4) In a typical electro-pneumatic transducer, an input pressure source is nominally (P) at 18 psig. That pressure is feed through a restriction with a flow resistance R into an expanding bellows chamber, as shown in the figure below. The bellows has expanding accordion pleat sides which expand or contract with zero force. However, this expansion distance (x) is limited by a compression spring with spring rate (k). The force generated by the air pressure in the bellows chamber which pushes on the spring equals its gage pressure times cross-sectional area (A). Derive the transfer function between changes of the inlet pressure (p.) and the spring compression (x). P + Pi Mixing Juh -X+X

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Section III: Pneumatic Systems
4) In a typical electro-pneumatic transducer, an input pressure source is nominally (P) at 18 psig. That
pressure is feed through a restriction with a flow resistance R into an expanding bellows chamber, as
shown in the figure below. The bellows has expanding accordion pleat sides which expand or contract with
zero force. However, this expansion distance (x) is limited by a compression spring with spring rate ( k ).
The force generated by the air pressure in the bellows chamber which pushes on the spring equals its
gage pressure times cross-sectional area (A).
Derive the transfer function between changes of the inlet pressure (p₁) and the spring compression (x).
P + Pi
R
Mixing
سر
P+Pa
-X+x
Transcribed Image Text:Section III: Pneumatic Systems 4) In a typical electro-pneumatic transducer, an input pressure source is nominally (P) at 18 psig. That pressure is feed through a restriction with a flow resistance R into an expanding bellows chamber, as shown in the figure below. The bellows has expanding accordion pleat sides which expand or contract with zero force. However, this expansion distance (x) is limited by a compression spring with spring rate ( k ). The force generated by the air pressure in the bellows chamber which pushes on the spring equals its gage pressure times cross-sectional area (A). Derive the transfer function between changes of the inlet pressure (p₁) and the spring compression (x). P + Pi R Mixing سر P+Pa -X+x
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