Elasto-plastic statistical model of strongly anisotropic rough surfaces for finite element 3D-contac
Elasto-plastic statistical model of strongly anisotropic rough surfaces
for ?nite element 3D-contact analysis
Ryszard Buczkowski a ,Michal Kleiber
b,c,*
a
Technical University of Szczecin,Division of Applied Mechanics,Piastow 41,71-065Szczecin,Poland
b
Institute of Fundamental Technological Research,Polish Academy of Sciences,Swietokrzyska 21,00-049Warsaw,Poland
c
Department of Mathematics and Information Sciences,Warsaw University of Technology,Poland
Received 23February 2005;received in revised form 15November 2005;accepted 15November 2005
Abstract
The complete elasto-plastic microcontact model of anisotropic rough surfaces is proposed.The description of anisotropic random surfaces is restricted here to strongly rough surfaces;for such surfaces the summits are represented by highly eccentric elliptic paraboloids having their semi-major axes oriented in the direction of the grain.The present model is based on the volume conservation of asperities in which the plasticity index is modi?ed to suit more general geometric contact shapes during plastic deformation process.This model is utilized to determine the total contact area,contact load and contact sti?ness which are a mixture of both the elastic and plastic com-ponents.For low nominal pressures both the elastic and elasto-plastic contact sti?ness is found to be almost linear in relation to the normal load.The elastic and elasto-plastic sti?ness coe?cients decrease with increasing variance of the surface height about the mean plane.The standard deviation of slopes and standard deviation of curvatures have no observable e?ects on the normal contact sti?ness.ó2006Elsevier B.V.All rights reserved.
Keywords:Rough surfaces;Statistical modelling;Contact sti?ness;Finite element method
1.Introduction
For machined metal surfaces the height,slope and curvature of asperities are random and have the Gaussian or nearly Gaussian probability distribution.This fact suggests that the geometry of such surfaces can be described statistically assuming they are described by a limited number of variables.On the basis of probability theory Greenwood and William-son [1](GW model),Whitehouse and Archard [2],Nayak [3,4],Bush et al.[5–7],Sayles and Thomas [8],Whitehouse and Phillips [9–11]and Greenwood [12]have made an important advancement in developing the asperity based-model.
The observation of Pullen and Williamson [13]that the volume of deformed asperities is conserved stimulated Chang,Etsion and Bogy [14](CEB model)to adopt it in their elasto-plastic model of deformed spheres.They introduced an improved model where the asperity deformations are primarily elastic but there is also a signi?cant number of asperities beyond their elastic limit.Recently,Horng [15]extended the CEB model to describe a more general case of an elliptical contact of asperities.On the other hand,surfaces machined by turning,honing or grinding,have orientation corresponding to the direction of motion of the cutting tools relative to the workpieces,and a model of anisotropic rough surfaces must be then employed.In such cases,it is necessary to include both the principal curvatures taking into account the directional
0045-7825/$-see front matter ó2006Elsevier B.V.All rights reserved.doi:10.1016/j.cma.2005.11.014
*
Corresponding author.Address:Institute of Fundamental Technological Research,Polish Academy of Sciences,Swietokrzyska 21,00-049Warsaw,Poland.
E-mail address:michal.kleiber@https://www.sodocs.net/doc/ca15487468.html,.pl (M.Kleiber).
https://www.sodocs.net/doc/ca15487468.html,/locate/cma
5142R.Buczkowski,M.Kleiber/Comput.Methods Appl.Mech.Engrg.195(2006)5141–5161
nature of surface roughness.To do so,the asperities may be replaced by elliptic paraboloid and then the analysis due to Hertz may be employed for elastic deformation of the surfaces.The statistical theory of Longuet-Higgins[16,17]in its gen-eral form provides a complete description of random anisotropic surfaces.Nayak[3]considered the application of the Longuet-Higgins[16,17]theory to anisotropic engineering surfaces and demonstrated how the spectrum moments up to order4can be obtained by knowing seven pro?le parameters(invariants)of the surface.These parameters,which are deter-minants of correlation matrices used in the multi-dimensional normal distribution theory are termed invariants of the surface and are independent of the orientation of the coordinate axes.Each of these invariants was discussed by Nayak [3]in terms of its respective physical interpretation.For a general analysis,?ve non-parallel pro?les are required to calcu-late the surface moments m ij in terms of the pro?le moments m n(h).A case of engineering importance is the surface with a grain pronounced to one direction.A theoretical analysis of such surfaces was presented by Bush et al.[5–7].They derived a joint distribution density function for random asperity heights and curvatures of elliptic paraboloids in elastic contact with a smooth rigid?at for both the isotropic[5,6]and anisotropic[7]surface.An interesting fact about non-isotropic sur-faces is that one needs nine constants(spectral pro?le moments m ij)to proceed with the analysis of the surface statistics. However,the properties of the surface are independent of the orientation of the plane reference surface coordinates(x,y). In relation to the anisotropic case Bush et al.[7]simpli?ed the general anisotropic rough surfaces to a strongly anisotropic one.In this case it is su?cient to consider?ve surface parameters:the variance of the surface height m00,two principal mean square slopes m02,m20and two principal mean square curvatures:m04,m40.A more general description of aniso-tropic surfaces was recently presented by So and Liu[18].This approach showed that the plastic part of the contact area increases signi?cantly as the degree of anisotropy increases.McCool and Gassel[19]gave the mathematical basis for aniso-tropic description using the Monte Carlo simulation technique.Another approach was taken by Kucharski et al.[20], Kogut and Etsion[21]and Larsson et al.[22]who proposed a?nite element model to determine a more realistic elasto-plastic or elasto-viscoplastic deformation for the analysis of a single-asperity behaviour,and then the relations derived were combined with a statistical description of the rough surface.
Di?erent approaches have been considered to describe micromechanical contact laws.The available formulations are based either on curve-?tting of experimental results or on statistical analysis of rough https://www.sodocs.net/doc/ca15487468.html,prehensive review of such models has been recently presented by Wriggers[23].An extensive survey of statistical models of rough surfaces was made by Thomas[24],Bhushan[25–27]and Whitehouse[28].Relations between surface parameters of the pro?lomet-ric and various asperity-based models were summarized by McCool[29].According to him,for the isotropic case the prediction of nominal pressure assuming the bandwidth parameter a=10is lower by nearly a factor of2in comparison to the elastic isotropic model taken from reference of Bush,Gibson and Thomas[5](BGT model)but is in good accordance with an asymptotic solution of the BGT model and the GW model.The question why the agreement is not better at higher bandwidth parameters a is not known[29].The suggestion of Mcool that it could be due to truncation errors in the numer-ical integrations is not justi?ed.A comparison of all simpli?ed models to the strongly anisotropic model of Bush,Gibson and Koegh[7](BGK)is therein not given.
It appears that the statistical roughness models given in the context to the?nite element procedure by Willner and Gaul [30],Zavarise and Schre?er[31](both related to the elastic case)and Buczkowski and Kleiber[32](the elasto-plastic case) were published?rst.
This study concentrates on building an elasto-plastic statistical model of rough surfaces for which the joint sti?ness can be determined in a general way.In Section3,we begin with a complete description of anisotropic random surfaces to be restricted here to strongly rough surfaces;for such surfaces the summits are represented by highly eccentric elliptic parab-oloids having their semi-major axes oriented in the direction of the grain.The statistical description of random,strongly anisotropic Gaussian surfaces based on the model of Bush et al.[7]is adopted.To calculate the forces and contact area for the single asperity in the elastic range the solution of Hertz is used(Section4).Section6presents an elasto-plastic micro-mechanical model of rough surfaces which is based on volume conservation during plastic deformation.Both the elastic and elasto-plastic normal contact coe?cients are derived in Sections5and7,respectively.Section8is devoted to the?nite ele-ment incremental solution of fully three-dimensional contact problem accounting for the normal contact sti?ness obtained using the statistical model of the strongly anisotropic rough surfaces.Some conclusions are presented in Section9.
2.How to describe surface roughness?
Modelling of the contact of rough surfaces has been treated using a number of approaches.One of the methods is a fractal description of engineering surfaces being presently a subject of the intensive discussion.Because the conventional parameters like slopes and curvatures are very scale-sensitive,attractiveness of the fractal model consists in its ability to predict the relationship between roughness parameters and sampling size or the resolution of the measuring instrument. The surface roughness can be adequately described using self-a?ne fractal models.A self-a?ne fractal object needs to be characterized by at least two parameters de?ned as the fractal dimension D which describes how roughness changes with scale and the amplitude parameter(sometimes called topothesy)K de?ned as the horizontal separation of pairs of points on
a surface corresponding to an average slope of one radian.A number of methods have been suggested in the literature to estimate both the D and K parametres.The structure function,spectral,the variogram,roughness-length and line scaling methods were used to calculate fractal parameters.Many authors showed that the fractal parameters are scale dependent,which arise from the sampling size,sampling interval and the resolution of the scanning instrument.Fardin et al.[33,34]used a 3D laser scanner having high accuracy and resolution to investigate the scale dependent behaviour of a large and rough rock fracture.Four sampling windows were selected from the central part of the modi?ed digital replica.Their results show that both D and K are scale dependent and their values decrease with increasing size of the sampling windows of the 3D-laser scanner.The authors obtained a power law relation between the standard deviations of the reduced asperity height and the window sizes for the all sampling windows.They concluded that the scale-dependency is always limited to a certain size,de?ned as the stationarity threshold,below which reliable statistical properties of the joint surface cannot be extracted.Moreover,rougher surfaces will have a larger stationarity limit and therefore,for accurate characterization of the rock fracture surface roughness,samples with a size larger than or equal to stationarity limit are necessary.In the note of Whitehouse [35]the author questions the philosophy of using fractals to describe engineering surfaces.Greenwood [36]in his comments on the paper of Whitehouse also doubts about the fractal concept.
The classical statistical model for a combination of the elastic and plastic contact between rough surfaces model of Greenwood and Williamson has been widely accepted.It assumes that asperities are modelled by a set of spheres of con-stant radius equivalent to an average curvature of the asperities and the deformation of any point in the roughness layer is independent of its neighbouring points.The last assumption,however,cannot be accepted for higher contact normal loads.On the basis of the ?nite element results according to Komvopoulos and Choi [37]interaction e?ects of neighboring asper-ities strongly depend on the distribution and radius of asperities and indentation depth.They concluded that the e?ect of neighboring asperities manifests itself through the unloading and superposition mechanisms.
A surface of GW model can be characterized by two following parameters:the standard deviation of surface heights r or R q which is referred to the square root of m 0and the area density of peaks and summits.Greenwood and Williamson [1]introduced the idea of studying three-point peaks.They de?ned the peak as a sample point on the pro?le which is higher than their immediate neighbours at the sampling interval,while the summit as a point on the two-dimensional surface higher than all its neighbours.In this case the summit of roughness is de?ned in the majority of cases as a point for which eight neighbouring points are situated below.The GW model assumes that summits on surface are equivalent to peaks on pro?les.Clearly it is not true,the summit density can be estimated from the peak density squared,but the factor is not 1as assumed by Greenwood and Williamson [1].According to the ?ve-point summits theory of Greenwood from 1984[12],the discrepancy between the density of summits and peaks increases when the sampling interval is larger and rises to the asymptotic value of 1.8.For complete description of the isotropic GW model we need also the information about the distance between the summit mean plane and the surface mean plane which depends on the bandwidth parameter a ,de?ned as
a ?m 0m 42
;
where m 0,m 2and m 4are known as the zeroth,second and fourth spectral moments of the pro?le.In the limit as the sam-pling interval tends to zero the moments of the power spectrum m 0,m 2and m 4become equal to the quantities r 2,r 2m and r 2
j which are the mean square values of the height,slope and curvature,respectively (see [12]).
The question that now remains to be answered is whether the pro?le parameters vary with the sampling size or the instrument resolution.Both the theory and experiment show that the density of peaks or summits and curvatures do all depend on the sampling interval.When the sampling interval is reduced by the factor of 10,the summit density increases by a factor of 40.Much the same holds for curvatures [12].Additionally,in the recent work of Greenwood and Wu [39],the authors stated that their idea based on assumption that peaks on a surface pro?le (points higher than their immediate neighbours at the sampling interval used)is quite wrong and gives false results according to both the number and the radius of curvature of the asperities.A similar problem occurs in the 3D description of surface.Radziejewska [40]have recently proposed entirely new method of surface roughness modelling with one e?ective radius which is much larger than the one obtained from measurements.The proposed method is based on the 3D analysis of size and shape of the surface intersec-tion asperities with planes parallel to the mean plane.It provides much more information than the standard bearing curve,which additionally enables to de?ne the contact process in the beginning phase of the approach.
Fortunately,the experimental data for the thin-?lm disks and magnetic tapes clearly show that the r.m.s.of m 0referred to r or R q does not change [41]or varies very little for machined surfaces with sampling interval [42]and can therefore be considered as scale independent for most surfaces and used to characterize a rough surface uniquely.The last conclusion ?ts very well to the present formulation because the standard deviation of slopes nad curvatures have no observable e?ects on the elastic or elasto–plastic normal sti?ness while both the elastic and elasto–plastic sti?ness coe?cients depend primar-ily on the variance of the surface height about the mean plane m 00(after Sayles and Thomas [38]and McCool [43],
m 00=m 0),which is not much sensitive over a large range of sampling intervals.Additionally,R q ???????
m 0p is the most useful and recognized parameter in the surface metrology thus being embedded in the international standards.
