Optimization of taper winding tension in roll-to-roll web systems

Abstract

Winding is an integral operation in almost every roll-to-roll system and the center-wound roll is one of the suitable and general schemes in a winding mechanism. The quality and performance of a center-wound roll are known to be related to the winding tension. In this paper, a novel optimization design method for winding tension using a special network structure is proposed. Firstly, based on the elasticity theory, the correlations between winding tension in the winding section and hoop stress distribution within a center-wound roll are analyzed. In addition, an analysis model for the residual stress due to the winding tension profile is developed. Then, according to the analysis model, the special network structure with back propagation training is developed to minimize the error of lateral residual stress, namely isostress-distribution. Finally, the experimental prototype of a roll-to-roll packaging system for glass-fiber fabric that can measure and control the winding tension is described, and actual experiments were carried out. Results show that the proposed method is very useful for determining the desirable taper-tension profile during the winding process and preventing defects of the center-wound roll.

Keywords

winding tension profile center-wound roll hoop stress residual stress isostress

The web is defined as a material that is thin, continuous, long, and easily bent. Web products can be easily found in our daily lives, such as paper, tissue, and aluminum foil.¹ As a typical web product, glass-fiber fabric either exists as rolls in its final shape or at least exists in the form of rolls at the transporting stages. Nowadays, the center-wound roll form is the most efficient and convenient storage format for glass-fiber fabric packaging.

The process of transforming the web into the form of center-wound rolls is called the winding process. The important manufacturing specifications in the process are the control of winding tension and transport velocity. The existing researches for such a winding process are mainly in the design of the tension controller (TC) to increase the web transport speed as much as possible.²

It is common practice in industrial web unwinder–winder systems (also called roll-to-roll systems) to use decentralized proportional-integral (PI)-type controllers. Overviews of problems, solutions, and perspectives on the topic of web tension control are presented by Shin.³ Recently, more efficient control strategies have been explored to improve web tension control to answer the requirement of higher productivity and the handling of thinner web materials. Advances in web longitudinal control up to year 2005 are well documented by Pagilla and Knittel.⁴ Nonlinear tension control via differential flatness and dynamic feedback linearization of roll-to-roll web systems is presented by Chang et al.⁵ A nonlinear slidingmode controller without a tension sensor for a multi-motor web-winding system is studied by Abjadi et al.⁶ Frechard and Knittel⁷ analyzed the influence of the master roller placement and the effects of velocity and tension bandwidths for roll-to-roll systems. Gassmann et al.⁸ analyzed the dynamic behaviors of web transport systems and presented a fixed-order H∞ TC using a pendulum dancer. More references on web control can be found in the bibliographies of Gassmann.⁸

Nevertheless, the internal stress within a center-wound roll will also change along with the outer hoop stress and radius, namely “wound on tension” loss, during the entire packaging process.⁹ As a result, it will also lead to an internal residual stress gradient even though it is under the condition of constant tension control. The internal residual stress gradient within a center-wound roll can cause damage such as buckling, wrinkling, interlaminar slippage, etc. It is therefore desirable to wind just adequate stress into a center-wound roll so that a stable package is wound without inordinate or insufficient stress.¹⁰

Previous studies prove that the problem of buckling within a center-wound roll can be relieved to some extent by using the taper-tension model.¹¹ In addition, the main factor for making a high-quality center-wound roll is the taper-tension profile in the entire winding process.¹² The existing researches on the taper-tension model are mainly focused on seeking the optimum taper factor. However, the internal stress within a center-wound roll is still non-uniform even using the taper-tension model, especially when the external radius is much larger than the core radius.¹³

In our glass-fiber fabric packaging system, however, we focused on the design of the tension profiles aiming at minimizing the distribution error of the residual stress within the center-wound roll. In this paper, we proposed a special network structure with a back propagation training, which can optimize the winding tension and each layer within the center-wound roll is subject to isostress-distribution.

Model of the residual stress distribution within a center-wound roll

In a large package, the external diameter of a center-wound roll is much bigger than its core diameter. Thus the relaxation effect in the internal layer web while winding external layers should be fully considered. In general, the winding speed of the web packaging system is relatively low (not exceeding 0.5 m/s); thus, the dynamic tension, impulse, and centrifugal force of the web were not disregarded temporarily. Since in most cases there will not be any plastic deformation of the web in the packaging processes, for simplicity in modeling, we assumed that the web is perfectly elastic. In addition, we also assumed that there is no slippage phenomenon between the roller and the web on the winding process so that the length of the web wound in the roll can be calculated easily. However, if there are some other ways to calculate the length, the following analysis is also applicable to those conditions that are not satisfied with the assumption.

