Design and finite element analysis of a wet cycle cement rotary kiln

Finite Elements in Analysis and Design 39 (2002) 17 – 42 www.elsevier.com/locate/!nel

Design and !nite element analysis of a wet cycle cement rotary kiln J.J. del Coz D'(aza; ∗ , F. Rodr'(guez Maz'ona , P.J. Garc'(a Nietob , F.J. Su'arez Dom'(ngueza a

Departamento de Construccion e Ingenieria de Fabricacion, Universidad de Oviedo, Edicio Dep. de Viesques no 7, 33204 Gijon, Spain b Departamento de Matem&aticas, Facultad de Ciencias, C= Calvo Sotelo s=n, Universidad de Oviedo, 33007 Oviedo, Spain Received 6 July 2001; accepted 12 November 2001

Abstract The !nite element method (FEM) is applied to the nonlinear analysis of a cement rotary kiln for the Ra7(s Hamidou factory (Algeria). The nonlinearity is due to contact conditions between the kiln body, tyres and foundations. The FEM is !rst used in a reduced model of the kiln in order to obtain the meshing criterion for the global model. Then, an overall FEM analysis is performed for the di9erent operating and live loads at di9erent positions of the rotary kiln. Stress and displacement components are evaluated based on the ASME rules (Asme Boiler and Pressure Vessel Code. VIII. Division 2—Alternative Rules. The American Society of Mechanical Engineers, 1995). Finally, in this work, the main design criterion is the out-of-roundness values at the kiln shell so that the thickness of the kiln shell is smaller in the central bend span than the values at the tyres. ? 2002 Elsevier Science B.V. All rights reserved. Keywords: Cement rotary kiln; Finite element analysis; Contact problem; Numerical simulation; Nonlinear analysis

1. Introduction The present paper aims to describe tasks and analyses for the calculation of a cement rotary kiln for the Ra7(s Hamidou Factory (Algeria). Procedures involved in the elaboration of this paper include • Structural modeling of the rotary kiln by the !nite element method. Previous analysis of a reduced model has been made. • Static nonlinear analysis of a full model. ∗

Corresponding author. E-mail address: [email protected] (J.J. del Coz D'(az).

0168-874X/02/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 8 7 4 X ( 0 2 ) 0 0 0 5 9 - 8

18

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

Fig. 1. Wet process clinker rotary kiln.

• Dynamic linear analysis of a full modi!ed model. • Structural veri!cation, including fatigue and ovalization of the kiln body, according to Asme [1–3] and AD-Merkbl7atter [4] rules. Depending on the manufacturing process, rotary kilns can be classi!ed into the following types [5]: • • • • •

Wet process kilns. Semi-dry process kilns. Dry process kilns. Preheater kilns. Pre-calciner kilns.

In the wet process, kiln feed material is in a slurry form containing 30 – 40% moisture. It is, therefore, necessary to dry the material in the kiln. There is therefore a drying zone and this part acts as a dryer. To facilitate drying, steel chains are used in the kilns. Due to the wet grinding of the material, the feed is more uniform in composition. Also, dust losses from such kilns are smaller. However, extra fuel is required to dry the feed material. This work analyzes a wet process rotary kiln similar to the one shown in Fig. 1. 2. Modeling and loading analysis 2.1. Description of the physical model Due to the di9erent chemical, mechanical and thermal requirements of the various sections of the rotary kiln, several zones can be distinguished:

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

19

Table 1 Magnitude

Value

Units

Cold real length Inner diameter Number of tyres Slope

124.4 4.2 5 4

Meters Meters %

• Inlet zone, dry zone and preheating zone: High wear-resistant castable or acid bricks, bricks of great porosity and !reproof (refractory) bricks or concrete refractory blocks resistant to abrasion are used. In this zone, the entrance ring is subjected to abrasion e9ort and in the case of very long rotary kilns a chain zone also supports this stress. In addition, there exist ceramic coatings with a good resistance to thermal stresses. • Calcination zone: In this zone of the rotary kiln which is less a9ected by chemical and thermal stresses, chamota bricks of di9erent qualities, chemically agglomerated, with 50 – 60% Al2 O3 are used. • Transition zone: Here extra aluminum bricks with corundum and bauxite on the basis of 50 –80% Al2 O3 are used. • Sintering zone: The coating consists exclusively of alkaline-resistant castable bricks of magnesium MgO–C2 O3 , bricks of chromium–magnesium and pressed dolomite. • Outlet and cooling zone: This section is made up of extra aluminum bricks with 65 –80% Al2 O3 and bricks of chromium–magnesium. The outlet ring is composed of bricks with 60% SiC and refractory concrete. 2.2. Geometry of the model The installation components are as follows: • • • • • • • • •

Rotary kiln shell. Kiln tyres. Tyre-bearing kiln shell sections. Roller stations. Drive components. Toothed ring and drive pinion. Cast steel kiln inlet and outlet segment system. Kiln inlet and outlet seals. Heating gas generator and burner assembly.

