis of D-ring by photoelastic experimental hybrid method

In this study, stresses in a D-ring seal under compression and various hydraulic pressures were analyzed using Photoelastic experimental hybrid method (PEHM). The fracture behaviors of the seal, namely the shape, location and origin of damage, were investigated. It was shown that fracture damage initiated from the region close to extrusion gap and propagated inward at an angle of about 60? with the horizontal as the reference and also along the circumference of the seal. The maximum contact length reached about 84 % of the cross sectional height. The attractive features of the seal makes it a suitable choice for high pressure sealing applications.     

Internal stress distribution of X-ring using photoelastic experimental hybrid method

Sealing elements are essential parts of many machines, and are used to prevent the loss of a fluid or gas. When such fluids are not properly sealed, catastrophic failures may result. Many different types of rings have been developed to suit various industrial needs. Considerable research has been done on the O-ring. We analyze the internal stresses developed in an X-ring under a uniform squeeze rate of 20%, which is suitable for static applications, using a photoelastic experimental hybrid method. The internal pressures applied were 0.98, 1.96, 2.94, 3.92, 4.90, and 5.88 MPa. We show that sealing rings with X geometry have considerably higher internal stresses than O-ring seals. In addition, we demonstrate that after extrusion, for an internal pressure of 5.88 MPa, the two lobes on the upper contact surface merge, thereby increasing the contact length of the upper side significantly. Extrusion in the X-ring occurred when the internal pressure was 4.90 MPa.     

Analysis for interior stress in various curvature radiuses on D-ring seal using hybrid photoelastic experimental method

When the seal is suffered from defected damage, it initiates a little leakage and finally becomes the critical abnormal condition. Sealing ring has very small than neighbored other components, it has to be considered as the most important thing due to intensity of its function. Sealing rings are designed with many kinds of cross-sections: O-ring, Square-ring, D-ring, X-ring etc. according to its different usage. The cross-section of D-ring is included with cross-sections of O-ring and Square-ring partially, in a other word, D-ring has both advantages of O-ring and Square-ring. In order to reduce the stress concentration, D-ring should be prepared with curvature radius in both sides of the lower square corner. In this work, the analyses on the interior stresses, and the behavior of D-ring with various curvature radius under uniform squeeze rate 20 % and various internal pressures of 0~20 MPa were studied by using the stress frozen photoelastic experiment and the photoelastic experimental hybrid method. From this research, it was founded that the geometrically optimal condition for curvature radius of D-ring under uniform squeeze rate and various internal pressures is r/D = 0.3.     

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%.     

Numerical modeling and experimental verification of compressible squeeze film pressure

The validity of using the Reynolds equation for compressible squeeze film pressure was tested with computational fluid dynamics (CFD). A squeeze film air bearing was instrumented with pressure sensors and non-contacting displacement probes to provide transient measurements of film thickness and pressure. The film thickness measurements also provided input parameters to the numerical prediction. However, numerical results showed a larger load capacity than those suggested from the experimental results. Furthermore, the nonlinear time averaged positive pressure described by the Reynolds equation was not evident in the experimental study.     

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.     

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

Using the photoelastic experimental hybrid method, we can obtain stress intensity factors and separate the stress components near the crack tip of any material under various loading conditions from only isochromatics. However, monochromatic light has, until now been used in the photoelastic experimental hybrid method to produce black and white isochromatics. The existing photoelastic experimental hybrid method using black and white isochromatics requires high order fringes to obtain sufficient experimental data for photoelastic hybrid techniques. If a photoelastic experimental hybrid method for colour isochromatics is developed, isochromatics with a maximum fringe order of 2 will be adequate for gathering the necessary experimental data for stress analyses using photoelastic hybrid techniques. Therefore, in this work, photoelastic experimental hybrid method for colour isochromatics of a crack problem was developed, and its superiority demonstrated by comparing its results with the results from black and white isochromatics. The use of few fringe orders in photoelastic experimental hybrid method for colour isochromatics is an important feature of this method. Because of this feature, this method, specifically the reflection type photoelastic method where low fringe orders are produced compared to the transmission type photoelastic method, can be widely used in stress analysis of real components.     