R.Buczkowski,M.Kleiber /Comput.Methods Appl.Mech.Engrg.195(2006)5141–51615143
3.Strongly anisotropic model of rough surfaces
Theories of isotropic surfaces are not applicable to the important practical case of ground surfaces which are strongly anisotropic.Bush,et al.[7]presented the random theory of strongly anisotropic rough surfaces which will be brie?y described here.In the model the cap of each asperity is replaced by elliptic paraboloid with summit n 1above the point (x 0=0,y 0=0)on the mean plane.The plane z =h intersects the paraboloid in an ellipse which has semi-axes of lengths (in a local deformed stage)A and B with one its principal radii of curvature at angle b =0to the positive x -axis (see Fig.1).Let us consider a rough surface whose heights above the mean plane of of the surface are de?ned by z (x ,y ),where x ,y are the Cartesian coordinates in the mean plane.De?ning
n 1?z ;n 2?
o z o x
;n 3?
o z o y ;n 4?o 2z o x
2;
n 5?
o 2z
o x o y
;n 6?o 2z o y
2;
e1T
the joint probability density of the normally distributed variables n i (i =1,2,...,6),each being the sum of a large number of independent variables with zero expectation,is
p en 1;n 2;...;n 6T?1e2p T3D 1=2
exp à1
2M ij n i n j
;e2Twhere M ij is the inverse of the
positive-de?ned covariance matrix N ij
N ij ?E ?n 21
E ?n 1n 2 ...E ?n 1n 6
E ?n 2n 1 E ?n 2
2 ...E ?n 2n 6 ..
......
....E ?n 6n 1 E ?n 6n 2
...E ?n 26
2
6
66
6643
7
7
7775e3T
and D is the determinant of N ij .Considering the random variables with zero mean,the components of the matrix N ij in
Eq.(3)are the expectations of n i n j which can be written in terms of the spectral moments m ij as
E ?n i n j ?m ij .
e4T
According to Longuet-Higgins [16]the spectral moments can then be de?ned by the power spectral density (called there the energy spectrum)
m ij ?
Z 1à1
Z 1
à1
U eu ;v Tu i v j d u d v ;e5Twhere U (u ,v )is the power spectral density and u and v are the wave numbers.(The power spectral density is the Fourier
transform of the surface autocorrelation function.)
Choosing the x -axis in the direction of the grain,symmetry implies that
m 11?m 13?m 31?0.
e6
T
5144R.Buczkowski,M.Kleiber /Comput.Methods Appl.Mech.Engrg.195(2006)5141–5161
Restricting the theory to the case of highly eccentric asperities with their axes closely aligned to the x-direction leads to m22 being negligible(see[7]).In this case it is su?cient to consider the probability density of the variables of n1,n2,n3,n4and n6, so that Eq.(2)becomes now
pen1;n2;n3;n4;n6T?
1
e2pT5=2D1=2
expà
1
2
M ij n i n j
;e7T
where M ij is the inverse of the simpli?ed matrix N ij given as
N ij?
m0000àm20àm02
0m20000
00m0200
àm2000m400
àm02000m04
2
66
66
66
4
3
77
77
77
5
.e8T
The determinant D of N ij is found to be
D?m00m40m04m20m02l;e9Twhere
l?e1àb1àb2T;e10Twhile b1and b2are de?ned by the bandwidth parameters a1and a2in the x-and y-directions,respectively,as
a1?1
b
1
?
m00m40
m2
20
;a2?
1
b
2
?
m00m04
m2
02
.e11T
For strongly anisotropic surfaces?ve parameters are required to describe such surfaces:(1)m00,i.e.variance of the sur-face height about the mean plane,(2)m02and m20,i.e.the principal mean square slopes,(3)m04and m40,i.e.the principal mean square curvatures.According to Longuet-Higgins[16],Nayak[3],Sayles and Thomas[38]these moments can be obtained from two pro?le measurements,one taken in the direction of the grain and the other across the grain assuming that both pro?les have the same variance m00.These surface moments are related to the the number of zero crossings D0 and extrema(minima and maxima)D e per unit length of pro?le by the following equations given by Nayak[4]:
D0ealong grainT?1
p
m20
m00
1=2
;D0eacross grainT?
1
p
m02
m00
1=2
;
D eealong grainT?1
p
m40
m00
1=2
;D eeacross grainT?
1
p
m04
m00
1=2
.
e12T
Assuming,for example,the bandwidth parameters a1and a2set equal to3and the value of m04/m40=6561=94,the pro?le in the direction of the grain will have an average of one-ninth of the number of zero-crossings and extrema of those across the grain.No experimental data are available to provide the mean square slopes(m20,m02)and the mean square curvatures (m40,m04)for anisotropic surfaces.Throughout the study we consider the?ctitious data related to the spectral moments given previously by McCool[29]and Bush et al.[7].
Furthermore,the random variables involved in Eq.(1)are written in non-dimensionalized form as follows:
x1?
n1
??????????
m00l
p;x4?à
n4
??????????
m40l
p;x6?à
n6
??????????
m04l
p.e13T
It is noted that necessary condition for the existence of relative maximum(not a saddle point)of the summit at the point z(x,y)requires that the slopes of a summit n2and n3must be zero and the principal curvatures n4and n6must be negative, i.e.n2=0,n3=0,n460,n660and n4n6àn5P0.
Using Eqs.(7)and(8)the probability that an ordinate is a summit of height x1and curvatures x4and x6is now
pex1;x4;x6T?
l2
e2pT5=2
??????????????
m04m40
p
??????????????
m02m20
p j x4x6j expeàX=2T;e14T
where
X?x2
1te1àb2Tx2
4
te1àb1Tx2
6
à2
?????
b1
p
x1x6à2
?????
b2
p
x1x4t2
?????????
b1b2
p
x4x6.e15TR.Buczkowski,M.Kleiber/Comput.Methods Appl.Mech.Engrg.195(2006)5141–51615145
In the theory which follows the probability distribution of summits is needed.To obtain it,Eq.(14)must be normalized by the ratio of summits to ordinates.The probability that an ordinate is a summit,D sum ,is found by integrating Eq.(14)over the standardized height x 1and the curvatures x 4and x 6
D sum ?Z t10
Z t11
Z t1
à1
p ex 1;x 4;x 6Td x 6d x 4d x 1.e16T
According to Bush et al.[7]the closed form of the density of summits is
D sum ?1e2p Tm 40m 04
m 20m 02
2.
e17T
This formula can be also taken as an ordinary check in the numerical evaluation of integrals Eq.(16).Finally,dividing Eq.(14)by Eq.(17)we obtain the joint probability density function of summits as
p sum ex 1;x 4;x 6T?l 2??????2p p m 04m 40
m 02m 20 3=2j x 4x 6j exp eàX =2T.e18T
4.Elastic contact
In the model a cap of each asperity is replaced by a paraboloid having the same height and principal curvatures as the
summit of the asperity.The asperities are parameterised by their height n 1and the semi-axes a and b of the ellipse obtained from the intersection of the asperity and a plane at height h above the point (x 0,y 0)on the mean plane of the rough surface as shown in Fig.1.The equation for an elliptic paraboloid asperity of summit height n 1above the point x 0and y 0is
n 1àz n 1àh ?ex àx 0T2
a 2tey ày 0T
2
b .e19T
Di?erentiating the above equation with respect to x and y yields the following relationships between the curvature and the semi-axes a and b ,see Eq.(1)
n 4?
à2en 1àh T
a 2
;n 6?
à2en 1àh T
b 2
.e20T
Using Eqs.(13)and (20),the semi-axes of the ellipse a and b can be expressed as functions of x 1,x 4and x 6by the fol-lowing expressions:
a 2
?2ex 1??????????m 00l p àh Tx 4??????????m 40l p ;b 2?2ex 1??????????m 00l p àh Tx 6??????????
m 04l p .e21TBased on this asperity model,the cross-sectional area per unit nominal area,called the bearing area A G is then A G es T?Z 1x 1?l
Z 1x 4?0
Z 1
x 6?0
p abp sum ex 1;x 4;x 6Td x 6d x 4d x 1;
e22T
where
l ?s ???l
p ;
s ?h ???????m 00
p .
e23T
The bearing area (or Abbott–Firestone bearing area)can be understood by imagining a straight smooth plane being brought slowly down towards the pro?le of the surface under https://www.sodocs.net/doc/ca15487468.html,ing Eqs.(21)and (22)the bearing area A G becomes
A G es T?l 2ea 1a 2T
1=4e2p T3=2
Z 1l Z 10Z 1
0ex 4x 6T1=2ex 1àl Texp eà1=2X Td x 6d x 4d x 1.e24TThe bearing area A B corresponding the Greenwood and Williamson [1]isotropic model is given by the integral
A B eh T?1????????????2p m 00p Z 1
h
exp àz
22m 00 d z .
e25T
The bearing area based on this asperity model can be compared with the true bearing area as a test of the validity of the
model for strongly anisotropic surfaces.In Fig.2the ratio A G /A B is plotted against s for various bandwidth parameters a 1and a 2taken from Eq.(11).For large separations as s !1the ratio A G /A B tends to 1.
5146R.Buczkowski,M.Kleiber /Comput.Methods Appl.Mech.Engrg.195(2006)5141–5161
The bearing area is a useful tool in characterising a large group of surfaces of some practical importance.Many technical surfaces employed in machine joints are not produced in a single operation but in a sequence of machining oper-ations.Such a sequence of operations superimposed on an earlier surface remove the higher parts of asperities of the ori-ginal process and produce a?ner texture leaving the deep valleys of the initial process untouched.It results in increasing the mean peak radius even more and reducing the plasticity index[1].Such processes are termed multiprocess or strati?ed surfaces(see Ref.[24])and their height distributions may contain useful information needed to categorise the surface multi?nish pro?les for quality control purposes.
The elastic deformation of the asperity causes the contact ellipse to be smaller than the geometric ellipse.If the contact ellipse has the semi-axes A and B then these are related to the semi-axes of the geometric ellipse a and b by the following equation[7]
A2 a2t
B2
b2
?1e26T
and
k2?b2
a2
?
kKàe1àk2Td K
d k
d K
;e27T
where a and b denote the semi-minor and the semi-major axes of the ellipse obtained from the intersection of the asperity (elliptical paraboloid)and a plane at height h,respectively making zero angles with the positive x-axis.K is the complete elliptic integral of the?rst kind
KeeT?
