The performance indexes of the elastomer hose.

1. Stiffness: the amount of load required for a member to produce a unit displacement is known as its stiffness. A constant value, usually denoted by "K," is used to indicate the stiffness of a member. If the elasticity of the member is not linear, the stiffness is not constant but varies with the load. For engineering applications, the stiffness of a spring-like member is limited to ±50% of its maximum allowable value. Most spring-like members have some degree of non-linearity and the stiffness is determined by the type of loading and displacement. Here are some typical methods for determining the stiffness of a spring-like member, based on its loading and displacement:

2. Energy method: the stiffness of a spring-like member is determined by energy methods.

3. Experienced formula method: the stiffness of a spring-like member is determined by the formula method.

4. Numerical method: the stiffness of a spring-like member is determined by numerical methods.

5. EJMA standard stiffness calculation method: the stiffness of a spring-like member is calculated by the formula method.

6. TOYO standard stiffness calculation method: the stiffness of a spring-like member is calculated by the formula method.

7. KELLOGG (new method) stiffness calculation method: stiffness of a spring-like member is also calculated by other methods. In addition to the above six methods of stiffness calculation, there are many other methods used in the theoretical research and experimental analysis of the spring. Among these, the most important method is:

(1) Oscillation method

(2) Numerical integral method with the initial parameter

(3) Integral equation method

(4) Oscillation finite element method

(5) Modified Kock formula stiffness calculation method

The above methods can be used to very precisely calculate the stiffness of a spring. However, due to the use of deep theoretical and calculation methods in mechanics, the practical application of these methods is difficult and difficult to control. It will take some time to widely promote their use.

Stiffness calculation of metal corrugated pipes combined with spiral tension springs



In the process of application, there is a high requirement for stiffness, and the stiffness of the metal corrugated pipe itself is relatively small. Therefore, it is recommended to first consider installing cylindrical spiral tension springs in the inner or outer cavity of the corrugated pipe. This not only improves the stiffness of the entire elastic system, but also greatly reduces errors caused by hysteresis. The elastic function of this elastic system is primarily based on the characteristics of the tension spring and the stability of the useful area of the bellows.



Bending stiffness of corrugated pipes



Stress calculation of corrugated pipes



As an elastic sealing component, metal corrugated pipes must first satisfy the strength conditions, that is, their stress does not exceed the allowable stress under given conditions. The allowable stress can be obtained by dividing the ultimate stress by the safety factor. According to the operating conditions of the corrugated pipe and the requirements for its application, the ultimate stress can be the yield strength, the critical stress when the corrugated pipe is unstable, or the fatigue strength. It is necessary to analyze the stress distribution in the corrugated pipe wall in order to calculate the working stress of the corrugated pipe.



The stress on the corrugated pipe is generated by the pressure in the system and the deformation of the corrugated pipe. Pressure generates circumferential stress on the corrugated pipe, while radial thin films and bending stresses are generated at the sidewalls, troughs, and peaks of the waves. Thin shells that cannot resist bending are sometimes referred to as thin films, while the stress calculated due to negligence in bending is called thin film stress. When the corrugated pipe deforms, it generates radial film stress and bending stress. During the operation of bellows, some accept internal pressure and some accept external pressure. For example, bellows of corrugated expansion joint and metal hoses accept internal pressure in most cases, while bellows used for valve stem sealing accept external pressure under normal conditions. Here, the stress of bellows under internal pressure is mainly analyzed, and bellows can only accept external pressure under normal conditions higher than that under internal pressure. With the widespread use of corrugated pipes, people have conducted many analytical discussions and experimental verification operations on the stress of corrugated pipes, and proposed many accounting formulas, procedures, and charts for engineering planning. However, some methods are inconvenient to use due to the complexity of charts or programs, while others assume that the conditions are either too simplistic or too ambitious, making it difficult to ensure safety and reliability in application. Many methods have not been accepted by the engineering community. Therefore, there are few ways to truly meet the useful requirements. There are two widely used methods:



1. Numerical method for calculating stress in corrugated pipes



Assuming that all the corrugations of the corrugated pipe are under the same conditions, only a single half wave of the corrugated pipe is considered in the calculation. In this way, the end ripple will not be considered in the discussion, although the boundary conditions of the end ripple are different from those of the center ripple. The numerical method is solved based on the nonlinear equation listed by E. Liesnel for the axial symmetric deformation of thin shells with variable wall thickness inversion. When deriving the E. Liesnel equation, the general assumptions of thin shell theory were used, which also include the assumption that the thickness is very small compared to the main radius of curvature of the annular shell; The assumption of homogeneity and isotropy of data. Choosing the above assumptions will also lead to certain errors in accounting. Because during the production of corrugated pipes, the rolling, drawing, and subsequent corrugated plastic forming of the pipe blank will result in anisotropy and non-uniformity in data mechanics.