For the convenience of analysis, the three related forces are defined as follows at first in this paper.

Winding tension $T (R)$ , where R is the current external radius of the center-wound roll; the unit for T is $kN / m$ . It shows the tension acted on per unit width of the web, and is generated by the TC and motor of the packaging system.

Internal tangential stress $σ (r, R)$ . This represents the hoop stress at the layer where the radius is r, while the external radius of the roll is R, the unit of which is $Mpa$ . If the average thickness of the web is h, it is obvious that $T = σ \cdot h$ .

Radial pressure $P (R)$ . This is used to express the pressure of the radial direction produced by the winding tension of the outer layer web.

Because the glass-fiber fabric is perfectly elastic, the linear superposition principle may be used to analyze the internal tangential stress distributions within the center-wound roll. Assume the radius of the rigid core module, namely the inner radius of a center-wound roll, is R₀, and the final package is formed with n layers of web. So the radius of the center-wound roll while winding the i th layer of the web can be expressed as $R_{i} = R_{0} + i \cdot h$ . Obviously, the largest outer radius of the package is R_n and the radial distributions of internal stress within the final package may be written as $σ (r, R_{n})$ , abbreviated as residual stress $σ (r)$ .

According to the superposition principle, the internal tangential stress $σ (r, R)$ at the arbitrary radius r within the center-wound roll is the result under the comprehensive function of the web in all layers with radii between $r and R$ . While winding the web, the distributions of internal tangential stress $σ (r, R)$ are influenced through the radial pressure $P (R)$ caused by the external fabrics. The geometry relationships among winding tension $T (R)$ , internal tangential stress $σ (r, R)$ , and radial pressures $P (R)$ are illustrated in Figure 1.

Figure 1.

Schematic of related forces within a center-wound roll.

According to the elasticity theory,¹⁴ the boundary condition is that the outside of the center-wound roll is stress free; therefore, the effects of hoop stress $Δ σ (r, R)$ caused by the radial pressures $P (R)$ are

Δ σ (r, R) = - P (R) \frac{R^{2}}{r^{2}} \frac{r^{2} - (1 - 2 γ) R_{0}^{2}}{R^{2} + (1 - 2 γ) R_{0}^{2}},

(1)

where γ is the Poisson’s ratio of the web material.

On the basis of the elasticity theory on a cylinder, the radial pressures $P (R)$ produced by the winding tension $T (R)$ can be calculated by the following formula:

P (R) = \frac{T (R)}{R} .

(2)

Then define constant $ρ^{2} = (1 - 2 γ) R_{0}^{2}$ , and substituting $P (R)$ of (2) for (1) leads to the hoop stress as follows:

Δ σ (r, R) = - T (R) \frac{R}{r^{2}} \frac{r^{2} - ρ^{2}}{R^{2} + ρ^{2}} .

(3)

From the above formula, we can see that the effects of the external winding tension $T (R)$ on internal tangential stress $σ (r, R)$ are obvious. For a center-wound roll of web, the distributions of $σ (r, R)$ may be analyzed using the superposition principle of elasticity theory.

Through the analyses and discussions above, it can be seen that the residual stress within a final package $σ (r)$ is the superposition effects of the hoop stresses such as $Δ σ (r, r + h)$ , $Δ σ (r, r + 2 h)$ , …, and $Δ σ (r, R_{n})$ . Therefore, the residual stress for the radial direction $σ (r)$ is presented as follows:

σ (r) = \frac{T (r)}{h} + Δ σ (r, r + h) + Δ σ (r, r + 2 h) + \dots + Δ σ (r, R_{n}) = \frac{T (r)}{h} + \sum_{i = 1}^{(R_{n} - r) / h} Δ σ (r, r + i \cdot h) .

