Bellows force and cover material

This note describes measurements of bellows force vs. extension, using a few different cover materials. The specimens are a few samples of 29x90 mm secondary windchest bellows, part of an ongoing effort to restore the Skandia Theatre organ in Stockholm, Wurlitzer style E opus 1254, installed in 1926. These bellows were originally covered with Zephyr skin, now mostly disintegrated.  It was decided to re-leather these bellows with somewhat heavier material, like also Wurlitzer did in later productions. This study was to verify this can be done without compromise to function.	Original Zephyr covered  bellows, with black dust accumulations in creases and cracks. (22x90 mm, a smaller one than those measured)
General layout of the note action inside the Wurlitzer windchest. (Adapted from D L Junchen: The Wurlitzer organ. ATOS 2005. ISBN 0-9763338-0-5) The figure shows components at rest. With no pressure applied the primary bellows should be supple enough that its valve is closed by gravity alone, and the spring should be able to lift the pallet and pry open the secondary bellows. When the chest is pressurized both bellows are inactive, and the pallets are held in place by an additional force from pressure times pallet area. When the mechanism is activated by the magnet valve, then the forces developed by the bellows must be able to overcome those forces to open their respective pallets against air pressure, gravity, and spring tension. The following measurements were made using a pressure/suction of 200mm (8") of water column. This is less than  normally used in the organ, but it adds a certain safety margin when evaluating what harm might come from an elevated stiffness in the bellows.
Measurements
This shows a measurement rig demonstrating how the force at the felt clad maneuver tab develops when the bellows is vented, and when fed with 200 mm WC under pressure. The 'fixed' bellows leaf is clamped to an arm and the bellows opening can be varied and measured by the number of coins piled up under its maneuvering tab. The bellows force is measured with an electronic household balance. Initially the balance is tared to zero with all coins and additional support structures on the balance table, with no contact with the bellows. Following that it is easy to successively move coins into the supporting pile and read the balance with and without suction applied. When the bellows is nearly collapsed and with no suction it does not reach the support pile. In that case the tab is held down by placing a few of the 'free' coins on top of it, such that you can read a meaningful negative value.

	These result diagrams show the weight read from the balance. The horizontal axis is for bellows relative opening, where zero is when the bellows is fully collapsed with suction applied. The various bellows were covered at different times, with slight accidental width variation in their cover strips. 100% indicates maximum opening without suction, where the cover material is stretched essentially flat.
Nominal working range for the opening is typically 20 to 70 %, as indicated with horizontal markers above. The sketches at right are idealized views of the bellows, seen from its short end.
The upper curves with markers are for the bellows with suction applied, the lower ones without markers when the bellows is vented. The green curves show theoretical force for an ideal cover material forming flat hinged bellows ribs (http://www.mmdigest.com/Gallery/Tech/airbounc.htm#2). With a soft cover as in the actual case, the folds rather take a rounded shape. This explains some of the difference to the measurements. Also stretching of the material contributes to a difference.
The more important result is indeed the lower curves without markers, those that represent the spring action of the cover material. This much reflects the subjective impression from exercising the bellows by hand. How hard to flatten the bellows folds toward 0%, and how much to pull to open up the bellows all the way. For this you need very little force having a zephyr or OSI tan covering. Conversely, the Tyvek covered one appears extremely stiff and rigid, to a degree you may feel it should be out of question to use it. But when you restrict the view to the limited 20-70% range of actual operation, then the difference between the various covering materials is relatively insignificant.
In one of the skins the thickness varies rather much, and this was not accounted for when covering strips were cut out from it. This figure shows a sequence of five releathered bellows (22 mm wide) where thickness varies from 0.3 to 0.6 mm. The stiffness of the leather makes zero force 'neutral' bellows opening vary accordingly. Measurements on these when passive are shown in the figure below. They should be representative even though these samples are 22 mm wide rather than 29.
The point of interest is what force is required from the bellows. a is the force to open the pallet against the air pressure. This applies only when the pallet is closed and decreases rapidly as the pallet opens. As computed from the dimensions of the pallet and its armature, at the pressure used here this force would be 50-70 grams. b is the force from the pallet closing spring. The diagram shows measurements from four samples, where the force refers to the bellows maneuver tab. This force has two essential characteristics. One is the spring constant, the slope of the line, how much force increases with extension. This depends on the length and diameter of the spring wire. The other is the bias, coming from how the spring is bent for pre-tensioning at its installation. The bias determines the vertical position of the characteristic in the diagram. The characteristic of necessary force is the sum of a and b and must fit in between the upper active and lower passive curves of the force the bellows can supply. It appears there is an ample safety margin what concerns the active bellows force. With some of the stiffer covering materials one might have to bend out the spring wires to increase the bias, such that the bellows is reliably opened and the pallet closed. This is easily checked at installation.

Primary bellows A similar measurement was made on one of the small primary bellows, covered with the Å&L tan leather. The width of the little rectangle in the diagram suggests the extent of the throw of the primary valve and its height corresponds to the force to open the valve disk against chest pressure. Again, it appears there is sufficient margin for this bellows to work well, despite its cover leather is much stiffer than the original Zephyr skin.