Metal corrugated pipe design theory basis is the theory of plates and shells, the material mechanics, computing mathematics. Many parameters bellows design, because the use of corrugated pipe in the system is different, the design and calculation of key is not the same. For example, a force balance element corrugated pipe, corrugated pipe requirements within the scope of work in the effective area of constant or change very little, for measuring element, elastic properties of bellows requirement is linear; used for vacuum switch tube for the vacuum seal, requirements for vacuum bellows seal, axial displacement and fatigue life for the valve; as the seals, bellows should have a certain degree of pressure resistance, corrosion resistance, temperature, displacement and fatigue life.

　　According to the structure characteristics of corrugated pipe, corrugated pipe can be put as the ring shell, shallow conical shell or ring plate. Design and calculation of bellows is design calculation of the circular shell, shallow conical shell or ring plate.

　　Parameter calculation of bellows design for stiffness, stress, effective area, instability, allowing the displacement, pressure resistance and service life.

　　Stiffness calculation of bellows

　　Stiffness of the bellows in accordance with the different nature of the load and displacement, divided into axial stiffness, bending stiffness, torsional stiffness etc.. At present, in the application of bellows, the overwhelming force in most cases is the axial load, displacement mode for linear displacement. The following are some of the main corrugated pipe axial stiffness calculation method for design:

　　Calculation of bellows stiffness 1 energy method

　　Bellows stiffness calculation of 2 empirical formula

　　Calculation of bellows stiffness 3 numerical method

　　Stiffness calculation method of 4.EJMA standard

　　Stiffness calculation method of 5 TOYO in Japan

　　6 KELLOGG (New) American stiffness calculation method

　　In addition to the above six kinds of stiffness calculation method, calculation method and many other foreign stiffness, then no longer be introduced. Mechanical workers in China have done a lot of work in the aspect of theoretical research and experimental analysis of bellows, achieved fruitful results. Study on the method of which the most important are: (1) the perturbation method (2) initial parameter method of numerical integration (3) integral equation method (4) perturbation finite element method

　　The above methods can be on the corrugated pipe for more precise calculations. However, because the method theory and applied and computational mathematics deeper, the engineering application has the certain difficulty, but also difficult to master, the need for further popularization.

　　Metal corrugated pipe and the spiral spring when combined with stiffness calculation

　　In the use process, the rigidity requirement is larger, and the metal corrugated pipe itself stiffness is small, can be considered in the inner or external configuration of cylindrical helical spring bellows. It can not only improve the elastic stiffness of the system, and the error caused by hysteresis can be greatly reduced. The stability of the effective area of the elastic properties of the tube elastic system mainly depends on the characteristics and the ripple in spring.

　　Corrugated pipe bending stiffness

　　Calculation of the stress of the bellows

　　Metal corrugated pipe as an elastic sealing parts, to meet the strength conditions first, i.e. the maximum stress does not exceed the allowable stress under given condition. Allowable stress can be obtained by the limit of safety coefficient of force divided by. According to the requirements of the bellows working conditions and the use of it, can be the ultimate yield strength stress, can also be a bellows critical stress instability, or fatigue strength. To calculate the bellows maximum working stress must analyze corrugated pipe stress distribution in the wall.

　　Stress of the bellows on the deformation caused by the pressure in the system and the corrugated pipe. Pressure produced by the ring on a corrugated pipe (axial direction) stress, while in the film side wall, wave trough and crest produce radial and bending stress. Not bending of the thin shell is sometimes referred to as a film, ignoring the bending stress is called the film stress. Corrugated pipe deformation caused radial membrane stress and bending stress. Bellows at work, some under internal pressure, some are subject to external pressure, such as bellows expansion joint and the metal hose in the majority of cases the bellows under internal pressure, and the valve stem seals for corrugated pipe generally subjected to external pressure here mainly analysis of bellows under internal pressure when the stress of bellows under internal pressure resistant ability is higher than the external pressure ability in general. With the wide application of corrugated pipe, people carry on research and experimental verification on the stress analysis of a large number of bellows, put forward many for engineering calculation formulas and design using computational procedures and chart. However, some methods or procedures are complicated because the chart is not convenient to use, some assumptions are not overly simplified method is too ideal, it is difficult to ensure the use of safe and reliable, many methods failed to accept for the engineering sector. Therefore, truly meet the practical requirements of the method is one of the few. At present, there are two kinds of methods widely applied:

　　Calculation of bellows stress 1 numerical method

　　Assume that all corrugated corrugated tube are in the same conditions, in the calculation of only single Bellow's half wave. So, in the study would not consider the end corrugation, although the end of a corrugated boundary conditions vary with the middle corrugated. The numerical method is based on the E. Liesinieer for variable wall thickness of revolution shells produce nonlinear equation of axial symmetry deformation of column to solution. In the derivation of the E. Liesinieer equation, application of the thin shell theory is generally assumed, including: thickness assumption compared with very little ring shell principal radius of curvature; assuming the material homogeneity and isotropy. With the above assumption will bring some errors to calculate. Because in the manufacture of bellows tube billet, rolling, drawing and subsequent corrugated plastic