(4)

In the practical winding system, the winding tension $F (R)$ is unequal at every part of the center-wound roll. Since the web thickness is much smaller than the radius of the center-wound roll, for the convenience of comparison, we assume that the radius of the ith layer in the center-wound roll is r, that is, R_i. Then substituting the hoop stresses $Δ σ (r, R)$ of (3) for (4) leads to the residual stresses in each layer as follows:

σ (R_{i}) = \frac{T (R_{i})}{h} + \sum_{j = i + 1}^{n} Δ σ (R_{i}, R_{j}) = \frac{T (R_{i})}{h} - \frac{R_{i}^{2} - ρ^{2}}{R_{i}^{2}} \sum_{j = i + 1}^{n} \frac{T (R_{j}) R_{j}}{R_{j}^{2} + ρ^{2}}, \times i \leq i < j \leq n .

(5)

In this formula, it is known that the Poisson’s ratio γ, the radius of the core module R₀, the external radius of package R_n, and the web thickness h are constant. Then, the internal tangential stresses $σ (R_{i}, R_{n})$ in each layer of web of the final package depend on the winding tension $T (R)$ only.

Considering the web thickness h is far less than the roll radius R, we can make h the differential operator of radius $dR$ . Then, the residual stress in a wound roll can be express as the integrated form:

σ (R) = \frac{T (R)}{h} - \frac{R^{2} - ρ^{2}}{{hR}^{2}} \int_{R}^{R_{n}} \frac{T (r) rdr}{r^{2} + ρ^{2}} .

(6)

Analysis of a typical tension model in the winding process

Several conventional models have been used to describe the tension behavior of a web in different winding processes. Without the tension close-loop in packaging systems, the winding roller will belong to a constant torque system. Then the winding tension with constant torque $T_{tor} (R)$ is inversely proportional to the roll radius as follows:

T_{tor} (R) = T_{0} \frac{R_{0}}{R},

(7)

where T₀ is the initial winding tension.

If the winding tension remains constant in the entire winding process, the tension control strategy is also known as the constant tension system, and the tension model is expressed as

T_{ten} (R) = T_{0} .

(8)

With the development of the control technology and the winding quality requirements, taper-tension models are being more and more applied in the winding process. Generally, the linear and hyperbolic taper-tension profiles are the most common two. These two winding tension profiles are defined as¹⁵

T_{lin} (R) = T_{0} (1 - t \frac{R - R_{0}}{R_{n} - R_{0}}),

(9)

T_{hyp} (R) = T_{0} (1 - t \frac{R - R_{0}}{R}),

(10)

where t,

0 \leq t \leq 1

, is the taper factor that represents the decrement of taper-tension profiles.

Figure 2 shows the tension changes in the winding process for the four different tension models, where the taper factor $t = 0.5$ and initial winding tension T₀ is set as $1 kN / m$ . In this case, the core module radius $R_{0} = 50 mm$ and the external radius of the package $R_{n} = 500 mm$ .

Figure 2.

Tension profiles for the four winding tension models.

From these curves, the constant torque profile variation is most remarkable, and is larger at the core and smaller on the outer layer. However, the constant tensile profile output has no correlation with the roll radius. The variations of taper-tension profiles are between that of the above two, and the linear taper-tension profile presents constant variation.

Substituting the winding tension of constant torque model (7) into (6), we can obtain the residual stress for the constant torque profile as follows:

σ_{tor} (R) = \frac{T_{0} R_{0}}{h} (\frac{1}{R} - \frac{R^{2} - ρ^{2}}{R^{2}} \int_{R}^{R_{n}} \frac{dr}{r^{2} + ρ^{2}}) = \frac{T_{0} R_{0}}{hR} (1 - \frac{R^{2} - ρ^{2}}{R ρ} arctg \frac{ρ (R_{n} - R)}{ρ^{2} + R_{n} R}) .

(11)

Furthermore, we substitute constant tension (8) into (6), which means the radial stress for the constant tension profile, that is:

σ_{ten} (R) = \frac{T_{0}}{h} (1 - \frac{R^{2} - ρ^{2}}{R^{2}} \int_{R}^{R_{n}} \frac{rdr}{r^{2} + ρ^{2}}) = \frac{T_{0}}{h} (1 - \frac{R^{2} - ρ^{2}}{2 R^{2}} \ln \frac{R_{n}^{2} + ρ^{2}}{R^{2} + ρ^{2}}) .

(12)

As for the linear taper-tension profile, the tensions in (9) can also be written as

T_{lin} (R) = (1 + \frac{{tR}_{0}}{R_{n} - R_{0}}) T_{0} - \frac{T_{0} t}{R_{n} - R_{0}} R .