Z p=2
e1àe2sin2/Tà1=2d/e28Tof the argument e(eccentricity of the ellipse)de?ned as
e2?1àeB=AT2.e29TTo express A and B(B e1?B A ? ????????????? 1àe2 p e30T and using as in Bush et al.[7]the following small e1expansion for K KeeT?ln 4 e1 t e2 1 4 ln 4 e1 à e2 1 4 .e31T Eq.(27)becomes k2?e2 1ln 4 e1 à1 ! .e32 TR.Buczkowski,M.Kleiber/Comput.Methods Appl.Mech.Engrg.195(2006)5141–51615147 This relation between k and e 1can be inverted numerically (see [7])to yield the following approximate relation between them e 1? 0:4777k 1à1:3211k . e33T Thus,Eq.(24)can be rewritten in the form A ?a k ek 2te 21T 1=2 e34T and B ?a k e 1k 2te 21 à á1=2. e35TIn the following,we will use the complete elliptic integrals of the ?rst and second kind,K and E ,respectively,in the form of the polynomial approximations (see [44]) K ee T?a 0ta 1m 1ta 2m 21àátb 0tb 1m 1tb 2m 2 1àáln e1=m 1Tt em Te36Twith error j (m )j 63·10à5, a 0?1:3862944; b 0?0:5;a 1?0:1119723;b 1?0:1213478;a 2?0:0725296;b 2?0:0288729 e37T and E ee T?1ta 1m 1ta 2m 21àátb 1m 1tb 2m 2 1àáln e1=m 1Tt em Te38T with error j (m )j 64·10à5, a 1?0:4630151; b 1?0:2452727;a 2?0:10778112;b 2?0:0412496. e39T It must be noted that in the above equations the parameter m is de?ned as m ?e 2 e40Ttogether with the complementary parameter m 1de?ned by m tm 1?1. e41T (Other approximate formulas for elliptic integral of the ?rst and second kind are available in the papers of Brewe and Ham-rock [45],Dyson et al.[46],and Greenwood [47].) When the bodies are pressed together displacements will occur in both of them.Motivated by the fact that the normal displacements within the loaded region at any point in one body is inversely proportional to the plane-strain modulus E /(1àm 2)(for details we refer to Johnson [48])and using the theory of superposition it can be shown that the sum of elastic normal displacements will be proportional to the harmonic (in tribology literature called also e?ective or contact)elastic modulus E *de?ned by 1E ??1àm 21E 1t1àm 22 E 2 ;e42T where E 1,E 2,m 1and m 2are the elastic moduli and the Poisson ratios for both the contacting bodies,respectively.Therefore,if one of contacting surfaces is much more elastic than the other,E *is just the plane-strain modulus E /(1àm 2);if the mate-rials are the same,E *is one half of it.For the purposes of this analysis contact between two rough un?at surfaces is equiv-alent to contact between a single deformable rough surface while the second surface is considered to be a rigid and smooth ?at plane.Hence,the deformable body is described by the e?ective modulus E *and mean e?ective radius R m expressed as R m =(R 0+R 00)1/2,where R 0and R 00 are de?ned as the principal relative radii of curvature of each surface [48]. We introduce the mean e?ective radius of a single asperity of curvature R m (or mean summit curvature j m )as follows: 1=R m ?j m ? j n 4tn 6j 2 ;e43T 5148R.Buczkowski,M.Kleiber /Comput.Methods Appl.Mech.Engrg.195(2006)5141–5161 where n 4and n 6are the curvatures in the two orthogonal directions.In comparison with the usual assumption that the asperity deformation is localized mainly in the vicinity of the contact,an alternative,more realistic approach can be adopted in which the values of curvatures may change during the process of asperity https://www.sodocs.net/doc/ca15487468.html,ing Eqs.(20)and (21),the mean curvature j m can be expressed as functions of x 6and k from Eq.(32),so Eq.(30)becomes j m ?12 x 6?????????? l m 04p e1tk 2T. e44T From the theory of elasticity the following expressions may be written in terms of the approach x given by x ?en 1àh T e45T for the contact area A i and the load W i of the individual asperity [48]: A i ex T?E ee T K ee Te1àe 2T1=2 ! p R m x ?f 1ee Tp e1=j m Tx e46T and W i ex T? p E ee T 1=2 2K ee T3=2e1àe 2T1=2 ! 43E ?R 1=2m x 3=2?f 2ee T4 3 E ?e1=j m T1=2x 3=2;e47T where f 1(e )and f 2(e )are the deviations from the circular contact model and elliptic one for contact area and contact load, respectively,j m is the mean curvature calculated by Eq.(44).E (e )denotes the complete elliptic integral of the second kind of the argument e E ee T? Z p =2 e1àe 2sin 2/T1=2 d /;e48Twhich can b e approximated by Eq.(38).Plots o f the function f 1(e )and f 2(e )in Fig.3can be valuable to visualize the in?u-ence of eccentricity e on the contact area and the load in Eqs.(46)and (47),respectively.For circular model (A =B ), f 1(e )=f 2(e )=1,and Eqs.(46)and (47)give the Hertz expressions for isotropic elastic contact. If the surfaces come together until their reference planes are separated by the distance h ,then all asperities are in contact if height n 1exceeds the separation h .Thus,the probability of making contact at any summit of dimensionless height x 1?en 1=?????????? m 00l p Twith given non-dimensionalized curvatures x 4and x 6is P el T Prob ex 1>l T?Z 1l Z 10 Z 1 p sum ex 1;x 4;x 6Td x 6d x 4d x 1.e49T If there are N summits in all,the expected number of summits above a given height x 1can be calculated for the normalized separation,l ?h =?????????? m 00l p (see Eq.(23))as n el T?N Z 1l Z 10 Z 1 p sum ex 1;x 4;x 6Td x 6d x 4d x 1;e50T R.Buczkowski,M.Kleiber /Comput.Methods Appl.Mech.Engrg.195(2006)5141–51615149 where N denotes the total number of summits equal to N?D sum A0.e51THere,A0describes the nominal contact area while the density of summits D sum is determined by Eq.(17).The nominal contact area A0will be considered later as a part nominal area corresponding to an area of the zero-thickness contact?nite element used.For x=(n1àh)and A i(x)given in Eq.(46)the mean contact area is A eelT?p D sum A0 ?????????? m00l p Z1 l Z1 Z1 f1eeTex1àlTe1=j mTp sumex6;x4;x1Td x6d x4d x1.e52T Similarly,with the help of Eq.(47)we can?nd the expected(elastic)load as W eelT?4 3 D sum A0E?em00lT3=4 Z1 l Z1 Z1 f2eeTex1àlT3=2e1=j mT1=2p sumex6;x4;x1Td x6d x4d x1.e53T The integrals(52)and(53)have been evaluated numerically using Gauss Legendre50point quadrature formula for various separations and surface moments and the results are shown in Figs.4and5.(It is of interest to note that a larger number of integrating points have no in?uence on results.)Fig.5demonstrates the approximately linear relationship between non-dimensional load and total contact https://www.sodocs.net/doc/ca15487468.html,ing asymptotic methods as shown in Bush et al.[7]it is observed that for large separations s(isotropic surfaces)tending to in?nity,s!1,we have(W e/X A e)! 1. 5150R.Buczkowski,M.Kleiber/Comput.Methods Appl.Mech.Engrg.195(2006)5141–5161 For purely elastic contact the results of the contact area and nominal pressure for the strongly anisotropic model are compared with equivalent Greenwood–Willimson approximation for anisotropic case (for details we refer to Ref.[29]).The results obtained for various bandwidth parameters a are given in Tables 1and 2.In respect to the elastic contact area there is rather good agreement between the two models.The di?erence in the nominal pressure are signi?cant at lower val-ues of a while at higher values of a the equivalent GW model a?ords an encouraging good approximation.5.Elastic normal contact sti?ness The coe?cient of the normal sti?ness for two asperities can be obtained by di?erentiating Eq.(47)with respect to approach w k n i ?2f 2ee TE ?e1=j m T1=2x 1=2. e54T The normal elastic sti?ness for the joint is obtained by integrating Eq.(54)for all the summits in contact,thus K e n ?2D sum A 0E ? em 00l T 1=4Z 1l Z 10 Z 10 f 2ee Tex 1àl T1=2e1=j m T1=2p sum ex 6;x 4;x 1Td x 6d x 4d x 1.e55T The same result can be obtained using Leibnitz rule di?erentiating Eq.(53)directly with respect to the interference w as shown in Ref.[32].We note that for the spherical model f 2(e )=1and Eq.(55)gives the normal elastic sti?ness obtained for elastic contact of the isotropic surfaces [32]. Alternatively,from Eqs.(55)and (53)the elastic normal sti?ness per unit area can be found as the function of the normal load W e (l ).It is given by k e N ? 