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Two very important factors which determine the effectiveness of a pump are its volumetric and power efficiencies. Yin and Ghoneim constructed a prototype of a Flexible-Matrix-Composite (FMC) body pump with a very high volumetric efficiency or pumping potential (the relative volume reduction due to a relative input stroke). The high volumetric efficiency is attributed to the geometry of the pump’s structure (hyperboloid) as well as the high negative effective Poisson’s ratio of the 3-layer [θ/β/θ] flexible-matrix-composite (carbon/polyurethane) laminate adopted for the body of the pump. However, the power efficiency of the pump was not evaluated. It is the objective of the current paper to obtain an estimate of the power efficiency of the pump. The viscoelastic properties of the 3-layer FMC (carbon/polyurethane) laminate are evaluated experimentally using the Dynamic Mechanical Analyzer (DMA) as well as analytically by applying the correspondence principle together with the micro-mechanics approach. In order to obtain an estimate of the power efficiency of the FMC body pump, the axial and shear loss factors of a laminated infinitely long cylindrical tube as functions of β and θ fiber orientation angles are determined employing the Adam and Bacon approach. The analysis engenders high loss factors (greater than 0.4), which suggests that the power efficiency of the proposed pump using the 3-layer carbon/polyurethane laminate may be low.

Flexible-Matrix-Composites (FMCs) are the branch of composite materials where the matrix is made of a compliant material (rubber, polyurethane, silicon). Flexible-matrix-composites have found a wide range of applications including flexible body pumps and vibration isolation mounts. The diaphragm pumps, the jellyfish-inspired flexible pump [

An attempt to find the overall loss factor (extensional and shear) of the 3-layer [q/b/q] FMC (carbon/polyu- rethane) laminate (plate) was undertaken by Kumar et al. [

The objective of the current work is two folds: to obtain a better estimate of the viscoelastic properties of the carbon/polyurethane (C/PU) laminate employed for the body of the novel pump; and to estimate the axial and shear loss factors of the 3-layer [q/b/q] laminated cylindrical tube as functions of the angles q and b. These loss factors are good estimates of the inherent damping in the C/PU cylindrical tube, and consequently are good indicators of the power efficiency of the flexible body pump adopting this 3-layer laminate.

Following the method adopted in the previous work [^{®} 121-31 urethane rubber) using the DMA (Perkins Elmer DMA 8000), and 2) apply the correspondence principle together with the micro-mechan- ics approach, assuming that the carbon fibers behave purely elastic, to estimate the viscoelastic dynamic properties of the C/PU lamina [

The DMA measures the variation of the storage and the loss moduli of viscoelastic materials as functions of frequency over a range of temperature. The temperature-frequency superposition principle is applied to generate a master curve [_{T}. The superposition principle uses a shift factor a_{T} to collapse the moduli’s curves at various temperatures into the master curve. In this analysis the William-Landel-Ferry (WLF) equation is selected for the shift factor:

where C_{1} and C_{2} are material constants to be determined experimentally, and T and T_{0 }are the temperature and reference temperature, in Kelvin, respectively. In this work, the reference temperature is taken as the room temperature (288 ^{0}K). Typical examples of the measured moduli (storage and loss shear and extensional) of the polyurethane as functions of the reduced frequency are displayed in ^{*}) and extensional (E^{*}) moduli are, respectively, given by:

where G' is the shear storage modulus, G'' is the shear loss modulus, E' is the extensional storage modulus, and E'' is the extensional loss modulus. All the four moduli are approximated by a quadratic polynomial fit (dotted lines in _{2 }x^{2} + a_{1}x + a_{0}, where E stands for any of the four moduli, and x = log(α_{T}f) . The values of the material constants a_{2}, a_{1}, a_{0}, C_{1} and C_{2} are displayed in

is estimated from the relationship

frequency/time dependent Poisson’s ratio by combining response functions such as E*(ω) and G*(ω). They stated that the determination of any bulk functions by calculation from any other parameters requires the source parameters to be obtained using a strict protocol known as the standard protocol [