(13)

Substitute the winding tension in (13) into (6), and rearrange to obtain the residual stress for the linear taper-tension profile as

σ_{lin} (R) = (1 + \frac{{tR}_{0}}{R_{n} - R_{0}}) σ_{ten} (R) - \frac{T_{0} t}{R_{n} - R_{0}} (\frac{R}{h} - \frac{R^{2} - ρ^{2}}{{hR}^{2}} \int_{R}^{R_{n}} \frac{r^{2} dr}{r^{2} + ρ^{2}}) = (1 + \frac{{tR}_{0}}{R_{n} - R_{0}}) σ_{ten} (R) - \frac{T_{0} t}{h (R_{n} - R_{0})} \times (R - \frac{R^{2} - ρ^{2}}{R^{2}} (R_{n} - R - ρ arctg \frac{ρ (R_{n} - R)}{ρ^{2} + R_{n} R})) .

(14)

The hyperbolic taper-tension profile may be regarded as the weighted sum of the constant tension and constant torque profiles, and where the taper factor t serves as the weight, that is:

T_{hyp} (R) = (1 - t) T_{0} - {tT}_{0} \frac{R_{0}}{R} = (1 - t) T_{ten} (R) - {tT}_{tor} (R) .

(15)

According to the elasticity superposition principle, the radial stress for the hyperbolic taper-tension profile is also considered as the synthesis of two distributions. So the residual stress can be obtained as

σ_{hyp} (R) = (1 - t) \frac{T_{0}}{h} (1 - \frac{R^{2} - ρ^{2}}{2 R^{2}} \ln \frac{R_{n}^{2} + ρ^{2}}{R^{2} + ρ^{2}}) + t \frac{T_{0} R_{0}}{hR} (1 - \frac{R^{2} - ρ^{2}}{R ρ} arctg \frac{ρ (R_{n} - R)}{ρ^{2} + R_{n} R}) .

(16)

Figure 3 shows the residual stresses within rolls wound using the four different tension profiles, where the parameter settings are the same as those in Figure 2.

Figure 3.

Residual stresses for the four different winding-tension models.

On the whole, the residual stress for the constant torque model is larger in the interior and smaller on the surface layer. When the web is wound under this winding-tension model, the slippage (generally called telescoping) is easily generated near the outermost radius of the wound roll. The cause of telescoping is a slippage that occurs between web layers because the radial pressures on external layers are unable to be supported due to the lowering of the winding tension and the entrainment of air in the wound roll. A typical slippage defect with the constant torque model is shown in Figure 4.

Figure 4.

Typical slippage (telescoping) in a center-wound roll.

On the other hand, when the web is wound under the constant tension model, some wrinkles (generally called star defects), as shown in Figure 5, will inevitably appear at the core. The star defect is thought to be a buckling phenomenon that occurs due to the fact that the residual stress σ becomes negative and a compressive force acts along the tangential direction of wound web layers.

Figure 5.

Typical star defect (wrinkling) in a center-wound roll.

Consequently, to prevent the above phenomenon, it is necessary to optimize the winding-up conditions so that the tangential stress in the wound roll is uniform and nonnegative, such that the radial pressures can maintain a suitable level to avoid the entrainment of air.

The taper-tension model is a tradeoff between the constant tension and constant torque profiles, and the residual stress for hyperbolic taper-tension has more equipollence than that for the linear one. However, as shown in Figure 3, the isostress within a center-wound roll is impossible to achieve using the above four winding tension profiles.

Optimization of winding tension

The winding tension exerts a large influence on the residual stress of the center-wound roll, and is the main cause of roll defects. In the winding process, the internal tangential stress within a center-wound roll will decrease while winding a new layer web on the outermost surface. In order to make a suitable distribution of residual stress in the final package, the winding tension $T (R)$ should be largest at the core and decrease gradually with the increase of the radius. For a long time, the method of decreasing the tension in proportion to the radial position of the wound roll has been used. However, this method was established depending on experience and without theoretical guarantee.

Through the above discussion, we can obtain the residual stress $σ (R)$ within a center-wound roll according to the winding tension $T (R)$ from (6). Nevertheless, the key of designing ideal winding tension is the inverse problem of that, that is, how to optimize a set of winding tensions $T (R_{i})$ , $i = 1, 2, \dots, n$ , to make the final $σ (R)$ meet the expected design requirements.