The main geometrical characteristics of the rotary kiln are given in Table 1. 2.2.1. Rotary kiln shell The thickness of the shells along the di9erent sections of the rotary kiln are given in Table 2. In Table 2 zero is placed in the upper end of the rotary kiln, called ‘amont’. The distances between supports, in millimeters, are given in Table 3. where ‘aval’ denotes the lower end of the rotary kiln.

20

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

Table 2 Section (mm)

Thickness (mm)

Section (mm)

Thickness (mm)

0 –7000 7000 –8000 8000 –11 000 11 000 –12 000 12 000 –36 500 36 500 –37 500 37 500 – 40 500 40 500 – 41 500 41 500 – 63 000 63 000 – 66 000 66 000 – 67 500

26 50 80 50 26 50 80 50 26 40 50

67 500 –70 500 70 500 –71 500 71 500 –84 400 84 400 –94 000 94 000 –95 000 95 000 –98 000 98 000 –99 000 99 000 –118 000 118 000 –119 000 119 000 –122 000 122 000 –124 400

80 50 30 40 50 80 50 40 50 80 50

Table 3 Supports

Distance

aval–I I–II II–III III–IV IV–V V–amont

3900 24 000 27 500 30 000 29 500 9500

2.2.2. Re-injection hole of dust At a distance of 35 ms from an amont, there are two holes in the rotary kiln wall, designed for the re-injection of dust. They have a rectangular form and a dimension of 0:4 ms length and 0:6 ms in circumference. 2.2.3. Kiln tyres The rotary kiln has a strip-rolled sheet per support known as a tyre. Each one is dimensioned with the same inner and outer diameters as well as the same contact length on the support rollers. However, strip sets III and IV vary in design in order to adapt to their interaction with drive components. The di9erent sections of each tyre are shown in Fig. 2. 2.2.4. Tyre-bearing kiln shell sections Between the support shell and tyres there are devices termed tyre-bearing kiln shell sections with two main functions: (1) to allow a gap between the rotary kiln and the tyre, in such a way that contact is adequately maintained, (2) to limit that gap in order to prevent excessive ovalization of the shell.

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

21

Fig. 2. Sections of kiln tyres.

Fig. 3. Roller stations.

2.2.5. Roller stations Each tyre is situated on a roller station with a diameter of 1724 mm and each roller station is supported on a concrete foundation. In this model, rollers are situated forming a triangle with the center of the clinker kiln body as shown in Fig. 3. 2.2.6. Drive components Since the rotation movement and slope of the kiln body induces longitudinal displacement, the devices called drive components correct this. Only tyres of types III and IV have these drives.

22

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42 Table 4 Component

Material

Shells Tyres Rollers Pinion

AH2CP o HII Cast iron GS-25 Mo.25 Cast iron GS-42 Cr Mo.5 30 Cr Ni Mo 8 (ISO R 638=II-68 Type 3)

2.2.7. Toothed ring and drive pinion To transmit rotation movement, the kiln has a toothed ring attached to the kiln body. It is !xed to the kiln body through moving links. Rotation velocity is 1:5 rev=min: and mass correspondent to this device is 14 000 kg. 2.2.8. Materials Materials used for the kiln are shown in Table 4. 3. Mathematical modeling of the contact problem 3.1. Contact conditions A particularly diQcult nonlinear behavior to analyze is the contact between two or more bodies. Contact problems range from frictionless contact in small displacements to contact with friction in general large strain inelastic conditions. Although the formulation of the contact conditions is the same in all these cases, the solution for the nonlinear problems can in some analyses be much more diQcult than in other cases. The nonlinearity of the analysis problem is now decided by the contact conditions [13–22]. The objective is to brieRy state the contact conditions in the context of a !nite element analysis and present a general approach for solution. 3.2. Continuum mechanics equations Let us consider N bodies that are in contact at time t. Let Sct be the complete area of contact for each body L; L = 1; : : : ; N ; then the principle of virtual work for the N bodies at time gives [6] 
  N  N  N 

t t B t t S t t

ij i eij dV =

ui (fi ) dV +

ui (fi ) dS +

uic (fic )t dS t ; L=1

Vt

L=1

Vt

Sft

L=1

SCt

(1) where the part given in brackets corresponds to the usual terms: tij are the Cartesian components of the Cauchy stress tensor (forces per unit areas in the deformed geometry), t eij the strain tensor corresponding to virtual displacements, ui the components of virtual displacement vector imposed on con!guration at time t, a function of xjt ; j = 1; 2; 3; : : : ; xit the cartesian