32W e el T A 0em 00l TF 1=2el TF 3=2el T ; e56T where the functions F 1/2(l )and F 3/2(l )are related by F m el T?Z 1l Z 10 Z 1 f 2ee Tex 1àl Tm e1=j m T1=2 p sum ex 6;x 4;x 1Td x 6d x 4d x 1 e57T with the probability density of summits p sum de?ned by Eq.(18)and m =1/2or m =3/2. Table 1 Comparison of the strongly anisotropic model at a =10and equivalent Greenwood–Williamson (GW)model for the anisotropic case h =m 1=2 00A e /A 0(%)W e /A 0(N/mm 2)GW Anisotropic GW Anisotropic 1.0 5.1497 6.122286.553493.38971.5 2.2210 2.542434.147036.59632.00.79080.867311.192211.90032.50.22860.2394 2.9972 3.16133.00.05290.05290.64700.67783.5 0.0097 0.0093 0.1114 0.1162 m 00=0.0625,m 20=8·10à5,m 02=8·10à4,m 40=1.04·10à6,m 04=1.04·10à4,E *=1.14·105N/mm 2. Table 2 Comparison of the strongly anisotropic model at a =3and equivalent Greenwood–Williamson (GW)model for the anisotropic case h =m 1=2 00A e /A 0(%)W e /A 0(N/mm 2)GW Anisotropic GW Anisotropic 2.0 1.05250.92802105.972877.812.50.31850.2589580.16796.573.00.07330.0570122.56175.173.50.01260.009919.47630.4354.00.001590.00135 2.2942 4.15684.5 0.000146 0.000143 0.1981 0.4397 m 00=3,m 20=1,m 02=81,m 40=1,m 04=6561,E *=1.14·105N/mm 2. R.Buczkowski,M.Kleiber /Comput.Methods Appl.Mech.Engrg.195(2006)5141–5161 5151 6.Plastic contact The total contact area consists of both the elastic and plastic parts.Therefore,critical interference x c has to be de?ned as a critical value at which an asperity deforms from elastic to plastic contact.The analysis of Pullen and Williamson[13] showed that volume beyond a critical value x c has to be preserved as the plastic deformation proceeds for x>x c.Based on plastic volume conservation,after Horng[15],it can be written that the plastic contact area is A p iexT?f3eeTpe1=j mTx2àx c x e2àf4eeTT h i ;e58Twhere f3eeT? EeeTe2 2e1àe2T1=2?EeeTàKeeTe1àe2T e59T and f4eeT?2?EeeTàe1àe2TKeeT KeeTe2 .e60T If asperities are spherical summits i.e.(a=b),f3(e)=1and f4(e)=1they produce the contact area A p i?pe1= j mTxe2àx c=xT,of the Chang et al.[14]elastic–plastic microcontact(CEB)model. Analytical results obtained by CEB model with the present3-D?nite element results(using commercial ABAQUS6.4 package)for the elasto-plastic frictionless contact of a deformable single spherical summit of radius R=2.448[mm]and a rigid?at can make an interesting comparison.The mesh consists of21894-node linear tetrahedral solid elements(C3D4) with9232nodes.Two?nite element models were considered.First,the material of the sphere was modelled as elasto-perfectly plastic while in the second,the material of the sphere was considered as elasto-plastic including linear isotropic with the strain-hardening modulus h of0.1E and large geometrical deformations.The dimensionless contact load obtained by Chang et al.[14]di?ers from present FE results.It overestimates?nite element results at small interferences(see also [21])and underestimates present results up to23%(without hardening)and29%(with hardening and large deformations) at x/x c=9,respectively.For the elastic–perfectly plastic the di?erence diminishes at large interferences down to6.5%at x/x c=47.For much more realistic assumptions regarding the hardening and large deformations the di?erence between CEB and FE models increases to46%at the same dimensionless interference.The corresponding?nite results vs.CEB model,for the elasto-perfectly plastic and the elasto-plastic with hardening models,at x/x c=47are W/W c=149.1and W/W c=205.4,respectively,where W c=88.684[N](see Ref.[21]for details).We note that the similar tendency has been recently observed by Kogut and Etsion[21]for the axisymmetric?nite element model. Considering FE results with the hardening and large deformations it is remarkable that with increasing load(or upset-ting of the sphere)the plastic zone(in the sense of the maximum of equivalent strains)moves from the center outwards as shown in Fig.6(a)–(d).Clearly the elastic–perfectly plastic model exhibits di?erent behaviour.As can be seen in Fig.7(a)–(d)the evolution of the plastic zone does not proceed from the center but spreads at the surface in the vicinity of the top of the sphere while the inner elastic core gradually shrinks and disappears completely at large interferences. It is known that the initial yielding occurs when the maximum contact pressure p m calculated as(cf.Eqs.(46)and(47)) p m ? 3 2 W e i A e i ? ??????????????????? KeeTEeeT p E? ????????? j m x pe61T reaches the value p m ?KY;e62Twhere Y is the yield strength and K represents the maximum contact yield coe?cient which is a function of Poisson’s ratio m only and can be linearly approximated[49]by K?1:282t1:158m.e63THence,from Eqs.(61)and(62)the critical value of interference x c=(n1àh)c which causes plastic deformation is x c?KeeTEeeT KY E? 21 j m .e64T Consequently from Eq.(58),the plastic load is W p iexT?f3eeTpe1=j mTx2àx c x e2àf4eeTT h i KY.e65T5152R.Buczkowski,M.Kleiber/Comput.Methods Appl.Mech.Engrg.195(2006)5141–5161 An empirical relation between the indentation hardness,H and the yield strength Y given by Tabor [50]is Y ?0:354H . e66T After Tabor,assuming m =0.3plastic ?ow will occur when the maximum Hertzian pressure p m between a ball and a plane reaches about p m =0.577H .However,for elliptical contacts the value for the ?rst yield in the material is not equal to 0.577H but is slightly dependent on the ratio (R y /R x ),where R x and R y are the principal relative radii of curvature in the x and y directions,respectively (for details refer to Wu and Zheng [51],Johnson [48],or Greenwood [47]).The plasticity index w was ?rst introduced by Greenwood and Williamson [1]to be de?ned by the equation w ?????????rj m p E ? H ;e67T where r is the standard deviation of summit heights about the summit mean plane.To express w in terms of the surface moments m ij the mean summit curvature j m and the standard deviation of summit heights r must be calculated in terms of the spectral moments.These were found in Bush et al.[7]as j m ?Z 1à1Z 10Z 1 0j n 4tn 6j 2p ex 1;x 4;x 6Td x 6d x 4d x 1????p 8r ???????m 04p t??????? m 40p eTe68Tand r 2 ?Z 1à1 Z 1 Z 1 en 1àd T2 p ex 1;x 4;x 6Td x 6d x 4d x 1?cm 00; e69T where c ?2àp 2 eb 1tb 2Tm 00 e70T R.Buczkowski,M.Kleiber /Comput.Methods Appl.Mech.Engrg.195(2006)5141–5161 5153 and d is the distance between the mean height of the summits and mean level of the surface(or mean surface plane)given as d? Z1 à1Z1 Z1 n1pex1;x4;x6Td x6d x4d x1? m00p 2 2 e ??? b p 1 t ??? b p 2 T.e71T Substituting for r and j m into Eq.(67),and removing the material constants E*and KY,the critical interference x? c expresse d in a non-dimensional form,becomes ex1àlT?x? c ? ????? 8c p KeeTEeeTe ???????m 04 p t ???????m 40 p T p3=2x6l ???????m 04 p e1tk2Tw2 .e72T In the elasto-plastic model the contact area and load of asperities are the sum of the elastic and plastic components.For x Therefore,after introducing the non-dimensional variables,the total contact area consists of the elastic and plastic parts AelT?A eelTtA pelTe73Twith the elastic area A eelT?p D sum A0 ?????????? m00l p Zeltx?cT l Z1 Z1 f1exTex1àlTe1=j mTp sumex6;x4;x1Td x6d x4d x1e74T and the plastic one A pelT?p D sum A0 ?????????? m00l p Z1 eltx?cT Z1 Z1 f3eeTe1=j mT2ex1àlTàx? c e2àf4eeTT ?? p sum ex6;x4;x1Td x6d x4d x1.e75T 5154R.Buczkowski,M.Kleiber/Comput.Methods Appl.Mech.Engrg.195(2006)5141–5161 Similarly,the total load can be split into W el T?W e el TtW p el T;e76T where W e el T?4 3D sum A 0E ?em 00l T3=4 Z el tx ?c T l Z 1 Z 1 f 2ee Tex 1àl T3=2e1=j m T1=2p sum ex 6;x 4;x 1Td x 6d x 4d x 1 e77T and W p el T?p D sum A 0?????????? m 00l p KY Z 1 el tx ?c T Z 1 Z 1 f 3ee T ?e1=j m T2ex 1àl Tàx ?c e2àf 4ee TT?? p sum ex 6;x 4;x 1Td x 6d x 4d x 1;e78T where the mean summit curvature of a single asperity j m is given by Eq.(44)and x ?c from Eq.(72)de?nes the critical inter-ference which can be now rewritten as x ?c ?c x 6;e79Twhere (cf.Eq.