Accordingly, a special network structure is proposed in this paper, with a back propagation iterative training, which not only optimizes the winding tension, but also minimizes the distribution error of residual stress $σ (R)$ within a center-wound roll. The topological structure of the network is illustrated in Figure 6.

Figure 6.

Special network structure for optimizing the winding tension.

In the topological structure, the weights of the hidden layer to the output layer $W_{i, j}$ , $1 \leq i \leq j \leq n$ , are defined as the influence factors of hoop stresses $Δ σ (R_{i}, R_{j})$ , which express the variations of internal tangential stress on the ith layer while winding the jth layer web. From (3), the weights $W_{i, j}$ can be obtained as

W_{i, j} = {\frac{1}{h}, i = j - \frac{R_{j}}{R_{i}^{2}} \cdot \frac{R_{i}^{2} - ρ^{2}}{R_{j}^{2} + ρ^{2}}, i < j .

(17)

Then, the iteration formula for the network outputs $σ (R_{i})$ is expressed as

σ_{k} (R_{i}) = \sum_{j = i}^{n} W_{i, j} T_{k} (R_{i}),

(18)

where the subscript k represents the number of iterations.

The output deviations of the network can be calculated using

e_{k} (i) = \overset{⌢}{σ} (R_{i}) - σ_{k} (R_{i}) .

(19)

Finally, according to the principle of error back propagation, we update the weights of the input layer to the hidden layer $ω (i)$ as follows:

ω_{k + 1} (i) = ω_{k} (i) + Δ ω_{k} (i) = ω_{k} (i) + α \frac{\partial F (R_{i})}{\partial ω (i)} e_{k} (i) = ω_{k} (i) + \frac{α}{T_{0} (R_{i})} e_{k} (i),

(20)

where α is the learning factor, which represents a compromise between the stability and convergence rate. If α is too small, the convergence rate of the network structure is greatly reduced. But if α is too large, the network easily causes the occurrence of oscillation result. The optimum α is 0.1–0.5 which is obtained through repeated experiments and seletions.

From the above iterative computations, the optimization process of winding tension only includes basic arithmetic operations. Therefore, the proposed network structure can be very convenient to realize using a micro control unit (MCU) or digital signal processing (DSP) system.

Generally, the initial winding tensions $T_{0} (R_{i})$ are all set as constant. Via the network weights $ω (i)$ , the winding tension $T (R)$ can be obtained in the hidden layer. The distributions of the residual stress $σ (R)$ in a center-wound roll are calculated with fixed weights $W_{i, j}$ . Following that, comparing the distributions with the expected one $\overset{\land}{σ} (R)$ , the deviation $\overset{⇀}{e}$ can be obtained. The weights $ω (i)$ are then adjusted and optimized using the updating algorithm (20).

Define the network error $‖ e ‖$ as $max {| e_{i} (k) |}$ , and determine a small parameter ɛ as the terminal condition. The network reaches convergence until $‖ e ‖ < ɛ$ . Then the outputs of the network node in the hidden layer are just the expected winding tension $\overset{⌢}{T} (R)$ .

Experiments

Experimental setup

Figure 7 shows the prototype of the winding process in the dipping and packaging system that has been built in this work for the experimental verification. The system consists of an unwinding roller, guide rolls, draw rolls, pacer rolls, three-layer cloth store-frames, a dip tank, a dip roll, a drying oven, a winding roller, etc.

Figure 7.

Structure of the automatic packaging system for glass-fiber fabric.

Firstly, the glass-fiber fabric is unwound from an unwinding roller by the draw rolls R₂, and pass by a guide roll R₁ and a storage frame S₁. The draw rolls R₂ are coupled with an alternating current (AC)-servo motor M₁ via gear reduction as the actuators, and a local inverter I₁ composed of a proportional-integral-derivative (PID) controller driving the motor M₁. The angular speed of a pacer roll is measured by a tachometer T, and used as the feedback of control loop in the PID controller to adjust the draw rolls R₂. As a result, the linear velocity of the web constantly equals 20 m/minute. Then the glass-fiber fabric is immersed in a coupling agent, and cured in a drying oven. Finally, passing by another storage frame S₂, the web material is roll-packaged into the form of a center-wound roll by the winding tension control system.

