Compensator Plane Instability Calculation: Understanding this can avoid the pit of pipeline failure

Find out first: What does compensator plane instability look like?

To put it bluntly, plane instability means that when the bellows is subjected to internal pressure or axial displacement, the bellows no longer expands and contracts along the axis honestly, but bends, twists and even rolls over in the plane perpendicular to the axis like a twist. Imagine: an originally straight metal bellows suddenly becomes S-shaped or wavy, with asymmetric wrinkles between the corrugations-this is the typical look of plane instability.

This instability is not the slow grinding of metal fatigue cracks, it often occurs instantaneously. Once it appears, the compensator is basically scrapped, and in severe cases, it directly leads to pipeline rupture, media leakage, and even the whole pipe system is paralyzed. The most exaggerated case we have ever seen in actual engineering is: the cement industryMetal Corrugated Expansion Joints in Cement IndustryLess than two months after it was put into operation, the bellows was completely twisted into a ball like a kneaded can.

Why does a good expansion joint suddenly "convulse" and become like this?

What factors are most likely to push the compensator into "plane instability"?

The reason is only three words-press, bend and twist. But breaking it down, there are a few things to blame:

• Internal pressure too high: Pressure is the direct pusher of plane instability. When the bellows is subjected to internal pressure, it will produce circumferential stress, which will bulge the corrugation outward. When the pressure exceeds a certain critical value, the corrugation will lose its stability. To put it bluntly, it is like blowing the balloon over-blown, and the balloon wall begins to bulge locally.
• Excessive axial displacement: The compensator is designed to absorb thermal displacement, but if the actual displacement exceeds the design value, the bellows is overcompressed or stretched, and the spacing between the corrugations changes too much, which can also induce instability. You see those expansion joints that are crushed and asymmetrical like an accordion on the spot, and nine times out of ten, the axial displacement is exceeded.
• Installation deviation: This one is too common. The center line of the pipeline is not aligned, and the expansion joint is forcibly screwed on; Or the fixing bracket is not done properly, causing the expansion joint to bear additional bending moment. Two days ago, I met a customer who said that they had installed a power station projectCorrugated expansion joint for power station industryAs a result, it collapsed directly during the pressure test-after checking, the eccentricity of the pipeline was two centimeters different during installation.
• Insufficient support: The bellows itself is a flexible element. Without suitable guide brackets and fixing brackets, it will twist like a snake without a skeleton. Especially those with long ripples, multiple wavenumbers, such asUniversal corrugated expansion jointIf the limiting device is lacking in the middle, the probability of plane instability soars.

The calculation formula of plane instability is not so mysterious. The key is to look at these parameters

Many designers are big when they mention the calculation formula, but the core calculation of plane instability is actually not complicated. At present, the formula in the American Association of Expansion Joint Manufacturers (EJMA) standard is commonly used in engineering:

Critical pressure P_cr = (0.34× π × E × t²) / (L_b × D_m²)
Where: E — — elastic modulus of corrugated pipe material, t — — wall thickness of single layer of corrugated pipe, L_b — — total length of corrugated pipe, D_m — — average diameter of corrugated pipe.

Do you see that? It is four parameters that really determine the instability boundary:Material stiffness (E), wall thickness (t), length (L_b) and average diameter (D_m)。 The longer the length and the larger the diameter, the lower the critical pressure and the easier the instability. On the contrary, the thicker the wall thickness and the harder the material, the stronger the ability to resist instability.

But many people just use the formula and ignore another implicit condition- -Wave distance and wave height ratio。 In practical engineering, the design of bellows should not only meet the critical pressure, but also consider the cumulative effect brought by wave number. Like aStraight pipe pressure balanced expansion jointIf there are too many wave numbers, even if the single wave calculation is qualified, the whole may be unstable. Therefore, there is an empirical value in the industry: the safety factor of single wave instability is usually above 1.5, and the overall safety factor of instability is above 2.0.

