Christophe Mobuchon

Pierre J Carreau

Marie-Claude Heuzey
email: marie-claude.heuzey@polymtl.ca

Maryam Sepehr

Gilles Ausias

Shear and extensional properties of short

INTRODUCTION

Composite materials such as polypropylene reinforced with glass fibers are used more and more in the automotive and other manufacturing industries. Glass fiber reinforcement is often an attractive way to improve the mechanical properties of thermoplastics, the improvement being attributed to the excellent mechanical properties of the fibers and to the better adhesion between the fibers and the polymer matrix when surface treated fibers are used [4]. The enhancement of the mechanical properties depends on the fiber lengths and the fiber macro-structure, i.e., the fiber orientation and distribution induced during processing [5]. The nucleating ability of the fibers inducing a transcrystallization of the matrix plays also a key role [6,7]. The correct prediction of any macro-structure development during flow using a simulation software requires an accurate rheological description of these reinforced polymers. Although numerous studies have been done, as shown below, on the rheological behavior of these materials, the literature lacks of a comprehensive understanding of the rheological properties of fiber composites, mainly transient and extensional properties. Moreover, there are many contradictions in the literature on the rheological properties of fiber composites.

RHEOLOGICAL OBSERVATIONS

The steady shear properties at low shear rates of short glass fiber suspensions in Newtonian media have been studied by Goto et al. [8]. They found that the volume fraction, the aspect ratio, and the flexibility of the fibers increased the shear viscosity, especially at low shear rates. Kitano and Kataoka [9] outlined that this shear rate dependence was more pronounced for larger fiber concentrations and larger fiber aspect ratios whereas Gananie and Powell [10] did not observe more shear-thinning effects for fiber suspensions, but their data have been obtained for lower shear rates and for smaller fiber aspect ratios. The same tendencies as noted by Goto et al. [8] for Newtonian suspensions have been reported for short fiber suspensions in viscoelastic media [10 -14]. Most of the authors cited above did not examine or mention the state of the fiber macro-structure. Milliken et al. [15] and Mondy et al. [16] using falling ball rheometry have shown that shear viscosity decreased as the fibers aligned in the flow direction. High-shear-rate capillary data [13,[17][18][19] have indicated also that the fiber orientation depended on the shear rate and, in particular, fiber alignment in the flow direction increased with residence time and the flow rate and decreased with fiber concentration [18,19]. The evolution of the fibers macro-structure at low frequencies during the dynamic shear measurements is cited by Kitano et al. [13] to explain the failure of the Cox-Merz rule. They found that the storage and loss moduli increased with fiber content and observed for the moduli at high frequencies short plateaus, which they explained by an evolution of the fiber macro-structure. The study of Kim and Song [20] supports this assumption of evolution of the macro-structure during a frequency sweep test. They observed that the complex viscosity decreased with increasing strain amplitude, frequency, and time. From a theoretical point of view, Harlen and Koch [21] justified the observations of Kim and Song [20]. Their simulations based on an Oldroyd-B fluid, confirmed by the experimental study of Petrich et al. [22], showed that fibers could be aligned by an oscillatory shear flow. Goto et al. [8] and Kitano and Kataoka [9] measured non zero steady-shear first normal stress differences for fiber suspensions in inelastic Newtonian fluids. Zirnsak et al. [23] verified that the loss angle was not affected by the fiber content and they concluded that the measured normal stress differences did not reflect the elastic behavior of those suspensions but the fiber-fiber interactions. Chan et al. [11], Czarnecki and White [12], Greene and Wilkes [14], Kitano et al. [13], Barbosa and Kataoka [24], and Sepehr et al. [25] concluded in the same manner. Sepehr et al. [25] have also shown that the relaxation of the shear and normal stresses of glass fiber suspensions in a Newtonian and elastic matrices following steady-shear flow was not affected by fiber content, indicating that the elasticity of the suspensions is that of the matrix.

Finally, the apparent extensional viscosity of fiber reinforced polymers was measured at low strain rates, from 10 -3 s -1 to 10 s -1 [11, 26 -28], using fiber spinning instruments [29,30]. Values for the extensional viscosity 1 to 20 times greater than the neat polymer were obtained depending on the volume fraction of the fibers and the extensional strain rate. Moreover, Chan et al. [11] observed a decreasing extensional viscosity of the reinforced polymers with extensional rate although the extensional viscosity of their neat polymer was constant over the same range of extensional rate.

Extensional Stress Predictions

Several constitutive models for fiber reinforced systems have been developed for semi concentrated systems [31][32][33]. For an extensional flow of a diluted or semi-concentrated suspension of aligned fibers in a Newtonian fluid, Batchelor [33] applied his body slender theory and obtained the following expression for the intrinsic particle stress:

͓͔ ϭ 2 9 r 2 ln͑␤͒ (1)
where [], the intrinsic particle stress, is defined by:

͓͑ ˙͔͒ ϭ ͑ ˙͒ Ϫ 0 ͑ ˙͒ 0 ͑ ˙͒ (2)
with ␤ ϭ ͌ / , 0 the tensile stress in the pure polymer, the tensile stress in the suspension, r the fiber aspect ratio, v the volume fraction of fibers, and ˙the extensional rate. Shaqfeh and Fredrickson [32] improved this analysis, which was afterwards extended for a power-law fluid by Goddard [3]:

͓͔ ϭ 2 9 r 1ϩn ΄ 1 n Ϫ 1 1 Ϫ ␤ 1Ϫ͑1/n͒ ΅ n B ( 3
)
where B ϭ ͑9/ 2 ϩ n͒ e ͑ ˙͒/͑ ˙͒ only if r Ͼ Ͼ ␤ Ͼ Ͼ 1, n is the power-law index, and e are the shear and the exten- sional viscosity, respectively, of the matrix.

Objective

The overall objective of this paper is to report shear and extensional rheological properties of short glass fiber reinforced polypropylene from low to large strain rates. Various commercial rheometers and a novel on-line rheometer mounted on an injection molding machine have been used to obtain the data. Furthermore, the extensional viscosity measurements are compared with the predictions of the Goddard model [3].

EXPERIMENTAL

Materials

A 10 and a 30 wt% short glass fiber reinforced polypropylene and the neat polypropylene used were supplied in pellet form by Basell (Hostacom G3 N01L). The 10 wt% composite corresponded to the semi-concentrated regime whereas the 30% composite was in the concentrated regime. For all the samples used in rotational rheometry, a thermal stabilizer (Irganox B225, 1 wt%) was added to the material using a Brabender internal mixer (40 RPM for 4 min at 200°C). The test samples were obtained by compression molding at 200°C. This processing method resulted in a planar random fiber orientation in the sample plane [34]. For the capillary and the on-line rheometry, the pellets were used as received. A test was also carried out using the capillary rheometer with a stabilized sample blended in the internal mixer. No significant differences were observed between the stabilized and nonstabilized samples. The fiber diameter was 14 m and the fiber lengths are reported in Table 1 in terms of L n and L w , the number average and weight average lengths, respectively, defined by:

L n ϭ ¥ i n i L i ¥ i n i (4) L w ϭ ¥ i n i L i 2 ¥ i n i L i . (5)
The length values of Table 1 are based on the manual measurement of 400 fibers using optical microscopy and image analyzer (Visilog) after pyrolysis of the polymer. The lengths of fibers measured after blending using the internal mixer are the characteristics for the samples used in rotational rheometry, while the lengths measured after injection molding are those of the samples for the on-line measurements. We note from Table 1 that the fiber length was considerably reduced by the processing and depended on the fiber content of the composite. From the samples as received from the supplier, the number average length L n was 610 and 430 m for the 10 and 30 wt% composite, respectively. After processing through the injection molding machine, the number average length was reduced to 530 and 330 m, respectively. The fiber damage was more severe in the internal mixer and the number average length was reduced to 440 and 300 m for the 10 and 30 wt% composite, respectively. As expected, longer fibers were more easily broken down in processing as indicated by the decreasing ratio of L w /L n . The aspect ratio of the fibers was larger than 20 in all cases and we assumed that the differences in length were not sufficient to affect the rheological properties of the fiber reinforced polypropylene composites at high shear rates. However, the observed differences between the average fiber lengths of the 10 and 30 wt% composites cannot be ignored when examining the effect of fiber content on the properties at low shear rates or in the dynamic mode.

Rotational Rheometry

Measurements of the linear viscoelastic properties were carried out using three stress controlled rheometers (AR 2000, TA Instruments; CSM, Bohlin Instruments; SR 5000, Rheometric Scientific). The parallel-plate geometry was used instead of the cone-and-plate geometry to avoid wall effects. According to Bibbo et al. [35], wall effects are not significant only when the gap between the parallel plates is much greater than the fiber length, a condition that the cone-and-plate geometry cannot guarantee. The downside of the parallel-plate geometry is that the shear rate is nonhomogeneous but varies linearly with the radial position, and consequently so does the deformation. For all experiments, the gap was set between 1.2 and 1.6 mm with a plate diameter of 25 mm. To reduce thermal degradation, all measurements were performed under nitrogen. The standard deviations reported (vertical error bars) are based upon three measurements done with fresh samples. Frequency sweep tests were performed from the highest to the lowest frequency in the linear domain. For steady-state measurements we proceeded from low to high shear rates and the torque was averaged during 60 s for low shear rates and 40 s for higher values until a constant value within 2% was obtained. The Rabinowitsch analysis was applied to the parallel plate viscosity data to account for shear-thinning effects [START_REF] Carreau | Rheology of Polymeric Systems: Principles and Applications[END_REF].

Capillary Rheometry

High shear rate data were obtained using an Instron rheometer with capillaries of aspect ratios (length to diameter) of 24.6, 35.5, 40, and 80.1 with 1.26 mm diameter and 90°entrance angle. The Bagley corrections were found to be negligible, but the Rabinowitsch analysis [START_REF] Carreau | Rheology of Polymeric Systems: Principles and Applications[END_REF] was applied to the capillary data.

