Within the frame of industrial automation, the mechanical power related to pneumatic actuator systems involves air flows along with mechanical component, such as valves, connecting tubes, cylinder chambers and possible linkages in order to finally actuate a specific objective. Gas dynamic of the air flowing into connecting ducts plays a fundamental role in the description of the global dynamic phenomena of these systems. Several studies deal with the dynamics of such pneumatic systems but through streamlined analysis where the influence of pressure-waves propagating in ducts is neglected or poorly described. The related models are even more complex when finite volumes are placed at the ends of connecting lines. In this paper, two different mathematical models describing transient pressure-waves propagating through lines closed by finite volumes are presented. The investigation regards pressure and velocity ranges normally operating in industrial pneumatic systems. Besides the value of new system modeling of different complexity, these models are compared from an analytical and numerical point of view; advantages, disadvantages, weakness, abilities, and inabilities are highlighted and, finally, the relevant analysis is corroborated through experimental validations of wave propagating pressure at fixed positions of ducts. This study results both in the presentation of models of practical interest, as well as in an attempt to provide an elucidation on the need to resort to an accurate model rather than a streamlined one with respect to the geometric and/or operative characteristics of industrial pneumatic systems.

1.
Messina
,
A.
,
Giannoccaro
,
N. I.
, and
Gentile
,
G.
, 2005, “
Experimenting and Modelling the Dynamics of Pneumatic Actuators Controlled by the Pulse Width Modulation (PWM) Technique
,”
Mechatronics
0957-4158,
15
(
7
), pp.
859
881
.
2.
Carducci
,
G.
,
Giannoccaro
,
N. I.
,
Messina
,
A.
, and
Rollo
,
G.
, 2006, “
Identification of Viscous Friction Coefficients for a Pneumatic System Model Using Optimization Methods
,”
Math. Comput. Simul.
0378-4754,
71
(
4–6
), pp.
385
394
.
3.
Schuder
,
C. B.
, and
Binder
,
R. C.
, 1959, “
The Response of Pneumatic Transmission Lines to Step Inputs
,”
Trans. ASME
0097-6822,
81
, pp.
578
584
.
4.
Brown
,
F. T.
, 1962, “
The Transient Response of Fluid Lines
,”
ASME J. Basic Eng.
0021-9223,
84
, pp.
547
552
.
5.
Andersen
,
B. W.
, 1967,
The Analysis and Design of Pneumatic Systems
,
Wiley
,
New York
, Chap. 4.
6.
Morton
,
K. W.
, and
Mayers
,
D. F.
, 1994,
Numerical Solution of Partial Differential Equations
,
Cambridge University Press
,
Cambridge, UK
, Chap. 4.
7.
Sim
,
W. -G.
, and
Park
,
J. -H.
, 1997, “
Transient Analysis for Compressible Fluid Flow in Transmission Line by the Method of Characteristics
,”
KSME Int. J.
1226-4865,
11
, pp.
173
185
.
8.
Hougen
,
J. O.
,
Martin
,
O. R.
, and
Walsh
,
R. A.
, 1963, “
Dynamics of Pneumatic Transmission Lines
,”
Control Eng.
0010-8049,
10
, pp.
114
117
.
9.
Messina
,
A.
, 2006, “
Progetto, Realizzazione e Test di un Filtro Analogico Passa Basso di Tipo Bessel-Thomson: BW2kHz
,” Private Report No. D16.
10.
Benson
,
R. S.
,
Garg
,
R. D.
, and
Woollatt
,
D.
, 1964, “
A Numerical Solution of Unsteady Flow Problems
,”
Int. J. Mech. Sci.
0020-7403,
6
, pp.
117
144
.
11.
Boyce
,
W. E.
, and
DiPrima
,
R. C.
, 1997,
Elementary Differential Equations and Boundary Value Problems
,
Wiley
,
New York
.
12.
Jaeger
,
J. C.
, 1955,
An Introduction to the Laplace Transformation
,
Wiley
,
New York
, Chap. 4.
13.
Murray Spiegel
,
R.
, 1965,
Theory and Problems of Laplace Transforms
,
McGraw-Hill
,
New York
, Chap. 1.
14.
Hamming
,
R. W.
, 1962,
Numerical Method for Scientists and Engineers
,
McGraw-Hill
,
New York
, Chap. 22.
15.
Whitmore
,
S. A.
,
Lindsey
,
W. T.
,
Curry
,
R. E.
, and
Gilyard
,
G. B.
, 1990, “
Experimental Characterization of the Effects of Pneumatic Tubing on Unsteady Pressure Measurements
,”
NASA
Technical Memorandum No. 4171, pp.
1
26
.
16.
Bulaty
,
T.
, and
Niessner
,
H.
, 1985, “
Calculation of 1-D Unsteady Flows in Pipe Systems of I.C. Engines
,”
ASME J. Fluids Eng.
0098-2202,
107
, pp.
407
412
.
17.
Ferrari
,
G.
, 1975, “
Simulazione del Processo di Aspirazione e Scarico di un Motore a Quattro Tempi
,”
La Termotecnica
,
7
, pp.
397
408
.
18.
Alfano
,
G.
, and
Betta
,
V.
, 1989,
Fisica Tecnica
,
Liguori Editore
,
Naples, Italy
, Chap. 7.
19.
Chester
,
C. R.
, 1971,
Techniques in Partial Differential Equations
,
McGraw-Hill
,
New York
, Chap. 13.
20.
Smith
,
G. D.
, 1985,
Numerical Solution of Partial Differential Equations, Finite Difference Method
,
Clarendon
,
Oxford
, Chap. 4.
21.
Holmes
,
M. H.
, 2007,
Introduction to Numerical Methods in Differential Equations
,
Springer
,
New York
, Chap. 4.
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