Free vibration analysis of rectangular plates with internal columns and uniform elastic edge supports by pb-2 Ritz method

Free vibration analysis of rectangular plates with internal columns and elastic edge supports is presented using the powerful pb-2 Ritz method. Reddy's third order shear deformation plate theory is employed. The versatile pb-2 Ritz functions defined by the product of a two-dimensional polynomial and a basic function are taken as the admissible functions. Substituting these displacement functions into the energy functional and minimizing the total energy by differentiation, leads to a typical eigenvalue problem, which is solved by a standard eigenvalue solver. Stiffness and mass matrices are numerically integrated over the plate using the Gaussian quadrature. The accuracy and efficiency of the proposed method are demonstrated through several numerical examples by comparison and convergency studies. Many numerical results for reasonable natural frequency parameters of rectangular plates with different combinations of elastic boundary conditions and column supports at any locations are presented, which can be used as a benchmark for future studies in this area.     

Theoretical,simulation and experimental investigation of 1D hybrid pressure distribution for internal gear motors and pumps

Journal of Mechanical Science and Technology - Internal gear motor and pump is the typical rotating machine which operates in hybrid regime of lubrication. Calculation of the pressure distribution...     

A study on the development of a loading device using a photoelastic stress freezing method for the analysis of o-ring stress

Typically, O-rings are used to prevent penetration of dust and alien substances from entering a cylinder during motion. Moreover, Orings are used to create an air tight seal around a stationary shaft. The stresses developed in O-rings depend on the squeeze rate, gap between the external diameter of the groove and internal diameter of the cylinder as well as internal pressure. In application, the stress distributions in O-rings can be very complicated and are almost always studied through experiment. Photoelastic experiment has been applied to the study of 3-dimensional stress distributions in O-rings. The loading device used in photoelastic experiment is important. Its function is to apply a uniform squeeze rate and internal pressure on the O-ring and to allow uniform squeeze rate to be controlled. In this research, a loading device was developed to perform these functions. The validity of this loading device was confirmed through the stress distribution, the configuration change and the contact length of the O-ring. When the squeeze rate was constant, the upper and lower contact lengths of the deformed O-ring were almost equal. When internal pressure was applied to the O-ring, while under a uniform squeeze rate the upper contact length increases slightly with increase in internal pressure, while the lower contact length of the O-ring is constant with an increase in internal pressure.     

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.     

On the stress distribution in prestressed extrusion dies under non-uniform distribution of internal pressure

Cold extrusion die stress distribution is normally calculated on the assumption that there is a uniform distribution of internal pressure, e.g. by application of the Lamé equations. With FE-analysis this assumption can be overcome by the introduction of arbitrary boundary conditions. However, as little information existed about realistic distribution of radial and axial stresses in container and die this possibility was not used very much. Only after a recent investigation of Bay [1] into friction and pressure distribution in forward extrusion an FE-calculation of stresses in a prestressed extrusion die under non-uniform distribution of radial pressure seemed to be promising. The results show very clearly that no negative effects on the stress state—e.g. increase of stress peaks—may be expected in case of combined continuous decrease of radial pressure in the container and discontinuous increase at the die entry.     

Limit analysis of strain-hardening viscoplastic cylinders under internal pressure by using the velocity control: Analytical and numerical investigation

The paper aims to assess plastic limit loads of thick-walled hollow cylinders of strain-hardening viscoplastic materials under internal pressure. Particularly, the problem concerned features in the interaction between strengthening and weakening behavior during the deformation process. Therefore, the relating onset of instability and the stability condition also deserve to be further investigated. Analytical and finite-element limit analysis efforts are both made for complete and comparative investigation. By the concept of sequential limit analysis, the plastic limit loads were acquired by solving a sequence of limit analysis problems via computational optimization techniques. Applying the velocity control as a computational strategy to simulate the action of pressure, the paper investigates analytically and numerically the plastic limit load, the onset of instability and the stability condition of plane-strain circular cylinders. Especially, analytical solutions of the onset of instability were solved explicitly by the fixed point iteration. Validation of the present analytical and finite-element efforts was made completely with good agreement between the analytical solutions and the numerical results.