On-Line Rheometry

To extend the previous data to injection molding conditions, a high strain rate rheometer was constructed and mounted in place of the mold in an all electric injectionmolding machine (Sumitomo SE50S). The injection speed of the Sumitomo SE50S electric injection molding machine ranges from 0.1 to 200 mm/s. The diameter of its screw is 16 mm and its rotation speed was set at 100 RPM. The on-line rheometer (Fig. 1) consists of a converging die, a slit die, and a diverging die made of steel (dimensions listed in Table 2 for converging and slit dies). The slit die with different gaps is suitable for measuring the shear viscosity, while the converging die is used to obtain the extensional flow behavior. Details about the converging die geometry are given in the following sections. The pressure profile along the rheometer was measured by five flushmounted pressure transducers (Grefan ISI 0101 and Dynisco TPT). The first and the last pressure transducers are located at the entrance of the hyperbolic converging section and of the entrance of the hyperbolic diverging section, respectively. The distance between the pressure transducers mounted on the slit die is equal to 35 mm. The two thermocouples located upstream and downstream of the slit die are used to measure the temperature of the fluid and to control the melt temperature within 2°C using two Omega CN491 temperature controllers. All data are sampled at a frequency of 40 Hz using a data acquisition card (PCI 6034E of National Instruments) with a software developed by Labview.

Two different converging dies have been designed fol-lowing suggestions of Kim et al. [START_REF] Kim | [END_REF] and James et al. [38].

If the shape of the converging section is hyperbolic (Fig. 2) a constant extensional rate is obtained. For a planar geometry along the z-axis, the average extensional rate, ͗ ˙͘, is defined by:

͗ ˙͘ ϭ d͗V z ͑ y, z͒͘ dz ϭ Q 4W d dz ͩ 1 h͑ z͒ ͪ (6)
where ͗V z (y,z)͘ is the average velocity at a given z, Q the volumetric flow rate, 2h the height and 2W the width of the converging die. Imposing a constant average extensional rate results in the following equation, representing a hyperbolic shape:

h͑ z͒ ϭ ͩ 4 ͗ ˙͘max Wz Q max ϩ 1 h i ͪ Ϫ1 (7)
where ͗ ˙͘ is the maximum average extensional rate obtainable corresponding to the maximum flow rate Q max , sup- plied by the injection machine. The resulting average extensional rate is then:

͗ ˙͑Q͒͘ ϭ Q 4WL ͩ 1 h f Ϫ 1 h 0 ͪ (8)
where h 0 is the initial height, h f the final height, and L the length of the converging die.

Interpretation of Data From the On-Line Rheometry

Assuming that the side walls of the slit die are of negligible flow resistance, for 2W Ͼ Ͼ 2h f , the power-law parameters, n and m, can be easily obtained using the following expression for the flow rate as a function of the pressure drop across the slit, P 0 -P L [START_REF] Carreau | Rheology of Polymeric Systems: Principles and Applications[END_REF]:

Q ϭ 4Wh 2 1 n ϩ 2 P 0 Ϫ P L L h m 1/n . ( 9
)
The analyses proposed by Cogswell [1] and Binding [2] have been used to estimate the extensional properties. These approximate methods correlate the flow rate and pressure drop for the flow through a contraction to an apparent extensional viscosity. Except in the case of lubricated flows [START_REF] Kim | [END_REF], the flow in a contraction is complex with shear and extensional components. In the Cogswell and Binding methods, the entry flow is separated into shear and extensional components. To measure a meaningful extensional viscosity, the shape of the converging section must be carefully designed. Four interrelated factors need to be examined: the contraction ratio, the homogeneity of the extensional strain rate, the shear and extensional contributions of the total pressure drop, and the residence time. These are discussed in the next three sub-sections.

Cogswell Analysis

In the Cogswell [1] analysis, the total pressure drop, ⌬P, is divided into a shear, ⌬P s , and an extensional, ⌬P e , term:

⌬P ϭ ⌬P s ϩ ⌬P e . ( 10
)
To estimate the pressure drop due to shear, Cogswell assumed that:

1) the viscosity under simple shear, , can be described by a power-law expression:

ϭ m͉␥ ˙͉nϪ1 (11) where ␥ ˙is the shear rate;

2) the extensional viscosity, e , is independent of the ap- plied stress; 3) the flow is laminar, locally fully-developed and under steady state.

The shear contribution for the converging die with geometry defined by Eq. 7 is therefore expressed as:

⌬P s ϭ ͩ Q͑2n ϩ 1͒ 4Wn ͪ n mL 2͑n ϩ 1͒ ͩ 1 h f Ϫ 1 h 0 ͪ ϫ ͫͩ 1 h f ͪ 2͑nϩ1͒ Ϫ ͩ 1 h 0 ͪ 2͑nϩ1͒ ͬ . (12)
For the contribution of the extensional flow component, Cogswell considered an average extensional stress yielding the following expression for the pressure drop:

dP e Ϸ ͗ zz ͘d ϭ e ͗ ˙͘d ( 13
)
where d is the extensional strain taken as dh/h. Hence, FIG. 2. View of the side cross-section of the two converging dies "a" and "b".

POLYMER COMPOSITES-2005 251

⌬P e Ϸ Ϫ ͵ h0 hf ͗ zz ͘ dh͑z͒ h͑z͒ ϭ Ϫ ͵ h0 hf e ͗ ˙͘ dh͑z͒ h͑z͒ ϭ Ϫ e ͗ ˙͘ ͵ h0 hf dh͑z͒ h͑z͒ . (14)
Finally, for a hyperbolic-shaped die the pressure drop due to the extensional flow component is given by:

⌬P e Ϸ e Q 4WL ͩ 1 h f Ϫ 1 h 0 ͪ ln ͩ h o h f ͪ . ( 15
)
The apparent extensional viscosity can be easily calculated from the experimental pressure drop once the powerlaw parameters for the shear viscosity are known.

Binding Analysis

Unlike Cogswell, Binding [2] used an energy balance and expressed the extensional viscosity as a power-law function of the extensional rate ( e ϭ l tϪ1 ). He derived the following expression for the power consumption, E ˙, for the flow in a converging planar die: (16) with:

E ˙ϭ mQ ͫ Q͑2n ϩ 1͒ 4Wn ͬ n ͵ 0 L 1 h͑ z͒ 2nϩ1 dz ϩ 4WlJ ntͫ Q͑2n ϩ 1͒ 4W͑n ϩ 1͒ ͬ tϩ1 ͵ 0 L h͑ z͒ ϫ ͫ 1 h͑ z͒ 2 ͩ Ϫ dh͑z͒ dz ͪͬ tϩ1 dz ϩ ͑2n ϩ 1͒ 2 Q 3 6͑3n ϩ 2͒͑4n ϩ 3͒W 2 ͵ 0 L 1 h͑z͒ 3 ͩ Ϫ dh͑z͒ dz ͪ dz
J nt ϭ ͵ 0 1 ͫ abs ͭ 1 Ϫ ͩ 2n ϩ 1 n ͪ 1ϩ͑1/n͒ ͮͬ 1ϩt d. ( 17
)
The first and last terms of the power consumption expression (Eq. 16) are the contributions from the shear component, E ˙s, and from inertia, respectively. They can be easily estimated if the shear behavior of the fluid and the profile of the converging section are known. The extensional parameters, l and t, are then obtained from the plot of the extensional contribution, E ˙e ϭ Q⌬P e , as a function of the flow rate. The extensional rate in the analysis of Binding [2] is a variable given by the following expression:

˙ϭ Q͑2n ϩ 1͒ 4W͑n ϩ 1͒ ͭͩ 2n ϩ 1 n ͪͩ y h ͪ 1ϩ1/n Ϫ 1 ͮ ϫ 1 h͑ z͒ 2 ͩ Ϫ dh͑z͒ dz ͪ . (18)
In our case of a constrained convergence in a hyperbolic die, the maximum extensional rate (at the center line) is related to the average extensional rate used in the Cogswell analysis (Eq. 6) by the following:

˙max ϭ ͑2n ϩ 1͒ ͑n ϩ 1͒ ͗ ˙͘. ( 19
)
Since the effect of the extensional flow is confined to the central region of the converging die, ˙max will be used to report the extensional viscosity calculated using the Binding analysis.

As pointed out by Binding [2], his analysis is based on the assumptions that the transverse velocity components are negligible and that the fluid elasticity will not significantly contribute to the pressure drop in the converging section. Finally, the analysis is applicable to constrained converging flows using the die profile, h(z), provided that the convergence angle of the hyperbolic die is not larger than that of the vortex generated in free convergence (case of a sudden contraction).

Residence Time in a Hyperbolic Converging Die

The residence time, t R , can be defined by the following equation:

t R ϭ ͵ 0 L 1 ͗V z ͘ dz ϭ 4W Q ͵ 0 L
h͑ z͒ dz (20) with:

͗V z ͘ ϭ Q 4Wh͑ z͒ . ( 21
)
So, for hyperbolic converging dies, defined by Eq. 7, the residence time is:

t r ϭ Q max ͗ ˙͘max Q ln ͩ 1 ϩ 4 W͗ ˙͘max Lh 0 Q max ͪ ϭ 1 ͗ ˙͘ ln ͩ 1 ϩ 4 W͗ ˙͘Lh 0 Q ͪ . ( 22
)

Design of the Two Converging Dies Used in This Study

For the purpose of this study two hyperbolic converging dies were designed with two different lengths as reported in Table 2. The range for the extensional rate is 0.2-200 s -1 for the shorter die and 0.1-100 s -1 for the longest one. However, the residence time (Eq. 22) for a specific extensional rate is the same for both dies. For a shear-thinning fluid, Eqs. 12 and 15 of the Cosgwell analysis can be used to calculate the ratio of the pressure drop for the two dies due to the shear and extensional contributions, respectively:

⌬P s converging die b ͉ ⌬P s converging die a ͉ ˙ϭ 2 nϩ1 ( 23
)
and

⌬P e converging die b ͉ ⌬P e converging die a ͉ ˙ϭ 1. (24)
The two converging dies give rise to the same extensional contribution but differ in their shear pressure drop contribution, which is more than double for the long converging die (b) compared to the shorter one (a).

The ratio of the extensional contribution, E ˙e, and the shear contribution, E ˙s, has been calculated using the Binding analysis (Eq. 16) for the two converging dies, and the results are reported in Fig. 3 in terms of pressure drop ratio as a function of the power-law index, assuming n ϭ t. Two different Trouton ratios were considered, l/m ϭ 4 and l/m ϭ 12. As expected, the extensional contribution is more important for the shorter die and for the larger Trouton ratio. It is interesting to note that the extensional contribution with respect to the shear contribution increases markedly as the shear-thinning character of the fluid becomes more pronounced (smaller power-law index).

