Holographic evolution of gauge couplings

a r X i v :h e p -t h /0208002v 2 25 O c t 2002BICOCCA-FT-02-16

Holographic evolution of gauge couplings

R.Contino 1,P.Creminelli 1,E.Trincherini 21Scuola Normale Superiore,Piazza dei Cavalieri 7,I-56126Pisa,Italy &INFN 2Physics Department,University of Milano-Bicocca,P.zza della Scienza 3,I-20126Milano,Italy &INFN

1Introduction

Grand Uni?ed Theories (GUT)with extra dimensions can address some of the longstand-ing problems of their 4-dimensional (4d)counterparts,while maintaining their virtues.The doublet-triplet splitting problem,for example,is elegantly solved in models where the GUT symmetry is broken by the boundary conditions of the gauge ?elds in the extra dimensions and not through a Higgs mechanism [1,2].The more and more stringent limits on proton decays [3],which are recently getting the minimal 4d SU (5)supersymmetric model into trouble [4],are satis?ed in 5-dimensional (5d)extensions [5].

Much attention has been devoted to the case of ?at extra dimensions.Here physics appears 4-dimensional in every experiment with typical energies below the inverse radius scale 1/R ,and therefore the running of gauge coupling constants is logarithmic as usual.

At higher energies however,nature becomes truly extra dimensional and gauge couplings increase with energy following a power law.By simple dimensional analysis,the loga-rithmic running comes from the evolution of boundary operators and is associated with a logarithmic divergence,while the power law dependence on external momentum re?ects a power divergence in the bulk gauge kinetic term.A power law increase with energy of the coupling constants seems an attractive way to obtain uni?cation of the elementary forces at much lower scales than the usual GUT models[6].Even more attractive if one speculates on scenarios with quantum gravity at the TeV,in which case uni?cation of strong and weak interactions with gravity seems a realistic ambition.Unfortunately,even if one postulates a su?cient separation of scales between1/R and the cuto?Λto have an extra-dimensional?eld theory regime,power law evolution comes together with power threshold corrections,which represent the dominant e?ect,spoiling completely the pre-dictability.The situation is even worse if one demands uni?cation to occur at the cuto?scale,because this is right the energy domain in which e?ective?eld theory breaks down and perturbation theory becomes unreliable.Therefore,if one is so ambitious to insist on predictive schemes,uni?cation has to occur as a result of the slow logarithmic running. This means that the paradigm of a desert between the electroweak scale and a high energy GUT scale1/R~1016GeV,is still valid.A very useful tool in this case is the e?ective ?eld theory approach of Weinberg[7]:a matching is performed at energyμ~1/R,be-tween the full extra-dimensional GUT theory and a4d theory with only the Standard Model(SM)gauge degrees of freedom.The heavy GUT states,which have masses of the order of1/R,are integrated out and contribute with calculable threshold corrections[8].

The picture drastically changes if we depart from the assumption of?atness.A very interesting situation is the case of just one compact extra dimension,in which the metric is that of Anti-deSitter(AdS)space:the Randall-Sundrum(RSI)model[9].This model has been originally constructed to address the hierarchy problem,with only gravity prop-agating in the bulk and the SM con?ned on the TeV brane.However,its many surprising features have led many groups to explore the possibility of realizing a GUT theory in this warped geometry,with gauge bosons propagating in the bulk[10]-[14].In RSI,physics appears5-dimensional at energies higher than the AdS curvature k(which is taken to be of the order of the Planck scale),when everything goes as in the?at limit.Below this scale and down to the weak scale,there is a huge range of energies in which the model is conjectured to be dual to a4d conformal?eld theory[15],along the prescription of the AdS/CFT correspondence[16,17,18].This duality allows us to infer that gauge couplings run logarithmically until very high energy,even if new GUT physics,namely the Kaluza-Klein(KK)resonances of the uni?ed gauge bosons,appears at the TeV scale revealing the uni?ed character of the fundamental forces[10].No surprise then that an e?ective theory description a l`a Weinberg does not exist beyond the TeV:changing the GUT group and its breaking modi?es the properties of the Conformal Field Theory(CFT) and consequently the evolution of gauge couplings until uni?cation,not only some minor threshold corrections.

In[11]the one-loop correction to the low energy coupling was computed in RSI for a non-abelian gauge theory,employing a momentum cuto?which depends on the?fth

dimension.In[13],using dimensional regularization,the case of massless scalar QED was considered,while in[14]also the massive case has been studied,adopting a Pauli-Villars regulator.In this work,we further study the scalar QED case with the computation of the gauge?eld zero-mode propagator in5d for di?erent choices of boundary conditions and for a generic scalar bulk mass.In doing that,we choose dimensional regularization that,we believe,is the most economical and transparent regulator which preserves the symmetries of the AdS background.All our results are compatible with what the holographic duality requires.This is su?cient to discuss the scalar contribution to gauge coupling evolution in di?erent GUT scenarios where the uni?ed group is broken by the boundary conditions or through a Higgs mechanism.