(72)) c ??????8c p K ee TE ee Te???????m 04p t???????m 40p Tp 3=2l ??????? m 04p e1tk Tw .e80T The variation of the plastic contact area A p /A and the dimensionless mean contact pressure W /AH with the plasticity index w are presented in Figs.8and 9.As can be seen from Fig.8at small values of w the ratio A p /A is very small even for the largest load.Only for small values of w the surface remains elastic.For w >1plastic ?ow will occur even at a very small load.At the high w value (w >2)the ratio A p /A approaches unity.Fig.9presents the dimensionless mean contact pressure W /AH as the function of the dimensionless load W /(HA 0)for various values of plasticity index w .The ratio W /AH rep-resents the real mean contact pressure W /A normalized by the indentation hardness H (see Eq.(66)).It is clear from Fig.9that for the greater value of w by given value of load (or separation)the degree of plastic deformation is dominant;that e?ect increases as the separation of surfaces becomes smaller (large separation means that there is little contact).At high values of w the normalized contact pressure W /AH approaches the value KH =0.577H which corresponds to the maxi-mum contact pressure at the inception of plastic deformation. Remark.Greenwood and Williamson [1]found that for most surfaces the mode of deformation is almost independent of load.It is elastic if the plasticity index is low and plastic if it is high.The idea that in general contact is elastic at low loads and becomes plastic as the load increases is not true.Sharp asperities would deform plastically even under lightest loads, R.Buczkowski,M.Kleiber /Comput.Methods Appl.Mech.Engrg.195(2006)5141–51615155 while blunt asperities would deform elastically even under heaviest loads.When w exceeds1plastic?ow will occur even at trivial nominal pressures and when w<0.6plastic contact can be caused only under very large nominal pressures.In the region0.6 From results given by Kogut and Etsion[52]it can be seen that at w=2only5%of asperities deform plastically and the yielded part of the real contact area A p/A is still very small even for the largest load.Their conclusion is di?erent from the one drawn by authors cited above and is also clearly contrary to the present results that for greater value of w the degree of plastic deformation is dominant.It should be noted,however,that in the present model the critical interference x? c from Eq.(72)and the limits of all integrals are the functions of the non-dimensional curvature(see Eqs.(13)and(20))de?ned by x6?2en1àhTb ?????????? m04l p; which changes systematically due to the deformation of asperities. 7.Elasto-plastic normal contact sti?ness The elastic normal sti?ness(Eq.(55))is valid as long as the plastic deformation of asperities is not considered;otherwise, the sti?ness of the elasto-plastic contact has to be calculated using Leibnitz rule di?erentiating of Eq.(76)directly with respect to the interference w as shown in Ref.[32].This di?erentiating is now more complicated because the derivation involves an integral with the interchange of the limits within the integral.We have for all the summits in contact K ep n ?2D sum A0E?em00lT1=4 Zeltx?cT l Z1 Z1 f2eeTex1àlT1=2e1=j mT1=2p sumex6;x4;x1Td x6d x4d x1 à 4 3 D sum A0E?em00lT1=4 Z1 Z1 f2eeTex1àlT1=2e1=j mT1=2p sumex6;x4;ltx? c Td x6d x4 t2p D sum A0KY Z l eltx?cT Z1 Z1 f3eeTe1=j mTp sumex6;x4;x1Td x6d x4d x1 tp D sum A0KY Z1 Z1 f3eeTf4eeTeltx? c Te1=j mTp sumex6;x4;ltx? c Td x6d x4.e81 T5156R.Buczkowski,M.Kleiber/Comput.Methods Appl.Mech.Engrg.195(2006)5141–5161 R.Buczkowski,M.Kleiber/Comput.Methods Appl.Mech.Engrg.195(2006)5141–51615157 The numerical results concerning the elastic(Eq.(56))and elasto-plastic(Eq.(81))sti?ness coe?cients are shown in Figs.10and11.Fig.10presents the dependence of the normal sti?ness coe?cients on the average pressure(the total load W per nominal area A0)for di?erent values of the variance of the surface height m00and the same value of the plasticity index w=1.For both the cases it can be seen that for higher values of m00which corresponds the higher roughness of the surface the contact sti?ness is smaller.A detectable di?erence between the elastic and elasto-plastic normal sti?ness for the high normal pressure is observed.In comparison to the elastic approach,the sti?ness curves obtained for the elasto-plastic model always underestimate them slightly which agrees with experimental observation.The decrease in the elasto-plastic sti?ness could be explained in terms of an increase in plastic deformation that has taken place.It was also found that the standard deviation of curvatures had no observable e?ects on the elastic normal sti?ness.It could be emphasized that the theoretical expressions for the normal contact sti?ness are in close agreement with those experimentally measured by Sho-ukry(see Ref.[53]). Fig.11presents the elasto-plastic normal sti?ness from Eq.(81)normalized by the hardness H vs.the dimensionless contact load W/HA0for various values of the plasticity index w and the same value of variance of the surface height m00.It can be seen from Fig.11that the sti?ness increases sharply with the load.Additionally,the contact sti?ness is prac-tically insensitive to the plasticity index w increasing slowly as the plasticity index w decreases.The similar tendency has been recently observed by Kogut and Etsion[52].The results of the present elasto-plastic model compare well with results load. of Kogut and Etsion model.There is only a slight di?erence between two models at very high contact 8.Numerical example 8.1.Prismatic beam on rigid base An elastic beam of rectangular cross-section of10·120mm and length of500mm lying with one of its longitudinal narrow faces against a?at rigid base(Fig.12)is chosen as numerical example. A total external load compressing the prism against the rigid base was applied at the prism mid-length and had the mag-nitude of1962N.The initial load was chosen as4.9N.The harmonic elastic modulus E*of1.127·105MPa(see Eq.(42)) that corresponds to the modulus of elasticity of the beam E1=1.057·105MPa and Poisson ratio of m1=0.25was taken. (If one of contacting surfaces is much more elastic than the other,therefore E??E1=e1àm2 1Tis just the plane-strain mod- ulus.)The numerical result is presented for a case in which the Young modulus of the foundation is105times larger than that of the beam;in e?ect,a rigid base is considered. Except for the contact zone the beam was discretized by20-noded hexahedral elements connected with the28-noded hexahedral transition elements(see Fig.13)in the neighbourhood of the contact zone.The contact zone is discretized by the32node cubic interface element of zero-thickness as shown in Fig.14.A complete description of both the special ?nite elements used is available in Ref.[54].Since the model is symmetric,suitable boundary constraints were imposed on nodes situated on the centre-line and only half of the structure is analysed.The contact constraints are introduced by the penalty technique combined with an active search strategy.For the incremental method employed the accuracy obtained depends upon the number of steps.This problem was analysed by using16load increments.For comparison results using the elastic and elasto-plastic normal contact sti?nesses are given in Table3.The maximum surface de?ections occur in the middle of the beam and these values strongly depend on the values of m00(see Fig.15;these results are given for elasto- 5158R.Buczkowski,M.Kleiber/Comput.Methods Appl.Mech.Engrg.195(2006)5141–5161 plastic model).There is no systematic di?erence between the results obtained by the elastic and elasto-plastic models.It was found that in the case without normal contact sti?ness some nodes at the outer edge of the beam were detected not be in contact (separation occurs).9.Conclusions 1.The results obtained in the paper demonstrate an approximately linear relationship between the elastic load W e and the contact area A e . 2.For low nominal pressure up to 12[MPa]the contact sti?ness is found to be almost proportional to the normal load.Both the elastic and elasto-plastic sti?ness coe?cients decrease with increasing variance of the surface height about the mean plane,m 00. 3.A detectable di?erence between the elastic and elasto-plastic normal sti?ness for the high normal pressure is observed.The elasto-plastic sti?ness increases slowly as the plasticity index w decreases. 