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

23

Fig. 4. Bodies in contact at time t.

coordinates of material point at time, V t the volume at time, (fiB )t the components of externally applied forces per unit volume at time t, (fiS )t the components of externally applied surface tractions per unit surface area at time t, Sft the surface at time t on which external tractions are applied, uiS the ui evaluated on the surface Sft (the ui components are zero and correspond to the prescribed displacements on the surface Sut ) and the last summation sign in Eq. (1) gives the contribution of the contact forces. The contact force e9ect is included as a contribution in the externally applied tractions. The components of the contact tractions are denoted as (fic )t and act over the areas Sct (the actual area of contact for body at time t), and the components of the known externally applied tractions are denoted as (fis )t and act over the areas Sft . It is possible to assume that the areas Sft are not part of the areas Sct , although such an assumption is not necessary. Fig. 4 illustrates schematically the case of two bodies, which are now considered in greater detail. In this paper, the two bodies in contact are denoted as body I and body J . Note that each body is ˜ IJ )t be the vector of supported such that without contact no rigid body motion is possible. Let (f IJ t ˜ ˜ JI )t . Hence, the contact surface tractions on body I due to contact with body J , then (f ) = −(f

24

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

Fig. 5. De!nitions used in contact analysis.

virtual work due to the contact tractions in (1) can be written as   

uiI (fiIJ ) t dS IJ +

uiJ (fiJI ) t dS JI =

uiIJ (fiIJ ) t dS IJ ; S IJ

S JI

S IJ

(2)

where uiI and uiJ are the components of the virtual displacements on the contact surfaces of bodies I and J , respectively, and

uiJI = uiI − uiJ :

(3)

The pair of surfaces S IJ and S JI are termed as ‘contact surface pair’ and note that these surfaces are not necessarily of equal size. However, the actual area of contact at time t for body I is Sct of body I , and for body J it is Sct of body J , and in each case this area is part of S IJ and S JI (see Fig. 5). It is convenient to call S IJ the ‘contactor surface’ and S JI the ‘target surface’. Therefore, the right-hand side of (2) can be interpreted as the virtual work that the contact tractions produce over the virtual relative displacements on the contact surface pair. Let ˜n be the unit outward normal to S JI and let ˜s be a vector such that ˜n and ˜s form a right-hand ˜ IJ )t acting on S IJ into normal basis (see Fig. 5). It is possible to decompose the contact tractions (f JI and tangential components corresponding to ˜n and ˜s on S : ˜ IJ )t = ˜n + ˜s; (f where  and

(4)

are the normal and tangential traction components. Thus,

˜ IJ )t ]T˜n;  = [(f

˜ IJ )t ]T˜s: = [(f

(5)

In order to de!ne the actual values of ˜n and ˜s that are used in the contact calculations, consider a generic point ˜x on S IJ and let ˜y ∗ (˜x; t) be the point on S JI satisfying ˜x − ˜y ∗ (˜x; t) = minJI {˜x − ˜y}: ˜y∈S

(6)

The distance from ˜x to S JI is then given by g(˜x; t) = (˜x − ˜y ∗ )T˜n∗ ;

(7)

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

25

τ

λ

+1

g

u -1

Normal Conditions

Tangential Conditions

Fig. 6. Interface conditions in contact analysis.

where ˜n∗ is the unit normal vector that is used at ˜y ∗ (˜x; t) (see Fig. 5) and ˜n∗ , ˜s∗ are used in Eq. (4) corresponding to the point ˜x. The function g is the gap function for the contact surface pair. Let w be a function of g and  such that the solutions of w(g; ) = 0 satisfy the conditions for normal contact: g ¿ 0;

 ¿ 0;

g = 0:

(8)

Similarly, let  be a function of and u˙ such that the solutions of (u; ˙ ) = 0 satisfy the frictional conditions, that is, let us assume that Coulomb’s law of friction holds pointwise on the contact surface and that  is the coeQcient of friction. This assumption of course means that frictional e9ects are included in a very simpli!ed manner [7,8]. Let us de!ne the nondimensional variable given by

=



;

(9)

where  is the ‘frictional resistance’, and the magnitude of the relative tangential velocity is J ˜u˙(˜x; t) = (˜u˙ |˜y ∗ (˜x; t) − ˜u I |(x; t) ) ·˜s ∗

