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As an elastic sealing component, a pipeline bellows must first meet the strength requirements, that is, its maximum stress must not exceed the allowable stress under given conditions. The allowable stress can be obtained by dividing the ultimate stress by the safety factor. Depending on the operating conditions of the bellows and the requirements for its use, the ultimate stress can be the yield strength, the critical stress at which the bellows loses stability, or the fatigue strength, among others. To calculate the maximum operating stress of a bellows, it is necessary to analyze the stress distribution within the bellows wall. Piping bellows can be divided into metal and non-metal types based on their material. 1. A metal bellows consists of the bellows itself, which is the main component that enables its function (an elastic element), along with accessories such as end tubes, supports, flanges, and ducts; it is considered a type of compensation element. By utilizing the effective expansion and contraction of its main working element, the bellows, it can absorb dimensional changes in pipelines, conduits, containers, etc., caused by factors such as thermal expansion and contraction, or compensate for axial, lateral, and angular displacements of these components. It can also be used for noise reduction and vibration damping, and is widely applied in modern industry. 2. Metal bellows can compensate for axial, lateral, and angular displacements of pipes. They feature no thrust generation, simplified support design, corrosion resistance, high-temperature tolerance, as well as sound and vibration reduction properties, making them particularly suitable for hot air ducts and dust exhaust ducts. The theoretical basis for the design of pipeline bellows includes plate-shell theory, mechanics of materials, computational mathematics, etc. There are many parameters involved in the design of pipeline bellows, and since these bellows serve different purposes within a system, the focus of their design calculations also varies. For example, in force-balancing components, it is required that the effective area of the bellows remain constant or change only slightly within its operating range ; Used for measuring components; the elastic properties of the bellows are required to be linear ; Pipe bellows are used as vacuum seals for vacuum switch tubes, and requirements include the vacuum sealing performance, axial displacement, and fatigue life of the bellows ; Used as seals for valves, the bellows are required to have certain pressure resistance, corrosion resistance, temperature resistance, operational displacement capacity, and fatigue life. Based on the structural characteristics of pipeline bellows, they can be regarded as being composed of annular shells, flat conical shells, or annular plates. Designing and calculating pipeline bellows means designing and calculating circular shells, flattened conical shells, or toroidal plates. The parameters of pipeline bellows are stiffness, stress, effective area, instability, allowable displacement, pressure resistance, and service life.