4.The standard deviation of slopes and standard deviation of curvatures have no observable e?ects on the normal sti?ness. Table 3 Contact de?ection values at the central,u N max and at end of the beam,u N min The case u N max el m Tu N min el m T1.m 00=0.6250(elastic,[54])à4.030à2.9052.m 00=0.3125(elastic,[54])à2.946à1.8743.m 00=0.0625(elastic,[54])à1.425à0.4704.m 00=0.6250(elasto-plastic)à4.443à3.2975.m 00=0.3125(elasto-plastic)à3.149à2.0606. m 00=0.0625 (elasto-plastic) à1.557 à0.584 m 20=8·10à5,m 02=8·10à4,m 40=1.04·10à6,m 04=1.04·10à4,E *=1.14·105N/mm 2,Y =300N/mm 2,K =1.62,w = 1. R.Buczkowski,M.Kleiber /Comput.Methods Appl.Mech.Engrg.195(2006)5141–51615159 5.For engineering applications,the normal contact sti?ness of anisotropic rough surfaces for low nominal pressure can be estimated by the following formula: k N?3 2 W eelT A0em00lT1=2 . Acknowledgment Sponsorship of the work by the Polish State Committee for Scienti?c Research(KBN)under grant No.4T07C05326 to the Technical University of Szczecin is gratefully acknowledged. References [1]J.A.Greenwood,J.B.P.Williamson,Contact of nominally?at surfaces,Proc.R.Soc.(Lond.)A295(1966)300–319. [2]J.Whitehouse,J.F.Archard,The properties of random surfaces in contact,Proc.R.Soc.(Lond.)A316(1970)97–121. [3]P.B.Nayak,Random process model of rough surfaces,J.Lubricat.Technol.Trans.ASME93(1971)398–407. [4]P.B.Nayak,Some aspects of surface roughness measurement,Wear26(1973)165–174. [5]A.W.Bush,R.D.Gibson,T.R.Thomas,The elastic contact of a rough surfaces,Wear35(1975)87–111. [6]A.W.Bush,R.D.Gibson,G.P.Keogh,The limit of elastic deformation in the contact of rough surfaces,https://www.sodocs.net/doc/ca15487468.html,mun.3(1976)169–174. [7]A.W.Bush,R.D.Gibson,G.P.Keogh,Strongly anisotropic rough surfaces,J.Lubricat.Technol.Trans.ASME101(1979)15–20. [8]R.S.Sayles,T.R.Thomas,Surface topography as nonstationary random process,Nature271(1978)431–434. [9]D.J.Whitehouse,M.J.Phillips,Discrete properties of random surfaces,Phil.Trans.Roy.Soc.Lond.A290(1978)267–298. [10]D.J.Whitehouse,M.J.Phillips,Two-dimensional discrete properties of random surfaces,Phil.Trans.Roy.Soc.(Lond.)A305(1982)441–468. [11]D.J.Whitehouse,M.J.Phillips,Sampling in a two-dimensional plane,J.Phys.A:Math.Gen.18(1985)2465–2477. [12]J.A.Greenwood,A uni?ed theory of surface roughness,Proc.Roy.Soc.(Lond.)A393(1984)133–157. [13]J.Pullen,J.B.P.Williamson,On the plastic contact of rough surfaces,Proc.Roy.Soc.Lond.A327(1972)159–173. [14]W.R.Chang,I.Etsion,D.B.Bogy,An elastic plastic model for the contact of rough surfaces,J.Tribol.Trans.ASME109(1987)257–263. [15]J.H.Horng,An elliptic elastic–plastic asperity microcontact model for rough surfaces,J.Tribol.Trans.ASME120(1998)82–88. [16]M.S.Longuet-Higgins,The statistical analysis of a random,moving surface,Phil.Trans.R.Soc.Lond.A249(1957)321–387. [17]M.S.Longuet-Higgins,Statistical properties of an isotropic random surface,Phil.Trans.R.Soc.Lond.A250(1957)157–174. [18]H.So,D.C.Liu,An elastic–plastic model for the contact of anisotropic rough surfaces,Wear146(1991)201–218. [19]J.I.McCool,S.S.Gassel,The contact of two surfaces having anisotropic roughness geometry,ASLE Spl.Publicat.SP7(1981)29–38. [20]S.Kucharski,T.Klimczak,A.Polijaniuk,J.Kaczmarek,Finite elements model for the contact of rough surfaces,Wear177(1994)1–13. [21]L.Kogut,I.Etsion,Elastic–plastic contact analysis of a sphere and a rigid?at,J.Appl.Mech.Trans.ASME69(2002)657–662. [22]https://www.sodocs.net/doc/ca15487468.html,rsson,S.Biwa,B.Stora?kers,Inelastic?attening of rough surfaces,Mech.Mater.31(1999)29–41. [23]P.Wriggers,Finite element algorithms for contact problems,https://www.sodocs.net/doc/ca15487468.html,put.Methods Engrg.2(1995)1–49. [24]T.R.Thomas,Rough Surfaces,second ed.,Imperial College Press,London,1999. [25]B.Bhushan,Tribology and Mechanics of Magnetic Storage Devices,Springer,New York,1990. [26]B.Bhushan,Tribology of solid contacts in magnetic recording devices,Appl.Mech.Rev.ASME47(1994)199–203. [27]B.Bhushan,Contact mechanics of rough surfaces in tribology:multiple asperity contact,Tribol.Lett.4(1998)1–35. [28]D.J.Whitehouse,Handbook of Surface Metrology,Institute of Physics Publishing,Bristol,Philadelphia,1994. [29]J.I.McCool,Comparison of models for the contact of rough surfaces,Wear107(1986)37–60. [30]K.Willner,L.Gaul,Contact description by FEM based on interface physics,in:D.R.J.Owen,E.On?ate,E.Hinton(Eds.),Proc.4th Int.Conf. COMPLAS,Pineridge Press,Swansea,1997,pp.884–891. [31]G.Zavarise,B.A.Schre?er,Numerical analysis of microscopically elastic contact problems,in:M.Raous,M.Jean,J.J.Moreau(Eds.),Proc.2nd Int.Contact Mech.Int.Symp.,Plenum Press,New York,1995,pp.305–312. [32]R.Buczkowski,M.Kleiber,A stochastic model of rough surfaces for?nite element contact analysis,Comput.Methods Appl.Mech.Engrg.169 (1999)43–59. [33]N.Fardin,O.Stephansson,L.Jing,The scale dependence of rock joint surface roughness,Int.J.Rock Mech.Mining Sci.38(2001)659–669. [34]N.Fardin,Q.Feng,O.Stephansson,Application of a new in situ3D laser scanner to study the scale e?ect on the rock joint surface roughness,Int.J. Rock Mech.Mining Sci.41(2004)329–335. [35]D.J.Whitehouse,Fractal or?ction,Wear249(2001)345–353. [36]J.A.Greenwood,Comments on‘Fractal or?ction’by D.J.Whitehouse,Wear252(2002)842–843. [37]K.Komvopoulos,D.-H.Choi,Elastic?nite element analysis of multi-asperity contacts,J.Tribol.114(1992)823–831. [38]R.S.Sayles,T.R.Thomas,Thermal conductance of a rough elastic contact,Appl.Energy2(1976)249–267. [39]J.A.Greenwood,J.J.Wu,Surface roughness and contact:an apology,Meccanica36(2001)617–630. [40]J.Radziejewska,Determination of3D roughness parameters in contact problems,Adv.Manufact.Sci.Technol.29(2005)5–19. [41]A.Majumdar,B.Bhushan,Role of fractal geometry in roughness characterization and contact mechanics of surfaces,J.Tribol.Trans.ASME112 (1990)205–216. [42]R.S.Sayles,T.R.Thomas,Measurements of the statistical microgeometry of engineering surfaces,J.Lubricat.Technol.Trans.ASME101(1979) 409–418. [43]J.I.McCool,Characterization of surface anisotropy,Wear49(1978)19–31. [44]M.Abramowitz,I.A.Stegun,Handbook of Mathematical Functions with Formulas,Graphs,and Mathematical Tables,Dover Publications, New York,1972. 5160R.Buczkowski,M.Kleiber/Comput.Methods Appl.Mech.Engrg.195(2006)5141–5161 第四章 等效电路模型参数在线辨识 通过第三章函数拟合的方法可以确定钒电池等效电路模型中的参数，但是在实际运行过程中模型参数随着工作环境温度、充放电循环次数、SOC 等因素发生变化，根据离线试验数据计算得到的参数值估算电池SOC 可能会造成较大的估计误差。因此，在实际运行时，应对钒电池等效电路模型参数进行在线辨识，做出实时修正，提高基于模型估算SOC 的精度。 4.1 基于遗忘因子的最小二乘算法 参数辨识是根据被测系统的输入输出来，通过一定的算法，获得让模型输出值尽量接近系统实际输出值的模型参数估计值。根据能否实时辨识系统的模型参数，可以将常用的参数辨识方法分为离线和在线两类，离线辨识只能在数据采集完成后进行，不能对系统模型实时地在线调整参数，对于具有非线性特性的电池系统往往不能得到满意的辨识结果；在线辨识方法一般能够根据实时采集到的数据对系统模型进行辨识，在线调整系统模型参数。常用的辨识方法有最小二乘法、极大似然估计法和Kalman 滤波法等。因最小二乘法原理简明、收敛较快、容易理解和掌握、方便编程实现等特点，在进行电池模型参数辨识时采用了效果较好的含遗忘因子的递推最小二乘法。 4.1.1 批处理最小二乘法简介 假设被辨识的系统模型： 12121212()()()1n n n n b z b z b z y z G z u z a z a z a z ------+++==++++L L （4-1） 其相应的差分方程为： 1 1 ()()()n n i i i i y k a y k i b u k i ===--+-∑∑（4-2） 若考虑被辨识系统或观测信息中含有噪声，则被辨识模型式（4-2）可改写为： 1 1 ()()()()n n i i i i z k a y k i b u k i v k ===--+-+∑∑（4-3） 式中， ()z k 为系统输出量的第k 次观测值；()y k 为系统输出量的第k 次真值，()y k i -为系统输出量的第k i -次真值；()u k 为系统的第k 个输入值，()u k i -为 系统的第k i -个输入值；()v k 为均值为0的随机噪声。 沙盘模型制作的方法和材料 一、确定模型比例 一般来说，在着手制作沙盘模型之前，得首先确定沙盘模型制作的总体方针和比例。城市规划、住宅区域规划等大范围的沙盘模型，比例一般为1：3000—1：5000；房地产楼盘等建筑模型的比例常为1：200—1：50；住宅模型，这与其他建筑模型的情况稍有不同，如果建筑物不是很大，则采用1：50左右的比例，目的是为了让人看得清楚。比例确定后，先做出建筑用的场地模型，模型的制作者必须清楚地形高差，景观印象等，通过大脑进行计划立意处理，多作研究分析，就可以开始着手制作模型了。 二、制作模型底座 比例确定之后，就可开始做模型了，大峡谷集团习惯先做模型底座与基地。如果建筑场地是平坦的，则制作模型也简单易行。若场地高低 不平，且表现要求上也有周围邻近的建筑物，则依测量方法的不同，模型的制作方法也有相应的区别。尤其是针对复杂地形和城市规划等大场地时，常常是先将地形模型事先做成，一边看着模型一边进行方案设计的情况较多，因而必须在地形模型的制作上多下些功夫，但也不需把地形做的过细。 三、用卡纸做模型 卡纸是最常用模型材料，你可以根据你的需要选择不同的卡纸，如：白卡，灰卡，色卡。 四、用木板做模型 灵活运用轻木料木材所具有的柔软而粗糙的才质质感及加工方便的 特点，可以做出各种不同的表现效果来。切割薄而细的软木材坂料时，要尽可能使用薄形刀具，细小的软木在切割时，应使用安全刀片的刃 口精心切下，切割范围很小时，应在木材下面帖上一层赛路硌透明纸带，这样可以增加其强度，是切割不受影响。我建议大家选用 0.7--2mm的航模木板。不过要注意的是垂直于木纹切割时不要太用力，否则很容易切坏。 五、用泡沫苯乙烯纸做模型 这种材料最适合做一些草模和研究模型，非常便于加工。 六、用有机玻璃做模型 由于这种材料很难切割，要用专门的刀才能切开，这种材料由于很透明，通常用来做外表面，可以看到内部空间。也可用来做一些研究性模型。 七、用塑料板做模型 这种材料模型公司用的多，非常正式的模型才会用，加工起来很麻烦。