Fully automatic modelling of cohesive discrete crack
propagation in concrete beams using local
arc-length methods
Zhenjun Yang
a,*,Jianfei Chen b a
School of Mechanical and Manufacturing Engineering,Queen’s University Belfast,Ashby Building,Strainmillis Road,Belfast BT95AH,UK b Institute for Infrastructure and Environment,School of Engineering and Electronics,Edinburgh University,
The King’s Buildings,Edinburgh EH93JN,UK
Received 23May 2003;received in revised form 11August 2003
Abstract
A ?nite element model for fully automatic simulation of multi-crack propagation in concrete beams is presented.Nonlinear interface elements are used to model discrete cracks with concrete tensile behaviour represented by the cohesive crack model.An energy-based crack propagation criterion is used in combination with a simple remeshing procedure to accommodate crack propagation.Various local arc-length methods are employed to solve the material-nonlinear system equations characterised by strong snap-back.Three concrete beams,including a single-notched three-point bending beam (mode-I fracture),a single-notched four-point shear beam (mixed-mode fracture)and a double-notched four-point shear beam (mixed-mode fracture),are https://www.doczj.com/doc/1417074340.html,parisons of the numerical results with experimental data show that this model is capable of fully automatically modelling concrete tensile fracture process with accurate pre/post-peak load–displacement responses and crack trajectories.Its mesh-objective nature,together with the high e?ciency of the energy crack propagation criterion,makes using coarse meshes to obtain reasonably accurate simulations possible.The local arc-length numerical algorithms are found to be capable of tracking complex equili-brium paths including strong snap-back with high robustness,generality and e?ciency.
ó2003Elsevier Ltd.All rights reserved.
Keywords:Finite element analysis;Discrete crack model;Arc-length method;Mixed-mode crack propagation;Concrete beams
1.Introduction
Developing ?nite element models (FEM)to simulate tensile fracture behaviour of concrete beams has been extensively carried out in the last two decades.Two types of crack models,i.e.,the smeared crack model and discrete crack model,are most frequently used to represent cracking.The smeared crack model *Corresponding author.Tel.:+44-28-90335523;fax:+44-28-90661729.
E-mail address:z.yang@https://www.doczj.com/doc/1417074340.html, (Z.Yang).
0020-7683/$-see front matter ó2003Elsevier Ltd.All rights reserved.
doi:10.1016/j.ijsolstr.2003.09.033
International Journal of Solids and Structures 41(2004)
801–826
https://www.doczj.com/doc/1417074340.html,/locate/ijsolstr
802Z.Yang,J.Chen/International Journal of Solids and Structures41(2004)801–826
assumes that an in?nite number of parallel cracks of in?nitely small opening are distributed over the?nite element based on a?xed?nite element mesh.The crack propagation is simulated by reducing the material sti?ness and strength.The constitutive laws are de?ned by nonlinear stress–strain relations with strain softening.The discrete crack model is based on displacement discontinuity,which is usually represented by nonlinear interface elements.The constitutive behaviour of such elements is represented by softening traction-crack relative displacement relations,as assumed by the cohesive crack model(CCM),or?ctitious crack model termed by Hillerborg et al.(1976).The smeared crack model has been much more popular than the discrete crack model because of its computational convenience(e.g.,De Borst,1986,1987;Rots and De Borst,1987;Bazant and Lin,1988;Rots,1988,1991;Yamaguchi and Chen,1990;Malvar,1993; Bolander and Hikosaka,1992;Duan,1994;Foster et al.,1996;Abdollahi,1996a,b;Ali,1996;May and Duan,1997;Ozbolt and Reinhardt,2002).The latter has been less investigated(e.g.,Ingra?ea and Gerstle, 1984;Carpinteri,1989;Bocca et al.,1990,1991;Rots,1991;Gerstle and Xie,1992;Xie,1995;Xie and Gerstle,1995;Cendon et al.,2000;Galvez et al.,2002;Yang and Proverbs,2004),mainly because of various numerical complexities compounded by the constant change of?nite element meshes caused by node separation to accommodate crack propagation.Besides a proper constitutive model for concrete tensile softening behaviour,a successful FEM based on discrete crack model must have additional four key features:a proper crack propagation criterion,an e?cient remeshing procedure,an accurate mesh-mapping technique to transfer structural responses of an old FE mesh to a new one,and a robust and e?cient numerical solution technique to solve nonlinear equation systems characterised with snap-through or snap-back.It is worth noting that besides the traditional smeared crack models and discrete crack models, another attractive type of models recently developed based on embedded displacement discontinuity(Moes et al.,1999;Wells and Sluys,2000;Alfaiate et al.,2002;Moes and Belytschko,2002),do not need reme-shing.
A proper crack propagation criterion is needed to determine when and in which direction a crack will propagate.The crack is usually assumed to propagate at the direction of the maximum principal stress of the crack-tip node,which is a basic assumption of the original CCM.This direction criterion has been most used.The CCM also assumes that the crack propagates when the maximum principal stress of the crack-tip node reaches concrete tensile strength.This stress-based assumption has been used by most existing studies (e.g.,Carpinteri,1989;Bocca et al.,1990,1991).Cendon and his co-workers used a maximum tangential stress criterion(Cendon et al.,2000;Galvez et al.,2002).However,nodal stresses are either interpolated from those of integration points in isoparametric?nite elements,or are constants when constant strain elements are used.In both cases,very?ne crack-tip meshes are necessary to predict accurate stresses.In order to reduce the required mesh density near the crack tip so as to simplify the remeshing procedure,Xie (1995)developed an energy-based cohesive crack propagation criterion.Because of the fast convergence rate of energy entities in FE analysis,crack propagation can be modelled more accurately even using coarse meshes(Xie,1995;Xie and Gerstle,1995).
An e?cient remeshing procedure is paramount in discrete crack modelling to accommodate crack propagation.The procedures currently available can generally be classi?ed into two categories.One may be termed‘‘remove-rebuild’’algorithm.In this algorithm,a new crack-tip node is determined by extending a speci?ed crack growth increment in the calculated propagation direction.The original mesh within a certain range around the new crack-tip node is then completely removed.A complex procedure is followed to form the new crack and regenerate the mesh within this range where a regular rosette is added.This regenerating procedure may be too complicated to be applied to composite structures such as reinforced concrete beams with dissimilar material interfaces.Representatives of such algorithm are the ones developed by Wawrzynek and Ingra?ea(1989)and Bocca et al.(1990,1991).The other type of algorithms may be termed ‘‘insert-separate’’algorithms such as one developed by Xie in his program AUTOFRAP(Xie,1995;Xie and Gerstle,1995).In this procedure,a new edge from the old crack-tip node is?rst inserted into the local mesh in the propagation direction.The intersection point of this edge with the original mesh is the new
Z.Yang,J.Chen/International Journal of Solids and Structures41(2004)801–826803 crack-tip node.The new crack is then formed by separating those nodes along the line through the new and old crack-tip nodes.A rosette can be?nally added to re?ne the tip-node mesh.Because this procedure neither completely removes nor rebuilds the new crack-tip mesh as the‘‘remove-rebuild’’procedure does, fewer elements are a?ected and the procedure is much simpler.After remeshing,the structural state vari-ables from the old mesh need to be transferred/mapped as accurately as possible to the new mesh as their initial values to be used in next loading step so as to ensure numerical convergence.The most widely used mapping methods are inverse isoparametric mapping(e.g.,James,1998)and direct interpolation(e.g., Harbaken and Cescotto,1990).
