How to choose the wave height and pitch of the compensator? Understand these points, pipeline design no longer steps on pits

Wave height and wave distance, what the hell are they talking about?

Don't be fooled by the words "wave height" and "wave distance". To put it bluntly, wave height is the vertical height of a ripple from peak to valley-you can think of it as the amplitude of the undulation of a wave; Wave distance is the horizontal distance between two adjacent peaks (or troughs). Placed on the bellows of the compensator (that is, the expansion joint), these two parameters directly determine how "soft and hard" it is and "how much displacement it can swallow".

The larger the wave height, the larger the spring coil diameter, the easier the bellows to deform, and the ability to compensate displacement is strong, but the pressure bearing capacity will decrease; The larger the wave pitch, the larger the pitch equivalent to the spring, the more rigid the bellows and can carry higher pressure, but the number of corrugations required under the same displacement is less. Therefore, selecting wave height and wave distance is essentially to find a balance between "flexible compensation" and "stable pressure resistance".

When designing pipeline, selection of compensator wave height and pitch? Who has the final say? Don't worry, read a negative textbook first.

What happens if the wave height and wave distance are selected wrong? A real case of pipeline failure

Two years ago, there was a problem with the steam pipeline of a chemical plant. The design temperature is 400℃, the pressure is 1.6MPa, and the displacement is 80mm. They chose a general-purpose corrugated expansion joint, which has a large wave height and a small wave pitch-to put it bluntly, it is "too soft". Results Less than three months after operation, the bellows became unstable, the wave crest collapsed, and the air leaked directly. When the scene was removed, the corrugation spacing had been squeezed together and completely lost its elasticity.

What's the problem? If the wave height is large, although it can easily cope with the axial displacement of 80mm, the local stress of the bellows wall is too high due to the small wave pitch. Under the superposition of high temperature and pressure, the creep of the material is accelerated and the fatigue failure is advanced. This is the typical pit of "compensator wave height and wave distance selection? Only focusing on displacement, ignoring pressure". Selection is never about patting your head, you have to break up the working condition parameters one by one.

Three core factors influencing the selection of wave height and pitch: pressure, displacement and fatigue life

There are only three things that really determine the height and distance of the wave:Design pressure, compensated displacement, expected fatigue life。 Let's disassemble them one by one.

Pressure: Determining the upper limit of wave height

The higher the pressure, the smaller the wave height. Why? Large wave height means that the curvature radius of the bellows wall is large, and the film stress is large when it is subjected to internal pressure, which is easy to bulge or burst. Therefore, for high-pressure working conditions (such as the main steam pipeline of the power station, the pressure is above 10MPa), bellows with small wave height and large wave pitch are generally selected, such asHigh temperature axial expansion jointOrExternal pressure single axial expansion joint。 Conversely, it is fine to use large wave heights for low-pressure pipes (such as flue gas pipes), likeRectangular non-metallic expansion jointOrNon-metallic expansion joint (fabric fiber expansion joint)It does not rely on the metal corrugation to bear pressure at all, and the constraint of wave height and wave distance is much smaller.

Displacement: a function of wave pitch and number of ripples

When the compensation displacement is large, the common practice is to increase the number of ripples instead of blindly increasing the wave height. Because excessive wave height is sensitive to pressure, the wave distance can be appropriately amplified. Such asUniversal corrugated expansion jointIn the selection table, for every 10mm increase in axial displacement, 1~2 waves are usually added. The wave pitch should be selected to ensure that there is sufficient gap between the corrugations, so as to avoid the collision of wave peaks during compression-the collision will directly lead to stress concentration and fatigue life drop.

Fatigue Life: The "Referee" of Model Selection

A lot of designers ignore this. ASTM or national standards have clear requirements for the fatigue life of compensators (such as 1000 cycles). The collocation of wave height and wave pitch directly affects the maximum stress amplitude of bellows, and then determines the life. As mentioned in the product information on our siteStiffness and Calculation Formula of BellowsIt is emphasized in (QA1) that the stiffness is inversely proportional to the cubic power of the wave height and directly proportional to the first power of the wave distance. When the wave height increases slightly, the stiffness decreases sharply, but the stress does not necessarily decrease-full stress check is needed. Therefore, applications with high fatigue life requirements (such as those for air-cooled island vacuum pipesDouble hinge expansion joint for air-cooled island vacuum pipeline), must take into account both wave height and wave distance, and iteratively calculate with special software. And guess what? The root cause of the failure of many factories is that only an "experience value" was taken during the fatigue life check.