RESULTS AND DISCUSSION

First, we verified that the wall slip effects were not significant for the parallel-plate and the on-line measurements. For both geometries we applied the Yoshimura and Prud'homme method [39] and no significant effects of the gap could be observed. Similar measurements were carried out with reinforced systems to investigate possible wall fiber interactions. It appeared that a ratio of the gap and fiber length close to 3 was sufficient to avoid significant wall effects. This ratio is greater than the limiting ratio of 1 suggested by Bibbo et al. [35].

The contribution of the lateral walls to the total pressure drop for the on-line rheometer was quantified numerically. The analytical expressions presented in the previous section, from which are obtained the shear and extensional viscosities, are 1D analyses that do not take into account the effect of the lateral walls. These walls represent 7.4% and 12.5% of the total surface areas for the slit and the converging dies, respectively. Hence, the lateral walls could contribute significantly to the total pressure drop, at least for the two converging dies. Flows (2D and 3D) for the on-line rheometer were computed using the finite element software packages Poly2D™ and Poly3D™ to assess the contribution of the lateral walls. The fluid was assumed to be inelastic and its viscosity described by the Carreau three-parameter model [START_REF] Carreau | Rheology of Polymeric Systems: Principles and Applications[END_REF]; the simulations were carried out for a flow rate of 100 mL/s FIG. 3. Ratio of extensional flow and shear flow contributions to the pressure drop for the converging dies "a" and "b" according to the Binding analysis with n ϭ t.

POLYMER COMPOSITES-2005 253

with the model parameters describing the polypropylene used in this work. In all cases, the pressure drop induced by the lateral walls of the slit die and of the converging section compared with the main walls represents less than 7%, confirming the previous results of Mourniac et al. [40]. The assumption of negligible lateral wall effects for the on-line rheometer is therefore justified.

Linear Viscoelastic Properties

As expected, the reinforced systems exhibited a nonlinear viscoelastic behavior down to very low strain amplitudes. However, we determined the linear region, which extended as far as the variation of the complex viscosity was less than 5% for a frequency of 0.628 rad/s. Consequently, for the frequency sweep tests, a strain amplitude of 0.05 was used for the neat polypropylene and the 10 wt% reinforced polypropylene, whereas a lower strain amplitude of 0.005 was used for the 30 wt% composite.

The effects of fiber concentration on the complex viscosity, *, and on the dynamic storage modulus, G', are shown in Fig. 4 for samples that had not been presheared before the test. We note that the behavior of * (Fig. 4a) and G' (Fig. 4b) is typical of homogeneous polymer melts. The properties of the 10 wt% (semidilute) composite are close to those of the neat polymer, but significant enhancements of both dynamic properties are observed for the concentrated fiber suspension (30 wt%). The increases of * and G' are independent of the frequency and the out-of-phase angle, ␦ (tan[␦] ϭ G"/G') is shown in Fig. 5 to be independent of the fiber content. This indicates that the elasticity of the suspensions is that of the matrix. A similar observation was recently reported by Hashemi et al. [41] for a Kraft (paper) fiber reinforced polypropylene. However, our G' data do not depict the plateau behavior at intermediate frequencies observed by Kitano et al. [42].

The previous results were obtained with tests samples prepared by compression molding. This process leads to an isotropic fiber orientation in the plane perpendicular to the disk axis (orthotropic orientation). As shown by Laun and Schuch [43] and Ausias et al. [34], the orientation state of the fibers macro-structure can be modified by a creep test. Figure 6 shows how a creep test, carried out until steady state was reached and applied before the frequency sweep test, affected the complex viscosity of the 30 wt% reinforced polypropylene. The relative complex viscosity, ⌬* r defined by

⌬* r ͑͒ ϭ * suspension Ϫ * matrix * matrix ͯ (25)
decreased with pre-shearing independently of the frequency. We note from Fig. 6 that the complex viscosity of the non-sheared sample is approximately twice that of the matrix. The complex viscosity of the 30 wt% com-posite dropped to 1.68 and 1.43 of that of the matrix after pre-shearing at a stress of 500 and 1000 Pa, respectively. Finally, the out-of-phase angle is shown in Fig. 5 to be independent of the fiber content and pre-shearing. This indicates that the characteristic elastic time of the composites, defined by Ref. 36:

ϭ GЈ GЉ ϭ 1 ͑tan ␦͒ (26)
is independent of fiber content and is equal to that of the matrix, confirming the findings of Hashemi et al. [41] for a different composite and Sepehr et al. [25] for the same composite.

Steady Shear Data

The steady state viscosity, , obtained from rotational rheometry as a function of the shear rate for different fiber contents is shown in Fig. 7. The viscosity behavior of the composites is similar to that of the matrix, but the increase with fiber content was more important at low shear rates, in contrast to the complex viscosity, for which the increases was about independent of the frequency (Fig. 6). However, the steady shear viscosity data were obtained for shear rates down to 10 -3 s -1 that is about a decade lower than the frequency range investigated. We note also that the zeroshear plateau was not reached yet at 10 -3 s -1 for the 30 wt% composite.

On-Line Viscosity Data

The temperature shift factor was applied for the shear viscosities measured with the on-line rheometer to verify how good the temperature control was. The temperature shift factor, a T , is defined by the following expression [START_REF] Carreau | Rheology of Polymeric Systems: Principles and Applications[END_REF]:

a T ϭ *͑T͒T 0 0 *͑T 0 ͒T ͯ ( 27
)
where T, T 0 , and 0 are the temperature, the reference temperature, the density, and the density at the reference temperature, respectively. The temperature shift factors used were determined thanks to the Arrhenius relationship:

a T ϭ exp E R ͩ 1 T Ϫ 1 T 0 ͪ ( 28
)
where R is the universal gas constant and E the flow activation energy. From dynamic data, E was found to be equal to 36.82 kJ/mol for the polypropylene for temperatures ranging from 180 to 220°C and T 0 equal to 200°C. This result is comparable to published values, which range from 36 to 50 kJ/mol for polypropylene. The master curve for the polypropylene is shown in Fig. 8. After corrections for the temperature, the viscosity data line up in a smooth curve, indicating that the shift factors used are accurate, i.e., the temperatures assumed to calculate them are accurate, and so that the temperature control during measurements is acceptable.

We are also showing in this figure the data for the 30 wt% composite obtained at the same three temperatures. The shift factors used were calculated using the same flow activation energy than the neat polypropylene. This is reasonable since the properties of the glass fibers and their indicating that the fiber content has no effect on the shear viscosity at high shear rates. This confirms the findings of Barbosa and Kenny [19] for similar composites. They found that the fibers near the die walls were at a lower concentration and totally oriented in the flow direction.

Cox-Merz Analogy

The shear and complex viscosities measured with the different devices are compared in Fig. 9 for the neat polypropylene (data multiplied by 0.1 to facilitate the com- parison) and the 30 wt% reinforced polypropylene. The Cox-Merz rule is well verified for the neat polypropylene and we note an excellent agreement between the capillary and parallel plate data. The on-line data are slightly lower than the data obtained with the other two rheometers, but the differences are acceptable. For the 30 wt% PP composite, the Cox-Merz rule is verified for the low frequencies or shear rates, but fails for rates larger than 10 s -1 . We should mention that the complex viscosity data presented for the reinforced system have been obtained after pre-shearing at 1000 Pa up to equilibrium. Consequently, the fiber macrostructure for this measurement was similar to that of the sample at the beginning of the simple shear viscosity measurement with the parallel-plate geometry. The similarity in the fiber macro-structures at low rates explains the superposition of the steady state and dynamic data. Conversely, the divergence at high rates are explained by the more pronounced orientation of the fibers under steady shear flow [18,19]. The differences between dynamic and steady shear measurements can also be explained by the presence of a dilute layer induced by the steady shear flow near the wall as outlined by Charrier and Rieger [44] and clearly illustrated by the modeling of Thomasset et al. [45].

First Normal Stress Difference

The first normal-stress difference, N 1 , was measured at low shear rates (10 -2 -1 s -1 ) with the parallel-plate geometry in steady state assuming that the secondary normal stress difference, N 2 , was negligible. Higher shear rate (10 -10 5 s -1 ) have been obtained with the on-line rheometer slit die using the Forgacs and Manson correlation [46]:

N 1 ͑ w ͒ ϭ P exit ( 29
)
that is, N 1 is equal to the pressure at the exit of a slit die referred as P exit . The exit pressure is obtained by extrapolating the measured pressure profile to the exit. We used also the Han correlation [47] given by:

N 1 ϭ P exitͩ 1 ϩ d ln P exit d ln w ͪ (30)
which adds a correction for the variation of the exit pressure as a function of the wall stress, W . The results are presented in Fig. 10 for the neat polypropylene. We observe that the data obtained from the parallel plate measurements do not extrapolate to the exit pressure data and to the values of the Han correlation. As shown by Choplin and Carreau [48], using a macroscopic mechanical energy balance, the exit viscous dissipation is not negligible as assumed by Forgacs and Manson [46] and Han [47]. Hence, Eqs. 29 and 30 could considerably overpredict the primary normal stress difference.

Laun [49] proposed the following expression to estimate the primary normal stress coefficient, 1 from dynamic data obtained in the range of 10 -2 to 10 3 s -1 :

⌿ 1 ͑␥ ˙͒ ϵ Ϫ N 1 ͑␥ ˙͒ ␥ ˙2 ϭ 2GЈ͑͒ 2 ͫ 1 ϩ ͩ GЈ GЉ ͪ 2 ͬ 0.7 ͯ ϭ␥ ˙. (31)
The parallel plate normal stress data and the values of 1 obtained using Eqs. 29 -31 are plotted in Fig. 11 for the neat polypropylene and the 30 wt% composite. The behavior depicted is similar to that of the shear and complex viscosities. The Laun relation [49] appears to be valid for both the neat polypropylene and the 30 wt% composite. For very small rates, Eq. 31 reduces to the prediction of an upperconvected Maxwell model [START_REF] Carreau | Rheology of Polymeric Systems: Principles and Applications[END_REF] with a constant 1 (zero- shear plateau). The trend of further increases of 1 for the 30% composite as the shear rate goes down to very small values is probably due to fiber-fiber interactions that become dominant, as observed by Sepehr et al. [25] for suspensions of the same glass fibers in a Newtonian matrix. The primary normal coefficient is somewhat larger for the 30 wt% composite than for the neat polypropylene, but as observed for the steady-shear viscosity (Fig. 7) the differences decrease at high shear rates. If we recall that the fiber orientation increases with shear rate [18] and consequently fiber-fiber interactions decrease, this observation supports the assertion of Zirnsak et al. [23] and Sepehr et al. [25] who claim that the increase of the primary normal stresses reflect the fiber-fiber interactions. The two correlations based on the exit pressure (Eqs. 29 and 30) overpredict the primary normal stress coefficient, in the range covered by the Laun relation [49], but the Forgacs and Manson correlation [46] appears to be reasonable at large rates. However, we need to obtain normal stress data at high rates using a more reliable method to verify the Laun empirical relation.