Section2is devoted to understand the meaning of the evolution of gauge couplings in AdS space.Planck brane correlators are the only meaningful observables at energies higher than the TeV scale,while mode-by-mode quantities become strongly coupled.We explicitly show how to interpret loop corrections to these observables from the holographic point of view.In section3we present the calculation of the scalar loop correction to the low energy gauge couplings,for generic boundary conditions and mass.We leave all the computational details to the appendix.We use these results in section4to discuss various mechanisms of GUT symmetry breaking pointing out the agreement with the holographic interpretation.Conclusions are drawn in section5,where we comment on possible phenomenological scenarios.

2Holographic interpretation of the running

The Randall-Sundrum model with two branes[9]is simply given by a slice of AdS space with metric

L2

ds2=

p2z at distances z p?1,which makes the

high energy processes on the Planck brane insensible of what is going on deep inside AdS: the local cut-o?for an observer living on the Planck brane is given by the AdS curvature k.The importance of these inclusive quantities is clear also from the holographic point of view,having the brane-brane correlators a simple4-dimensional meaning.In our case, the gauge propagator between two points on the Planck brane tells us the strength of the gauge interaction in the4-dimensional dual theory and it remains perturbative despite the fact that the KK gauge bosons become strongly coupled above the TeV.This dual picture allows us to understand why the gauge coupling running is still logarithmic above the TeV scale:the CFT composites become broader and broader and the true degrees of freedom emerge,but their contribution to the running still remain perturbative and4-dimensional, i.e.logarithmic.In a uni?ed model,brane-brane gauge correlators for di?erent groups are the same much above the uni?cation scale and this may happen in a regime(E?TeV) in which only boundary correlators make sense.

At energies much greater than the TeV scale,but smaller than the AdS curvature k, the tree level Planck brane-brane gauge propagator is given by[10]

g25/L

G(q)=

??+

Figure1:The brane-brane correlator in AdS corresponds holographically to the free gauge propagator corrected by the LO contribution in1/N of the CFT(of order~O[N2(α/4π)]

with respect to the tree level).The grey circle represents the JJ insertion.

What changes if we add the Planck brane?The rough picture is the following.Cutting

o?the part of AdS space near its boundary corresponds to a UV modi?cation of the CFT,which is now smeared over a distance of order k?1:degrees of freedom of shorter

wavelength have been integrated out.Moreover the4d role of?elds living in AdS space

changes.In the full AdS case they are not dynamical from the4d point of view:their

boundary behaviour at in?nity just acts as a source for the corresponding operator of the

CFT.With the addition of the Planck brane,bulk?elds become dynamical also from the

4d viewpoint,as we must integrate over their boundary value on the brane.

We thus expect that radiative corrections to brane correlators in presence of the Planck

brane describe not only1/N subleading CFT terms,but the additional contribution of

the4d?elds made dynamical by the introduction of the brane.If we have a scalar?eld in

AdS cut by the Planck brane,the4d theory contains a dynamical scalar,coupled to the

CFT through an operator O(x),which has dimension4if the scalar is massless.Loops of this4d scalar will enter the running of the gauge couplings.

As depicted in?gure2,the one-loop AdS correction corresponds to the sum of dif-

ferent terms:the contribution from the4d scalar(a),whose propagator gets itself a

CFT correction(c),and the NLO CFT insertion(b).It is worth noting that the various

terms can be arranged in a double expansion:the?rst is the standard series in powers of

(α/4π),the second is the expansion of the CFT correlators in powers of1/N.The two

expansions are related,as the holographic prescription tells us that1/N2~g25/16π2L. Diagrams(a)and(b)are of order O(α/4π)with respect to the tree level;diagram(c)is

completely negligible in this case,being the CFT coupled to the4d scalar only through

M Pl-suppressed operators.The corresponding diagram in the case of vector boson loops

is O[N2(α/4π)2],but still subleading with respect to the other two contributions,as4d perturbativity requires N2(α/4π)?1.

We can look at the contribution(b)and(a)in?g.2as coming respectively from the

limiting case of a5d loop deep inside AdS or close to the Planck brane.This is quite

intuitive,as the4d scalar?eld comes from the integration over the boundary conditions

on the Planck brane.In the complete AdS case,the boundary valuesφ0,A0μ,g0μνfor the

?

?

+

(a)(b)

+ (c)

Figure2:The one-loop(rainbow)scalar correction to the brane-brane correlator in AdS corresponds holographically to three di?erent diagrams:a4d scalar loop graph(a),

the same diagram with the scalar propagator corrected by the CFT(c),and the NLO contribution in1/N of the CFT(b).Diagrams(a),(b)are both O(α/4π)with respect to the tree level;diagram(c)is negligible because the scalar coupling to the CFT is M Pl-suppressed.The grey circle(square)represents the JJ ( OO )insertion.A similar holographic interpretation holds for the seagull diagram.