How to choose under different working conditions? From general purpose to high temperature to non-metallic compensators

After talking about theory, talk about practice. According to the existing product series of this site, the selection of several typical scenes is sorted out:

• General Low Pressure Pipeline (Water, Oil, Low Pressure Steam): SelectUniversal corrugated expansion jointThe wave height is 0.1 to 0.15 times of the nominal diameter, and the wave distance is 0.8 to 1 times of the wave height. For example, DN100 pipeline has a wave height of 10~15mm and a wave pitch of 8~15mm. When the pressure is lower than 1.0MPa, it can still be usedrubber compensatorOrRubber PTFE compensatorThe wave height and pitch are determined by rubber molding, so there is no need to worry about it.
• High temperature and high pressure steam pipeline (main steam and reheated steam of power station): Must go onHigh temperature axial expansion jointOrCorrugated expansion joint for power station industry。 The wave height should not exceed 20mm (even above DN600), and the wave distance should be appropriately increased (15~25mm) to reduce the film stress. At the same time, the internalexpansion joint guide tubeAvoid high-speed steam scour ripples.
• Cement/flue gas industry (large displacement, low pressure, dusty): PreferredNon-metallic expansion jointOrRectangular non-metallic expansion joint。 In fact, the concept of wave height and wave pitch is not applicable to fabric fibers, but the "band width" and "interlayer spacing" in structural design are similar to logic: the band is too wide (equivalent to too large wave height) and it is easy to dust, and the compensation is too narrow (the wave pitch is too small). This type of product is pressed byNational standard for non-metallic expansion joints(JB/T 12235-2015) can be selected.
• Corrosive media (acid, base)：PTFE-lined hoseOrPTFE compensatorEnter the stage. Wave height and wave pitch are limited by the molding ability of PTFE. Usually, the wave height is small (8~12mm), and the wave pitch is uniform, so it cannot be over-stretched, otherwise the PTFE layer will crack.

The wave height and wave distance of different working conditions are very different, so you can't take a template everywhere in the selection. Two days ago, a customer asked: What is the selection of compensator wave height and wave distance? Can you give me a watch directly? I say yes, but only if you list the pressure, temperature, displacement, number of cycles-otherwise the table given is waste paper.

Measured Data Speak: Relationship between Wave Height and Wave Pitch and Compensator Stiffness

We use a set of typical data to illustrate the problem (based on the factory laboratory measurement, non-theoretical formula calculation). Take 304 stainless steel bellows with wall thickness of 1.2mm and corrugated inner diameter DN150 as an example:

• Scheme A: Wave height 15mm, wave pitch 12mm → axial stiffness about 400N/mm, single wave compensation amount 5mm, fatigue life 3000 times (at 1.0MPa).
• Scheme B: wave height 20mm, wave pitch 12mm → axial stiffness drops to 220N/mm, single wave compensation amount 7mm, but fatigue life drops to 1200 times.
• Scheme C: The wave height is 15mm, the wave pitch is 18mm → the axial stiffness rises to 600N/mm, the single wave compensation is only 3.5mm, and the fatigue life is reduced to 800 times due to stress concentration.

See? The wave height increases, the stiffness decreases exponentially, and the compensation amount goes up, but the fatigue life is severely sacrificed. The wave pitch increases, the stiffness increases, but the compensation amount is too small, more ripples are needed, and the cost goes up. The core of the selection is to find the practically available intersection in this triangle (stiffness-compensation-life).

This is why professional manufacturers (such as the technical accumulation behind the 23 types of products in our station) are doing itExpansion joint selectionWhen, finite element will be used to assist calibration, rather than relying on hand calculation alone.

Summary: Selection is not patting the head, just follow these four steps

After so much verbose, it is summarized into a four-step operation guide. Next time you design the pipeline, you will go directly against it:

1. Explicit boundary conditions: Pressure (maximum operating pressure + hydraulic test value), temperature (maximum + minimum), displacement (axial/transverse/angular, note thermal expansion and contraction and installation deviation), allowable fatigue life (usually 1000 times or more).
2. Initial wave height and wave distance: According to the pressure level, refer to the industry experience (such as high-pressure wavelet height, low-pressure large wave height), choose a gear first. Recommended wave height for high pressure =0.03~0.06 times nominal diameter, 0.08~0.15 times for medium and low pressure.
3. Calculate the number of corrugations required: Divide the total displacement by the allowable compensation amount of single wave (note that the safety factor is 0.6~0.7) to get the minimum number of corrugations, and then multiply by the wave pitch to get the effective length of the bellows. While considering space constraints.
4. Fatigue checking and fine-tuning: The maximum stress is calculated using software or a formula (e.g. EJMA standard) and the fatigue curve of the material is compared. If the fatigue life is not enough, the wave height should be reduced or the number of corrugations should be added, and the single wave compensation amount should be reduced. Go back and adjust the wave distance again, and iterate again and again.

Compensator wave height and pitch selection? There is no standard answer to this question, only the answer "best for your working conditions". Don't be superstitious about the so-called "universal type"-find a professional manufacturer. After all, if something happened to the pipe, it was not as simple as replacing the bellows.