In the present paper, the gasket stress distributions, hub stress and a variation in axial bolt force in bolted gasketed pipe flange connections under internal pressure are analyzed using elasto-plastic FEM taking into account the nonlinearity of gasket behavior. Non-asbestos spiral wound gaskets were employed. The effect of nominal flange diameter is examined on the gasket contact stress distributions, the hub stress and the variation in axial bolt force (the load factor) is examined. Using the obtained gasket contact stress distribution and the fundamental data of the relationship between gasket compressive stress and gasket leak rate according to JIS B 2490, a method for predicting the leak rate is demonstrated. Experiments to measure the amount of leakage, the hub stress and the variation in axial bolt force when the joint is under internal pressure were carried out. The numerical results of the leak rate, hub stress and the load factor are in a fairly good agreement with the measured results. Then, a method is demonstrated for determining the bolt preload under given conditions, that is, taking into account assembly efficiency, leak rate and internal pressure In addition, bolt preload is determined using the actual gasket contact stress which can be estimated using the value of the load factor. As a design example, the procedure for determining the bolt preload in 3″ and 20″ nominal diameter pipe flange connections is shown for the allowable leak rate of 1.0−3Pa • m3/s. The results are validated by the experiments.
Cold forging is a metal forming that which uses localized compressive force at room temperature. During the cold forging process, the tool is subjected to extremely high loads and abrasive wear. Lubrication plays an important role in cold forging to improve product quality and tool life by preventing direct metallic contact. Surface roughness and residual stress also greatly affects the service life of a tool. In this study, variations in surface roughness, residual stress, and specimen deformation with the number of cold forging cycles were investigated under different forging conditions. Specimens that were made of heat-treated SKH51 (59–61 HRC), a high-speed tool steel with a polished working surface, were used. The specimens were subjected to an upsetting process. Compressive residual stress, surface roughness, and specimen deformation showed a positive relationship with the number of forging cycles up to a certain limit and became almost constant in most of the forging conditions. A larger change in residual stress and surface roughness was observed at the center of the specimens in all the forging conditions. The effect of the magnitude of the forging load on the above discussed parameters is large when compared to the effect of the lubrication conditions.
In designing a bolted joint, it is important to estimate an increment in axial bolt force when an external tensile load is applied to an assembly. The ratio of the increment Ft in the axial bolt force to the external tensile load W is called the load factor φ(= Ft/w). The formula φ = Kt/(Kt+Kc) proposed by Thum has been applied for estimating the value of the load factor φ, where Kt is the spring constant of bolt-nut system and Kc is the compressive spring constant of clamped parts. It has been found that the value of the load factor varies with the position of load application to the assembly. Then, a method to compensate Thum’s formula was proposed. However, this compensation is made empirically and the theoretical background is not made clear. In this paper, the concept of the tensile spring constant Kpt for clamped parts is introduced newly when an external load is applied to the outer circumference of clamped parts (hollow cylinders) and a method for estimating the value of the load factor exactly is proposed by using Kpt. The value of Kpt is analyzed using an axisymmetric theory of elasticity. For verification of the proposed method, experiments were carried out to measure the load factor. A fairly good agreement is seen between the analytical and the experimental results of the values of the load factor while the values of the load factor obtained from Thum’s formula were so different with the experimental results. The reason why the difference in the values of the load factor is substantial between values and the values obtained from Thum’s formula is elucidated. It is found that the value of the load factor decreases as the outer diameter of the hollow cylinder increases and the as thickness of the clamped parts decreases. In addition, FEM calculations for the load factor are carried out. The FEM results are in a fairly good agreement with the theoretical results.
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