A variety of numerical procedures have been used to solve nonlinear equation systems associated with material softening,such as Newton iteration and its extensions(e.g.,Abdollahi,1996a,b),dynamic re-laxation(Xie,1995;Xie and Gerstle,1995),and various arc-length controlled procedures(e.g.,De Borst, 1986;Cris?eld,1986;Rots and De Borst,1987;Cris?eld and Wills,1988;Rots,1991;May and Duan,1997; Hellweg and Cris?eld,1998;Alfano and Cris?eld,2001;Cris?eld et al.,1997).These solutions,however, have not necessarily led to ideal predictions.Various problems have been reported when the post-peak part of the load–displacement relation is desired,especially when sharp snap-back phenomenon happens in mixed-mode fracture modelling.The Newton iteration methods with load control fail to converge once the limiting point is reached and the post-peak responses cannot be predicted.Displacement controlled Newton methods can tackle structural problems exhibiting snap-through but fail to model snap-back behaviour. The dynamic relaxation method used in a few analyses(Xie,1995;Xie and Gerstle,1995)has been criticized for its slow convergence rate and numerical instability due to uncertainties in selecting various pseudo-parameters(e.g.,Underwood,1983).The arc-length method,initially proposed by Riks(1979)and sub-sequently adapted by Cris?eld(1981)and others,succeeded for the?rst time in tracing the limiting point and post-peak responses by constraining the iterative path along a normal plane or a cylindrical/sphere controlled by a prescribed arc-length.This method has been widely used.However,it has been often re-ported that these traditional normal-plane and cylindrical/spherical arc-length methods may still fail to converge at or near the limiting points when they are applied to problems involving softening materials (Cris?eld,1986;De Borst,1986,1987;Rots and De Borst,1987;Cris?eld and Wills,1988;Duan,1994; Cris?eld et al.,1997;May and Duan,1997;Hellweg and Cris?eld,1998;Alfano and Cris?eld,2001).Even the combination of line searches and acceleration techniques(e.g.,quasi-Newton)with arc-length method
804Z.Yang,J.Chen/International Journal of Solids and Structures41(2004)801–826
only achieved limited improvements(May and Duan,1997).De Borst(1987)and Rots and De Borst(1989) pointed out that this inability should be attributed to the global constrain equations including all the de-grees of freedom,which was contradictory to the fact that the failure zone or fracture process zone in concrete beams is highly localised.They thus used only the crack sliding displacement(CSD)and the crack opening displacement(COD)in the constraint equations,respectively.Duan(1994)further devised a new local arc-length procedure to tackle this problem.By automatically distinguishing the strain-localized zones,the selection of relative displacements becomes problem-independent.They reported close agree-ments with the experimental data based on the local constraint methods using the smeared crack model.
However,very few studies using arc-length methods in the context of discrete crack modelling have been reported.In addition,almost all such studies used pre-de?ned interface elements.For example,Rots(1991)
Z.Yang,J.Chen/International Journal of Solids and Structures41(2004)801–826805 used pre-de?ned interface elements with the COD controlled arc-length method.Alfaiate et al.(1997) developed a‘‘non-prescribed’’crack propagation model that limited the cracks along the edges of the?nite elements without changing the original FE meshes.This model thus approximates a smooth crack tra-jectory with a zigzagged one.Recent studies reported by Cendon and his co-workers(Cendon et al.,2000; Galvez et al.,2002)used a two-stage approach:predicting crack paths using linear elastic fracture me-
806Z.Yang,J.Chen/International Journal of Solids and Structures41(2004)801–826
chanics(LEFM)and incorporating CCM into the crack paths by nonlinear springs.The conclusions drawn from a recent comparative study carried out by the authors(Yang and Proverbs,2004)was also based on pre-de?ned crack paths although some initial automatic modelling of crack propagation was carried out on a single-edge notched shear beam.More investigation of the application of arc-length methods to fully automatic discrete crack modelling of fracture process in concrete structures is still desired.
This paper presents a fully automatic discrete crack propagation model for fracture analysis of concrete structures.It uses the remeshing procedure and the energy-based crack propagation criterion proposed by Xie(1995)and Xie and Gerstle(1995).An in-house program,incorporating a modi?ed version of Xie?s AUTOFRAP and implementing various numerical techniques,was developed and used in this study.The following?rst describes the key aspects of the model.Four concrete beams,including a single-edge notched three-point bending beam(mode-I fracture),a single-edge notched four-point shear beam(mixed-mode fracture)and a double-edge notched four-point shear beam(mixed-mode fracture),are then modelled.
Table1
Parameters of bilinear COD-traction curves of three example beams
Beam G f(N/m)r0(MPa)w0(mm)r1(MPa)w1(mm)w c(mm)k0(MPa) SENB137.0 3.330.00001 1.110.03290.14833,000 SENS150.0 4.00.00001 1.330.030.13540,000 DENS100.0 2.00.000010.670.040.1820,000
Various local arc-length strategies are examined and their computational e?ciency and e?ectiveness are discussed as well as the robustness and mesh objectivity of the model.
2.Discrete crack ?nite element model
A thorough description of this model and its computer implementation (Yang,2002)are beyond the scope of this paper.Fig.1illustrates its key steps.The critical physical and numerical aspects of the model are brie?y presented as
follows.
Fig.9.Initial ?nite element meshes for SENB beam:(a)L max >25mm,(b)L max ?25mm and (c)L max ?10
mm.
Fig.10.Initial ?nite element meshes for SENS beam:(a)L max >20mm and (b)L max ?20mm.
Z.Yang,J.Chen /International Journal of Solids and Structures 41(2004)801–826807
Fig.11.Initial?nite element meshes for DENS beam:(a)L max>22mm and(b)L max?22
mm.
Fig.12.Cracking process of the SENB beam using L max?25mm(a)F?0:6KN,(b)F?0:8KN(peak load),(c)F?0:464KN and (d)F?0:30KN(on collapse):390nodes and9interface elements.
808Z.Yang,J.Chen/International Journal of Solids and Structures41(2004)801–826
2.1.Cohesive crack model and unloading paths
CCM can accurately model the energy dissipation process in quasi-brittle materials such as concrete.It assumes that a?ctitious crack or a fracture process zone(FPZ)exists ahead of a real crack tip.The FPZ has the capability of transferring stresses through mechanisms such as aggregate interlock and material bonding until the COD reaches a critical value.The CCM has become the basis of nonlinear discrete crack modelling and has been incorporated into some?nite element codes in the form of two-dimensional four-node,six-node and three-dimensional eight-node interface elements to model mode-I and mixed-mode crack propagation(e.g.,Ingra?ea and Gerstle,1984;Gerstle and Xie,1992;Xie,1995;Xie and Gerstle, 1995).The four-node interface elements developed by Gerstle and Xie(1992)are used to represent the cohesive cracks in this study.Fig.2schematically shows the FPZ in concrete structures and two interface elements used to model the FPZ.
The Petersson?s bi-linear curve(Petersson,1981)is used here to model the softening behaviour of the cohesive interface elements.Fig.3shows the bi-linear COD-traction curve with unloading path indicated. The initial sti?ness should be high enough to represent the uncracked material prior to the concrete tensile strength as long as numerical ill-conditioning does not occur.Most existing research used an irreversible unloading path or an elastic damage model(Path1in Fig.3).It assumes that after reaching a value w?,for decreasing value of w an elastic unloading occurs with a reduced sti?ness which represents the secant from the current point to the origin(A?C)(Rots and De Borst,1987;Rots,1988;Rots,1991;Ali,1997; Alfaiate et al.,1997;Alfano and Cris?eld,2001).Hellweg and Cris?eld(1998)distinguished another un-loading mechanism,i.e.,reversible unloading,which assumes a completely reversible COD-traction con-stitutive law(Path2in Fig.3)(A?B?C).Physically,the irreversible unloading represents cracking more realistically than the reversible unloading because when a crack is closing,it cannot transfer higher stresses
because the stress-transferring mechanisms such as aggregate interlock and material bonding have
been
Fig.13.Deformed con?gurations of the SENB beam on collapse.(a)L max>25mm(F?0:53KN,242nodes and5interface elements) and(b)L max?10mm(F?0:167KN,513nodes and16interface elements).
