Sealing Statistics Characterization the Sealing Behavior: Talking Statistics

Author / Editor: Ibrahim Kar, Michael Berz* / Dominik Stephan

Characterization the behavior of sealing elements using statical testing plays a vital role — When developing sealing solutions, statical testing is a mighty tool. Thus, understanding its methodology, its disturbances and variables becomes a decisive factor in the development process. Is there any standard procedure to determine sealing behavior?

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Major influencing variables and their correlation to the targeted variables in the description of sealing behavior.
Major influencing variables and their correlation to the targeted variables in the description of sealing behavior.
(Source: Kar/Berz)

Companies that are developing new products need to take the necessary experiments into account. For this purpose, statistical testing can be very useful: They allow for a better exploitation of experimental results regarding the quantification of affecting variables with respect to key performance indicators. There is an empirical model that uses statistical testing to determine the behavior of sealing elements. In these calculations, the total leakage rate becomes the emission characteristic value, which is the targeted value of the experimental investigations. Experience and theory show that the relationship between most influencing and target variables are non-linear. Based on that assumption, a non-linear model using one of the following procedures is considered:

  • Square experimental procedure,
  • Factorial procedure, and
  • Response Surface procedure.

The square experimental procedure is used to investigate influencing variables with more than two settings or stages. The factorial procedure on the other hand limits the stages two to keep the effort low, yet allows for an unlimited number of influencing variables. Response Surface is suitable for recording characteristic curves or the detailed examination of correlations.

In the first step, the initial situation or the corresponding system must be analysed to come up with a model assumption. During the analysis, influencing and target variables must be defined. A model assumption is made, based on investigations or using a priori knowledge. Experimental planning distinguishes between linear experimental designs (with a linear relationship between influencing and target variables) and non-linear experimental designs (non-linear relationship).

A Closer Look at Experimental Design

It must be considered that the experiment is not adapted to the procedure rather the experimental design is adapted to the experiment. This is made possible by the use of D-optimal experimental designs which can be constructed with the help of Hadamard matrices. The name D-optimal derives from the fact, that the determinant (XTX) in the determination equation for the effects or model coefficients (regression coefficients) is as large as possible in terms of error propagation. Advantages of D-optimal experimental procedures are:

  • Freedom of choosing for the mathematical model.
  • Freedom of choosing the number of test points, considering the absolute minimum specified by the number of coefficients.
  • Free selection of the influencing factors for the number of stages and possible deviation of the number of stages.
  • Possibility of expansion through new influencing factors.
  • An alternative to include tests already performed in the evaluation of the design.

The experimental designs can be created with suitable software, such as Umetrics’ Modde or Visual-Xsel 2000XT DoE from Crgraph.

The behavior of a sealing element can be described by various variables. The total leakage rate, one of the most significant, is a combination of the primary and secondary leakage rates. Primary leakage develops in leakage channels. A distinction is made between three different flow types, which can be described as:

  • Viscous flow,
  • Knudsen flow, and
  • Molecular flow, respectively.

The flow type encountered in a specific case can be defined with the help of the Knudsen number.

Which Factor has the Greatest Influence on Seals?

As calculations and experiments show, the contact pressure has the greatest influence on the leakage rate: As the pressure increases, the total leakage rate decreases (a so-called negative correlation). Other influencing variables are positively correlated: If they increase, the leakage rate also increases. Examples are the temperature, which has the second biggest influence, or the seal height, which has the least.

From this consideration it can be concluded that, when optimizing a seal, first the contact pressure and finally the seal height should be considered. The reciprocal effect has a lower influence between 10 % and 15 %. Physically, this model is plausible: With increasing contact pressure, a higher sealing force is applied, leading to a lower total leakage rate. An increase in differential pressure and temperature on the other hand also increases the concentration gradient, resulting in a higher leakage rate. Last but not least, smaller seal heights indeed do show a lower total leakage rate. This is probably because thinner sealing elements can fill rough surface structures better and thus seal a larger part of the cross-section area.

This shows, that a regression function describing the behavior of sealings can be set up using statistical methods. This way, it is possible to calculate the significance of individual variables and the reciprocal effect. The use of statistical testing is not limited to experiment design but can also be used to plan numerical analyses. For an entire description of the behavior of sealing elements, both experimental and numerical investigations are necessary. As this article shows, the actual emission parameters can be gathered from experiments. In addition to the contact parameters are to be analysed numerically with the aid of FEM. By combining these two and integrating the statistical testing methodology, production cycle and costs can be effectively reduced when designing a sealing element.

* * Kar is a specialist for cost estimates, time scheduling and artificial intelligence at Shell, Berz works as a Senior Cost Estimator at Jacobs Engineering