Transient Behavior

The complex transient behavior for creep and stress growth measurements of the same reinforced polypropylene samples has been presented and discussed in Sepehr et al. [50]. Here, we illustrate in Fig. 12 the effect of a dynamic pre-conditioning on the creep data in terms of the instantaneous viscosity as a function of strain, ␥ for the 30 wt% reinforced polypropylene. For the preconditioning, various frequency and strain amplitude conditions were applied during one hour. Immediately after the pre-conditioning, creep experiments were conducted for an applied shear stress of 600 Pa. Without pre-conditioning, the creep viscosity of the fiber reinforced suspension exhibited a large overshoot, due to the fiber macro-structure evolution [10,34,35,51,52]. The amplitude of this overshoot was reduced by the preconditioning, especially at large strain amplitude and high frequency. The overshoot almost vanished for a strain amplitude of 0.1 and frequency of 6.28 rad/s. The observations of Fig. 12 are explained by the fact that a large amplitude oscillatory shear affects the fiber-fiber interactions and leads to a shear aligned fiber macrostructure, as previously shown by Kim and Song [20].

Apparent Extensional Viscosity

Figure 13 reports the total pressure drop and calculated shear and extensional contributions for the neat polypropylene as functions of the flow rate for hyperbolic die (a). The extensional contributions were calculated using the experimentally determined pressure drops and the calculated shear contributions using Eq. 12 or the first term of Eq. 16. For the shear rate range experimentally covered in the converging dies, the polymer does not obey a simple powerlaw expression. Three zones were then defined for which we used the following power-law parameters: For each flow rate, the converging die was separated in different zones for which the appropriate power-law expression was used, based on the calculated shear rate at the wall. The extensional flow contribution is shown in Fig. 13 to be significant, representing about 40% of the total pressure drop for the shorter converging die (a). If the total pressure drop is believed to be accurate within a few percents, the accuracy of the extensional contribution is, however, not better than Ϯ 15%. The extensional contributions have been described by three different power-law expressions for cal-culating the apparent extensional viscosity using the Binding method.

␥ ˙Ն 100 s Ϫ1 f n ϭ 0.
The apparent extensional viscosity, e , of the neat polypropylene estimated for the shorter converging die (a) using the Cogswell and the Binding analyses are presented in Fig. 14 (error bars indicating estimated errors). The complex and shear viscosity data are shown to illustrate some differences in the behavior. The Binding analysis (Eq. 16) takes into account the strain dependence of the extensional viscosity as well as that of the shear viscosity. As mentioned above, the parameter t was obtained from the log-log plot of the extensional contribution to the pressure drop vs. flow rate in three zones as shown in Fig. 13. We took into account the variations of the power-law parameters for the shear viscosity, as we did for calculating the contributions of the shear viscosity to the pressure drop. The apparent extensional viscosity values calculated using the Binding method are presented in Fig. 14 as a function of the extensional rate at the centerline of the converging die compared to the average extensional rate for the calculations based on the Cogswell method. The apparent extensional viscosity for the Binding analysis is probably more meaningful, but the overall trend in both sets of calculated values is the same, although the values based on the Binding method are somewhat smaller. For simplicity reasons, we chose to present only the extensional data for the 30% composite based on the Cogswell method.

For the data presented in Fig. 14, based on the Cogswell method, the Trouton ratio, T R , defined as e /, was evalu- ␥ ˙ϭ␥ ˙ϭ 2 ˙. The ratio was found to be around 40 at low strain rates, and decreased rapidly as the extensional rate increases from 0.2 to 200 s -1 to reach a value of 4, which is the theoretical Trouton ratio for a Newtonian fluid in planar extension. Our results at low strain rates are in agreement with those of Binding et al. [53] for another polypropylene. However, the value of the Trouton ratio of 4 at large strain rates is much smaller than that reported by Binding et al.

The corresponding data for the reinforced polypropylenes containing 10 and 30 wt% are compared to the neat polypropylene data in Fig. 15. For these results, we use only the simpler Cogswell method and data obtained using the shorter converging die, which induces higher rates and for which the extension flow contributions are the largest. The complex viscosity data of the neat polypropylene are also shown for comparison. We observe that the apparent extensional viscosity of the composites increases slightly with fiber content. The relative extensional viscosity increase is defined by: ⌬ er ͑ ˙͒ ϭ e suspension Ϫ e matrix e matrix ͯ ˙.

(

) 33
For the data presented in Fig. 15, ⌬ er was found to be almost independent of the extensional rate. It is equal to 35 and 5% for the 30 and 10 wt% reinforced polypropylenes, respectively. The 5% increase for the 10 wt% composite is not significant considering the experimental uncertainty. The effect of fiber content on the extensional properties is considerably less compared to that observed for dynamic data (Fig. 6).

The Goddard model predicts a relative stress, ⌬ r (ϭ ⌬ er ), equal to 0.54 and 0.22 for the 30 and 10 wt% reinforced systems, respectively. These results are 1.5 and 4.4 times larger than the values based on the experimental data of Fig. 15. The same unsatisfactory agreement was found by Goddard [54] between his non-Newtonian theory and the experimental data of Chan et al. [11]. According to Goddard, the lack of alignment of the fibers in the flow direction and the lack of adhesion between the fibers and the matrix were the most plausible causes of this discrepancy. The lack of fiber orientation as observed from micrographs of samples taken at the exit of the converging section appears to be the reason for the difference between the model prediction and our data.

CONCLUDING REMARKS

We have reported a rather complete rheological characterization of a commercial glass fiber reinforced polypropylene, using conventional rheometers and a novel on-line rheometer mounted on an injection molding machine. The experimental conditions were comparable to those encountered in polymer processing. The on-line rheometer consisted of a slit die and planar hyperbolic converging and diverging dies. The apparent extensional properties were obtained from the pressure drop in the converging die using the Cogswell [1] and Binding [2] analyses. The steady-shear viscosity could be obtained from the pressure profile along the slit die measured by three flushed-mounted transducers.

All the dynamic properties as well as the steady shear viscosity were found to increase with fiber content. However, the loss angle was shown to be independent of fiber content, indicating that the elasticity of the composites was not affected by the presence of fibers. The enhancement of the steady shear viscosity was more important at very low strain rates, mainly for the 30 wt% composite. Moreover, the rheological properties were affected by the fiber macrostructure or fiber orientation. Pre-shearing was shown to decrease the complex viscosity and the viscosity overshoot during transient experiments, respectively. The Cox-Merz rule was found to be valid for the neat polypropylene, but important deviations were observed for the composites at large rates, and these have been attributed to fiber orientation induced by large shear rates.

The primary normal stress difference was evaluated using the parallel plate geometry and empirical correlations based on the dynamic data, as well as exit pressure data from the slit die. The Laun relation [49] based on dynamic data gave a satisfactory description of the primary normal stress coefficient for the neat polypropylene, whereas the correlations based on the exit pressure overestimated the normal stresses, except possibly for very large shear rates. The Laun relation appeared to well describe the normal stress data for the 30% composite, except at very low shear rates where the fiber-fiber interactions were dominant and responsible for larger normal stresses.

The apparent extensional viscosity of the neat polypropylene was found to exhibit a similar behavior as the shear or complex viscosity, but the extensional viscosity of the polypropylene was found to be much larger than the shear viscosity at low strain rates. The Trouton ratio of about 40 decreased rapidly with increasing strain rate down to the value of 4 at 200 s -1 . The extensional viscosity of the composites was also found to be close to that of the matrix, with values of 35 and 5% larger for the 30 and 10 wt% reinforced polypropylenes, respectively. These values are much lower than those predicted by the Goddard [3] model.

FIG. 1 .

 1 FIG. 1. Schematic of the on-line rheometer.

FIG. 4 .

 4 FIG. 4. Complex viscosity * (a) and dynamic storage modulus G' (b) vs. frequency for reinforced polypropylene with various fiber contents; T ϭ 200°C. The samples had not been pre-sheared before the dynamic measurements.

FIG. 7 .

 7 FIG. 7. Viscosity vs. shear rate ␥ ˙for reinforced polypropylene with various fiber contents; T ϭ 200°C.

FIG. 9 .

 9 FIG. 9. Shear viscosity and complex viscosity curves of neat polypropylene (unfilled symbols) and 30 wt% fiber reinforced polypropylene (grey symbols); T ϭ 200°C. The data for the neat polypropylene have been multiplied by 0.1 for convenience.

FIG. 12 .

 12 FIG. 12. Effect of dynamic pre-conditioning on the creep viscosity of 30 wt% fiber reinforced polypropylene, (␥ ϱ ): viscosity at the equilibrium; T ϭ 200°C.

  22 and m ϭ 3.04 ϫ 10 4 Pa ⅐ s n 10 s Ϫ1 Յ ␥ ˙Ͻ 100 s Ϫ1 f n ϭ 0.40 and m ϭ 1.516 ϫ 10 4 Pa ⅐ s n (32) ␥ ˙Ͻ 10 s Ϫ1 f n ϭ 0.60 and m ϭ 1.014 ϫ 10 4 Pa ⅐ s n .

FIG. 13 .

 13 FIG. 13. Total pressure drop and contributions of the shear and extensional components vs. flow rate Q for the neat polypropylene; converging die "a"; T ϭ 200°C.

FIG. 14 .

 14 FIG. 14. Apparent extensional viscosity e calculated using the Cogswell and Binding methods for neat polypropylene; converging die "a"; T ϭ 200°C. The simple shear and complex viscosity data are shown for comparison.

TABLE 1 .