沙盘模型制作的材料可以是五花八门，各种环保型材料，可回收材料应有尽有。 浅析电力系统模型参数辨识 （贵哥提供） 一、现状分析 随着我国电力事业的迅猛发展, 超高压输电线路和大容量机组的相继投入, 对电力系统稳定计算、以及其安全性、经济性和电能质量提出了更高的要求。现代控制理论、计算机技术、现代应用数学等新理论、新方法在电力系统的应用，正在促使电力工业这一传统产业迅速走向高科技化。 我国大区域电网的互联使网络结构更复杂，对电力系统安全稳定分析提出了更高的要求，在线、实时、精确的辨识电力系统模型参数变得更加紧迫。由于电力系统模型的基础性、重要性，国外早在上世纪三十年代就开始了这方面的分析研究，[1,2]国内外的电力工作者在模型参数辨识方面做了大量的研究工作。[3]随后IEEE相继公布了有关四大参数的数学模型。1990年全国电网会议上的调查确定了模型参数的地位，促进了模型参数辨识的进一步发展，并提出了研究发电机、励磁、调速系统、负荷等元件的动态特性和理论模型，以及元件在极端运行环境下的动态特性和参数辨识的要求。但传统的测量手段，限制了在线实时辨识方法的实现。 同步相量测量技术的出现和WAMS系统的研究与应用，使实现在线实时的电力系统模型参数辨识成为可能。同步相量是以标准时间信号GPS作为同步的基准，通过对采样数据计算而得的相量。相量测量装置是进行同步相量测量和输出以及动态记录的装置。PMU的核心特征包括基于标准时钟信号的同步相量测量、失去标准时钟信号的授时能力、PMU与主站之间能够实时通信并遵循有关通信协议。 自1988年Virginia Tech研制出首个PMU装置以来，[4]PMU技术取得了长足发展，并在国内外得到了广泛应用。截至2006年底，在我国范围内，已有300多台P MU装置投入运行，并且可预计，在不久的将来PMU装置会遍布电力系统的各个主要电厂和变电站。这为基于PMU的各种应用提供了良好的条件。 二、系统辨识的概念 系统模型是实际系统本质的简化描述。[5]模型可分为物理模型和数学模型两大类。物理模型是根据相似原理构成的一种物理模拟，通过模型试验来研究系统的 模型制作资料 1、模型分类：方案模型（形式表现要求不高）和展示模型（材料及制作深度高的成品） 2、：测绘：三棱尺、直尺、三角板、弯尺、圆规、游标卡尺、模板、蛇尺剪裁：勾刀、手术刀、推拉刀、45°切刀、切圆刀、剪刀、手锯、钢锯、电动手锯、电动曲线锯、带锯、电热切割器、优耐美模型机组、电脑雕刻机。打磨喷绘：砂纸、砂纸机、锉刀、什锦锉、木工刨、小型台式砂轮机、喷枪。热加工：塑料板亚克力弯板机、火焰抛光机。 3、：主材：泡沫聚苯乙烯板、有机玻璃板、塑料板、ABS板PVC板（abspvc 电脑加工）、木材版（轻木软木微薄木）辅材：金属材料：单面金属板、双色板、确玲珑、纸粘土、油泥、石膏、即时贴、植绒即时贴、仿真草皮、绿地粉、泡沫塑料、水面胶=A、B 水、软陶、石蜡、型材-基本、仿真成品。 胶黏剂：纸类：白乳胶、胶水、喷胶、双面胶带。 塑料类胶黏剂：三氯甲烷、502胶黏剂、建筑胶、热熔胶、hart 胶、Araldite 胶、无影胶。 木材类胶黏剂：乳胶、4115建筑胶、hart 胶。面层喷色材料：自喷漆、醇酸调和漆、硝基磁漆、聚酯漆、模型专用漆、丙烯颜料。 4、环艺模型制作设计：主题制作设计：总体与局部、效果表现、材料选择、模型色彩。基本介绍 建筑模型（architectural model）是建筑设计及都市规划方案中，不可缺少的审查项目。建筑及环境艺术模型介于平面图纸与实际立体空间之间，它把两者有机的联系在一起，是一种三维的立体模式，建筑模型有助于设计创作的推敲，可以直观地体现设计意图，弥补图纸在表现上的局限性（见建筑制图）。它既是设计师设计过程的一部分，同时也属于设计的一种表现形式，被广泛应用于城市建设、房地产开发、商品房销售、设计投标与招商合作等方面。 基本特征使用易于加工的材料依照建筑设计图样或设计构想，按缩小的比例制成的样品。建筑模型是在建筑设计中用以表现建筑物或建筑群的面貌和空间关系的一种手段。对于技术先进、功能复杂、艺术造型富于变化的现代建筑，尤其需要用模型进行设计创作。 在初步设计即方案设计阶段的称工作模型，制作可简略些，以便加工和拆卸。材料可用油泥、硬纸板和塑料等。在完成初步设计后，可以制作较精致的模型——展示模型（见图），供审定设计方案之用。展示模型不仅要求表现建筑物接近真实的比例、造型、色彩、质感和规划的环境，还可揭示重点建筑房间的内部空间、室内陈设和结构、构造等。展示模型一般用木板、胶合板、塑料板、有机玻璃和金属薄板等材料制成。模型的制作务求达到表现设计创作的立意和构思。 主要分类 黏土模型 黏土材料来源广泛取材方便价格低廉经过“洗泥” 工序和“炼熟过程其质地更加细腻。黏土具有一定的粘合性可塑性极强在塑造过程中可以反复修改任意调整修刮填，补比较方便。还可以重复使用是一种比较理想的造型材料,但是如果黏土中的水分失去过多则容易使黏土模型出现收缩龟裂甚至产生断裂现象不利于长期保存。另外，在黏土模型表面上进行效果处理的方法也不是很多, 黏土制作模型时一定要选用含沙量少，在使用前要反复加工，把泥和熟，使用起来才方便。一般作为雕塑、翻模用泥使用。[1] 油泥模型油泥是一种人造材料。凝固后极软，较软，坚硬。油泥可塑性强，黏性、韧性比 基于最小二乘模型的Bayes 参数辨识方法 王晓侃1，冯冬青2 1 郑州大学电气工程学院，郑州（450001） 2 郑州大学信息控制研究所，郑州（450001） E-mail ：wxkbbg@https://www.sodocs.net/doc/ca15487468.html, 摘 要：从辨识定义出发,首先介绍了Bayes 基本原理及其两种常用的方法,接着重点介绍了基于最小二乘模型的Bayes 参数辨识,最后以实例用MATLAB 进行仿真,得出理想的辨识结果。 关键词:辨识定义；Bayes 基本原理；Bayes 参数辨识 中国图书分类号：TP273+.1 文献标识码：A 0 概述 系统辨识是建模的一种方法。不同的学科领域，对应着不同的数学模型，从某种意义上讲，不同学科的发展过程就是建立它的数学模型的过程。建立数学模型有两种方法:即解析法和系统辨识。L. A. Zadehll 于1962年曾对”辨识”给出定义[1]:系统辨识是在对输入和输出观测的基础上，在指定的一类系统中，确定一个与被识别的系统等价的系统。一般系统输出y(n)通常用系统过去输出y(n-m)和现在输入u(n)及过去输入u(n-m)的函数描述 y(n)=f(y(n-1),y(n-2)，...，y(n-m y ), u(n),u(n-1),... ,u(n-m u ))=f(x(n),n) x(n)=[y(n-1),y(n-2),...y(n-m y ), u(n),u(n-1),...,u(n-m u )]’ 这里f(,)为未知函数关系，一般情况为泛函数，可以是线性函数或非线性函数，分别对应于线性或非线性系统，通常这个函数未知，但是局部输入输出数据可以测出，系统辨识的任务就是根据这部分信息寻找确定函数或确定系统来逼近这个未知函数。但实际上我们不可能找到一个与实际系统完全等价的模型。从实用的角度来看，系统辨识就是从一组模型中选择一个模型，按照某种准则，使之能最好地拟合由系统的输入输出观测数据体现出的实际系统的动态或静态特性。接下来本文就以最小二乘法为基础的Bayes 辨识方法为例进行分析介绍并加以仿真[4]。 1 Bayes 基本原理 Bayes 辨识方法的基本思想是把所要估计的参数看做随机变量,然后设法通过观测与该参数有关联的其他变量,以此来推断这个参数。 设μ是描述某一动态系统的模型，θ是模型μ的参数，它会反映在该动态系统的输入输出观测值中。如果系统的输出变量z(k)在参数θ及其历史纪录(1) k D ?条件下的概率密度函 数是已知的，记作p(z(k)｜θ，(1) k D ?)，其中(1) k D ?表示（k-1）时刻以前的输入输出数据集 合，那么根据Bayes 的观点参数θ的估计问题可以看成是把参数θ当作具有某种先验概率密 度p （θ，(1) k D ?）的随机变量，如果输入u(k)是确定的变量，则利用Bayes 公式，把参数θ 的后验概率密度函数表示成[2] p (θ，k D ）= p (θ｜z (k ),u(k ), (1) k D ?)=p (θ｜z (k ),(1) k D ?) = (k-1) (k-1) p(z(k)/,D )p(/D ) (k-1)(k-1)p(z(k)/,D )p(/D )d θθθθθ∞∫?∞ (1) 在式(1)中,参数θ的先验概率密度函数p(θ｜(1) k D ?)及数据的条件概率密度函数p(z(k)｜θ， 模型制作资料 一、 模型制作材料、工具及其使用 1、主材类 2、纸质材料 3、打印纸 4、绘图（卡）纸-----制作卡纸模型采用白色卡纸。如果需要其他颜色，可在白色卡纸上进行有色处理。卡纸模型还可以采用不干胶色纸和各种装饰纸来装饰表面，采用其他材料装饰屋顶和道路。 5、厚纸板-----厚纸板是以其颜色与白色的卡纸做区分，有灰色和 棕色制模用的厚纸板------它有一个由泡沫塑料制成的坚固核心，而此核心的两边是用纸张覆盖(粘合)的。 6、瓦楞纸-----波浪纹是用平滑的纸张粘合在一面或是两面上的， 因为具备可卷曲的特性。瓦楞纸的波浪越小、越细，就越坚。 各色不干胶：用于建筑模型的窗、道路、建筑小品、房屋的立面和台面等处的贴饰。 吹塑纸：适宜制作构思模型和规划模型等，它具有价格低廉、易加工、色彩柔和等特点。 仿真材料纸：仿石材、木纹和各种墙面、屋顶的半成品纸张。 各色涤纶纸：用于建筑模型的窗、环境中的水池、河流等仿真装饰。 锡箔纸：用于建筑模型中的仿金属构件等的装饰。 砂纸：砂纸是用来打磨材料，可做室内的地毯和球场、路面、绿地。 二、 木质材料 1．木工板 （木工用平板 细木工板） 2．胶合板-----胶合板是用三层或奇数多层刨制或旋切的单板，涂胶后经热压而成的人造板材，各单板之间的纤维方向互相垂直(或成一定角度)、对称，克服了木材的各向异性缺陷。 3．硬木板(密度板、刨花板)----- 硬木板是利用木材加工废料加工成一定规格的碎木，刨花后再使用胶合剂经热压而成的板材。 4．软木板-----软木板是由混合着合成树脂胶粘接剂的木质颗粒组合而成的。 5．航模板----- 航模板是采用密度不大的木头(主要是泡桐木)经过化学处理而制成的板材。 6．其他人造装饰板-----仿金属、仿塑料、仿织物和仿石材等效果的板材，各种用于裱糊的装饰木皮等。 三、塑料板材 1.ABS 板：ABS 板是一种新型的模型制作材料，称之为工程塑料,ABS 板是现今流行的手工及电脑雕刻加工制作的主要材料。 2.PVC 板：主要成分为聚氯乙烯分为软PVC 板(柔软耐寒，耐磨，耐酸、碱)和硬PVC(易弯曲、 上海交通大学 硕士学位论文 Bouc-Wen滞回模型的参数辨识及其在电梯振动建模中的应用 姓名：周传勇 申请学位级别：硕士 专业：机械设计及理论 指导教师：李鸿光 20080201 Bouc-Wen滞回模型的参数辨识 及其在电梯振动建模中的应用 摘 要 电梯导靴是连接轿箱系统与导轨的装置，它能起到导向和隔振减振的作用。同时，在电梯的运行过程中它又将导轨由于制造或安装所造成的表面不平顺度传递给轿箱系统，从而引起轿箱系统的水平振动。国内外学者在电梯水平振动的建模和分析中，往往把导靴视为线性弹簧-阻尼元件来建模而忽略了非线性因素。事实上导靴与导轨之间存在非线性的迟滞摩擦力，本文通过实验的方法，采用Bouc-Wen 滞回模型来建立导靴-导轨非线性摩擦力模型。 Bouc-Wen滞回模型因其微分形式的非线性表达式而使得其参数辨识存在较大的困难，本文利用模型中部分参数的不敏感性，通过数学变换将非线性参数辨识问题转化为线性参数辨识问题，从而使得问题大大简化，参数辨识的效果也能满足要求。 基于以上导靴-导轨间摩擦力模型，本文进而建立了轿箱-导轨耦合水平振动动力学模型，该模型将轿箱系统等效为2自由度的平面运动刚体，将导靴等效为质量-弹簧-阻尼单元，同时考虑了导靴-导轨间的非线性摩擦力，以及导靴靴衬与导轨间接触的不连续性等。 在建立了轿箱-导轨耦合水平振动动力学模型后，利用Matlab/Simulink，建立了相应的仿真模型，开展了几种典型导轨不 平顺度激励（弯曲、失调和台阶）下的仿真分析。研究结果表明，这些分析对于电梯结构优化设计和动力学建模与分析有理论指导意义。 关键词：迟滞，参数辨识，非线性，动力学建模，系统仿真 模型制作资料收集 一、制作工具 一．常用刀具 1.常用美工刀又称为墙纸刀，主要用于切割纸板、卡纸、吹塑纸、软木板、即时贴等较厚的材料。 2.美工钩刀切割有机玻璃、亚克力板、胶片和防火胶版的主要工具。 （美工刀） 3.手术刀 主要用于各种薄纸的切割与划线，尤其是建筑门窗的切、划。 (手术刀） 4单、双面刀片 单、双面刀片的刀片最薄，极为锋利，用于切割薄型材料 5.木刻刀 用于刻或切割薄型的塑料板材。 6.剪刀 用于裁剪纸张、双面胶带、薄型胶片和金属片的工具。根据用途通常需要几把不同型号。 7.微型机床、切割机 7.微型机床、切割机 相比手工切割，使用小型或者微型机床进行切割能够更好地提升工作效率，同时，使用高精度的锯片，能够使切割面更加整齐、平整。微型切割机搭配不同的锯片，能够用于切割比较厚、硬的板材。 二．常用度量工具 1.T形尺 用于测量尺寸，同时辅助切割。 2.三角板、圆规、量角器等 用于测量平行线、平面、直角，画圆、曲线等。 3.钢角直尺 画垂直线、平行线与直角，也用于判断两个平面是否相互垂直，辅助切割。 4.卷尺 用于测量较长的材料。 4.卷尺 用于测量较长的材料。 三.修整工具 1.砂纸 用于研磨金属、木材等表面，以使其光洁平滑。根据不同的研磨物质，有干磨砂纸、耐水砂纸等多种。干磨砂纸（木砂纸）用于磨光木、竹器表面。耐水砂纸用于在水中或油中磨光金属表面。 (砂纸） 锉 用于修平和打磨有机玻璃和木材，分为木锉和钢锉，木锉主要用于木料加工，钢锉用于金属材料与有机玻璃加工。按锉的形状与用途，可分为方锉，半圆锉，圆锉，三角锉，扁锉，真挫，可视工作的形状选用。 按锉的锉齿分为粗锉，中粗锉，细锉。锉的使用方法有横锉法，直锉法和磨光搓法。 其他工具 各种铅笔 用于做记号，在卡纸材料上通常用较硬的铅笔 镊子 制作细小构件时需要镊子来辅助工具 3，鸭嘴笔，勾线笔 画墨线的工具 4，清洁工具 模型制作过程中模型上会落有很多毛屑和灰尘，还会残留一些碎屑，可以用板刷，清洁用吹气球来清洁处理。 其他工具 一般最常用的五金工具，如老虎钳，小型锤、精密钢锯，卷尺，尖嘴钳等，在不同的材质制作模型中会需要用到。 纸质材料 按模型的使用特征分类，通常分为建筑结构和框材料，建筑表面和装饰材料，环境装饰材料和底盘材料。 制作建筑模型的材料 Company number：【0089WT-8898YT-W8CCB-BUUT-202108】 建筑模型设计制作员：把“大家伙”变成工艺品职业定义 建筑模型设计制作员指的是能根据建筑设计图和比例要求、选用合适的模型制作材料，运用模型设计制作技能，设计制作出能体现建筑师设计思想的各种直观建筑模型的专业模型制作人员。 从事的主要工作包括 (1)读懂建筑图，理解建筑师设计思想及设计意图；(2)模型材料的选用及加工；(3)计算模型缩放比例；(4)制定模型制 作工艺流程；(5)制作模型。 职业概况 我国目前建筑模型设计制作业从业人员有120万多人，其中从事实物建筑模型(非计算机模拟模型)的专业制作人员占20%以上，按此计：建筑模型制作员从业人数可达24万。从业人员主要分布情况大致如下：70%的建筑模型制作员就业于模型制作公司；15%左右就职于各类展台布置装潢公司；10%开设独立的建筑模型设计制作工作室；5%分布在各大设计院、设计公司、设计师事务所。 目前的建筑模型设计制作员从业人员素质情况如下：水平参差不齐，很多从业人员都是半路出家，没有经过系统的学习与培训，靠师傅带和自己琢磨成才。有些模型制作人员无法读懂建筑设计图，使制作出来的建筑模型与要求相差太远。建筑模型设计制作不需要很大的场地，对人员的文化水平、年龄、性别等条件相对限制不是很多，没有各类污染，是花费少投入多的都市产业，对促进就业、发展社会经济作用很大。规范本职业的意义在于：提高本行业从业人员的素质、对衡量建筑模型库制作从业人者从业资格和能力提供依据；促进就业；加强建筑模型制作员这一新职业的科学化、规范化和现代化管理，从而从根本上提高从业人员整体素质。 目前本职业在劳动分工中主要有以下岗位：建筑模型设计公司模型制作工、展台布置装潢公司模型制作工、房产公司模型制作工等。 目前国内院校与本职业相关的专业设置没有。但在国内院校的建筑系有相关劳技课程，课时不多。 建筑模型设计制作员在国外的职业状况和我国相近，从业人员比我国少很多，制作水平更专业化。 蔬菜主要病虫害种类 十字花科蔬菜病虫：主要有小菜蛾、菜青虫、黄曲条跳甲、斜纹夜蛾、甜菜夜蛾、蚜虫、菜螟、软腐病、黑腐病、菌核病、霜霉病、炭疽病、白锈病等。 豆科蔬菜病虫：主要有豆荚螟、豆蚜、斜纹夜蛾、豆芫菁、斑潜蝇、烟粉虱、朱砂叶螨、白粉病、炭疽病、枯萎病、锈病、轮纹病、病毒病等。 葫芦科蔬菜病虫：主要有黄守瓜、芫菁、瓜娟螟、蚜虫、蓟马、斑潜蝇、烟粉虱、灰霉病、疫病、霜霉病、白粉病、炭疽病、黑斑病、叶斑病、蔓枯病、枯萎病、细菌性角斑病、病毒病等。 茄科蔬菜病虫：主要有蓟马、棉铃虫、二十八星瓢虫、茶黄螨、青枯病、早疫病、晚疫病、褐纹病、炭疽病、白粉病、灰霉病、根结线虫病等。 葱蒜类蔬菜病虫：主要有蓟马、潜叶蝇、斜纹夜蛾、甜菜夜蛾、灰霉病、疫病、霜霉病等。 蔬菜主要病虫害种类及适用农药品种 乐斯本基立甲霜灵百菌清农药杂谈分类：农业 病虫种类： 1、苗期病害（猝倒病、立枯病）发生作物：叶菜类、瓜类、茄果类苗期。适用农药：恶习霉灵、甲基立枯磷、苗菌净、多氧霉素、甲霜灵锰锌。 2、霜霉病类发生作物：瓜类、葱类、叶菜类。适用农药：甲霜灵锰锌、百菌清、氰霜唑、杀毒矾、克露、氟吗锰锌、疫霜灵。 3、疫病类型发生作物：瓜类、葱类、叶菜类。适用农药：甲霜灵锰锌、百菌清、氰霜唑、杀毒矾、克露、氟吗锰锌、疫霜灵。 4、早疫病类发生作物：辣（甜）椒、黄瓜、葱、芋等。适用农药：代森锰锌、可杀得、百菌清、甲霜灵锰锌、杀毒矾、异菌。 5、晚疫病类发生作物：番茄、马铃薯。适用农药：甲霜灵锰锌、氟吗锰锌、氰霜唑、金雷多米尔、克露、蓝保、可杀得。 6、炭疽病类发生作物：甜（辣）椒、白菜、黄瓜、菜豆。适用农药：炭特 模型制作大全 INDEX 上手快速索引：关键词按拼音首字母的顺序排列，基础篇涵盖素组所需的大部分技术。 B 补土/无缝 D 打磨 G 工具勾线 K 刻线 Q 去色 S 渗线砂纸术语水口素组 T 贴纸 X 消光/光油 B 关键词：补土/无缝 Q：什么叫补土啊? A：分3种： 1）牙膏补土：补缝,填小气泡 2）宝丽补土/AB土：都可以用来塑型,填较大的洞等 3）水补土：上色前喷可以统一底色,检查无缝是否完美,也能补一些很小的气泡 Q：我的补土不是挤牙膏一样的：上面有两条，一条白色一条淡土黄色，说明书上指示使用的时候要把两种混合在一起。 