The winding tension control system consists of the following parts: tension meter (TM), revolution meter (RM), TC, magnetic particle clutch (MC), direct current (DC)-motor M₂, and core module. The rotational speed of the core module is adjusted by the DC-motor M₂ via a MC controlled by the TC. The radius of the center-wound roll can be presumed indirectly according to the rotational speed of the core module, and the practical linear velocity of the web detected by the pacer. The output signals of the TM and RM are used as the feedback of the TC; therefore, the winding roller belongs to a closed-loop control system. The controlled quantities are computed by a DSP TMS320F2812 within the TC in order to adjust the winding tension to meet the desired distribution.

Results and discussions

The optimization method has also been implemented in a real-time DSP2812-based environment for the prototype winding section in the packaging system. Taking the packaging process of FR-4 high-strength epoxy glass-fiber fabric, for example, testified the validity of the proposed method.

The experimental setups are schematically shown as follows: the average thickness of the glass-fiber fabric $h = 0.35 mm$ , the Poisson’s ratio of the web $γ = 0.36$ , the radius of the core module $R_{0} = 50 mm$ , and the size of the package was $2200 m$ per coil. The design requirement for winding tension was to make the residual stresses at each layer within the roll $1 Mpa$ with a tolerance of $\pm 0.1 Mpa$ .

By means of the average thickness of the web and the size of the package, it can be calculated that the roll radius $R_{n} = 500 mm$ and the layer number n was 1286. According to the design requirements, the expected residual stresses $\overset{⌢}{σ} (R_{i})$ in the network were all $1 Mpa$ , and the initial winding tensions $T_{0} (R_{i})$ were all $2.86 kN / m$ , namely $1 Mpa / 0.35 mm$ . In our case, the learning factor of network α was 0.5 and the iterative terminal condition was set as $‖ e ‖ < 0.01 Mpa$ .

On the DSP TMS320F2812-based TC, the proposed network structure reached convergence through 22 iterations, and the residual error and computing time were 0.0081 $kN / m$ and 0.8 s, respectively. The optimization process of winding tension and the corresponding distribution changes of residual stress are shown in Figure 8.

Figure 8.

Optimization process of winding tension: (a) winding tension; (b) distribution changes of residual stress.

In practice, the tension response usually fluctuates. To improve the tension variation, an external PID feedback control to the MC was also implemented in the TC. The voltage signal to the TC, generated by the TM that was attached at the idle roll bearings, adjusted the winding tension of the web. The roll radius of the center-wound roll was estimated according to the angular velocity and linear velocity detected by the TM and pacer, respectively. In the experiments, the packaging system started from rest, and the tension responses were recorded at every sampling period of 1 s. Figure 9 shows the experimental results for the tension control of the packaging system.

Figure 9.

Experimental results for optimal winding tension: (a) performance of the tension control; (b) residual stress within the center-wound roll.

In view of this result, the winding tension design using the optimization method is effective for overcoming the quality problems existing in large packages. Because the winding roller started form rest, the initial tension control also started from scratch, which caused tension overshoot at the core. Except for the above region, the residual stress within the center-wound roll in the experiment is basically consistent.

Figure 10 represents the picture of the winding process and an actual center-wound roll with an optimization winding tension profile. Defects such as buckling, wrinkling, and slippage were not observed in the center-wound roll. The results from the experiments indicate that the proposed optimization method of the advanced taper-tension profile is useful in actual manufacturing systems.

Figure 10.

Actual center-wound roll with optimization winding tension.

Conclusion

The linear superposition principle of elasticity theory was used to analyze the internal stress distribution of a center-wound roll. By modeling we reveal the variation of residual stress caused by winding tensions. The performances for four typical winding tension models were discussed. Although the taper-tension model has more equipollence than the constant tension and constant torque profiles, the isostress within a center-wound roll is impossible to achieve even using the taper-tension profiles.

A special network structure was proposed with a back propagation iterative training, which not only optimizes the winding tension, but also minimizes the distribution error of residual stress within a center-wound roll. The presented method has been implemented in a real-time DSP2812-based environment for the prototype winding system. Its performance has been verified by experiments.

Footnotes

Funding

This work was supported by the Natural Science Foundation of Fujian Province (2010J01310), China (51177141), the Aviation Science Foundation (2012ZD68003), and Basic Research Universities Special Fund Operations (2010121041-ZK1007).

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