 1 Fiber characteristics.

					L w , m	L n , m
	Reference	m ; (%)	; (%)	Mixing method	(Ϯ10 m)	(Ϯ10 m)	L w /L n
	PP10	10	3.8	As supplied	790	610	1.3
				Injection machine	660	530	1.24
				Brabender internal mixer	520	440	1.18
	PP30	30	13.2	As supplied	520	430	1.2
				Injection machine	400	330	1.22
				Brabender internal mixer	350	300	1.15

TABLE 2 .

 2 Dimensions of the on-line rheometer.

		Inlet	Outlet
		thickness,	thickness,	Width, 2W,	Length, L,	Strain rate range,
	Geometry	2h 0 , mm	2h f , mm	mm	mm	s Ϫ1
	Slit die	2 & 3.04	2 & 3.04	25	70	10 1 -10 5
	Converging die a	8	2	25	12	0.2-200
	Converging die b	8	2	25	24.1	0.1-100

POLYMER COMPOSITES-2005

POLYMER COMPOSITES-2005

POLYMER COMPOSITES-2005

POLYMER COMPOSITES-2005

ACKNOWLEDGEMENTS

The materials used in the study were provided by Basell, for which the authors wish to thank Dr. G. Krotkine.

Contract grant sponsor: Natural and Engineering Research Council of Canada (NSERC).


Pascal Cosson
email: pascal.cosson@ec-nantes.fr

Antoine Leroy

Bernard Peseux

Jean-Pierre Regoin

A MULTIBODY APPROACH FOR THE MODELLING OF A MILLING MACHINE

Keywords: machine-outil, modélisation, approche multi-corps, comportement dynamique, analyse modale

De nombreuses études expérimentales ont mis en évidence que les premiers modes de vibration d'une machine-outil pouvaient être excités lors d'opérations d'usinage à grande vitesse (UGV). L'étude des déformations sous l'effet de sollicitations dynamiques d'une machine-outil dédiée à l'UGV est donc essentielle afin d'imposer pour cette machine des raideurs statique et dynamique importantes, tout en conservant des masses en mouvement faibles, ce qui assure des valeurs de fréquences de résonance élevées. Pour définir le comportement dynamique d'une machine, nous présentons une méthode simplifiée de modélisation basée sur une approche multi-corps. A partir d'une mesure expérimentale du comportement dynamique obtenue avec des essais de type choc, une représentation de cette machine à l'aide de solides indéformables est élaborée, chaque solide étant associé à une partie de la machine : portique, broche ... Pour modéliser les déformations des différentes parties ainsi que d'éventuels défauts au niveau des liaisons, des rotations supplémentaires sont introduites entre les solides. A chaque rotation, sont associés une raideur et un amortisseur. Le modèle construit est donc défini par les raideurs et les coefficients des amortisseurs. Ces paramètres sont identifiés à partir des mesures expérimentales. La méthode est appliquée pour étudier une fraiseuse de type portique.

Introduction

High Speed Machining (HSM), by lowering times of manufacturing, seems to be a suitable way for industrials to increase productivity. In order to reach high spindle speeds and high feed rates required for HSM, machine tool designers have realized many studies concerning motorization, spindles and control systems. But new problems induced by the machine tool behaviour have raised with the use of HSM. On top of difficulties which concern the fact that the tool tip has to follow the tool path with a given feed rate and a given spindle speed, the machine tool can no longer be regarded as a rigid body with no strains. Indeed, many measured data have focused on the fact that the first vibration modes of a machine tool can be excited by dynamic sollicitations which occur during HSM. If in the past, a static designing of a machine tool was sufficient, such a point of view is no longer possible. To obtain HSM conditions requires a better understanding of the machine tool behaviour in dynamics. This paper describes a simplified way of taking into account the vibratory behaviour of a machine.

To carry out the analysis of the dynamic behaviour of a machine tool needs to overcome at least three main difficulties :

-the different parts of the machine tool have to be represented with a sufficient accuracy ;

-another aspect of the problem is the description of phenomena which happen at lumped joints between components of the machine ; generally, it is considered that connections introduce local flexibilities and non-linearities [6], [START_REF] Persianoff | Etude expérimentale et numérique d'une liaison glissière de machine-outil[END_REF] and [8] even if for small displacements, a linear behaviour is commonly applied ; on top of these nonlinearities, it must be taken into account that a great part of the loss of mechanical energy which occurs in a real structure is localized in the lumped joints ;

-finally, the third main difficulty concerns the fact that the behaviour of the machine tool depends on the state of the machine [START_REF] Lauroz | Modèle eléments finis et plans d'expériences pour la validation de critères de conception des machines utgv[END_REF] ; static and dynamic stiffnesses are linked to the location of the tool in the working space ; however, one can notice that this influence of the state of the machine is higher for a machining centre than for a portal-frame-type machine.

It exists at least three main approaches to model the dynamic behaviour of a machine tool in order to take into account the strains of the machine for a machining simulation :

-the first method attempts to represent interactions among the workpiece, the tool and the machine with a transfer function [START_REF] Tounsi | Modélisations du système Pièce-Outil-Machine, du Procédé de Coupe et de leur Interaction[END_REF]; this transfer function is a 3×3 matrix experimentally built by measuring cutting forces and relative accelerations between tool and workpiece in three orthogonal directions ; for this method, a representation of the machine is not necessary ;

-the second method is based on a finite element approach ; it needs a fine desciption of the components of the machine ; moreover, very precise models of joints between components (including non-linearities and damping) are required ; finite element models of machine tools are usually characterized by a high number of degrees of freedom (DOF), more than 10,000 DOF [START_REF] Duverger | Modélisation et simulation du comportement dynamique d'une machine-outil à grande vitesse[END_REF] and [START_REF] Lavabre | Dynamic behavior analysis of machine tool structures in the high speed machining context and its utility in design[END_REF] ;

-in the third approach, it is considered that a machine is composed of rigid bodies connected together by lumped joints ; in order to take into account strains, additional DOF are introduced ; these DOF are associated with springs and dashpots for the modelling of elasticity and damping ; this third method that we call a multibody approach can be refined by modelling the most rigid parts of the machine with undeformable bodies and the other parts of the machine with flexible bodies [5].

This third method has been applied to get a quite rough model of an existant machine. In order to predict the dynamic behaviour of this machine and to detect its shortcomings for HSM, our model has to provide :

-natural frequencies, -an estimate of stiffnesses and damping ratios of lumped joints between components, -an estimate of displacement levels for many points of the structure.

Our work can be divided into three parts :

(i) in a first experimental part, the vibratory bahaviour of the machine has been studied ; receptance has been measured at the spindle nose to find natural frequencies and modal damping ratios have been deduced from a fit of experimental data ;

(ii) in order to design a kinematic chain for the modelling of strains which occur in the machine, a system of angular coordinates has been established ; every coordinate has to be understood as a relative rotation between two rigid bodies associated in a given joint ;

(iii) mechanical parameters of the model (stiffness and damping ratio of each lumped joint) have been identified from measured data by optimization method.

The support of this study is the DROOP & REIN n o 486/1 milling machine, a plane milling machine of EADS in Toulouse.

Experimental modal analysis of the DROOP & REIN milling machine

The machine that we have studied -a table on which the workpiece is clamped ; -two guideways ; -a travelling gantry which can move on the guideways ; this travelling gantry is formed by a crossing-beam supported by two columns ; -a sliding block which can translate on the crossing-beam ; -a saddle which can have a relative vertical displacement with respect to the sliding block ; this saddle supports two motorization devices which motor-drive the two spindles.

For the experimental modal analysis, the machine was excited by impacts using a dynamometric hammer TECHDIS PCB 086B50. Impacts were produced in many points of the machine along three orthogonal directions when possible. The impacting forces induced in the structure were measured with a force transducer. An accelerometer B & K 4367 with a conditioning amplifier B & K 2635 were used to measure the response along three orthogonal directions. The two signals were treated with a dynamic signal analyser HP3562A to obtain receptance. Due to noise-like disturbances, the frequency response functions were determined on the frequency range [ 0 Hz , 500 Hz ] .

The first information which can be deduced from measurement concerns natural frequencies of the machine and damping ratios of vibration modes which can be attached to each natural frequency. Experimental data were carried out by bumping the tool along x, y and z directions and measuring acceleration along these three orthogonal directions. To rule out local resonances, impacts were also produced on the tool holder and on the lower spindle tip. The most significant results were obtained with impacts along x and y axes. Natural frequencies and damping ratios of vibration modes were taken out from experimental data with a curve fitting using rational functions. For the jth vibration mode, natural frequency f j and damping ratio η j were given by :

f j = | λ j | 2 π and η j = Re(λ j ) | λ j | (1)
where λ j and λ j are the two poles which define the jth vibration mode.

In comparison with results for the DROOP & REIN milling machine, natural frequencies for a SABRE 500 milling unit [START_REF] Cosson | Essais réalisés sur un centre d'usinage sabre 500[END_REF] and for a HURON EX 14 milling centre [START_REF] Bezy | Analyse vibratoire sur le cu huron ex 14[END_REF]

Identified values of the damping ratios

For the modelling of the plane milling machine with discrete lumped inertias interconnected by springs, dampers and massless links if necessary, a characterization of joints and couplings between the main components of the structure was needed. With this experimental modal analysis, it was shown that in a first approach, it did not matter to take into account table and guideways. On top of that, it also appeared from these measurements that coupling between table and travelling gantry was so weak that it could be neglected.

Besides these results, experimental data provided that the translation of the travelling gantry with respect to guideways had no effect on measurements. Actually, measured data were independent of the travelling gantry position on guideways. Furthermore, it was just the same behaviour for the sliding block with respect to the crossing-beam. The influence of its position on measured frequency response functions was so insignificant that it could be given up.

Definition of a complementary kinematic schema

The experimental modal analy-Fig. 2: Moving part of the milling machine sis focused on the fact that among all components which constituted the milling machine, only moving elements had to be modelled for a simplified approach. The main goal of this second part of our work was to establish a complementary kinematic schema which could describe strains of the constituents of the machine and shortcomings of joints between these constituents.

As it is shown on Figure [START_REF] Bezy | Analyse vibratoire sur le cu huron ex 14[END_REF], the moving part of the milling machine is composed of the travelling gantry, the sliding block, the saddle, the two motorization devices and the two spindles.