What if the calculation is unqualified? The easiest way is to reduce the wave number or increase the wall thickness. But don't forget that the increase in wall thickness will make the stiffness greater and the compensation ability decrease. This is a game-you have toCompensation amount, pressure class, structure dimensionsFind a balance between.

Wrong selection, inadequate installation, no matter how accurate the calculation is, it is useless-a guide to avoiding pits in actual combat

The formulas were so wild that they were all in vain when they arrived at the scene- -I've seen this a lot. Here are a few pits that you'd better avoid:

• Ignore the influence of temperature on elastic modulus during model selection: Many designers calculate it at room temperature and think everything will be fine. However, with four or five hundred degrees of steam in the power station pipeline, the E value of stainless steel will drop by more than 30%. The critical pressure was also cut in half. Therefore, under high temperature working conditions, selectHigh temperature axial expansion jointThe elastic modulus at high temperature must be used for recalculation.
• Misuse of tie rod as support: Some scene drawings save trouble, takeexpansion joint tie rodUsed as a guide bracket. The tie rod can only limit axial displacement and cannot resist lateral bending. The initial stage of plane instability is lateral bending, and the tie rod can't stop it at all. The right thing to do is to install separate guide brackets, one every two to three wave pitches.
• Excessive cold tightening operation: Pre-tensioning or pre-compression (cold tightening) is to reduce the stress in the working state, but the amount of cold tightening is too large, which is equal to initially giving the bellows an additional displacement. If the design margin of the compensator itself is insufficient, the cold tightening directly triggers instability. There's a case whereDouble hinge expansion joint of air-cooled island vacuum pipeThe cold tightness exceeded the design value by 20%, and it became unstable after one week of operation.
• Ignore wall thickness reduction caused by media corrosion: The environment of desulfurization flue is highly corrosive, if the materials are selected incorrectly, such as usingNon-metallic expansion joint (fabric fiber expansion joint)However, without considering acid-alkali corrosion, the wall thickness gradually becomes thinner, and the original critical pressure fails. Regular thickness measurement is a life-saving means.

Talk about the cases of rollover due to plane instability in power stations and cement industries

Let's start with the power station. A 300MW unit was installed on the main steam pipelineCompound hinge transverse expansion jointThe design pressure is 4.0 MPa and the temperature is 540 °C. After half a year's operation, the inspection found that the bellows had obvious local bulging, which was orange peel-shaped. After stopping for inspection, it was found that the plane instability of the bellows had occurred, and the corrugation spacing changed from a uniform 10mm to 8mm on one side and 12mm on the other. The cause of the accident is very typical: the elastic modulus used in design is the normal temperature value, and the high temperature attenuation is not considered; In addition, the length of the bellows is too long, and the critical pressure is only 10% higher than the working pressure, so the safety factor is not enough. Finally, the whole expansion joint was scrapped, and the front and rear pipelines were replaced, and production was stopped for three days, resulting in a loss of seven figures.

Let's say cement. Used in the cement industryMetal Corrugated Expansion Joints in Cement IndustryIt is often arranged at the outlet of the preheater, and the air duct has large diameter, high temperature and large dust content. I have a project to chooseSingle-axis double-flapper doorWith an expansion joint, but the guide tube of the expansion joint (i.e.Specific Function of Expansion Joint Guide TubeThe liner mentioned in) is worn out so badly that the bellows are directly exposed to the high-temperature dusty airflow. Dust accumulates in the trough, destroying the uniform force of the bellows. Coupled with the large spacing between pipe supports and hangers, the expansion joint is subjected to additional bending moment, and finally the bellows has serious twisting and instability. From the photos at the scene, the bellows looks like a kneaded paper ball, which is terrible to see. The solution is to use insteadRectangular non-metallic expansion jointIt is equipped with wear-resistant guide tube and two guide brackets are added at the same time.

Alas, these lessons were all earned for real money. Plane instability calculation is not armchair, it is directly related to the safety of pipeline system and project cost. When you select or check the expansion joint next time, don't just turn through the sample. Go through the pressure, temperature, displacement, material and support conditions, and then make the safety factor-at least 80% of the pits can be avoided.