# What will be the future of the new flange calculation methods?

About 50 years ago, when the main pressure vessel standards were composed only by a few pages, and the sliding rule was the only available tool for the pressure vessel designer, the Taylor Forge method for the calculation of flanges was regarded as a very advanced and sophisticated procedure for the design of these complicated vessel components. The method seems to be based on a sound analytical model: in fact two essential requirements are established in order to get the leak tightness of a flanged joint: the first requirement is to compress the gasket (made of a material relatively soft compared to the flange material) during the assembly, so that its plasticization against the flange surfaces is assured; in this way it will be possible to fill the microscopic machining grooves existing on the seats, thus stopping any possible escape path for the internal fluid. The second requirement is to assure a contact pressure on the gasket during operation conveniently higher than the internal pressure, in order to avoid a separation of the gasket from the seats. To fulfil these requirements the method provides, for all the main gasket types, two factors: a minimum contact pressure y (MPa or psi) on the gasket surface during the first assembly, and a non-dimensional multiplication coefficient m for the internal pressure, in order to guarantee a gasket compression in service m times higher than the internal pressure.

It is interesting to note that these two requirements (sufficient initial gasket compression and sufficient residual pressure on the gasket in service) are still the basis of all the more modern and sophisticated methods for the calculation of bolted joints. However the determination of these two factors and the consequent determination of the actual bolt loads is not at all an easy job, if you consider the following.

1. In order to calculate the loads, the y and m factors are to be applied to the effective contact surface between the seats and the gasket, surface which is determined by the different deformations of all the parts composing the joint, starting from the initial bolt tightening, and going, through the hydrostatic pressure test, towards the normal operating condition.
2. The y and m factors are certainly dependent not only on the characteristics of the gasket material (which may be different for different gasket manufacturers, even for the same gasket type), but also on the surface roughness of the gasket seats.
3. They are also dependent on the nature and the characteristics of the internal fluid: considering that for gases and vapours a total filling of all the possible microscopic escape channels existing between the gasket and the seats is virtually impossible, whatever is the degree of plasticization of the gasket material, it is clear that an absolute leak tightness of the gasket in presence of gaseous fluids will never be achieved, even in presence of high values of the y and m factors. Therefore leak tightness of gaskets in presence of such fluids should be evaluated only on the basis of a “tightness class”, that is, on the basis of an acceptable leakage rate, of course using higher y and m values with lower acceptable leakage rates. On the contrary an absolute leak tightness of the gasket in presence of liquids, thanks to their higher viscosity and to their surface tension, can still be considered as a realistic goal, of course if the proper y and m factors (lower than in the case of gases) are used.
4. Some kind of tolerance has to be considered for the bolt loads, particularly if they are tightened with the application of a torque by means of any kind of wrench: in fact with such tools, even in those where the torque is controlled, the actual load applied to the bolts using a specified torque value is strongly dependent on the friction between the nut and the flange face from one side, and between the nut and the bolt screws on the other side.

In the Taylor Forge method these considerations are partially neglected and partially taken into account with a very approximate solution. For example the deformation behaviour of the flanged joint between the assembly and the operating conditions is not at all considered in the calculation of the bolt loads, which are in fact calculated separately for each condition: in the assembly condition the bolt load is the one which is needed to get a surface pressure y on the gasket during tightening, while in the operating condition the bolt load is the one which is needed in order to get a gasket compression in service m times higher than the internal pressure. The required bolt area is therefore the maximum value which is determined by the loads calculated for these two separate situations. Simple correlations are given in order to take into account the reduction of the gasket surface in contact with the seats, and a standard table containing the recommended y and m factors for all possible gasket materials and shapes (whatever is the roughness of the seats and the physical state of the fluid) is provided.

Moreover, very high safety factors are provided both for the calculation of the bolts and for the calculation of the flanges: no consideration is therefore needed to take into account possible differences dependent on the tightening device. Therefore the loads resulting from a Taylor Forge calculation must not be regarded as the effective bolt loads to be used to actually tighten the assembly, but only as conventional figures needed for the calculation itself, without any feedback for the operators.

I remember how I have discovered this discrepancy for the first time, 45 years ago, when I was working for an important Italian heat exchanger manufacturer. I was very proud to have prepared a specific computer program for the calculation of flanges in accordance with ASME VIII division 1, the first international Pressure Vessel standard that had adopted the Taylor Forge method. I had written this program for a device which was really only a programmable calculator, using a sort of credit cards as a storage medium for the software: the output consisted in a long strip of paper, containing only numbers, that, in order to be properly understood, had to be pasted on a specific calculation form which contained the symbols. Once, in a large job where I had to make the mechanical design of several shell and tube exchangers, the customer’s specification requested the actual torque values by which the bolts had to be tightened: this was not usual, therefore the shop manager asked the technical department to give them all the torque values of all the flanged joints. Well, I simply took the values of the loads obtained from my program, made some reasonable assumptions in order to convert them into torsional moments (trying to be rather pessimistic about friction factors, and considering  also a multiplication factor to take into account the ratio between test and design pressure). Then I forwarded all the data to the shop.