-Displacements along x axis of the travelling gantry with respect to guideways are allowed by a prismatic joint.

-Between the crossing-beam of the gantry and the sliding block, there is a prismatic joint which allows displacements of the latter along the y axis.

-Displacements along z axis of the saddle with respect to the sliding block are allowed by a prismatic-joint.

-The two motorization devices are clamped on the saddle and each spindle is linked to its motorization device by a rotoïd joint.

As the components of the moving part were modelled by rigid bodies, further DOF have been added to the kinematic schema of the Figure [START_REF] Bezy | Analyse vibratoire sur le cu huron ex 14[END_REF] in order to take into account strains in the constituents of the moving part and shortcomings of joints between these constituents. These additional DOF have been introduced to allow supplementary translational or rotational motions between the different components on top of motions described just before.

With the assumption of small displacements of the spindle around a given state of the machine, the displacements of the lower spindle tip were directly related to the additional DOF by a linear transformation, namely :

   u x u y u z    = [ G ] { X } (2)
where -{ u x , u y , u z } were the displacements of the lower spindle tip along x, y and z directions ;

-{ X } represented the vector of additional DOF ; -[ G ] was a constant 3 × n matrix where n was the size of vector { X }.

The vector of additional DOF could be deduced from equation (2) by minimizing the euclidian norm :

   u x u y u z    -[ G ] { X } 2 (3)
-If there were three additional DOF, the vector { X } was merely given by :

{ X } = [ G ] -1    u x u y u z    (4)
-If the number of additional DOF was different from three, the vector { X } was obtained by using a singular value decomposition of the matrix [ G ] (the QR decomposition of the matrix [ G ] led to the same values of vector { X }).

In order to take into account strains and shortcomings of joints, many kinematic chains have been tested. To compare these chains, displacements calculated from additional DOF have been correlated with measured displacements. We also have had a look on self-consistency of the results. Among all the tested kinematic chains, the best feet with measured data have been performed with a model including five additional rotations : one rotation θ for the travelling gantry around y axis, one rotation β for the sliding block around the crossing-beam, one rotation α around z axis for the saddle and two rotations ζ and γ for the spindle around x and y axes. With this model, displacements at the lower spindle tip were related to additional rotations θ, β, α, ζ and γ by the following linear transformation :

  u x u y u z   =   z h + z P z P -y J -y P z P 0 0 0 x J + x P 0 -z P -x h -x K -x J -x P -x K -x J -x P 0 -x P y P         θ β α ζ γ       (5)
where { x h , 0 , z h } represented the coordinates of the point H in the travelling gantry coordinate system, { x K , 0 , 0 } were the coordinates of the vector --→ HK in the sliding block reference system, { x J , y J , 0 } represented the coordinates of the vector --→ KJ in the saddle reference system, { x P , y P , z P } were the coordinates of the vector --→ JP in the spindle reference system ; The point P represented the lower spindle tip which the accelerometer was fixed on.

Remarks : points H , K and J are defined on the Figure (3) ; for a given state of the milling Fig. 3: Complementary kinematic chain for the milling machine machine, when this machine is unstrained, these points have the same z coordinate in a global coordinate system ; on top of that, the point J is on the spindle axis. On the Figure [START_REF] Cosson | Essais réalisés sur un centre d'usinage sabre 500[END_REF], only the bumped spindle has been represented. This part of our work has also provided that it was not possible to define a more complex kinematic chain. Actually, when we attempted to feet measured data with a model characterized by n additional DOF (with n ≥ 6), it resulted in a lot of disturbances on identified values. In fact, to define a more complex model needs at least : -to obtain less noise-like disturbances on measured data, -to use an experimental device which allows measurements in many points simultaneously.

Identification of the parameters of the numerical model of the milling machine

The third part of this work has tackled about the identification of parameters of the numerical model of the milling machine which is associated with the kinematic schema of Figure [START_REF] Cosson | Essais réalisés sur un centre d'usinage sabre 500[END_REF]. It is an optimization problem which could be achieved by minimizing a gap function between measured and estimated values of natural frequencies, modal damping ratios and compliances. These calculated values were performed with the numerical model of the machine by solving equations which governed motions of the structure.

Classically, according to the fact that components of the moving part of the machine were modelled with rigid bodies, the calculus of kinetic energy corresponding to motions defined by rotations θ, β, α, ζ and γ has led to the expression of the mass matrix M .

As this model is devoted to represent small motions of the milling machine around a given state, elastic behaviour of joints has been assumed. Therefore, five linear springs k θ , k β , k α , k ζ and k γ have been associated to the five rotations θ, β, α, ζ and γ.

In addition to these springs, in order to take into account losses of mechanical energy due to external damping at joints, five viscoelastic dampers b θ , b β , b α , b ζ and b γ have been introduced. As one can see, the assumption of proportional damping has been dismissed essentially because it is a more restrictive framework well suitable for lightly damped structures.

It follows that small motions of the structure were governed by the differential equation (6) :

0 M M B Ẍ Ẋ + -M 0 0 K Ẋ X = 0 -Φ p + F x .Φ x + F y .Φ y + F z .Φ z (6)
where -F x -→ x + F y -→ y F z -→ z represented the force applied at the lower spindle tip ;

-Φ x , Φ y , Φ z were load vectors due to unit forces applied respectively along x, y and z directions ;

-Φ p was a load vector due to gravity ;

-M represented the mass matrix of the structure ;

-B was the damping matrix of the structure given by B =

      b θ b β b α b ζ b γ       ;
-K , the stiffness matrix of the structure, could be written as

K = K p +       k θ k β k α k ζ k γ      
where K p was a matrix due to gravity.

As matrix M, B and K were symmetric ones, compliance X(Ω) satisfied the relation :

X(Ω) = j=10 j=1 U j U t j a j ( i Ω + λ j ) { F ( F x ) .Φ x + F ( F y ) .Φ y + F ( F z ) .Φ z } (7)
where -the vector Z j = -λ j U j U j was carried out by solving the eigenvalue problem

-M 0 0 K Z j = λ j 0 M M B Z j (8)
-the coefficients (a j ) were given by a j = -2 λ j U t j M U j + U t j B U j , -F ( F x ) , F ( F y ) and F ( F z ) represented the FOURIER transformations of F x , F y and F z . As it can be readily shown from equation ( 7), the compliance X(Ω j ) could be performed from the solutions of the eigenvalue problem defined by equation ( 8). The eigenvalues (λ j ) represented the poles of the system from which numerical values of natural frequencies and modal damping ratios could be calculated by using equation [START_REF] Bezy | Analyse vibratoire sur le cu huron ex 14[END_REF]. Therefore, we were able to build an objective function Ξ with respect to parameters k

θ , k β , k α , k ζ , k γ b θ , b β , b α , b ζ
and b γ . This objective function was choosen as it follows :

Ξ = a 1 i=5 i=1 f i,cal -f i,meas f i,meas + a 2 i=5 i=1 η i,cal -η i,meas η i,meas + a 3 j=N M EAS j=1 w = x, y, z ρ w X w,cal (Ω j ) -X w,meas (Ω j ) X w,meas (Ω j ) 2 0.5 (9)
where -compliances X w,cal (Ω j ) for w = x, y and z were performed with relation ( 7), -coefficients ρ w (for w = x, y, z) were set to 1 or 0 whether experimental data concerning w direction were assumed to be significant or not, -a 1 , a 2 , a 3 were weighting coefficients.

This objective function was minimized with MATLAB by using the NELDER-MEAD simplex method. Equation [START_REF] Lavabre | Dynamic behavior analysis of machine tool structures in the high speed machining context and its utility in design[END_REF] states that values of parameters which issued from the optimization process were those which minimized differences between measured and calculated values of natural frequencies, modal damping ratios and compliances.

Conclusions

In this paper, we have developed a method for the study of the dynamic behaviour of a machine tool. This approach leads to models which supply natural frequencies, modal damping ratios and an estimate of displacement levels for many points of the structure. These models are defined by lumped inertias interconnected by springs and viscoelastic dampers. We believe that in some cases, this method provides a useful way for characterizing a machine tool behaviour which avoids doing an accurate finite element mesh of the machine.

According to us, it would be of great interest to measure experimental data with a device which allows measurements in many points simultaneously. Moreover, it would be better to obtain data with less noise-like disturbances. It could be achieved for instance by applying an excitation to the machine tool with an inertial shaker or with the use of the own system control of the machine.

From our point of view, the optimization process has to be improved too. Actually, the identification of parameters of the machine tool model has presented many instabilities. The results were strongly dependent on the starting vector from which the optimization process was initialized. This drawback can be overcome by the development of identification methods. Particularly, it could be relevant that residues which are issued from the curve fitting of experimental data with rational functions would be related to the solutions of the eigenvalue problem defined by equation (8).

Fig. 1 :

 1 Fig. 1: Kinematic schema of the DROOP & REIN milling machine during this work is a DROOP & REIN plane milling machine of EADS company. The portal-frame-type architecture of this machine gives the structure high stiffness. This machine can be divided into five main parts :-a table on which the workpiece is clamped ; -two guideways ; -a travelling gantry which can move on the guideways ; this travelling gantry is formed by a crossing-beam supported by two columns ; -a sliding block which can translate on the crossing-beam ; -a saddle which can have a relative vertical displacement with respect to the sliding block ; this saddle supports two motorization devices which motor-drive the two spindles.

This work constitutes one of the studies led during a technological project concerning HSM. More detailed results are available in [2]. This project was supported by the French Ministry of Education, Research and Technology (MENRT).


Hong Thai Tran
email: hongthai.tran@uts.edu.au

George Feuerlicht
email: george.feuerlicht@uts.edu.au

Improving Reliability of Cloud-based Applications

Keywords: Reliability of Cloud Services, Fault Tolerance, RFT, RBFT, DSFT

With the increasing availability of various types of cloud services many organizations are becoming reliant on providers of cloud services to maintain the operation of their enterprise applications. Different types of reliability strategies designed to improve the availability of cloud services have been proposed and implemented. In this paper we have estimated the theoretical improvements in service availability that can be achieved using the Retry Fault Tolerance, Recovery Block Fault Tolerance and Dynamic Sequential Fault Tolerance strategies, and we have compared these estimates to experimentally obtained results. The experimental results obtained using our prototype Service Consumer Framework are consistent with the theoretical predictions, and indicate significant improvements in service availability when compared to invoking cloud services directly.