With the complex shear and extensional moduli of the polyurethane (PU) matrix material known, and with the assumption of purely elastic behavior for the carbon fibers (E_{f} = 231 GPa, and n_{f} = 0.2), the in-plane viscoelastic

a_{2 } | a_{1 } | a_{0 } | |||
---|---|---|---|---|---|

G' (KPa) | 15.49 | 24.08 | 259.3 | C_{1 } | 0.53 |

G'' (KPa) | 13.26 | −0.84 | 26.03 | C_{2} (^{0}K) | 46.45 |

E' (KPa) | 97.61 | 31.12 | 965.3 | C_{1 } | 0.47 |

E'' (KPa) | 71.51 | −30.41 | 111.8 | C_{2} (^{0}K) | 43.36 |

properties of the C/PU lamina can be evaluated using the principle of correspondence and the micromechanics approach. It should be understood that the composite lamina is assumed to be transversely isotropic [

where v is the fiber volume fraction, x is a curve fitting parameter, which is also a measure of the reinforcement of the matrix by the fibers, and the subscripts m and f stand for the matrix and fiber, respectively.

_{0} is taken as 288 ^{0}K, and the curve fitting parameter x = 2 for the calculation of the shear modulus and x = 3 for the transverse modulus.

The correspondence principle in combination with the classical lamination theory has been employed to calculate the global longitudinal, transverse and shear complex moduli of C/PU laminates.

The analytical results for some laminates with moduli that satisfy the upper limit measurement of the DMA are compared with the corresponding experimental results. Samples of the results are shown in

・ The application of the simple micromechanics theories of the Rule of Mixture and Halpin-Tsai.

・ The testing specimens were manually produced and despite the meticulous care taken, the quality of the specimens, in particular the accuracy of the fiber angle orientation and perfect wetting and bonding, was limited.

・ The shear test involves applying an optimum pressure to hold the test specimen by gently squeezing it between two plates [

The correspondence principle, in combination with the classical lamination theory and the method employed by Adams and Bacon [_{ }of the laminate are considered. In general, the effective loss factor h is given by

where W^{e} is the total elastic strain energy per cycle of loading, W^{d} is the total dissipated energy per cycle, and k is the layer (lamina) number. If W is the total work done per cycle, then

where s_{k}, and e_{k} are the in-plane stress and strain vectors in the material coordinates, respectively. An estimate of the extensional and torsional loss factors of the hyperboloid FMC body pump can be realized by analyzing an infinitely long laminated cylindrical tube subjected to axial and torsional loading, respectively.

Herakovitch [

・ In the vicinity of q = b (diagonal lines) the effective damping experiences a very high gradient (any slight deviation from q = b renders a huge change in h). Consequently, this region is impractical for h-based design.

・ The loss factor is influenced mainly by the fiber orientation angle of the outer q-layers.

・ The 3-layer tubular laminate exhibits a very high inherent damping factor (h > 0.4). In general, the results indicate that there is no practical fiber angle orientation, which may render low loss factor (h < 0.01). More specifically, the results clearly confirm that the fiber-angle orientation, which renders a high negative Poisson’s ratio [5/40/5] and selected for the design of the flexible body pump [

The viscoelastic properties of the FMC carbon/polyurethane (C/PU) laminate, adopted for the body of the novel pump proposed by Yin and Ghoneim, are estimated experimentally using the Dynamic Mechanical Analyzer (DMA) as well as analytically applying the correspondence principle together with the micro-mechanics approach. The agreement between the predicted viscoelastic properties of the C/PU laminates and the corresponding experimental ones, in general, is fair. In addition, the loss factor of the 3-layer [q/b/q] laminate is estimated employing Adam and Bacon approach. More specifically, the axial and shear loss factors of a laminated infinitely long cylindrical tube as functions of b and q fiber orientation angles are determined. It is found that, in general, the 3-layer [q/b/q] laminated cylindrical tube exhibits high axial and shear loss factors and consequently may render a low power-efficiency pump.

N. P. Kumar,H. Ghoneim, (2016) Damping Factor Estimation of a Flexible-Matrix-Composite Body Pump. Journal of Materials Science and Chemical Engineering,04,59-66. doi: 10.4236/msce.2016.47009