Z.Yang,J.Chen/International Journal of Solids and Structures41(2004)801–826809
Fig.14.Cracking process of the SENS beam using L max ?20mm.(a)F ?140KN (peak load),(b)F ?120KN,(c)F ?60KN and (d)F ?20KN (on collapse):519nodes and 25interface elements.
810Z.Yang,J.Chen /International Journal of Solids and Structures 41(2004)801–826
damaged.However,the authors?previous study(Yang and Proverbs,2004)showed that the unloading paths played an important role in numerical strategies in modelling a mixed-mode concrete beam.In view of this both unloading paths will be investigated in this research.
2.2.Energy-based crack propagation criterion
Based on the principle of energy conservation,Xie(1995)derived the following energy-based cohesive crack propagation criterion
Gàu T o f
o A
?0e1T
where u is the displacement vector,f is the cohesive forces and A is the crack surface area.G is the total strain energy release rate(SERR)calculated by
G?à1
2
u T
o K
o A
utu T
o P
o A
e2T
where K is the total sti?ness matrix of the elastic bulk and P the total equivalent nodal force due to external tractions and body forces.In planar mixed-mode fracture problems,the displacement?eld and SERR can be decomposed to Mode-I and Mode-II components as
u?u Itu IIe3TG?G ItG IIe4TFig.4presents a simple method for conducting a virtual crack extension(VCE)as proposed by Xie (1995)to compute SERR,in which only the crack-tip elements contribute to the energy release rates.By using a?nite di?erence approximation from Eq.(2),the Mode-I and Mode-II SERRs in Eq.(4)may be expressed as
G I?à
1
2D A
X N ce
i?1
u e T
I i
D K e
i
u e
I i
t
1
D A
X N cef
j?1
u e T
I j
D P e
j
e5aT
G II?à
1
2D A
X N ce
i?1
u e T
II i
D K e
i
u e
II i
t
1
D A
X N cef
j?1
u e T
II j
D P e
j
e5b
T
Fig.15.Deformed con?gurations of the SENS beam using L max>20mm on collapse:F?23KN,283nodes and11interface ele-ments.
Z.Yang,J.Chen/International Journal of Solids and Structures41(2004)801–826811
in which N ce and N cef are the total number of elements and the number of elements with applied force
around the crack tip respectively;u e I i and u e II i are the Mode-I and Mode-II displacement vectors of the i
th
Fig.17.Deformed con?guration of the DENS beam using L max >22mm:F ?20KN,241nodes,14interface
elements.Fig.16.Cracking process of the DENS beam using L max ?22mm (a)F ?42KN (peak load),(b)F ?36KN,(c)F ?27KN,(d)F ?23KN:388nodes and 24interface elements.
812Z.Yang,J.Chen /International Journal of Solids and Structures 41(2004)801–826
crack-tip element respectively;D K e
i is the change of i th crack-tip element sti?ness matrix due to VCE;D p e
j
is
the change of the nodal force vector of the j th crack-tip element due to VCE;and D A is the increase of crack surface area after a VCE D a and D A?t D a for a2D structure with a thickness t.
Interested readers are referred to Yang et al.(2001)for detailed discussion of calculating SERR.The second term of Eq.(1)can be explicitly derived using the four-node interface elements(Xie,1995).The crack is assumed to propagate in the direction of the maximum principal stress of the crack-tip node. 2.3.Remeshing procedure
When a crack is judged to propagate,a remeshing procedure is carried out to accommodate its propa-gation.The basic steps of Xie?s remeshing procedure(Xie,1995)are outlined as follows.
Z.Yang,J.Chen/International Journal of Solids and Structures41(2004)801–826813
?delete the existing rosette around the old crack-tip node;
?locate the next tip according to calculated crack propagation direction.Two cases are identi?able(Fig.
5):
Case1:the next crack tip is an existing node connected to the old crack tip;
Case2:the next crack tip is on the edge of a crack-tip element;
?for Case1,the edge connecting the new crack-tip node and the old one is split up.For Case2,the node closest to the new crack-tip position is dragged to the new crack-tip place and is treated as the new crack-tip node.In this way Case2becomes Case1(Fig.5);
?re?ne the new crack-tip mesh according to a speci?ed maximum crack propagation length;?triangularize all elements around the new crack tip;and
?add a rosette around new crack tip.
For each crack during this procedure,the old three-node crack-tip interface element is altered to a four-node interface element.One three-node tip interface element and one four-node one are created.
2.4.Mesh mapping
The model adopts a direct mapping method proposed by Harbaken and Cescotto(1990).It evaluates the nodal values in the new mesh by directly interpolating those from the old mesh.The following equation is used to map a variable Z,which can be stress,displacement and other state variables at point j
Z j?
P N
k?1
Z k
R2
kj
tCZ p
R2
pj
P N
k?1
1
R2
kj
tC
R2
pj
e6T
where N is the number of points for interpolation in the old mesh,Z k is the value of Z at the point k,Z p is the value of Z at the nearest point p to point j,and R kj is the distance between points k and j.The technique requires the user to specify N points for interpolation,the maximum distance R max,the minimum distance R min and the coe?cient C.Those points outside the radius R max are not considered.If there is a point k very Table2
Total number of increments and total iterations for SENB beam
Algorithm N d?20N d?30
Total number of increments Total number of
iterations
Total number of
increments
Total number of
iterations
SEC-REV-V137******** SEC-REV-V23366822664 SEC-REV-V348117225991
SEC-IRE-V137******** SEC-IRE-V23468122666 SEC-IRE-V348117225991
TAN-REV-V11579415597 TAN-REV-V21744515610 TAN-REV-V316751101200 TAN-IRE-V11579513592(failed) TAN-IRE-V21942115618 TAN-IRE-V3147468580(failed) 814Z.Yang,J.Chen/International Journal of Solids and Structures41(2004)801–826
Z.Yang,J.Chen/International Journal of Solids and Structures41(2004)801–826815 close to j so that their distance is smaller than R min,Z k is assigned to the value of Z j.The main advantages of this method are the simplicity and?exibility in choosing C,R max and R min.Their optimum values to achieve best mapping results are mesh and problem dependent.This study uses a set of empirical values as follows: C?0:8,R min?0:1L e and R max?3L e where L e is the length of the longest edge of the element in the old mesh in which the mapped point is located.
2.5.Local arc-length method
The comparative study carried out by the authors(Yang and Proverbs,2004)has shown that the local arc-length algorithms are much more superior than the global ones in terms of numerical robustness and e?ciency.The term‘‘global’’used herein means that the arc-length constraint equations include all the degrees of freedom whereas only selected degrees of freedom of dominant nodes are included in a‘‘local’’
arc-length method.The Duan?s local updated normal plane constraint equation(Duan,1994;May and Duan,1997)is used in this study.The local arc-length formulations in one loading increment can be written as
X
e
reD u1TTáreD u kT?l2;ek?2;3;4;...Te7aT
d k1?
l
???????????????????????????????????????
P
e
red u TTáred uT
pe7bT
d k k?d k1àP
e
red u TTáereD u kà1Ttred u?TT
P
e
red u TTáred uT
;ek?2;3;4;...Te7cT
816Z.Yang,J.Chen/International Journal of Solids and Structures41(2004)801–826
Z.Yang,J.Chen/International Journal of Solids and Structures41(2004)801–826817 where l is the speci?ed arc-length,u is the displacement vector and k is the loading factor.The symbols D and d represent incremental and iterative change respectively.k is the iterative number.d u and d u?are iterative displacement vectors(Cris?eld,1997).Eq.(7a)de?nes the constraint equations;Eq.(7b)deter-mines the loading factor at the beginning of a loading increment d k1;and the iterative loading factors are calculated by Eq.(7c).