(10)

corresponding to the unit tangential vector ˜s at ˜y ∗ (˜x; t). Hence, ˜u˙(˜x; t)˜s∗ is the tangential velocity at time of the material point at ˜y ∗ relative to the material point at ˜x. With these de!nitions Coulomb’s law of friction states that | | 6 1; | | ¡ 1 ⇒ u˙ = 0; | | = 1 ⇒ sign(u) ˙ = sign( ):

(11)

The solution of the contact problem in Fig. 6 therefore entails the solution of the virtual work equation (1) (specialized for bodies I and J ) subject to conditions (8) and (11). 3.3. Solution approach for contact problems Let w be a function of g and  such that the solutions of w(g; ) = 0 satisfy the conditions for normal contact (8), and similarly, let v be a function of and u˙ such that the solutions of

26

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

v(u; ˙ ) = 0 satisfy the frictional conditions (11). Then, the contact conditions are given by w(g; ) = 0;

(12)

v(u; ˙ ) = 0:

(13)

These conditions can now be imposed on the principle of the virtual work equation using a penalty approach (PA), Lagrange multiplier method (LMM) or augmented Lagrangian method (ALM). This work uses the technique of ALM since it proves to be more eQcient from a numerical point of view [9 –11,6]. The variables  and can be considered as Lagrange multipliers, and so let  and be variations in these quantities. Multiplying (12) by  and (13) by and integrating over S IJ (the contactor surface), we obtain the constraint equation  [ w(g; ) + v(u; ˙ )] dS IJ = 0: (14) S IJ

In summary, the governing equations to be solved for the two-body contact problem are the usual principle of virtual work equation (1), with the e9ect of the contact tractions included through externally applied (but unknown) forces, plus the constraint equation (14). The !nite element solution of the governing continuum mechanics equations is obtained by using the discretization procedures for the principle of virtual work, and now, in addition, using even discretizing the contact conditions. 4. Finite element analysis of a reduced model 4.1. Initial approach A set of reduced models (Fig. 7) consisting of a body section of the kiln with its corresponding tyre and roller station has been constructed. The aim of this process was to develop suQcient knowledge regarding contact between shells and tyres and between tyre and rollers. Another important aspect to consider in this reduced analysis was the convergence process related to !nite element mesh re!nement. Di9erent approaches regarding contact boundary conditions and mesh density were investigated. Normal actions and sliding, with PA, LMM and ALM methods have been included. Some valuable conclusions obtained with this approach are presented below. 4.2. Solid modeling and meshing The model has been developed in Ansys 5.7.1 [12]. Finite elements used were as follows: • Shell93 is a shell that has eight nodes and double curvature, with six degrees of freedom at each node. This is used to model the rotary kiln shells. • Solid95 is a solid that has 20 nodes with three degrees of freedom at each node, used in the modeling of the bricks for tyres.

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

Fig. 7. Reduced models.

Fig. 8. Element point-to-point ‘Contact52’. Element ‘Target170’.

27

28

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

Fig. 9. Element ‘Contact174’.

Fig. 10. Elastic modulus and thermal expansion coeQcient.

• Contact52 is a three-dimensional gap of kind point-point (Fig. 8), with three degrees of freedom at each node, with possibility of friction, Rexibility, slide and preload. It was employed in the gaps between tyre-bearing and roller stations. • Contact174 is a three-dimensional surface gap (Fig. 9), with three degrees of freedom at each node, eight nodes, with the possibility of slide and elastic strain on target elements. • Target170 represents the surface of strain gap, with their corresponding physical properties. The contact elements are shown in Figs. 8 and 9. 4.3. Material properties The material has been modeled as isotropic and linear, elastic temperature dependent, according to the elastic properties of the steel used in Table 4. Fig. 10 shows the variation curves of elastic modulus and thermal expansion coeQcient taken from ASME rules [2].

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

29

Fig. 11. Boundary conditions of reduced model.

4.4. Boundary conditions Boundary conditions are represented in Fig. 11. Basically, rotations of the kiln have been constrained. In the same way, pairs of nodes corresponding to tyres and kiln body have been coupled in the longitudinal direction, and the tyre itself has been constrained in Z direction. 4.5. Loading analysis. Load cases Loads considered are basically body loads, including refractory bricks and chains, material weight and crust from the clink itself, added to the refractory. Since bricks and chains are attached to the shell, mass correspondence to these was modeled as an ‘addmass’ property of the Shell93 elements. It is a consequence of rotation that clink is dragged with the shell, so that it presents a natural ◦ slope of 20 . Consequently, this load condition is modeled as it is represented in Fig. 12. 4.6. Finite element analysis Stresses developed in contact and ovalizations of the kiln body are the primary results we are concerned with. Ovalization is one of the most important aspects in these devices because of its inRuence on the integrity of the refractories attached to the kiln body. So special care was taken regarding this issue. Tresca failure criteria (stress intensity in Ansys) were considered in this analysis and ovalization was evaluated from the formulas presented below: Ov = 43 (OD )2 WH; Ov = 2