A：AB土，用来塑型和填大窟窿用的，用的时候就将同样长度的两条剪下，捏，充分混合后填到洞里，或者捏想要的形状，等完全硬化后再修。如果要做无缝的话还是得用那种牙膏包装的补土。 Q：AB补土使用时，把两块补土捏在一起，之后要捏到什么程度呢？颜色完全统一？A：当然是捏到匀了。 Q：AB补土是不是直接粘在零件上造型并完全干透后就把能自行粘合在零件上还是要另加接合剂？ A：自己会粘住的。 Q：组好以后零件之件的细缝只能用补土来填吗?用502的话会不会对塑料造成伤害呢?素组的是不是不用填缝呀?还是填了缝后一定要上色呢? A:无缝作业的话胶水和补土都需要，模型胶和502都可以用。做了无缝后还是上色好些，打磨会影响模型表面的。素组的概念因人而异，但如果做了无缝，不上色的话，会很难看的还有就是用502的话，要注意不要按的太死，不然会把塑料溶掉的。 Q：在用田宫补土补缝的时候发现田宫的补土刚放到模型上不久就干掉了，有什么办法可以让补土不用那么快干呢？ A：可以用田宫溶剂稀释。但要注意：牙膏补土越稀释，干时的收缩就越明显。 Q：请问做无缝除了用补土还有什么办法?用胶水又怎么做?等胶水干又要多久? A：以下的网址里的5至11楼有教用胶水做无缝： https://www.sodocs.net/doc/ca15487468.html,/forum/index.php?showtopic=10462也可参见：https://www.sodocs.net/doc/ca15487468.html,/viewthrea ... 1%26filter50Ddigest Q：请问在上补土（做无缝的）之后处理比较圆的地方时有什么秘诀吗？还有！上补土时有什么要注意的？ A：弧面的地方要慢慢磨，小心不要将弧面磨平即可。上补土的话我比较喜欢先用溶剂湿润一下补土后再上。 Q：拿什么来稀释这些“补土”呢？ A：牙膏补土的话，可以用郡士的溶剂来稀释，或者田宫的Lacquer溶剂（黄色盖，水油通吃，也可用于除去漆膜）。 Q：罐装水补土HOBBY分几种？ A：有灰的和白的两种颜色，有500，1000，1200等号数，号数越高粒子越细。 Q：水补土能用笔涂吗? A：效果会不均匀。如果做铸造感的特殊效果的话，可以用水补土干扫。 Q：500号和1000号的水补土有什么不一样？ A：参见上面。水补的编号和砂纸的编号都是细腻度的意思。越大越细腻。 Q：如果不上补土直接上油性漆的话会有什么不好的后果？ A：不上补土当然也可以上色，当然油性漆要经过稀释，只是附着力不会很好就是了。油性漆比水性的腐蚀性要大（指的是稀释液），如果不喷补土可能（有可能）塑料会变脆，尤其是透明件。 Q：罐装水补土要注意什么？ A：可以参看进阶篇喷罐相关。简单的说，就是距离30cm左右，快一点来回碰，少量多次的原则。 Q：不喷漆想要做到无水口、无缝还需要什么工具？ A：不涂装，做无缝比较难些，因为总是要打磨的，一打磨塑料表面就花了，基本不可能做到无痕迹。白色零件上可以尝试，痕迹不会很明显。模型胶水，砂纸必须。 D 关键词：打磨 Q：问下打磨高达用的砂纸除了田宫的还有别的种类吗？ A：高目的砂纸就别省这个钱了。田宫的砂纸的确非常好用。（还可以用3M的砂纸，很好用）粗目的用五金砂纸也行，几毛钱一张。不过不耐用。美国3M打磨布，很好用，贵。 参数辨识 参数辨识的步骤 飞行器气动参数辨识是一个系统工程，包括四部分：①试验设计，使试验能为辨识提供含有足够信息量且信息分布均匀的试验数据；②气动模型结果确定，即从候选模型集中，根据一定的准则和经验，选出最优的气动模型构式；③气动参数辨识，根据辨识准则和数据求取模型中待定参数，这是气动辨识定量研究的核心阶段；④模型检验，确认所得气动模型是否确实反映了飞行器动力学系统中气动力的本质属性。这四个部分环环相扣，缺一不可，要反复进行，直到对所得气动模型满意为止。 参数辨识的方法 参数辨识方法主要有最小二乘算法、极大似然法、集员辨识法、贝叶斯法、岭估计法、超椭球法和鲁棒辨识法等多种辨识方法。虽然目前参数辨识的领域己经发展了多种算法，但是用于气动参数估计的算法主要有：极大似然法(ML)，广义Kalman滤波(EKF)法，模型估计法(EBM )、分割及多分割算法(PIA及MPIA)、最小二乘法，微分动态规划法等。 因为最小二乘法和极大似然法是两种经典的算法，目前己经发展得相当成熟。最小二乘法适于线性模型的参数辨识，可以用于飞行器系统辨识中很多的线性模型，如惯性仪表误差系数的辨识，线性时变离散系统初始状态的辨识及多项式曲线拟合等。目前最小二乘法已经广泛应用于工程实际中。而极大似然算法因其具有渐进一致性、估计的无偏性、良好的收敛特性等特点而被广泛应用于飞行器参数辨识领域。 最小二乘法大约是1975年高斯在其著名的星体运动轨道预报研究工作中提出来的。后来，最小二乘法就成了估计理论的奠基石。由于最小二乘法原理简单，编程容易，所以它颇受人们重视，应用相当广泛。 极大似然估计算法在实践中不断地被加以改进，这种改进主要表现在三个方 Bouc-Wen模型因数字处理方便简单而得到较为广泛的应用，力可以表示为： 利用遗传算法工具箱（GA）对Bouc-Wen模型进行参数识别。 实验数据来源于对磁流变阻尼器（MR damper）进行性能测试，试验获得的数据包括力F，位移x，采用频率已知，速度和加速度可以由位移求导得出。 参数识别出现程序如下：（文件名：Copy_0_of_BoucWen） function j=myfung(x) y0=[0]; yy=y0; tspan=[]'; s=[]'; v=[]'; Ft=[]'; rr=max(size(s));%计算数据个数 i=1; while (i 模型手工制作工具及主要材料 ?常用刀具 1?常用美工刀 又称为墙纸刀，主要用于切割纸板、卡纸、吹塑纸、软木板、即时贴等较厚的材料。2?美工钩刀 切割有机玻璃、亚克力板、胶片和防火胶版的主要工具。 美工刀美工钩刀 3?手术 刀 单、双面刀片的刀片最薄，极为锋利，用于切割薄型材料。 5?木刻 刀 用于刻或切割薄型的塑料板材。 6?剪刀 用于裁剪纸张、双面胶带、薄型胶片和金属片的工具。根据用途通常需要几把不同型号。 7?微型机床、切割机 相比手工切割，使用小型或者微型机床进行切割能够更好地提升工作效率，同时，使用高精度的锯片，能够使切割面更加整齐、平整。微型切割机搭配不同的锯片，能够用于切割比较厚、硬的板材。 ?常用度量工具 1.T形尺 用于测量尺寸，同时辅助切割。 2?三角板、圆规、量角器等 用于测量平行线、平面、直角，画圆、曲线等。 三角板钢直角尺 3?钢角直尺 画垂直线、平行线与直角，也用于判断两个平面是否相互垂直，辅助切割。 4.卷尺 用于测量较长的材料。 三.修整工具 1.砂纸 用于研磨金属、木材等表面，以使其光洁平滑。根据不同的研磨物质，有干磨砂纸、耐水砂纸等多种。干磨砂纸（木砂纸）用于磨光木、竹器表面。耐水砂纸用于在水中或油中磨光金属表面。 2 .锉 用于修平和打磨有机玻璃和木料。分为木锉与钢锉，木锉主要用于木料加工，钢锉用于 金属材料与有机玻璃加工。 按锉的形状与用途，可分为方锉、半圆锉、圆锉、三角锉、扁锉、针锉，可视工件的形 状选用。 按锉的锉齿分粗锉、中粗锉和细锉。锉的使用方法有横锉法、直锉法和磨光锉法。 四.其他工具 2.镊子 制作细小构件时需要用镊子来辅助工作。 3.鸭嘴笔、勾线笔 画墨线的工具。 4?清洁工具 模型制作过程中，模型上会落有很多毛屑和灰尘，还会残留一些碎屑。可以用板刷、清 洁用吹气球等工具来清洁处理。 砂纸 锂 1.各种铅笔 用于做记号，在卡纸材料上通常用较硬的铅笔（ H —3H ）。 白菜类蔬菜病虫害识别与防治 白菜类蔬菜属于十字花科芸苔属一年生或两年生草本植物，按照它们的形态，可以分为大白菜、小白菜、菜薹、乌塌菜以及芜菁等。 大白菜就是结球白菜，在全国都有分布，以北方栽培为主，是华北秋季栽培的主要蔬菜。 小白菜就是不结球白菜，我国北方俗称它为小油菜，南方地区成为青菜。 菜薹又称菜心，是我国著名的特菜之一。 乌塌菜含有丰富的矿物质和维生素，所以人们又叫它“维生素菜”。 总的来说，白菜类蔬菜的叶片、叶球、花薹和嫩茎等，富含各种维生素和矿物质，符合人们的食用习惯，再加上它们栽培面积广、产量高、耐于贮运、供应期长，所以，白菜类蔬菜称得上我国最重要的蔬菜之一。 在白菜类蔬菜的生长过程中，经常会出现各种各样的病虫害，如果不及时地进行防治、或是防治方法不对的话，会对蔬菜的产量和品质造成严重影响。接下来的节目中，我们首先来认识几种典型的病虫害，然后再看看如何防治。 病害 白菜类蔬菜的病害可以分为侵染性病害和生理性病害，而侵染性病害又分为细菌性病害、真菌性病害和病毒性病害。 细菌性病害 细菌性病害是植株由于受到细菌侵染而引起的一种病害，一般表现出坏死、腐烂、萎蔫、畸形的特点。 软腐病 您瞧这颗大白菜，叶球直接露出来了，叶柄基部和根茎处的心髓部组织已经完全腐烂，充满了灰黄色的粘稠物，还散发出很大的臭味，这就是软腐病的典型症状。 软腐病又叫做烂疙瘩、烂葫芦、腐烂病、水烂病等，发生极为普遍。它的主要特点是轻轻一掰，植株就倒了，病部呈黏滑软腐状．并伴有恶臭味。小白菜、菜心等白菜类蔬菜发生软腐病时，症状与大白菜基本相似。 拿大白菜来说，大白菜定植后直到形成心叶的这个过程是长外叶的过程，这个过程中软腐病不会发生。而当植株外叶即将罩严地面的时候，大白菜渐渐进入壮心期，这时软腐病开始发生，从壮心开始至收获的整个过程中都有发病的可能，如果在这个时期，一开始植株外围的叶片在烈日下表现出萎蔫，但早晚尚能恢复，慢慢儿地外叶不能恢复的话，那您就要注意了，这有可能是得软腐病的早期症状。 黑腐病 您瞧这棵大白菜，从叶片的边缘往两侧和里边扩展，形成“V”字形黄褐色枯斑，病斑的周边呈淡黄色，这就是黑腐病的症状。以后，病原菌还会沿着叶脉向里扩展，形成大块黄褐色病斑或网状黑脉，并感染叶柄。大白菜一般在莲座期以后容易得这种病，它也是由细菌引起的。 做模型用什么材料好 有很多朋友问我们做模型材料的，如果要用来做模型都是需要一些什么材料呢？那么用什么材料是最好的呢？这样的问题涉及面很 广泛，如果说要一一介绍到模型材料，可能三天三夜也不能完全介绍完，如果说要介绍用什么材料最好呢？其实每种模型都有最适合的模型材料，各个材料有各个材料的优点，当然也有缺点，关键是要看你怎么做这个模型！对于朋友们提的问题，我将会成系列的例举下来，文章每天都会有更新，请大家多多关注，多多支持！ 材料系列（一） 材料是建筑模型构成的一个重要要素，它决定了建筑模型的表面形态和立体形态。 在现代建筑模型制作中，材料概念的内涵与外延随着科学技术的进步与发展，在不断的改变，而且，建筑模型制作的专业性材料与非专业性材料界限的区分也越加模糊。特别是用于建筑模型制作的基本材料呈现出多品种、多样化的趋势。由过去单一的板材，发展到点、线、面、快等多种形态的基本材料。另外，随着表现手段的日臻完善和对建筑模型制作的认识与理解，很多非专业性的材料和生活中的废弃物也被作为建筑模型制作的辅助材料。 这一现象的出现无疑给建筑模型的制作带来了更多的选择余地，但同时，也产生了一些负面效应。很多模型制作这认为，材料选用的档次越高，其最终效果越好。其实不然，任何事物都是相对而言，高档次材料固然很好，但是建筑模型制作所追求的是整体的最终效果。如 果违背了这一原则去选用材料，那么再好、再高档的材料也会黯然失色，失去它自身的价值。 模型材料的分类：材料有很多种分类方法，有按照材料产生的年代进行划分的，也有按照材料的物理特性和化学特性进行划分的。我们之后要介绍的材料分类，总分类为：主材料和辅助材料，再对两大类进行详细的分类。主要是从建筑模型制作角度进行划分，由各种材料在建筑模型制作过程中所充任的角色不同划分。（未完待续。。。。。。） 蔬菜——不用农药怎么防止病虫害？ ?A+ ?A- 2017-04-05 10:01:47农产信息网关注 说实话，作物病虫害防治不用农药很不现实，比较麻烦且费人力，但要有想学习如何不用农药来防治病虫害的朋友可以来看一下。 蔬菜虫害是蔬菜种植户们非常头疼的问题，若是用传统的农药喷洒方式解决虫害，会因为农药残留影响蔬菜的品质。这里和大家分享一下蔬菜虫害的科学防治方法。 一、伴生植物法： 1.青椒和大蒜间作。由于大蒜有一种特殊气味，能使为害青椒的害虫闻之即逃，避免青椒受害。 2.番茄和甘蓝套种。番茄的叶片会散发一种特殊的气味，可驱赶走为害甘蓝的菜青虫和蚜虫。除此之外，这两种蔬菜吸收的营养有很强的互补性，能充分发挥地力。 3.葱头与胡萝卜间作。它们各自散发的气味能驱走相互间的害虫。若单一种植胡萝卜，为防止虫害，可在地内或四周种上几棵葱头，这也能起到驱虫的作用。 并非所有的蔬菜都可以间作，如甘蓝和芹菜、黄瓜和番茄等不宜间作在一起，因为它们各自的分泌物能抑制对方的生长。 这种方法对适用于种植户和家庭小面积种植者。 二、自然材料治虫 1.草木灰液治虫。草木灰10千克对水50千克浸泡24小时，取滤液喷洒可有效地防治蚜虫、黄守虫。若葱、蒜、韭菜受种蝇、葱蝇的蛆虫危害，每亩沟施或撒施草木灰20~30千克，既治蛆又增产。 2.红糖液防治病。害红糖300克溶于500毫升清水中，加入10克白衣酵母，置于温室或大棚内，每天搅拌1次，发酵15~20天，待其表面出现白膜层为止。然后将此发酵液再加入米醋、烧酒各100克，对入100千克水。每隔10天1次，连喷4~5次，防治黄瓜细菌性斑点病和灰霉病有良好效果。 3.兔粪治地老虎每10千克水加兔粪1千克，装入瓦缸内密封沤15~20天，用时搅拌均匀，浇于瓜菜根部，可防治地老虎。 4.尿洗合剂治菜蚜用洗衣粉、尿素、水按1∶4∶400的比例制成混合液，可防治菜蚜，杀虫率达90％以上。 5.猪胆液治病虫10％浓度的猪胆液加适量小苏打、洗衣粉，能防治茄子立枯病、辣椒炭疽病，能驱赶长豆角、四季豆、瓜类等蔬菜上的蚜虫、菜青虫、蜗牛等多种害虫。稀释液可保持10天有效。 6.大蒜、番茄叶巧杀红蜘蛛用大蒜（捣烂成泥状）2份，水1份混拌均匀，取其滤液喷治。或用新鲜的番茄叶（捣烂成浆）加清水2倍并浸泡5小时然后取滤液喷洒果树、花木或蔬菜，都可有效将红蜘蛛杀死。 7.糖醋、烂果诱捕金龟子选用熟烂酸臭的无花果、烂西瓜等，与糖醋液（红糖、醋、水比为1：3：16），一起放入陶钵，支撑分布在果园或菜园中，每2—3天收集钵中的金龟子即可。 8.三合板涂漆聚捕微型害虫在较大的三合板两面涂上橙黄色油漆，干后再涂一层机油、黄油混合油，分布挂在果园或菜园中，蚜虫、白粉虱、美洲斑潜蝇等害虫就会自投罗网。1周后更换涂刷油漆、混合效果更好。 模型手工制作工具及主要材料 一．常用刀具 1.常用美工刀 又称为墙纸刀，主要用于切割纸板、卡纸、吹塑纸、软木板、即时贴等较厚的材料。 2.美工钩刀 切割有机玻璃、亚克力板、胶片和防火胶版的主要工具。 美工刀美工钩刀 3.手术刀 主要用于各种薄纸的切割与划线，尤其是建筑门窗的切、划。 4单、双面刀片 单、双面刀片的刀片最薄，极为锋利，用于切割薄型材料。 5.木刻刀 用于刻或切割薄型的塑料板材。 木刻刀剪刀 6.剪刀 用于裁剪纸张、双面胶带、薄型胶片和金属片的工具。根据用途通常需要几把不同型号。 7.微型机床、切割机 相比手工切割，使用小型或者微型机床进行切割能够更好地提升工作效率，同时，使用高精度的锯片，能够使切割面更加整齐、平整。微型切割机搭配不同的锯片，能够用于切割比较厚、硬的板材。 二．常用度量工具 1.T形尺 用于测量尺寸，同时辅助切割。 2.三角板、圆规、量角器等 用于测量平行线、平面、直角，画圆、曲线等。 三角板钢直角尺 3.钢角直尺 画垂直线、平行线与直角，也用于判断两个平面是否相互垂直，辅助切割。 4.卷尺 用于测量较长的材料。 三.修整工具 1.砂纸 用于研磨金属、木材等表面，以使其光洁平滑。根据不同的研磨物质，有干磨砂纸、耐水砂纸等多种。干磨砂纸（木砂纸）用于磨光木、竹器表面。耐水砂纸用于在水中或油中磨光金属表面。 砂纸锉 2．锉 用于修平和打磨有机玻璃和木料。分为木锉与钢锉，木锉主要用于木料加工，钢锉用于金属材料与有机玻璃加工。 按锉的形状与用途，可分为方锉、半圆锉、圆锉、三角锉、扁锉、针锉，可视工件的形状选用。 按锉的锉齿分粗锉、中粗锉和细锉。锉的使用方法有横锉法、直锉法和磨光锉法。四．其他工具 1.各种铅笔 用于做记号，在卡纸材料上通常用较硬的铅笔（H—3H)。 2.镊子 制作细小构件时需要用镊子来辅助工作。 3．鸭嘴笔、勾线笔 画墨线的工具。 4.清洁工具 模型制作过程中，模型上会落有很多毛屑和灰尘，还会残留一些碎屑。可以用板刷、清洁用吹气球等工具来清洁处理。 建筑模型制作所需材料和工具 一.基本设备: 简单工具,能够应付大多数的建模工作 1．测绘工具、三棱尺(比例尺) 、直尺、三角板、弯尺 (角尺) 、圆规、游标卡尺、模型、蛇尺等。 2．剪裁、切割工具 勾刀、笔刀、裁纸刀、角度刀(45o) 、切圆刀、剪刀、手锯、钢锯、电动手锯(积梳机) 、电动曲线锯、电热切割器、电脑雕刻机。 3．打磨喷绘工具 砂纸、砂纸机、锉刀、什锦锉、木工刨、台式砂轮机。 二. 材料 1简易的建筑模型用聚苯泡沫塑料块切割成建筑模型实体部分的毛坯，也可用泡沫极做简易模型的底盘；用茶色涤纶纸，茶色不干胶纸作模型的窗、底盘粘面；用吹塑板、吹塑纸作阳台、墙面、地面、道路、台阶、屋顶等；用绒纸、砂纸作绿地草坪、步行道、广场等；用彩色橡皮块、海绵作汽车、树木等配景。以上几种材料价格低，易加工制作。一般视为同一档次的模型材料。这些材料灵活配合使用，可快速制成比较理想的设计模型或表现模型。 2. 建筑模型是使用易于加工的材料依照建筑设计图样或设计构想，按缩小的比例制成的样品。它是在建筑设计中用以表现建筑物或建筑群的面貌和空间关系的一种手段。对于技术先进、功能复杂、艺术造型富于变化的现代建筑，尤其需要用模型进行设计创作。那么制作一般的建筑模型需要哪些材料呢？以下做了一个简单的归类： 1、主体墙面：模型专用"747"型ABS高分子工程塑料板（厚度0.8 mm -33 mm） 2、主体玻璃：模型专用ICI高透明有机玻璃（厚度0.8 mm -1.2 mm） 3、路面、硬质铺装及加工方式：全部使用模型专用LG ABS板材。 4、绿化草坪：模型专用FALLER草坪 5、植物：软化铜丝、高弹海绵、高质量颜料及模型专用FALLER草粉 6、粘合剂：优质三氯甲烷、日本A-A超能胶、德国UHU胶、喷胶 三、制作流程 做建筑模型用的材料一般是ABS.用卡纸。 1、把图纸按需要的比例进行缩放，比如要做一比一百，就缩放到一比一百。 2、把建筑的各个面分解出来，单独出图，然后一比一打印出来。 3、把打印出来的纸贴在卡纸上，然后裁出门窗和边框。等效电路模型参数在线辨识
沙盘模型做的所用材料
浅析电力系统模型参数辨识
模型制作材料
基于最小二乘模型的Bayes参数辨识方法
模型制作材料、工具及其使用
Bouc-Wen 滞回模型的参数辨识
模型制作材料
制作建筑模型的材料
蔬菜虫害分类
模型制作大全
参数辨识示例 报告
遗传算法工具箱识别(GA)Bouc-Wen模型参数辨识_识别
(完整版)手工建筑模型制作工具、材料及步骤概要
白菜类蔬菜病虫害识别与防治
做模型用什么材料介绍
蔬菜病虫害防治
(完整版)手工建筑模型制作工具、材料及步骤概要
建筑模型制作所需材料和工具(2)