The summation in Eq.(7)is calculated in an element-by-element way.Only the elements contributing to structural nonlinearity are included in the constraints.In the smeared crack models,they are?nite elements in the damage and failure zones.In CCM based discrete crack models,they are nonlinear interface ele-ments.The symbol r denotes the relative displacement vector(RDV)of dominant elements, reaT?a1àa n a2àa1a3àa2áááa nàa nà1
? Te8Twhere vector a is any displacement vector in Eq.(7).
For discrete crack modelling in which the nonlinear interface elements are the dominant elements,an-other formulation of RDV may include only two CODs and two CSDs of the two pairs of nodes of all four-node interface elements(Fig.2),i.e.,
reaT?a2àa8a4àa6a1àa7a3àa5
? Te9TSimpler forms may include only COD or CSD at the crack mouth such as
reaT??a2àa8 Te10aTreaT??a1àa7 Te10bTThis set of formulations(Eqs.(7–10))have three advantages(Duan,1994;May and Duan,1997):(i)Eq. (7a)limits the iteration trajectory on a spherical surface,which always has an intersection with the equi-librium path;(ii)it does not need to choose a proper root as spherical/cylindrical constraints do since there is only one root of loading factor;and(iii)the sign of the loading factor will be changed automatically if necessary within the iterations if a total secant sti?ness is used;(iv)this local algorithm using RDV guarantees a rapid and stable convergence because it is able to catch the structural nonlinearity and remove the adverse e?ects of the rigid body movement on the accurate representation of nonlinearity.These ad-
vantages have also been demonstrated in(Yang,2002;Yang and Proverbs,2004).
The authors ?study has also shown (Yang and Proverbs,2004)that this constraint method does not inherently defy using the tangential sti?ness.When the tangential sti?ness is used,Eq.(7b)should be modi?ed as follows
d k 1?sign eK 1t Tl ???????????????????????????????????????P
e red u T Táred u Tp e11T
where j K 1t j is the determinant of the tangential sti?ness matrix K 1t calculated at the ?rst iteration of a loading increment.
At the beginning of each loading step,the arc-length l (Eq.(7))must be determined to ensure the e?ciency of the algorithms.Bellini and Chulya (1987)found that the de?nition of l had a direct e?ect on the performance of cylindrical/spherical arc-length algorithms applied to geometrically nonlinear problems.The arc-length of the i th loading increment l i is often predicted by (Cris?eld,1997)
818Z.Yang,J.Chen /International Journal of Solids and Structures 41(2004)801–826
l i?
N d
N ià1
m
l ià1;i?2;3;4; (12)
where N ià1and l ià1are the iteration number and arc-length used by the(ià1)th loading step respectively. N d is a desired optimum iteration number which is problem-dependent.The coe?cient m ranges from0.25 to0.5(Bellini and Chulya,1987).Eq.(12)tends to shorten l to keep the iteration number down when it exceeds N d.
The arc-length in the?rst loading increment l1can be determined from Eq.(7b)by specifying an initial loading factor based on a proper reference loading condition,e.g.,d k1?0:1.Special considerations are needed for the second loading increment when Eq.(12)is used in some cases.For example,in the three numerical example beams modelled in this study(ref.Sections3and4),there are no initial cracks and thus no interface elements in the?rst loading increment.Interface elements are added in the second increment. This means all the nodal displacements are used in Eq.(7b)(i.e.,global arc-length method),which results in a relatively large l1.If a comparable l2calculated from Eq.(12)is used in Eq.(7b),d k1for the second
Z.Yang,J.Chen/International Journal of Solids and Structures41(2004)801–826819
loading increment will be very large because only RDVs of the added interface elements are used in Eq.(7b).Too many iterations or even divergence may be caused by the large d k 1.In order to avoid this,Eq.(12)is modi?ed as d k 1i ?k ini i ?1;...;j l i ?N d N i à1
m l i à1i ?j t1;...(e13Twhere j is the loading increment in which the interface elements are ?rst added and k ini is an initial loading factor for the ?rst j increments.The following default values are used:N d ?20,m ?0:5and k ini ?0:1.
2.6.Iterative numerical algorithms and convergence criterion
The modi?ed Newton–Raphson iterative procedure is used for all the analyses,i.e.,the global sti?ness matrix is formed at the ?rst iteration of every loading increment and remains unchanged during iterations afterwards.
820Z.Yang,J.Chen /International Journal of Solids and Structures 41(2004)801–826