2. US EJMA stress accounting method

Calculation of useful area of corrugated pipes



The useful area is one of the fundamental functional parameters of corrugated pipes, which characterizes their ability to convert pressure into concentrated force. In situations where corrugated pipes are used to convert pressure into concentrated force output, the useful area is an important parameter.



When corrugated pipes are used for force balanced surfaces, the stability of their useful area directly affects the accuracy of the surface. So in this situation, it is not only required that the corrugated pipe has a reasonable useful area, but also that the useful area does not change with the working conditions during the operation process.



1. The concept of useful area and changes in useful area



The useful area is an equivalent area, and the pressure effect on this area will generate a flat axial force. Under normal conditions, as the internal pressure increases, the useful area of the corrugated pipe decreases, while the useful area increases with the addition of external pressure.



2. The useful area of the volume of the corrugated pipe



The ratio of the volume change of a corrugated pipe under external force or pressure difference to the corresponding useful length change is called the volume useful area.



3. Calculation of useful area of corrugated pipes



The requirements and accounting methods for the useful area of corrugated pipes depend on their usefulness. If the corrugated pipe is used as an elastic seal or pipeline thermal compensation, the meaning of the useful area is only used to calculate the axial force during the forming of the corrugated pipe and the thrust in the application system. There are some differences between the calculated and measured useful area values of corrugated pipes. Under normal circumstances, using a specialized formula to calculate the useful area of corrugated pipes can completely satisfy the demand.



When corrugated pipes are used to balance the appearance of force and convert pressure into force, their useful area should be accurately confirmed and measured one by one.



2. Sensitivity



The displacement of metal corrugated pipes and other elastic components when subjected to unit load is called the sensitivity of the component. Stiffness and sensitivity are the fundamental functional parameters of corrugated pipes and other elastic components, but they are two different ways of indicating the same application characteristics. For different occasions, for the convenience of analyzing the problem, any parameter can be selected between them.





3. Useful area



Another important functional goal of elastic components for achieving pressure to force or force to pressure conversion is the useful area. Useful area refers to the size of an elastic element that can be converted into a concentrated force when its displacement is zero under a unit pressure effect.



4. Conventional usage of longevity



There are two conditions when working on elastic components; One type of operation is to operate under certain load and displacement conditions, and adhere to the principle that the load and displacement remain constant or rarely change, which is called static operation; Another application scenario is the constant cyclic replacement and change of load and displacement. The component is in a cyclic operation state. Due to different operating conditions, the forms of component damage or failure also vary. The operation of external elastic sensitive components is fundamentally in a static state within the elastic scale, and the lifespan of conventional applications is very long, usually reaching tens of thousands to hundreds of thousands of times. The corrugated pipe components used in engineering sometimes operate on an elastic-plastic scale or under alternating stress conditions, with a lifespan of only hundreds of times. It is necessary to give the allowable lifespan of the component during cyclic operation, as well as the number of regular cycles, time, and frequency.



The additional lifespan of elastic components is the expected usage lifespan set during component planning, and it is required that the components do not exhibit fatigue, damage, or failure during this period.





5. Sealing performance



Sealing refers to the function of ensuring that components do not leak under a certain internal and external pressure difference. When working on corrugated pipe components, the inner cavity is filled with gas or liquid medium and has a certain pressure, so it is necessary to ensure sealing. The new methods for detecting sealing include air pressure sealing test, leakage test, liquid pressure test, and detection using soap water or helium mass spectrometer leak detector.



6. Natural frequency



Elastic components used in industry often experience certain degrees of oscillation in their operating environment. Some components are used as isolation components and are themselves under oscillation conditions. Regarding elastic components used under special conditions, it is necessary to prevent the natural frequency (especially the fundamental frequency) of the components from being near the frequency of any oscillation source in the system, in order to prevent resonance and damage. Corrugated pipe components have been widely used in various fields. To prevent resonance surface damage to the corrugated pipe, the natural frequency of the corrugated pipe should be lower than the oscillation frequency of the system, or at least 50% higher than the vibration frequency of the system.





7. Application temperature



The application temperature scale of metal corrugated pipe components is very wide, and they are generally given before the planning and production of elastic components. Some particularly useful corrugated pipes have an inner chamber that passes through liquid oxygen (-196 ℃) or lower temperature liquid nitrogen, with a pressure resistance of up to 25MPa. The large corrugated expansion joint (nominal diameter sometimes exceeds lm) used for the connection of pipe network system is required to have a pressure of 4MPa, a temperature resistance of 400 ℃, and a certain corrosion resistance stability. The temperature adaptation ability of elastic components depends on the temperature resistance function of the selected elastic material. Therefore, based on the application temperature scale of elastic components, elastic materials with appropriate temperature functional parameters can be selected to process and produce qualified corrugated pipe components.