Introduction

With the increasing use of cloud services the reliability of enterprise applications is becoming dependent on the reliability of consumed cloud services. In the public cloud context, service consumers do not have control over externally provided cloud services and therefore cannot guarantee the levels of security and availability that they are typically expected to provide to their users [START_REF] Zibin | A Distributed Replication Strategy Evaluation and Selection Framework for Fault Tolerant Web Services[END_REF]. While most cloud service providers make considerable efforts to ensure the reliability of their services, cloud service consumers cannot assume continuous availability of cloud services, and are ultimately responsible for the reliable operation of their enterprise applications. In response to such concerns, hybrid cloud solutions have become popular [START_REF] Zhengping | Improving Cloud Service Reliability --A System Accounting Approach[END_REF]; according to Gartner Special Report on the Outlook for Cloud [START_REF] Rivera | Gartner Says Nearly Half of Large Enterprises Will Have Hybrid Cloud Deployments by the End of 2017[END_REF] half of large enterprises will adopt and use the hybrid cloud model by the end of 2017. Hybrid cloud solutions involve onpremise enterprise applications that utilize external cloud services, for example Paypal Payment Gateway (www.paypal.com), cloud storage service Amazon S3 (aws.amazon.com/s3), or entire SaaS (Software as a Service) applications. With a hybrid delivery model where enterprise applications are partially hosted on premise and partially in the cloud, enterprises can balance the benefits and drawbacks of both approaches, and decide which applications can be migrated to the cloud and which should be deployed locally to ensure high levels of data security and privacy. However, from the reliability point of view, hybrid cloud introduces a number of significant challenges as IT (Information Technology) infrastructure and enterprise applications become fragmented over multiple environments with different reliability characteristics.

Another reliability challenge concerns service evolution, i.e. changes in functional attributes of services that may impact on existing consumer applications. Services are often the subject of uncontrolled changes as service providers implement functional enhancements and rectify defects with service consumers unable to predict when or how services will change [START_REF] Andrikopoulos | On the Evolution of Services[END_REF]. Consequently, service consumers suffer service disruptions and are forced to upgrade their applications to maintain compatibility with new versions of cloud services, often without any notification. As the complexity of service-oriented applications grows, it is becoming imperative to develop effective methods to manage service evolution and to ensure that service consumers are protected from service changes.

In this paper we describe the reliability features of the Service Consumer Framework (SCF) designed to improve the reliability of cloud-based enterprise applications by managing service outages and service evolution. In the next section (section 2) we review related literature dealing with the reliability of cloud-based solutions. In section 3 we describe three reliability strategies (Retry Fault Tolerance, Recovery Block Fault Tolerance, and Dynamic Sequential Fault Tolerance) and calculate their expected theoretical impact on the probability of failure and response time. In section 4 we discuss how these reliability strategies are implemented using the SCF framework. Section 5 describes our experimental setup and gives a comparison of the theoretical results calculated in section 3 with the experimental measurements of availability and response time. Section 6 contains our conclusions and proposals for future work.

2

Related work

Traditional approaches to developing reliable, fault tolerant on-premise SOA (Service Oriented Architecture) applications include fault prevention and forecasting. For example, Tsai, Zhou [START_REF] Tsai | On Testing and Evaluating Service-Oriented Software[END_REF] propose a SOA testing and evaluation framework that implements group testing to enhance test efficiency. thors identify the most critical components of cloud applications and then determine an optimal fault-tolerance strategy for these components. Based on this work, Reddy and Nalini [START_REF] Reddy | FT2R2Cloud: Fault tolerance using time-out and retransmission of requests for cloud applications[END_REF] propose FT2R2Cloud as a fault tolerant solution using time-out and retransmission of requests for cloud applications. FT2R2Cloud measures the reliability of the software components in terms of the number of responses and the throughput. Authors propose an algorithm to rank software components based on their reliability calculated using a number of service outages and service invocation.

In recent research, Zhengping, Nailu [START_REF] Zhengping | Improving Cloud Service Reliability --A System Accounting Approach[END_REF] propose the S5 system accounting framework to maximize reliability of cloud services. The framework consists five different layers: service existence examination, service availability examination, service capability and usability examination, service self-healing layer, and system accounting user interface. Authors also propose a new definition of quality of reliability for cloud services. In another work, Adams, Bearly [START_REF] Adams | An introduction to designing reliable cloud services[END_REF] describe fundamental reliability concepts and a reliability design-time process for organizations. Authors provide a guideline for IT architects to improve the reliability of their services and propose processes that architects can use to design cloud services that mitigate potential failures. More recently, Zheng and Lyu [START_REF] Zheng | Selecting an Optimal Fault Tolerance Strategy for Reliable Service-Oriented Systems with Local and Global Constraints[END_REF] identified major problems when developing fault tolerance strategies and introduced the design of static and dynamic fault tolerance strategies. Authors identify significant components of complex service-oriented systems, and investigate algorithms for optimal fault tolerance strategy selection. A heuristic algorithm is proposed to efficiently solve the problem of selection of a fault tolerance strategy. The authors describe an algorithm for component ranking aiming to provide a practical fault-tolerant framework for improving the reliability of enterprise applications. Zheng, Lyu [START_REF] Zheng | Service fault tolerance for highly reliable serviceoriented systems: an overview[END_REF] describe a Retry Fault Tolerance (RFT) that involves repeated service invocations with a specified delay interval until the service invocation succeeds. This strategy is particularly useful in situations characterized by short-term outages.

Focusing on improving the reliability of cloud computing, Chen, Jin [START_REF] Chen | A lightweight software fault-tolerance system in the cloud environment[END_REF] present a lightweight software fault-tolerance system called SHelp, which can effectively recover programs from different types of software faults. SHelp extends ASSURE [START_REF] Sidiroglou | ASSURE: automatic software self-healing using rescue points[END_REF] to improve its effectiveness and efficiency in cloud computing environments. Zhang, Zheng [START_REF] Zhang | BFTCloud: A Byzantine Fault Tolerance Framework for Voluntary-Resource Cloud Computing[END_REF] propose a novel approach called Byzantine Fault Tolerant Cloud (BFT-Cloud) to manage different types of failures in voluntary resource clouds. BFTCloud deploys replication techniques to overcome failures using a broad pool of nodes available in the cloud. Moghtadaeipour and Tavoli [START_REF] Moghtadaeipour | A new approach to improve load balancing for increasing fault tolerance and decreasing energy consumption in cloud computing[END_REF] propose a new approach to improve load balancing and fault tolerance using work-load distribution and virtual priority.

Another aspect of cloud computing that impacts on reliability involves service evolution. Service evolution has been the subject of recent research interest [START_REF] Andrikopoulos | On the Evolution of Services[END_REF][START_REF] Eisfeld | Complex environment evolution: Challenges with semantic service infrastructures[END_REF][START_REF] Romano | Analyzing the Evolution of Web Services Using Fine-Grained Changes[END_REF][START_REF] Zhenmei | Small-World Based Trust Evaluation Model for Web Service[END_REF][START_REF] Ziyan | User's Requirements Driven Services Adaptation and Evolution[END_REF][START_REF] Feuerlicht | Service consumer framework: Managing Service Evolution from a Consumer Perspective[END_REF], however, the focus of these activities so far has been mainly on developing methodologies that help service providers to manage service versions and deliver reliable services. In the cloud computing environments where services are provided externally by independent organizations (cloud service providers) a consumer-side solution is needed to ensure the reliability of cloud-based service-oriented application [START_REF] Zheng | Service fault tolerance for highly reliable serviceoriented systems: an overview[END_REF].

Reliability Strategies

In this section we discuss three reliability strategies that are implemented in the SCF framework: Retry Fault Tolerance (RFT), Recovery Block Fault Tolerance (RBFT), and Dynamic Sequential Fault Tolerance (DFST). As noted above in section 2, these strategies have been described in the literature for on-premise systems [START_REF] Zibin | Component Ranking for Fault-Tolerant Cloud Applications[END_REF], [START_REF] Reddy | FT2R2Cloud: Fault tolerance using time-out and retransmission of requests for cloud applications[END_REF], [START_REF] Zheng | Service fault tolerance for highly reliable serviceoriented systems: an overview[END_REF]. We have adapted the RFT, RBFT and DFST reliability strategies for cloud services to address short-term and long-term service outages, and issues arising from service evolution. Short-term outages are situations where services become temporarily inaccessible, for example as a result of the loss of network connectivity; automatic recovery typically restores the service following a short delay. Long-term service outages are typically caused by scheduled and unscheduled maintenance or system crashes that require service provider intervention to recover the service. Service evolution involves changes in functional characteristics of services associated with functionality enhancements and changes aimed at improving service performance. Service evolution may involve changes to service interfaces, service endpoints, security policy, or may involve service retirement. Most cloud service providers maintain multiple versions of services to limit the impact of such changes on service consumers, and attempt to ensure backward compatibility between service versions. However, in practice it is not always possible to avoid breaking consumer applications, resulting in a situation where service consumers are forced to modify their applications to ensure compatibility with the new version of the service. Service overload occurs when the number of service requests in a given time period exceeds the provider limit.

Retry Fault Tolerance

Retry Fault Tolerance (Figure 1) is a relatively simple strategy commonly used in enterprise application. Using this strategy, cloud services are repeatedly invoked following a delay period until the service invocation succeeds. RFT helps to improve reliability, in particular in situations characterized by short-term outages. The overall probability of failure ( ) can be calculated by:

= ( 1
)
where PF is the probability of failure of the service and m is a number of retry attempts. While RFT reduces the probability of failure, it may increase the overall response time due to delays between consecutive service invocations. The total delay can be estimated as: where D is the delay between retry attempts and is the response time of i th invocation. The above calculations assume independent modes of failure of subsequent invocations; this assumption only holds in situations where the delay D is much greater than the duration of the outage, i.e. for long duration outages the invocation will fail repeatedly, invalidating the assumption of independence of failures of subsequent invocations.

= ∑ ( ( ) + × ( -1)) × ( ) (2)

Recovery Block Fault Tolerance

Recovery Block Fault Tolerance (Figure 2) is a widely used strategy that relies on service substitution using alternative services invoked in a specified sequence.