centrifugemodelling离心模拟centrifuge离心机centripetalacceleration向心加速度centripetalforce向心力centripetal向心的centrode瞬心轨迹centroidaxis重心轴线centroidofarea面心centroid质心centroidalprincipalaxesofinertia重心诌性轴centrosymmetric中心对称的ceramicbearing陶瓷轴承ceramicbond陶瓷结合剂ceramiccoating陶瓷涂层ceramicengine陶瓷发动机ceramicfilter陶瓷过滤器ceramicindustry陶瓷工业ceramici ulater陶瓷绝缘子ceramictip陶瓷刀片ceramictool陶瓷车刀ceramic 陶瓷的ceramics陶瓷cermettool金属陶瓷刀具cermet金属陶瓷cesium铯cetanenumber十六烷值CF 吸顶型风机CeilingMountedTypeFancfrp碳纤维增强塑料cg ystemcgs单位制cgsunit厘米克秒单位chai eltconveyor链带输送机chai elt链带chai lock链动滑轮chai rake链闸chai ridge链桥nondime ional无量纲的nondirective非定向的nondi ersivewave非弥散波nonelasticbuckling非弹性屈曲nonelasticscattering非弹性散射nonelastic非弹性的nonequilibriumplasma非平衡等离子体nonequilibriumproce非平衡过程nonequilibriumstate非平衡态nonequilibriumstate非平衡状态nonequilibriumsurfacete ion非平衡表面张力nonequilibriumthermodynamics非平衡态热力学nonequilibrium非平衡nonevanescentwave无阻尼波nonferrousalloy非铁合金nonferrousmetal有色金属nonferrousmetallurgy非铁金属冶炼术nonflatne不平面度nonfreepoint非自由质点nongeostrophicflow非地转怜nonholonomicco traint非完整约束nonholonomicsystem非完整系统nonholonomicvelocitycoordinate非完整速度坐标nonhomogeneou oundary非齐次边界nonidealflow非理想怜noninertia无惯性noninertialsystemofcoordinates非惯性坐标系noninertialsystem非惯性系nonisentropicflow非等熵怜nonisotropicmaterial非蛤同性材料nonisotropy非蛤同性nonius游标nonlinearaerodynamics非线性空气动力学nonlineardistortion非线性失真nonlinearelectrodynamics非线性电动力学collarbearing环状止推轴承collarheadscrew带缘螺钉collarjournal有环轴颈collarnut凸缘螺collarpin凸缘销collarthrustbearing环状止推轴承collarvortex涡环collar凸边collateralmotion次级运动collectivemodeofmotion集体运动模式collectivemotion集体运动collectorefficiency集热僻率collectorring滑环collector集电器colletchuck弹簧夹头collier运煤船collimation视准collimation准直collimator视准仪Collimator准直仪collisionchain碰撞链collisioncro ection碰撞截面collisiondiameter 碰撞直径collisiondiffusion碰撞扩散collisionexcitation碰撞激发collisionfrequency碰撞频率
全自动面条机改变了面条供不应求的现状今天，小编与大家一起探讨一下中国关于吃的一些发展方面，所谓舌尖上的中国。在悠久的历史先河当中，吃一直是一个人们经常会谈及的话题，在我国每个家庭绝大多数都是一日三餐，而三餐的主食主要是米饭或面食，说到面食，小编首先想到的就是面条啦。 面条在主食行列中一直占据着重要的位置，而且面条具有很多的优势和特点，比如说，面条有汤有面，含有丰富的碳水化合物，具有暖胃、好消化、能提供足够的能量、营养高的作用，所以面条在中国的历史悠久，食用范围广，喜欢面条的人群面广，在现在的21世纪，虽然人们的生活水平提高了，但是面条作为 我国最传统的美食依然受到广大国人的欢迎。正因为如此，面条的需求量一直很大，据数据统计，每年超市或者市场面条的消费水准是最高的，面条的消费量高于其他产品类，由于人们对其主要的需求，也是为了适应机械化的生产活动，全自动面条机应运而生。 接下来，咱们就讲一讲这个帮助面条业跟上时代步伐的大咖——全自动面条机。 全自动面条机是现在新一代面条机的代表，它最重要的特点就是全自动化，自动化程度高于其他种类面条机。有很多用户在购买时都会担心会不会用，会不会操作起来特别繁琐啊这些个问
题，全自动面条机也正是考虑到这个大众问题，所以设计出的成品操作简便，灵活应用，在业内人士都称其为傻瓜式操作，足见其使用起来简单易懂。然鹅，操作简单归简单，主要参数可不能落下，甚至于全自动面条机的主要参数相对于其他面条机来说更加科学规范化。 如果你以为全自动面条机就只有这几个优势那就错了，全自动面条机还有很多优势的，下面由我来一一阐述。 就材质方面，全自动面条机全身采用的是不锈钢材料，使得全自动面条机拥有耐腐蚀耐磨经久耐用的优势，不仅如此，全自动面条机还可以为我们节约成本，提高生产水平，用最小的投资赢得最大的收益。全自动面条机还有一个最大的特点就是可以利用全自动化省去人力操作，多功能一体化具有全自动的特点一次成型,节省劳动力，并且可以大批量的生产面条，在面条最后一 道制作工艺中采取自动挑面技术。 当然了，在使用全自动面条机的时候一定要按照操作规范走，切记安全第一。下面也为大家整理了一些全自动面条机在使用中的安全操作须知： 第一，全自动面条机在开机操作之前一定要先阅读机械说明书，并牢记操作步骤；第二，在开机前仔细检查机械有无异常情况发生，一旦发现有异常情况，一定要禁止使用；第三，一定记得定期给面条机涂抹润滑油，防止机器生锈影响生产；最后，在使用过程中一定要注意安全用电。
果蔬切丁机技术参数 【诸城市德川工贸】不知道大家吃没吃过牛肉炖萝卜丁、猪肉炖土豆丁，热乎乎，香喷喷的菜端到餐桌上，怕是各位都忍不住想多吃几口吧。那么在罐头加工工厂，这种萝卜丁、土豆丁以及各类果蔬切成丁不可能都用人工来切，这也就用到了小编这次要说的果蔬切丁机。那么今天我们一起了解一下关于果蔬切丁机技术参数 #详情查看#【德川工贸：果蔬切丁机】 【诸城市德川工贸：果蔬切丁机特点】 我公司根据市场需要，综合各类技术所研发此类果蔬切丁机，适合各种果蔬切丁需要。本机采用304不锈钢制做，符合食品安全卫生标准，客户可以放心使用。所切蔬菜丁小规格为1.8mm，大规格为
120mm，调整范围广，可满足各类切丁厂家的需要。设备制做外型美观，操作简单，果蔬切出来的丁形状规则，大小均等，是果蔬切丁厂家的不二之选。 【诸城市德川工贸：果蔬切丁机简介】 切丁机结构紧凑，采用优化卫生设计， 机壳，切割刀栅均采用不锈钢材料制 成，切刀采用切削，工作效率高，可 以切制5、8、10、15mm的立方体 或长方体，调整厚度切割旋纽，可对 推杆进行无级调速，以满足不同切割 厚度的要求。采用了预压力设计，保 证在切割过程中切出的物料均匀光 滑并保证切割尺寸正确。本机可适应土豆、萝卜、芋头、苹果以及各种根、茎类蔬菜的切丁，是果蔬加工中的的设备。 切丁机采用复合刀具，一次成形，形状规则，切面光滑，成形率高。本机设计先进，操作方便，耗能低，效率高，采用铝镁合金及不锈钢材料，防腐，美观，符合卫生标准。拨盘带动被切物体高速旋转，利用物体离心力，借助立刀将被切物体切成片状，然后经过圆盘切刀切成条状，并将被切物料送入横切断刀口，由横切断刀切成所需要的立方体或长方体。 【诸城市德川工贸：果蔬切丁机参数】 1.生产能力：在切制15mm立方体时产量为1000kg/h。 2.切菜规格：可切制5、8、10、15mm的立方体或长方体，也可以根据要求定做其他尺寸的刀具。 3.总功率：0.75kw/380v 4.外形尺寸：710*660*1010mm 5.机器重量：100kg
Fifth Generation Communication Automotive Research and innovation Deliverable D3.2 Report on Channel Modelling and Positioning for 5G V2X Version: v1.0 2018-11-30 This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 761510. Any 5GCAR results reflects only the authors’ view and the Commission is thereby not responsible for any use that may be made of the information it contains. http://www.5g-ppp.eu
Deliverable D3.2 Report on Channel Modelling and Positioning for 5G V2X
Abstract 5GCAR has identified the most important use cases for future V2X communications together with their key performance indicators and respective requirements. One outcome of this study is that accurate positioning is important for all these use cases, however with different level of accuracy. In this deliverable we summarize existing solutions for positioning of road users and justify that they are not sufficient to achieve the required performance always and everywhere. Therefore, we propose a set of solutions for different scenarios (urban and highway) and different frequency bands (below and above 6 GHz). Furthermore, we link these new technical concepts with the ongoing standardization of 3GPP New Radio Rel-16. An important prerequisite for this work is the availability of appropriate channel models. For that reason, we place in front a discussion of existing channel models for V2X, including the sidelink between two road users, their gaps, as well as our 5GCAR contributions beyond the state of the art. This is complemented with results from related channel measurement campaigns.