Di max − Di min 100 Di max + Di min

(15) (16)

30

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

Fig. 12. Load from material weight.

where OD is the outside diameter and WH , Di max ; Di min are the radial displacement and the inner ◦ diameters, measured at 90 in each section around the shell. The maximum allowable ovalization for the kiln is 10% of the nominal diameter, according to standard rules [1,4]. 4.7. Conclusions Some conclusions were obtained from this reduced method: • The augmented Lagrange method (ALM) is adequate for contact simulation in this kind of analysis because it has a faster convergence ratio than penalty approach (PA) and Lagrange multiplier method (LMM). This method is basically the LMM with additional penetration control. • Sliding stresses are negligible in comparison with the normal ones. Typical values are about 4000 Pa and the contact pressures are about 1:46 MPa with the friction values of 0.1, 0.2 and 0.5. • The ovalization of the kiln body shell is the most important e9ect in the design and we have observed that the gap between the kiln shell and the tyres is very important. • The values of ovalization are very similar (smaller than 10%) among all the analyzed models from one to three, as shown in Fig. 13. • Convergence of results with mesh re!nement (Fig. 7) shows a reasonable limit between precision and computational e9ort. Consequently, we adopt a meshing criterion of the model number one to carry out the full model without Coulomb friction between the kiln body and the tyres. Therefore, the ALM method is used in the nonlinear analysis for contact simulation.

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

31

Fig. 13. Ovalization of the kiln body shell (magni!cation ×50).

5. Full model analysis The full model analysis (FMA) was developed based on the conclusions obtained from the reduced model analysis. Some modi!cations were added to this FMA: • The rotary kiln was analyzed in N di9erent positions. Each of these positions consists of a rotation ◦ of 30 about the kiln axis. The aim of this approach was to simulate the rotation of the kiln on a daily basis. This is necessary because the presence of dust injection holes in the kiln body breaks the symmetry conditions. Rotation is suQcient to consider each case as static. • Thermal load was considered variable throughout the rotary kiln according to manufacturer speci!cations as shown in Fig. 14. • Three accidental loads were considered: ◦ Material weight ◦ Crust rings ◦ Detachment of refractory bricks and crust. The rotary kiln has been modeled structurally (shown in Fig. 15) by means of the same type of elements indicated in Section 4 and this one • Structural mass (point mass) having three degrees of freedom (MASS21), used in the modeling of the transmission gear mass distributed around the shell. The thicknesses used in this preliminary analysis with shell elements have been those given by the reference book [5] in its predesign. The ‘gap’ elements have been fashioned to support only compression as well as to slide with friction according to Coulomb’s law with a friction coeQcient of 0.05.

32

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42 300

Temperature (˚C)

250

200

150

100

50

0 0

20

40

60

80

100

120

140

Length of the kiln body (m)

Fig. 14. Temperatures throughout the kiln body.

Fig. 15. Full model of the rotary kiln.

The boundary conditions are set to allow an axial displacement on kiln tyres and roller stations without friction except support number IV (see Table 3), the latter being !xed in axial direction. Also, the gap elements that simulate the kiln tyre–roller stations contact are immobilized at the end corresponding to the roller, by supposing that the foundation is capable of supporting the reactions transmitted without small di9erential displacements.

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

33

5.1. Analysis In this work, two di9erent analyses have been performed: nonlinear static analysis and dynamical analysis. Nonlinear static analysis: According to the model described above, the loads are applied at the adequate points so that their e9ect is equivalent to the real actions. Such loads include the dead and live loads. As load cases we considered the following: • Body loads: Every elements of the model including refractory bricks, crust and chains. • Operating loads: Due to the distribution of product at the bottom of the kiln. • Operating temperature: According to the manufacturer, without variation in the thickness. • Accidental load: Due to crust ring and 120% overload. The following combinations of load have been analyzed: 1. Body loads + operating loads + operating temperature. 2. Body loads + accidental charge + operating temperature. Since the rotary kiln has no revolution symmetry due to dust re-injection holes, the analyses have ◦ been carried out for seven di9erent positions of the kiln (every 30 rotation). Therefore, 14 di9erent cases of load are studied. Dynamical analysis: The dynamical analysis performed was transitory time-dependent, taking into account the degrees of freedom in the model [8]. • Structural model: Constituted by shell elements of thickness between 26 and 400 mm, to simulate the tyres. • Loads: The following loads have been considered: ◦ Static: The gravity acceleration that acts on the elements constituting the model. ◦ Dynamical loads: In the section between 111 and 116 mm from ‘amont’ a drop or settling of ◦ refractory corresponding to 120 sector and a 500 mm length are supposed. The settling velocity, v, is v=