It is used to improve the availability of critical applications. The failover configuration includes a primary cloud service used as a default (active) service, and stand-by services that are deployed in the event of the failure of the primary service, or when the primary service becomes unavailable because of scheduled/unscheduled maintenance. Now assuming independent modes of failure, the overall probability of failure for n services combined can be computed by:

= ∏ ( ) ; = 1 - ( 3
)
where n is the total number of services and is the probability of failure of the i th alternative service. The overall response time ( ) can be calculated by:

= ( ) + ∑ ( ( ) × ∏ ( ) ) (4)
where is response time of first service invocation and is response time of i th alternative service invocation. In the online shopping scenario illustrated in Figure 3, the composite payment service uses eWay payment service as an alternative (standby) service for the PayPal (primary) service. Assuming that the availability of both PayPal and eWay services is 99.9% (corresponding to an outage of approximately 9 hour per year), and that the probability of failure PF = 0.01 for each service, the overall RBFT probability of failure = 10 -6 , and the overall availability s = 99.9999% (this corresponds to an outage of approximately 5 minutes per year).

Dynamic Sequential Fault Tolerance

The Dynamic Sequential Strategy (Figure 4) is a combination of the RFT and RBFT strategies. When the primary service fails following RFT retries, the dynamic sequential strategy will deploy an alternative service. The overall probability of failure for the n services combined is given by:

= ∏ ( ) ; = 1 - (5)
where ( ) is the probability of failure of the i th alternative service using the RFT strategy calculated in equation (1), and ( ) is the overall availability of the composite service using the DSFT strategy. The overall response time ( ) can be calculated by:

= T ( ) + ∑ (T ( ) × ∏ PF ( ) ) (6)
where T ( ) is the response time of the first service using the RFT strategy in equation (2), T ( ) is response time of i th alternative service calculated in equation ( 2), and PF ( ) is the probability of failure of the k th alternative service using the RFT strategy calculated using equation [START_REF] Zibin | A Distributed Replication Strategy Evaluation and Selection Framework for Fault Tolerant Web Services[END_REF]. Table 1 indicates the suitability of the RFT, RBFT, and DSFT strategies to different types of reliability challenges.

Implementation of Reliability Strategies using the SCF

The SCF framework is designed to manage hybrid cloud environments and aims to address the main issues that impact on the reliability of enterprise applications. The SCF framework implements RFT, RBFT and DSFT strategies and is briefly described in the following sections. The framework consists of four main components: Service Repository, Workflow Engine, Service Adaptors and a Notification Centre. Detail description of the SCF framework can be found in [START_REF] Feuerlicht | Service consumer framework: Managing Service Evolution from a Consumer Perspective[END_REF]. Figure 5 illustrates how service adaptors and the workflow engine can be configured to implement the various reliability strategies.

Service repository

Service repository maintains information about the available services and adaptors, including metadata that describes functional and non-functional attributes of certified services. The information held in the service repository is used to manage services and to design reliable applications. The functional and non-functional QoS (Quality of Service) attributes held in the service repository enable the selection of suitable services by querying the service repository specifying desired service attributes. Services with identical (or similar) functionality are identified to indicate that these services can be used as alternatives to the primary service to implement the RBFT strategy.

Service adaptors

Service adaptors are connectors that integrate software services with enterprise applications. Each cloud service recorded in the repository is associated with a corresponding service adaptor. Service adaptors use a native interface to transform service requests to a request that is compatible with the current version of the corresponding cloud service, maintaining compatibility between enterprise applications and external services. The function of a service adaptor is to invoke a service, keep track of service

Workflow engine

The workflow engine implements service workflows, facilitates service failover and the composition of services. The workflow engine executes workflows and routes requests to corresponding cloud services. Workflows can be configured to implement the RBFT strategy by using a number of alternative services redundantly. Another important function of the workflow engine is load balancing. Service adaptors can be configured as active or stand by. By default, active service adaptors are used to process the requests and stand by adaptors are deployed in situation when the primary (active) adaptor requests fail or when the primary adaptor becomes overloaded.

Notification Centre

The SCF framework maintains execution logs and updates service status records in the service repository. When service faults occur, notification centre notifies application administrators so that a recovery action can take place. The administrators are able to rapidly react to service failures and maintain application availability minimizing downtime. In addition, execution logs are used to monitor services and to analyze QoS attributes.

Experimental Verification of Reliability Strategies

Figure 6 illustrates the experimental configuration that was used to verify the theoretical calculations in section 3. The experimental setup consists of two servers that Fig. 6. Experimental Configuration host the SCF framework and a separate Monitoring Server. Both SCF servers implement identical payment scenario illustrated in Figure 3 using PayPal Pilot service (pilot-payflowpro.paypal.com) and eWay Sandbox (https://api.sandbox.ewaypayments.com). The payment requests are randomly generated and sent to the PayPal and eWay payment servers from two different locations. The US West Server uses Amazon Web Services (AWS) cloud-based infrastructure located on the West Coast of the United States and has a high quality server with a reliable network connection. The Sydney server is a local server in Sydney, Australia with a less reliable Internet connection.

Experimental Setup

We have collected experimental results from both servers for a period of thirty days, storing the data in the logs on the Monitoring Server deployed on AWS. The log data records were analyzed computing the experimental values of availability and response time for the composite payment service using different reliability strategies. Both SCF servers generate payment requests in intervals varying randomly between 5 and 10 seconds, and use the following four strategies:

Experimental Results

We have collected the payment transaction data independently of the values available from the cloud service providers, storing this information in the log files on the Monitoring Server (Table 2 shows a fragment of the response time measurements). The use of two separate servers in two different locations enables the comparison of availability and response time information collected under different connection conditions. As shown in Table 3, using Strategy 1 (i.e. without deploying any reliability strategy) the availability for PayPal and eWay services on the US West server is 90.4815% and 93.8654%, respectively. Deploying the RFT strategy (Strategy 2) the availability increases to 97.9033% and 97.2607%, for PayPal and eWay services, respectively. Using the RBFT strategy (Strategy 3), the availability of the composite service (Pay-Pal and eWay) increases to 99.8091%, and finally using the DSFT strategy (Strategy 4) the availability of the composite service (PayPal + eWay) increases further to 99.9508%. The theoretical values obtained in section 3 are slightly higher than the experimental values; this can be explained by noting that connection issues may affect both PayPal and eWay services concurrently, invalidating the assumption of independent modes of failure. Table 4 shows the average response time of PayPal and eWay services using different reliability strategies during the period from March 15 th to April 15 th 2016. The average response time of the US West Server is considerably lower than the Sydney Server when connecting to the PayPal service in the US. However, for the eWay service (https://www.eway.com.au/), which is located in Australia, the response time of the Sydney Server is slightly better than for the US West server. The bar charts in Figure 7 and 8 give a comparison of the availability values for various reliability strategies for the period of March 15 th to April 15 th 2016. As the figures illustrate, the availability of PayPal and eWay services using any of the reliability strategies is significantly higher than without deploying a reliability strategy. During the measurement period the availability of the PayPal service varied between 88% and 92%, but the availability of the combined PayPal-eWay services using the DSFT strategy remained above 99.9%.

CONCLUSIONS

With the increasing availability of various types of cloud services many organizations are becoming reliant on providers of cloud services to maintain the operation of their enterprise applications. Different types of strategies designed to improve the availability of cloud services have been proposed and implemented. These reliability strategies can be used to improve availability of cloud-based enterprise applications by addressing service outages, service evolution, and failures arising from overloaded services.

In this paper we have estimated the theoretical improvements in service availability that can be achieved using the Retry Fault Tolerance, Recovery Block Fault Tolerance, and Dynamic Sequential Fault Tolerance strategies and compared these values to experimentally obtained results. The experimental results obtained using the SCF framework are consistent with theoretical predictions, and indicate significant improvements in service availability when compared to invoking cloud services directly (i.e. without deploying any reliability strategy). In the specific case of payment services, the availability for PayPal and eWay services increased from 90.4815% and 93.8654%, respectively for direct payment service invocation, to 97.9033% and 97.2607%, for PayPal and eWay services, respectively when the RFT strategy was used. Using the RBFT strategy, the availability of the composite service (PayPal + eWay) increased to 99.8091%, and using the DSFT strategy the availability of the composite service (PayPal + eWay) increased further to 99.9508%.

Deploying multiple alternative services using the RBFT strategy also alleviates issues arising from service evolution that results in incompatible versions of services released by service providers. We are currently extending the functionality of the SFC framework to detect such situations and automatically redirect requests to alternative services.

Fig. 1 .

 1 Fig. 1. Retry Fault Tolerance

Fig. 2 .

 2 Fig. 2. Recovery Block Fault Tolerance

Fig. 3 .

 3 Fig. 3. Online shopping scenario using a composite payment service

Fig. 4 .

 4 Fig. 4. Dynamic Sequential Strategy

Fig. 5 .

 5 Fig. 5. Service Consumer Framework reliability features

Strategy 1 : 2 :Strategy 3 :Strategy 4 :

 1234 Payment requests are sent directly to the payment service without applying any reliability strategy Strategy Payment requests are sent to the payment service using RFT strategy with three retry attempts (R=3) and a delay of five seconds (D=5) Payment requests are sent to a composite payment service using the RBFT strategy Payment requests are sent to a composite payment service using the DSFT strategy which is combination of RBFT and RFT with PayPal (R=3, D=5) and eWay (R=3, D=5)

Fig. 7 .Fig. 8 .

 78 Fig. 7. Availability of reliability strategies from 15th to 31st of March

Table 1 .

 1 Suitability of reliability strategies

	Method	Short Outages	Long Outages	Service Evolution	Service Overload
	RFT	yes	no	no	no
	RBFT	yes	yes	yes	yes
	DSFT	yes	yes	yes	yes

Table 3 .

 3 Availability of payment services

	Server	PayPal	eWay	PayPal RFT	eWay RFT	PayPal-eWay RBFT	PayPal-eWay DSFT
	US West	90.48%	93.86%	97.90%	97.26%	99.80%	99.95%
	Sydney	90.18%	93.53%	97.28%	97.03%	99.29%	99.82%

Table 4 .

 4 Response time of payment services in seconds

	Server	PayPal	eWay	PayPal RFT	eWay RFT	PayPal-eWay RBFT	PayPal-eWay DSFT
	US West	1.35	1.84	2.33	2.66	2.06	2.44
	Sydney	3.70	1.75	5.67	3.02	4.98	5.43