家用面条机的设计与分析 -----机械系统设计课程论文 姓名：肖虎 学号： 2009092553 学院：机电学院 班级： 09机制 3班 指导老师：李盛林 2012年12月20日
目录 一、目的及背景 (3) 1.1 目的： (3) 1.2 背景： (3) 二、方案设计 (4) 2.1 背景： (4) 2.2 黑箱法分析： (5) 三、各工步设计 (6) 3.1 放面团 (6) 3.2一级输送 (6) 3.3压面 (6) 3.4二级输送 (6) 3.5 切面机构 (6) 四、各子系统设计 (6) 4.1 动力系统选取 (6) 4.2 传动系统设计 (6) 4.3 压面机构 (6) 4.4 切面机构 (7) 4.5 机械生产效率计算 (7) 五、产品前景 (8) 产品优势 (8) 产品前景 (8) 六、参考文献 (8)
摘要：该机械采用小功率驱动，经济节能；通过2次压面工艺，提高面条的品质；一次出面，效率高，省事，省时，省心，方便，快捷。 关键词：清洁，2次压面，封闭，品质 一、目的及背景 1.1 目的： 针对传统手工制作面食存在的劳动强度大、工序复杂、效率低、不卫生等缺陷，运用机械原理，设计了家用面条机，以适应市场对面条机节能、体积小、造型新颖、操作简单、维修方便、光洁卫生等需求。 1.2 背景： 随着生活水平的不断提高，生活节奏日益加快，饮食制作快捷化就自然想到用饮食机械来代替传统手工制作。市场上已经出现许多如和面机、洗面机、面条机、饺子机等形状各异、种类繁多的面食品加工机械，但是大多为大型面食品加工机械，面条家用加工机械并不多，且功能单一，纵观世界面条机, 一方面向高生产率、全自动的方向发展, 另一方面由敞开型向封闭型、重量轻、体积小、造型美. 一次成条方向发展。随着人们对食品各方面要求的提高，家用面条机开始受到家庭厨子的喜爱，面对全国广大市场，家用面条机发展空间广阔，经济前景好。纵观世界面条机, 一方面向高生产率、全自动的方向发展, 另一方面由敞开型向封闭型、重量轻、体积小、造型美. 一次成条方向发展 面条的规格： 品质规格：根据麦类作物学报中中国面条的标准化实验室制作与评价方法研究，西北农林科技大学学报中面条品质评价方法研究进展，把面条的色泽、外观、软硬度、粘弹性、光滑性、食味;作为评价面条的标准，其中外观，软硬度，粘弹性，光滑性很大程度受到机械加工的影响。 尺寸规格：南方以2X2mm方截面型面条为主，北方以5mm圆形面条为主，长度从150-250mm不等。
摘要： 二十一世纪以来，我国的食品行业的发展大大改革在加工食品的早期开放的日益提高，人们的生活和高要求的食品包装食品机械的食品工业的发展，提高人民的物质生活不断为了满足食品行业促进各类食品机械和食品机械的发展，机器的自动化和加工食品中的社会发展必然的一种先进的发展需求促进社会主义经济建设的不断发展，人们的物质生活旁边的新要求，食品的质量，为水果量的变化来满足人们的日常需求，和小食品包装市场供应系统方便法就提到了议事日程，，其优势是用来节省时间，提高效率，为大规模生产劳动释放保证效处理的实现是否手工制作，产品质量，降低了原材料的浪费通过蜗轮蜗杆传动电机在表盘的切碎机的基本工作原理，拨号环周运动剑架圈，它是负责由和3线切丁机目前市场上的主要大尺度，主要的大型酒店和食品加工厂，餐厅设计这些切丁在一个大酒店，至少一个切丁切丁和广泛的应用，然而，国内的多功能机切丁种类很多，现在出现了一片碎机，效率高，使用方便操作，能耗低，大产量高，适合工厂，只有在学校的食堂，食品加工厂，用作一种蔬菜，不能满足家庭生活的改善的多功能机，切丁的需求，更好的满足用户的需求，和实用价值，这些小机器，和功能，可以满足普通家庭的需求巨大 关键词:食品,机,发展
Abstract： Since the 21st century, the development of food industry of our country greatly the reform open early in the processed food is improved day by day, people's lives with the high demand from the food packaging Food machinery of the development of the food industry The improvement of people's material life continually in order to meet the demand of the food industry to promote the development of various types of food machinery and development An advanced development in food machinery and automation of the machine and the social development inevitable in processed foodsPromoting the development of socialist economic construction constantly, people's material living next to the new requirements The quality of food, fruit quantity change in order to meet the demands of the people's daily, and convenient method of the supply system of small food packaging market supply immediately mentioned the agenda, extensibility and, Behold, no hard crusts cut of each fruit fruit julienne slices of fruit Application of food machinery's [1] this machine Application of food machine, reduces the labor intensity of the workers, the advantage is used to save time, improve efficiency, large labor production release In order to guarantee the special effect processing to realize whether the handmade, product quality, reduces the waste of raw materialsThe basic work principle of shredded machine via the worm gear worm drive motor on the dial, dial ring week exercise sword rack
全自动一次成型挂面机操作方法技巧 我们一共将制面的整个过程分为3大步骤进行操作分析 1.和面：将面粉倒入拌面机内，然后按规定25%左右的比例进行加水，启动运力，把面和水拌均匀达颗粒状(10分钟后使用最佳)，即可倒入面条机使用。 2.调整：用手轮进行调整轧辊间隙，各组轧辊间隙的参考数据是：(330以上机组例外)在调整过程中，调紧或放松手轮的多少，有时不易一次调准，关键是要弄清道理，耐心把握，不熟练时可停机调整，正常后锁紧手轮。 3.操作：把拌好的面粉放入面斗内，按刀并固定挡刀板，就可开机运转，第三组下来面板要用手引到下一组(多组照此类推)经过面条机压辊压制，出面条操作完毕。
重庆友乐乐机械专业生产各种款式的面条机，热门搜索词：重庆全自动面条机、重庆面条机、重庆压面机、贵州面条机、四川面条机、云南面条机、重庆面条机厂、面条机多少钱一台、多功能家用面条机价格、重庆面条机厂家。欢迎大家登录我公司网址详细咨询，友乐乐竭诚为您服务！！ 产品关键词：全自动面条机、重庆老牌面条机、重庆老式面条机、重庆传统面条机
2. 3. 面通过拉丝处理 结构紧凑，造型新颖，辊具有揉面功能，生产面条时不需另外熟化，广受客户的青睐。 4. 转动部位采用高精轴承，经久耐用，运转灵活，性能稳定。 5. 护板采用不锈钢，面斗木质部分用不锈钢板装
重庆友乐乐机械有限公司位于重庆市巴南区金竹工业园内，前身为“重庆永利食品机械厂”，因自身发展需要，2015年底由重庆的合川区搬迁到了巴南区金竹工业园区内，不但交通地理环境更加便利，而且大大提升了我公司在研发、制造领域同周边“重庆大江工业集团”和“长安铃木公司”配套厂的综合协作能力。“友乐乐”是一家专业从事食品机械设计、制造、销售、服务为一体的企业，公司不断开拓创新，迅速发展。公司主打产品为面条机、米粉机和粉条机、凉皮机等，企业以创新、科技、服务和经济效益为设计理念，以优越的性能和人性化的智能设计赢得了广大新老客户的信赖，以过硬的质理和精湛的技术，在行业内享有较高的声誉! 我们的目标：创业路上友(有）乐乐！ 我们的宗旨：销售的不仅仅是产品，更重要的是服务；最终目的是帮助选择我们的朋友获取适宜的利润！！ 产品关键词：全自动面条机、重庆老牌面条机、重庆老式面条机、重庆传统面条机
元谋县果蔬物流中心 方案设计书 班级：物流0912 组长：姚富有 组员：王瑜刘芫杏