2gh;

(17)

where g is the gravity acceleration and h is the drop height of the refractory. • Application of load as a function of time: The former loads are modeled as a function of time (see the Fig. 16). Dynamical load is broken down into four phases: • First phase (0 –0:001 s): Corresponds to the imposition of the initial conditions, which contain gravity (both longitudinal and vertical), and operating load. The inertial e9ects are neglected in this phase since it is a purely static load. • Second phase (0.001–0:101 s): The load due to the impact of refractory is introduced in this phase as well as the inertial e9ects in the integration scheme with 25 time steps in each load case. The application of the load is supposed as linear as indicated in Fig. 15. • Third phase (0.101–0:201 s): Now, a gradual load is applied, by means of a linear ramp and an integration scheme in time, in which the inertial e9ects are taken into account and the load applied previously is removed so that the ‘rebound’ of the product at the bottom is simulated.

34

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42 1.2 Phase 2 : 0.001 - 0.101

1.0 Phase 3 : 0.101 - 0.201 s

Load (%)

0.8

0.6 Phase 4 : 0.201 - 1.0 s

Phase 1 : 0 - 0.001 s

0.4

0.2

0

-0.5

-0.3

-0.1

0

0.1

0.3

0.5

0.7

0.9

Time (s)

Fig. 16. Load as a function of time.

• Fourth phase (0.201–1:0 s): The inertial e9ects derived from unloading carried out in the previous phase are analyzed.

6. Results: analysis of the full model analysis 6.1. Stress analysis The security of the kiln body was veri!ed by means of the preliminary analysis of obtained stresses. In order to do so, the ASME VIII norm, Appendix 4 (‘Design based on stress analysis’) was adopted as a criterion [1]. In general, in order to check the previous design, a value of equivalent stress is calculated at each point of the equipment. Subsequently, this value is compared with the mechanical properties of material obtained by uniaxial stress tests. The criterion for calculating the aforementioned equivalent stress is the maximum shear stress (Tresca failure criteria). Such a criterion admits as a value the semi-di9erence between the bigger value and the smaller value of the principal components of the stress in the point of analysis considered. Hence, a design is considered acceptable if it is satis!ed with the following: • The stress is smaller than the limits given by paragraph 4-130 of the ASME VIII rule [1]. • In the cases involving compression stress, in addition to the foregoing point, it is necessary to consider the buckling critical values, given by AD-330 [1]. The stress limit obtained by means of the rule, without the presence of fatigue, is of 131:6 MPa for the value of allowable stress Sm.

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

35

Fig. 17. Stress categories and limits.

In this way, the stress values calculated by the !nite element technique must not exceed the limits shown in Fig. 17, such maximum values are indicated by the adjacent circles to each of the check made, extracted from ASME alternative rules [1]

6.2. Ovalization analysis This analysis is based on the radial displacement criterion. This criterion aims to assess the integrity of the refractory bricks attached to the kiln body and therefore, it limits the transversal section out-of-roundness. The expressions of the ovalization parameter are indicated in formulas (15) and (16). The displacement results of analysis were post-processed by macros in an Excel Worksheet.

6.3. Stress results According to the criteria indicated in the above section the values of stresses in the di9erent structural elements that made up the kiln were evaluated at di9erent components: Kiln Kiln Kiln Kiln Kiln

shell of shell of shell of shell of tyres.

26 mm 40 mm 50 mm 80 mm

thickness, thickness, thickness, thickness,

The results are shown in Figs. 18–22.

36

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

Fig. 18. Kiln shell of 26 mm thickness between supports IV and V.

Fig. 19. Kiln shell of 50 mm thickness in support V.

6.4. Ovalization results According to the criteria pointed out in the above section, the values of out-of-roundness at the kiln shell were calculated for the following transversal sections: • Central line of kiln tyres. • Central bend span of the kiln body.

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

Fig. 20. Kiln shell of 80 mm thickness in support V.

Fig. 21. Kiln shell of 40 mm thickness between supports III and IV.

• Kiln inlet and outlet seals. The maximum results for each position are shown in Table 5.

