Abstract
Quantitative understanding of mechanical actuation of intricate Pneumatic Artificial Muscle (PAM) actuators is technically required in control system design for effective real-time implementation. This paper presents mathematical modeling of the PAM driven by hydrogen-gas pressure due to absorption and desorption of metal hydride. Empirical models of both mechanical actuation of industrial PAM and chemical reaction of the metal hydride-LaNi5 are derived systematically where their interactions comply with the continuity principle and energy balance in describing actual dynamic behaviors of the PAM actuator (PAM and hydriding/dehydriding-reaction bed). Simulation studies of mechanical actuation under various loads are conducted so as to present dynamic responses of the PAM actuators. From the promising results, it is intriguing that the heat input for the PAM actuator can be supplied to, or pumped from the reaction bed, in such a way that absorption and desorption of hydrogen gas take place, respectively, in controlling the pressure of hydrogen gas within the PAM actuator. Accordingly, this manipulation results in desired mechanical actuation of the PAM actuator in practical uses.
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Abbreviations
- A:
-
Coefficient of polynomial function
- c0, c1:
-
Constant coefficients of PAM geometry
- cp, H:
-
Specific heat at constant pressure of hydrogen
- cp, La:
-
Specific heat at constant pressure of lanthanum
- cp, MH:
-
Specific heat at constant pressure of metal hydride
- cp, Ni:
-
Specific heat at constant pressure of nickel
- cv, H2:
-
Specific heat at constant volume of hydrogen gas
- Ca, Cd:
-
Material-dependent constants for absorption and desorption, respectively
- Ea, Ed:
-
Activation energy of absorption and desorption, respectively
- F:
-
Pulling force
- ΔH:
-
Reaction heat of formation; absorption or desorption
- I:
-
Index of polynomial order
- L:
-
Instantaneous length of PAM
- Ls:
-
Stretched length
- Lu:
-
Unstretched length
- K:
-
Stiffness parameter of PAM
- mH:
-
Mass of hydrogen atom
- mMH:
-
Mass of metal hydride
- mH,sat:
-
Saturated mass of hydrogen atom
- \(m_{H_{2}}\) :
-
Mass of hydrogen gas
- ṁf:
-
Hydride formation rate
- MH:
-
Atomic mass of hydrogen
- \(M_{H_{2}}\) :
-
Molecular moles of hydrogen gas
- MLa:
-
Atomic mole of lanthanum
- MMH:
-
Molecular mass of metal hydride
- MNi:
-
Atomic mole of nickel
- n:
-
Highest order of polynomial function
- P:
-
Absolute pressure
- Ṗ:
-
Rate of change in pressure
- Peq:
-
Equilibrium pressure
- Pg:
-
Gauge pressure within PAM
- Q̇:
-
Rate of heat transfer to reaction bed
- r:
-
Equivalent radius
- \(R_{H_{2}}\) :
-
Gas constant of hydrogen gas
- Rg:
-
Universal gas constant
- xH/MH:
-
Hydrogen-to-metal atomic ratio
- t:
-
Time
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Leephakpreeda, T. Mathematical Modeling of Pneumatic Artificial Muscle Actuation via Hydrogen Driving Metal Hydride-LaNi5. J Bionic Eng 9, 110–118 (2012). https://doi.org/10.1016/S1672-6529(11)60103-0
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DOI: https://doi.org/10.1016/S1672-6529(11)60103-0