孙丽娟施丽蓉 目录 前言 1、我国冷藏业当前存在的问题-----------------------------------------------------------3 2、我国冷藏库建设未来发展方向的探索- ------------------------------------------------------3 1、基本设计 1.1果蔬冷链仓库平面图----------------------------------------------------------------------- -------6 1.2果蔬冷链必要设施及设备------------------------------------------------------------------------7 1.21国际形势-------------------------------------------------------------------------------------------7 1.22果蔬冷链物流仓储设施设----------------------------------------------------------------------7 2.库存优化选择 2.1出入库流程-------------------------------------------------------------------------------------------- 9 2.11仓库作业过程---------------------------------------------------------------------------------------9 2.12入库作业流程---------------------------------------------------------------------------------------9 2.13 出库作业流程- -------------------------------------------------------------------------------------9 2.2货物优化方案-----------------------------------------------------------------------------------------10 2.21物动量分析表- -------------------------------------------------------------------------------------10 2.22 堆码示意- ------------------------------------------------------------------------------------------11 2.23 货物存储及货位分配----------------------------------------------------------------------------11 2.24 货物盘点-------------------------------------------------------------------------------------------12 2.25 库
系列切丁机使用说明书必须仔细观看使用说明书才能开机，否则机器损坏为人为的责任。 苏州中名机械制造有限公司 地址：江苏省苏州市相城区黄桥镇生田路6号 邮编：215031 公司主页：
前言 首先衷心地感谢您惠购本公司的产品，希望本公司的产品能为贵公司带来更多的经济效益。 本使用说明书是为了安全使用本机器而制作的参考简介。 本机的操作人员或保养人员在进行操作或检修保养之前，必须仔细阅读使用说明书并正确理解其操作方法及各项注意事项，然后再进行操作或检修保养。 如果不是使用说明书进行操作，可能会造成重大事故的发生。 请讲本使用说明书放置于机器附近的容易查看处，并妥善保管，以便随时查看。 当把本机出售或转让给他人时，请务必将本使用说明书一同交给用户，以便用户操作和检修等。 本使用说明书如丢失或破损等，请尽快与本公司或销售代理店联系购取。 温馨提示 一、必须由专人使用本机。 二、开机之前必须先确认电源电压为380V，无缺相现象。 三、为了保护刀具和人身安全，开机前先检查设备上是否有异 物，如果有异物，请先断电、清理、再开机操作。 四、为了操作人员的安全，在切割时禁止谁意开关门并把手伸 进去，必须把设备电源切断并等刀具停稳方可开门，否则 造成的人身安全由购方自行负责。
五、操作完毕后必须及时关机并切断本设备电源。 六、切割工作完成后必须对设备进行清洗及保养。 七、清洗刀具或更换刀具前必须先关机再切断本设备电源。 八、不得切带硬骨的或冷冻的肉类进行切割，本机只适合切割 麻冻状态-4℃以上的纯肉。
目录
一、概述 ZJTS系列切丁机参照国际先进设计制造，结构合理，该机械能做到精确切“丁”、“丝”、“片”且工作效率高。 ZJTS切丁机是肉类制品生产制作工艺中的一个重要设备。将肉块，脂肪等主要原料，切割成用户所需要的肉丁，调整刀栅的尺寸可切除肉丝、肉片。肉丁尺寸的大小由刀栅中刀片数量来决定。本厂生产的350型和550型切丁机适用于大，中，小型肉类食品加工厂，也可按用户提出的要求，制定生产特殊工艺要求的产品。 本厂生产的切丁机结构紧凑，安全实用，维修清洗方便，组装灵活，具有下列优点： 1.安全防护性能良好，前门打开后转动的切刀立即停转。 2.刀栅及大切刀装拆方便，不用工具即可全部卸下，便于清洗更换刀栅。 3.测压机构可使一次切割的肉料的量增加，并有助于预压力加快达到设定 值，提高生产效率。 4.拨叉结构的设计提高了产品切割质量，减小噪声、降低机械故障率。 5.调整预压力旋钮，可保证产品在切割过程中始终如一。 6.肉料可步进进料，可最大限度地减少在切割过程中对产品的挤压。 7.改变刀栅中刀片的数量，可切割出不同尺寸的肉丁，组合方便。
郑州大型面食设备制作厂家哪家比较专业，下面小编介绍下这类设备的基本信息： 一．冷风定条区：通常采用不加温，而加强空气流动的办法，以大量干燥空气来促进面条去湿，使挂面形状初步固定，除去表面水份。表面硬化，由塑体向弹性转变，雨天（或梅雨）要提前开扇和排潮，冬季送温略提前，因湿面表面蒸发缓慢不易定条，避免温度过度，会使面条湿性差，面表面水份蒸发过多，影响内蒸发阶段的湿度降低，保潮湿度过度，造成面条拉伸，断条上薄下厚，相互粘连等现象。
二、内蒸发区（保潮发汗）： 此区以水份内扩散为主，强化通风，使空气循环畅通，此时跨区温度上升，不要过“急”，要使温度形成“梯度”，保持一定湿度，一方面是向面条中心转移热能，缩小表面与内部的温差，另一方面加快内部水份的扩散，使表面水份汽化速度与内部水份转移速度一致，水份慢慢蒸发，如果此时温度、湿度差过大，会造成表层干得快，表面“结膜”、“关门”、“龟裂”等现象，内外水份不平衡，最后挂面外干内湿，导致面条酸面、酥面等质量问题，存放期短。 郑州大杰食品机械有限公司位于郑州市马寨经济开发区，临近郑州西四环环城高架及郑州西区CCD四个中心、郑州绕城公路陇海西路站下口。 本厂遵循以创新经营高科技为导向，以客户需求为焦点，不断开发新产品。以质量求生存的经营理念和诚信销售热情服务为广大客户提供优质产品。 我公司以生产食品机械为主，专业生产挂面机、方便面机、中低温挂面成套设备、热干面自动生产线、全自动成套熟面机、生鲜面机设备、手盘面机生产线、波纹面机成套设备、面叶生产线、饺子皮机、混沌皮机、凉皮机、米皮机等食品机械的研发与制造，产品远销三十多个省、市、自治区，和非洲等国家和地区。 长期以来，本公司坚持以创新经营、精致为本的经营理念，让顾客满以为宗旨，不断开发新产品，以优质的产品和良好的信誉，赢得了用户的信赖和好评。
财务模型培训
今天的议题
财务预测模型介绍 工具与数据 构建简单的财务预测模型 构建复杂的财务预测模型
财务模型可以用来做什么？ 财务模型可以用来做什么？
预算Budgeting 成本估算Cost Estimating 销售预测Sales Forecasting 销售预测 市场表现预测Market Share Forecasting 市场表现预测 投资项目的选择Project Selection & Management 投资项目的选择 业务/产品组合管理－ 业务 产品组合管理－组合方案与优化 产品组合管理 实时的市场分析Time-to-Market Analysis 战略决策的评估Real Options Valuation 并购M & A
战略规划项目中的财务预测模型是什么？用来干什么？ 战略规划项目中的财务预测模型是什么？用来干什么？
战略规划项目中的财务预测模型是 模拟各业务在不同运营策略/ 各业务在不同运营策略 模拟各业务在不同运营策略/业务模 式下及不同市场环境下各项业务的 式下及不同市场环境下各项业务的 大体财务表现及发展趋势。因此， 大体财务表现及发展趋势。因此，
在模拟业务表现时，先不考虑股权比 例、投资收益、少数股东权益等问 题；在最后并总表时，可以综合考虑 最后计数单位宜采用“千元”、“百 万元”等较大计量单位，切忌采用 元、角、分等极其精准的单位计量
财务预测模型绝对不能直接作为： 财务预测模型绝对不能直接作为： 直接作为
–
精准的预算 绩效考核的标准
–
但是，可以作为制定预算时的初步参 照，且其中部分有关运营方面的假设 项，例如产能利用率、损耗率等也可在 绩效考核中作为参照
在战略项目中， 财务预测模型将用于 在战略项目中，财务预测模型将用于 在战略项目中， 在战略项目中， 比较不同战略备选方案的经济价值 比较不同战略备选方案的经济价值 促进战略规划、行动方案的细化，并进行验证，反过来指导战略的制定 促进战略规划、行动方案的细化，并进行验证，反过来指导战略的制定 根据财务计划对未来进行资源安排提供依据 根据财务计划对未来进行资源安排提供依据