37

38

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

Fig. 22. Kiln tyres in support III. Table 5 Item

Maximum value

Support I Support II Support III Support IV Support V Kiln shell between supports Kiln shell between supports Kiln shell between supports Kiln shell between supports Aval (kiln inlet) Amont (kiln outlet)

0.25167208 0.32166218 0.25816529 0.38099704 0.37198828 0.27567326 0.28179605 0.30034064 0.35318739 0.29816008 0.25944230

I and II II and III III and IV IV and V

6.5. Dynamic analysis results According to the criteria mentioned in the above section, the values of stresses in the dynamic analysis were evaluated in the kiln shell and are shown in Figs. 23 and 24. 6.6. Fatigue test In order to carry out the fatigue analysis, the ASME VIII rule section 5-110 [3] was processed. The conditions and procedures for the analysis are based on the comparison between peak stress values and fatigue alternative stress.

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

39

Fig. 23. Kiln shell for dynamic analysis.

Fig. 24. Re-injection holes and tyres of the kiln shell.

Such a rule furnishes graphs for di9erent alloys and temperature ranges that relate to the admissible amplitude of alternative stress to the number of cycles, for the calculation. This stress amplitude is calculated in the elastic zone, but it does not represent a real stress when the elastic zone is surpassed. The stress curves are obtained from uniaxial stress cycles, where the prescribed stresses have been multiplied by the elastic modulus, in order to compare the stress intensity and the admissible stress amplitude.

40

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

Table 6 Main stresses in the kiln shell (MPa) S1 Position Position Position Position Position Position Position

1 2 3 4 5 6 7

S2

S3

S1max .

S1min .

S2max .

S2min .

S3max .

S3min .

70.9 71.1 71.1 71.1 71.1 71.1 71.1

− − − − − − −

23.8 23.7 22 22 21.9 23.3 23.8

−30 − 30.4 − 30.4 − 30.3 − 30.4 − 30.4 − 30.3

0.196 0.196 0.195 0.196 0.196 0.195 0.196

−89 − 89.4 − 89.3 − 89.3 − 89.4 − 89.3 − 89.3

0.609 0.609 0.609 0.608 0.609 0.609 0.608

The procedure followed to calculate the alternative stress amplitude is as follows: Firstly, the maximum and minimum main stresses are determined in the distinct considered positions. It is assumed that the main directions (S1 ; S2 and S3 ) did not vary during one entire cycle. For the kiln body, these main stresses taking into account the load due to proper weights, the operating temperature and the operating loads can be seen in Table 6, for the di9erent considered positions. We have calculated the di9erent stresses in the distinct positions, at an absolute value. These di9erences will be identi!ed as Sij, where Sij = Si − Sj. The greatest variation range above all the main stresses, corresponding to the maximum of the foregoing Sij (at absolute value) was also calculated, which it is denoted as Srij, obtained as Srij = 160:5 MPa: It requires to be veri!ed that Srij ¡ 3Sm, Sm being the stress limit obtained previously, by applying the Section 4-130 of the same rule. It is observed that 160:5 MPa ¡ 3 (131:6 MPa). The value of alternative stress amplitude SALT , as the average value of Srij is as follows: SALT = 80:25 MPa: With the value of the obtained stress amplitude (SALT ), multiplied by the material elastic yield, it is possible to enter into the axis of ordinates of the diagram in Fig. 25, attaining 2 186 618 cycles. The kiln rotation velocity is 1.5 cycles per minute and it is assumed for 320 days per year in operation. With these data, the number of cycles of the kiln per year is: 1:5×60×24×320=691 200 cycles=year. Thus, the fatigue life can be estimated as 2 186 568=691 200 = 3 years: This result can be considered acceptable taking into account the factor design carried out in the calculation of the alternative stress amplitude (SALT ). This majoration takes place in the calculation of the di9erences between the main stresses Sij = Si − Sj, due to the maximum and minimum values of the main stresses that are not applied to the same point during one cycle. These are the maxima and minima throughout the entire kiln, obtaining Sij and SALT greater than the real ones. This simpli!cation is a consequence of security. Besides, the kiln has to carry out annual stoppings of inspection and repairings.

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

41

Fig. 25. Design fatigue curves for carbon low alloy [3].