I still remember the phone call that I received from the shop when the exchangers were subject to the final pressure test. As usual, the shop people have a very bad opinion about designers (normally considered as pure mathematicians, without any practical experience): that day I was able to understand, by the tone of that phone call, that my torque values had greatly contributed to re-enforce that opinion. The content of the telephone call was more or less the following: “Please, come down to see” (not sure about the word “please”). Well, when I came down to the shop the reason of the call became at once evident: the shop floor was filled with puddles, because of the water leaking abundantly from all the flanged connections of ten or twelve exchangers under hydrostatic test pressure. At the end, it was clear that my torque values were absolutely too low to properly tighten the gaskets. After a short discussion, we decided to tighten the flanges with the normal device used in the shop (an impact wrench, substantially the same device used in all tire shops), and then to measure the torque using a calibrated torque wrench: this will have been the value to be marked on the drawings. I confess I was a little bit frightened when I realized that the measured torque values were 2 or 3 times higher than the values calculated with my program: in any case it was clear that these were the normal values used by our shop to tighten the flanges, and that explosions of flanges due to sudden rupture of the bolts were never experienced in the exchangers fabricated by our company. But what would have happened if our customer had decided to require the calculations made in order to get the torque values? Well, this was an absolutely inevitable risk. At the end, all the exchangers were successfully tested and shipped, and, as far as I know, they might be still in service in some oil refinery of the Middle East.

Coming back to my calculations, I realized that the actual tensile stress of the bolts determined by the torque values used in the shop was about 350 MPa, against a theoretical ASME allowable stress a little bit higher than 172 MPa. Well, considering that the yield point of the bolt material was higher than 700 MPa and the corresponding tensile strength was more than 800 MPa, it was clear that even under these conditions an overstress of the bolts was certainly not to be expected. A similar consideration is valid also for the flange: in fact the flange stresses are simply proportional to the bolt load, and its main circumferential stress, according to the rules of the modern elastic stress analysis (certainly almost unknown when the Taylor Forge method was formulated for the first time) is a primary bending stress, which therefore could be 1,5 times higher than the primary membrane stress used in the method.

More recently, an ASME publication (PCC-1, latest edition in 2013) has officially recognized that in the tightening of a flanged joint the bolt stresses (and consequently also the flange stresses) to be achieved are much higher than the theoretical values given by the Taylor Forge calculations.

From the above considerations it is clear that the Taylor Forge method, still prescribed by all the main Pressure Vessel standards (ASME VIII division 1 and 2, CODAP, PD 5500, ISPESL VSR, EN 13445.3-Clause 11), used with all the above approximations and limitations, gives raise to flange joints which are reasonably safe, although the details of the calculation are to be regarded as a mere convention. This situation is particularly appreciated by the users: in fact no maximum bolt load is prescribed by the method, therefore they have no limitations about the maximum load to be used in service in order to tighten a possibly leaking joint: and the experience proves that the best way to stop a leak (without stopping the entire plant to replace a gasket or to machine a gasket seat) is to increase the bolt load, by tightening the flange maybe up to the yield point of the bolts. Whoever has worked in an oil refinery or in another chemical or petrochemical plant under continuous service knows very well that such plants, which have a daily production whose value is measured in millions Euro, require long shutdown and start-up procedures: their normal operating time is about three years, so that all the possible maintenance operations (such as the repair of a leaking flange joint) are to be generally condensed in a single month between two subsequent operating periods. A plant manager who decides to stop the plant before the scheduled shutdown date (thus causing to his company a loss of several millions Euro) must have very good and sound reasons to do so, if he wants to be sure to keep his job when the plant is restarted: therefore in case of problems he will adopt all the possible alternative procedures other than stopping the plant. You can be sure that to tell him that the flanges of his plant must be tightened only with a specific device and only up to a prescribed limit will not make him very happy.

Knowing all the above, it is very easily understandable why the gasket tables used in the different versions of the Taylor Forge method are substantially equal to each other, apart from small corrections and approximations due to a possible change of units: in other words, everybody knows that the value of the table are too low, that do not provide differences between gases and liquids, etc. Nevertheless, using these values and the resulting bolt and flange stresses, the flanged joints calculated with the method are reasonably safe, and may be tightened until visual distortions will take place. Even when, some years ago, asbestos gaskets were banned from certain national legislations, there was no update of the corresponding values on the gasket tables: simply the word “asbestos” was deleted, and replaced with other expressions, such as “mineral fiber” or “vegetal fiber”, while the values of the y and m factors remained unchanged, although the characteristics of these materials are certainly not the same of asbestos gaskets.

One of the problem that EN 1591.1:2001 and EN 1591.2:2001 failed to solve was the difference between parameters to be used for liquids and parameters to be used for gases and vapours: in EN 1591.2:2001 the only reference to acceptable leakage rates was the statement that the m values of all the tables is the one which guarantees a leakage rate of 1ml/min Nitrogen under a pressure of 40 bar in a flat gasket having an OD of 90 mm and an ID of 50 mm: which of course is of very little use in order to find a general rule to consider actual leakage rates of other fluids with different gasket dimensions. All the tables are preceded by the statement that all gasket data should in any case be confirmed by the gasket manufacturer.

A further refinement of the EN method is contained in the 2013 Edition of EN 1591.1:2013, while EN 1591.2 has also been updated in 2008 considering the results of the PERL project and a further standard prepared by CEN TC74 (EN 13555: Flanges and their joints – “Gasket parameters and test procedures relevant to the design rules for gasketed circular flange connections”). With EN 1591.1:2013 is now possible (provided all the required gasket characteristics are available) to make the calculation of a bolted joint containing a gaseous fluid on the basis of a “tightness class”, that is considering an acceptable leakage rate (leakage rates are normally expressed in mg/s/m, that is in mg/s per unit length of the gasket perimeter). Note that leakage rates are conventionally referred to the leakage rate of a specified fluid under a specified pressure difference at a specified temperature, therefore to determine the effective leakage rate of any given fluid at any given temperature and pressure suitable equations are specified in EN 1591.1:2013.