自动揉面机的揉面特点及工作原理 一、自动揉面机(也称自动压面机)是一种安全、高效、实用的面食加工机具。经它揉和后的面片可以提高面的筋度，增加面的白度和韧性。经过揉压的面团制作面馒头及各类食品、面包、糕点，香甜、劲道、光泽度好，口感好。该机效率高，安全系数高，可以代替传统的人工揉面和繁重的体力劳动，使用方便，具有别的机型不可代替的待征和优越性。广泛适用于机关、学校、厂矿食堂、个体食品经营者、面食加工单位，也是配置馒头生产线的理想设备。 二、揉面机结构特征：自动揉面机主要有机架、传动部分、压面部分、输送折叠部分、外罩五大部分组成。传动部分主要采用链条、轧辊齿轮、主动齿轮组成，具有传动平稳，噪音小的特点。压面部分主要有可调轧辊、上轧辊、下轧辊组成，实现自动翻面的功能。输送折叠部分主要有左右支架、输送带组成，运用不同线速原理，实现自动传送自动折叠，代替了繁重的手工操作，既卫生又安全。同时为保证轧辊两端间一致，采用蜗轮、蜗杆、偏心轮调整机构，可实现无极调整，使压面厚度两侧一致。
三、揉面机的工作原理： 将定量的面团放在下输送带上，开动机器，自动输送到轧辊间，面团在输送带和轧辊的作用下自动完成喂入和压面过程。压完后经上输送带自动传送到下输送带上，由于采用不同线速度，使面皮自动完成折叠和输送、喂入，转入下一轮揉压。经过反复折叠、揉压，反复数遍达到理想压面效果，使面的结构更为紧密，更具光滑度，使压制后的面团获得较好的层次和口感。
重庆友乐乐机械专业生产各种款式的面条机，热门搜索词：重庆全自动面条机、重庆面条机、重庆压面机、贵州面条机、四川面条机、云南面条机、重庆面条机厂、面条机多少钱一台、多功能家用面条机价格、重庆面条机厂家。欢迎大家登录我公司网址详细咨询，友乐乐竭诚为您服务！！ 产品关键词：全自动面条机、重庆老牌面条机、重庆老式面条机、重庆传统面条机
摘要 随着近年来我国蔬菜出口的迅速崛起，蔬菜加工出口已成为我国的重要创汇渠道。但疏菜加工机械却远远滞后于蔬菜出口的发展，并且价格昂贵。由此我们研制了多功能蔬菜加工机，一机多用，取代了部分功能单一、效率低下、价格昂贵的进口机械。本文首先研究了蔬菜切割、输送、定位、成型的基本理论，然后设计了多功能蔬菜加工机的切削装置、送料装置和传动机构等，使之能够达到对块根状及叶菜状蔬菜进行切片、丝、段等规格形状的加工。同时应用新科技，采用先进的数字调速电机，省去复杂的变速机构与调节机构。试验表明，该设备出成率、效率达到进口机械水平，价格较进口设备降低50%以上，可填补此类机械的国内空白，取得良好的经济效益和社会效益 关键词:多功能，蔬菜，加工机 第一章引言 1.1 课题的目的和意义 蔬菜是人生活中必不可少的营养丰富的食品之一，可为人体提供必需的维生素、矿物质、膳食纤维等有益于人体健康的功能成分。随着人们生活水平的不断提高，生活节奏加快，对食用方便、营养丰富、经过加工的精细蔬菜的需求越来越大，对产品的品质要求越来越高。蔬菜出口在我国起步虽晚，但由于中国蔬菜富含营养、品种齐全、质优价廉，深受各国消费者的青睐，因而近几年蔬菜出口发展十分迅速，己成为创汇农业的支柱产业。 调查结果显示，目前我国蔬菜加工机械却远远滞后于蔬菜出口的发展，现在主要靠合资外方从国外进口，价格昂贵，如牛芬、胡萝卜切丝机，从日本进口一台普通(长短、粗细不可调)切丝机，需人民币1.2万多元。为适应蔬菜加工的需要，我们设计多功能蔬菜加工机，一机多用，只需更换切刀和部分零件，即可加工各种异型块根状蔬菜，如铅笔屑状(牛芬)、各种异型状片(胡萝卜、土豆的梅花状、菊花、树叶状、球拍状等)、丝条(胡萝卜、牛芬等)、自由片(牛芬、胡萝卜、姜、蒜等)及酱菜等。该机的多功能化，取代了部分功能单一、价格昂贵的进口机械，蔬菜加工厂家只需购买一台设备就可加工多适合出口需要的不同规格的产品。投资少，效益高，适应于多品种、批量生产的需要，提高了设备利用率。 加快蔬菜机的发展，提高企业技术装备水平，无疑将成为山东蔬菜出口发展的战略突破口，增值增效潜力巨大。本课题旨在研制一种高效、可靠、实用、多功能蔬菜加工机械，重点解决我国蔬菜加工机械功能单一、进口机械价格昂贵的问题。 1.2 蔬菜加工机械的种类 （1）多功能旋转式切菜机，其原理是使需要的切的蔬菜高速旋转，利用离心力使蔬菜紧贴刀片进行加工，是一个蔬菜加工行业、食品行业、脱水蔬菜厂、速冻食品二次加工常用的机器。使用它可将有固定形状的如：芥菜、萝卜、土豆等块切制成所需要厚度的片和丝，一般采用防腐铝外壳及高级合金刀片，具有结构紧凑、合理、操作简便、调整维修方便、耐腐蚀的特点。其缺点是：切片或切丝的形状不规则。厚度不均。 （2）离心式切菜机采用先进工作原理，其特点为结构紧凑、坚固耐用、易于维修，可提高生产率，降低劳动强度，对萝卜、土豆、白薯、圆白菜等根茎类可加工成菜丝、菜条、菜片、广泛适合大、中型酱菜厂和速冻食品厂使用。 （3）切丁机性能优于其它机器，可一道工序完成块条的加工，省时省力，操做方便，适合芥菜、萝卜、黄瓜（包括咸制黄瓜）、土豆、洋葱、香瓜、胡萝卜、
大小五组面条机压辊的调整说明 大小五组面条机压辊的调整说明： 第一道辊：1-2毫米 第二道辊：1.5毫米 第三道辊：0.5毫米 第四道辊：0.5毫米 2调整时压辊两端间隙须一致。 3各压辊之间面片如发现拉断或折叠现象可调整压辊间隙，拉断时缩小下对压辊间隙或加大上对压辊间隙，折叠时加大对压辊间隙或缩小上对压辊间隙。 调整适合后锁紧压辊方可进行面条加工。
友乐乐面条机厂家、半自动面条机、全自动面条机价格
双面撒粉，自动挑条一次成型，流水线式生产，双面撒粉，自动化程度高，操作简单，效率高。 2. 3. 面通过拉丝处理 结构紧凑，造型新颖，辊具有揉面功能，生产面条时不需另外熟化，广受客户的青睐。 4. 转动部位采用高精轴承，经久耐用，运转灵活，
重庆友乐乐机械有限公司位于重庆市巴南区金竹工业园内，前身为“重庆永利食品机械厂”，因自身发展需要，2015年底由重庆的合川区搬迁到了巴南区金竹工业园区内，不但交通地理环境更加便利，而且大大提升了我公司在研发、制造领域同周边“重庆大江工业集团”和“长安铃木公司”配套厂的综合协作能力。“友乐乐”是一家专业从事食品机械设计、制造、销售、服务为一体的企业，公司不断开拓创新，迅速发展。公司主打产品为面条机、米粉机和粉条机、凉皮机等，企业以创新、科技、服务和经济效益为设计理念，以优越的性能和人性化的智能设计赢得了广大新老客户的信赖，以过硬的质理和精湛的技术，在行业内享有较高的声誉! 我们的目标：创业路上友(有）乐乐！ 我们的宗旨：销售的不仅仅是产品，更重要的是服务；最终目的是帮助选择我们的朋友获取适宜的利润！！
毕业论文（设计） 题目：蘑菇切丁机的设计 姓名： 学院： 专业： 班级： 学号： 指导教师： 年月日
目录 摘要....................................................................... I Abstract ........................................................................................................................................... II 1绪论. (1) 1.1研究的目的及意义 (1) 1.2国内外研究现状 (3) 2切丁机总体方案的确定 (3) 2.1切丁机的总体构成 (6) 2.2整机结构设计 (6) 3主要零部件的设计与计算 (4) 3.1传动方案的确定 (4) 3.2滚筒的设计 (5) 3.3部分零件的规格设计 (5) 3.4 电动机的选择................................................................................ 错误！未定义书签。 3.5 V带的设计计算 (6) 3.6V带轮的设计 (8) 3.7直齿圆柱齿轮的设计计算............................................................. 错误！未定义书签。 3.8轴的结构设计计算......................................................................... 错误！未定义书签。 3.9轴承的选择及校核......................................................................... 错误！未定义书签。 3.10键的选择和校核 (17) 3.11切刀的设计 (18) 3.12机体结构设计 (22) 4结论............................................................................................................ 错误！未定义书签。 4.1 本设计的优点................................................................................ 错误！未定义书签。 4.2 存在的不足和建议........................................................................ 错误！未定义书签。5总结............................................................................................................ 错误！未定义书签。参考文献....................................................................................................... 错误！未定义书签。致谢............................................................................................................... 错误！未定义书签。