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 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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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 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.     

Deformation analysis of plastic strain rate hardening material using stress function under plane strain condition

The two-dimensional plane strain equation of plastic flow in accordance with the Levy-Mises constitutive relation is expressed in terms of stress functions of complex variables. Expressions for the stress, strain rate and velocity are derived for plastic flow in a non linear viscous medium assuming the stress function in the form of both the summation and product of conjugate stress functions. The plastic states are derived, also using a mixed mode solution expressed in terms of non-seperable, independent conjugate complex variables.The analysis of the block indentation associated with a nonlinear viscous (strain rate hardening) material under plane strain condition using the product form solution is performed. The effect of the variation in the strain-rate hardening exponent on the contact stress is investigated. The predicted behavior of the vertical component of the contact stress suggests the possibility of the development of a specially instrumented plane strain block indentation tests, for the rapid determination of the strain-rate sensitivity of the real material. The vertical contact stress and strain-rate obtained from the product of the complex conjugate stress function are compared with those obtained from the summation form of the complex conjugate stream function.     

Transverse vibration of a uniform Euler-Bernoulli beam under varying axial force using differential transformation method

This paper presents the application of techniques of differential transformation method (DTM) to analyze the transverse vibration of a uniform Euler-Bernoulli beam under varying axial force. The governing differential equation of the transverse vibration of a uniform Euler-Bernoulli beam under varying axial force is derived and verified. The varying axial force was extended to the more general case which was high polynomial consisted of many terms. The concepts of DTM were briefly introduced. Numerical calculations are carried out and compared with previous published results. The accuracy and the convergence in solving the problem by DTM are discussed.     

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...     

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.     

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.     

Re-rounding analysis of API X60 pipelines containing an unconstrained dent subjected to internal pressure using finite element method

Journal of Mechanical Science and Technology - As a common defect on pipelines, a dent normally re-rounds under internal pressure, which impacts the integrity of a dented pipeline. In this study, a...     

爬壁机器人的力学分析与实验

运用键图理论建立了爬壁机器人负压吸附动力学过程模型,并对其进行了仿真及实验分析.针对爬壁机器人的特点,对负压吸附系统的技术要求进行了详细分析,设计了高效率负压吸附系统.在对负压吸附系统进行合理的假设和流体力学分析的基础上,运用键图理论针对不同物理域具有参数等效的特点,把负压吸附流体系统参数等效为机械动力学中的力、位移、刚度和阻尼;负压吸附动力学模型等效为一阶的机械系统,建立了键图模型,应用20sim软件进行仿真.仿真结果显示,爬壁机器人负压吸附过程在负压形成过程中是一阶响应过程,系统响应时间为1.5 s.最后进行了试验测试,测试结果证明了所建立模型的正确性.