7. Conclusions and recommendations In all cases, the stresses are smaller than the allowable ones according to the ASME rules (3Sm = 394:8 MPa). Likewise, it is observed that the inertial e9ects derived from the impact are almost negligible, since this entails comparing the high total mass of the kiln to the tiny mass of the clinker brick. After the analysis of the representative model of the rotary kiln pre-design, with the modi!cations, it can be concluded that the thicknesses of the kiln body chosen as a !rst choice are, in general, rights. However, in the initial section of the kiln, between the outlet and support IV, the shell thickness must be reduced below 24 mm. However, according to the rule employed [1], the stresses would be within the prescribed limits, while ovalization in the central part of Sections IV and V is higher than the stress of refractory integrity. The deviation, even so, is not excessive: with a limit value of 0.42, an ovalization of 0.434 is obtained. This fact inclines us to suggest the increase in the thickness of the kiln body from 24 to 26 mm. Finally, the check corresponding to the mentioned modi!cation also includes the recommendation to increase the thickness (from 30 to 40 mm) of the kiln body in the !rst 12 m of Sections II and III, from support II. A new approach for the control of size and morphology of the cement rotary kiln geometry using !nite element analysis was proposed and the e9ects of this study were con!rmed by the measurements and the observations of the kiln. The distributions of stress and radial displacements (ovalization) were also studied. The bene!ts of these calculations can be achieved without

42

J.J. del Coz D&/az et al. / Finite Elements in Analysis and Design 39 (2002) 17 – 42

signi!cantly compromising the simplicity and reliability of a conventional measurement system. The model developed here can be used as one part of a more extensive one that may include other phenomena to forecast the actual geometry of the kiln. Acknowledgements The authors express deep gratitude to Construction Department and Department of Mathematics at Oviedo University for useful assistance. Helpful comments and discussion are gratefully acknowledged. The student’s collaboration including Mr. Jos'e Mart'(nez-Chaveli Amandi for his thesis work to the study of the cement oven that is presented here, with the No. 1001040, as well as the Project of Investigation No. CN-99-229-B1 at Oviedo University are also appreciated. References [1] Asme Boiler and Pressure Vessel Code VIII, Division 2—Alternative Rules, The American Society of Mechanical Engineers, 1995. [2] Asme Boiler and Pressure Vessel Code II—Material Properties, The American Society of Mechanical Engineers, 1995. [3] Asme Boiler and Pressure Vessel Code VIII, Division 2—Alternative Rules, Appendix 5, ”Design based on fatigue analysis”, 1995. [4] AD-Merkbl7atter, Technical Rules for Pressure Vessels, Carls Heymanns, Verlag KG, 1997. [5] Frederic Olsen, The Kiln Book: Materials, Speci!cations and Construction, Chilton Book Company, 1997. [6] J.C. Simo, T.A. Laursen, An augmented Lagrangian treatment of contact problems including friction, Comput. Struct. 42 (1992) 97–116. [7] E. Rabinowicz, Friction and Wear of Materials, Wiley, New York, 1965. [8] J.T. Oden, J.A.C. Martins, Models and computational methods for dynamic friction phenomena, Comput. Methods Appl. Mech. Eng. 52 (1985) 527–634. [9] W. Ames, Numerical Methods for Partial Di9erential Equations, Academic Press Inc., San Diego, 1992. [10] P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. [11] R.L. Burden, J.D. Faires, Numerical Analysis, Brooks Cole Publishing, San Francisco, 1998. [12] Ansys Help and Documentation., SAS IP, Inc., 1992–2000. Agreement Number #104834. [13] K. Bathe, Finite Element Procedures, Prentice-Hall, Englewood Cli9s, NJ, 1996. [14] S.S. Rao, The Finite Element Method in Engineering, Pergamon Press Inc., Maxwell House, New York, 1982. [15] S. Moaveny, Finite Element Analysis: Theory and Application with Ansys, Prentice-Hall, Englewoods Cli9s, NJ, 1999. [16] A. Quarteroni, A. Valli, Numerical Approximation of Partial Di9erential Equations, Springer, Berlin, 1997. [17] P.A. Raviart, J.M. Thomas, Introduction a l’Analyse Num'erique des Equations aux D'eriv'ees Partielles, Masson, Paris, 1983. [18] E.P. Popov, T.A. Balan, Engineering Mechanics of Solids, Prentice-Hall Inc., Englewood Cli9s, NJ, 1999. [19] R.C. Hibbeler, Mechanics of Materials, Prentice-Hall Inc., A Simon & Schuster Company, Engelwood Cli9s, NJ, 1997. [20] T.R. Chandrupatla, A.D. Belegundu, Introduction to Finite Elements in Engineering, Prentice-Hall Inc., Upper Saddle River, NJ, 1999. [21] O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method: Solid and Fluid Mechanics and Non-linearity, Vol. 2, McGraw-Hill Book Company, UK, 1991. [22] W.C. Young, ROARK’S Formulas for Stress & Strain, McGraw-Hill Book Co., New York, 1989.