various?elds at in?nity act as sources for the corresponding operators in the CFT[18]: e? d4x O(x)φ0(x)+Jμ(x)A0μ(x)+Tμν(x)g0μν(x) CFT=e?S AdS(φ0,A0μ,g0μν).(3) The right hand side of this equation must be regularized[18],and this procedure leads us closer to the truncated AdS case we are interested in.The standard procedure is to limit the z integration to z>?(which corresponds to introducing an explicit UV cut-o?on the CFT),add a proper local counterterm action(divergent for?→0)function of φ0,A0μ,g0μνand their derivatives,and then take the limit?→0.In the case with only a scalar?eld,eq.(3)becomes

e? d4x O(x)φ0(x) CFT=lim?→0e?S AdS(φ0,?)e?S count(φ0,?).(4) Suppose now not to perform the?nal limit,keeping an explicitly truncated AdS space. As we have integrated out a portion of space which corresponds to the UV of the CFT, we expect this to correspond to a smearing procedure in which fast modes are integrated out1[15,23,24].At this stage,the scalar loop correction in AdS of?gure2gives a

subleading contribution to the JJ φ

CFT correlator in the external backgroundφ0.

The last step to get the Randall-Sundrum scenario is to integrate over the boundary valuesφ0,A0μ,g0μν,which become dynamical?elds,introducing a generic brane action S bound(φ0).Consider for instance a brane action with only a kinetic term proportional to

an arbitrary parameterξ:

S bound(φ0)=ξ

g?μφ?νφ?gμν.(5)

By varyingξone changes the kinetic term of the4d scalar and therefore the relative

importance between its loop contribution(?g.2a)and the CFT correction(?g.2b)2.In

the limitξ→+∞,the4d scalar is frozen out and we are left with the CFT correction;

the same result holds by choosing Dirichlet boundary conditions on the Planck brane.

From these considerations,it should be clear the strict connection between boundary

terms in AdS and the4d scalar mode.Moreover,all the features of the AdS bulk re?ect

on the CFT.In particular,if the GUT symmetry is unbroken in the bulk,the CFT is

GUT-preserving at all orders.

2.2The CFT contributions

We now concentrate on the pure CFT corrections,as if we had pushed the Planck brane

to in?nity,recovering the complete AdS space.We have shown that at leading order the

JJ correlator does not distinguish among the unbroken subgroups of a uni?ed theory, while at NLO the CFT correction is GUT invariant or not depending on the mechanism

we choose to break the GUT symmetry.If the symmetry is broken by the boundary

conditions,the AdS bulk remains GUT invariant as well as the dual CFT3.In this case,

at subleading order the CFT still gives a common running to all the unbroken subgroups.

Another possibility is that the uni?ed theory is broken in the bulk,through a vev

of a charged scalarΣ.If the expectation value of the scalar is constant along the?fth

dimension,the conformal symmetry is still unbroken(all AdS isometries are preserved)

but the GUT symmetry is not4.In the holographic theory,we have turned on an operator OΣcoupled to the4dΣscalar,transforming under the GUT symmetry,which therefore results spontaneously broken5.In this scenario,GUT-breaking corrections to Planck brane propagators correspond to analytic or non-analytic operators,involvingΣ,in the

5d e?ective action.The contribution due to analytic operators is not calculable,and can be only estimated through a naive dimensional analysis.For instance,in the case of the ΣF F operator,naive dimensional analysis gives a ratio between the O(1)and O(N2) corrections to the CFT beta-function:

b NLO

CFT

Λ=

M GUT

1+log M GUT/TeV~8,(8) where the numerical bound is obtained for b0i given by the SM matter content.An opposite bound on b CFT,or equivalently on N,comes from the requirement of perturbativity in

5d,namelyΛ/kπ?1,whereΛis the5d cuto?:the inequality

b CFT=8π2L

3

(9)

follows.

The general conclusion is that the leading CFT running cannot be much greater than other contributions which separate the unbroken subgroups,coming from additional particles coupled to the CFT.The limit on N is not so strong to spoil the perturbativity of the AdS picture,as we see comparing eqs.(8)and(9),even if the allowed window is not too wide.This limit on the CFT leading contribution implies,in turn,that subleading corrections,coming from bulk loops and higher dimension operators are negligible with respect to the non-CFT running.

In principle we could discuss the gauge coupling running even in absence of a uni?ed group in the bulk and check if the gauge couplings cross at a certain energy.In this case the CFT contribution to the running of each group is di?erent at leading order,so that the running may be much faster with a consequent lowering of the uni?cation scale[11]. However,the CFT beta-function for the three groups,given at leading order by the three independent gauge kinetic terms,is incalculable,so that no?rm prediction seems possible.

Before moving to the explicit calculations,we want to stress an important conceptual di?erence between the standard models of uni?cation and the ones built in AdS space.In the standard case,Weinberg’s approach of e?ective gauge theory is very useful and it tells us that the details of GUT-symmetry breaking,resulting only in threshold corrections, are not crucial to test uni?cation.Here the situation is di?erent.Modifying the uni?ed gauge group we are at the same time changing the CFT excitations,hopefully around the corner,at the TeV scale.The pattern of symmetry breaking does not in?uence only the physics at far-away energies,but also the subleading CFT corrections to the running down to the TeV scale.All this follows from the fact that AdS space describes at the same time the CFT properties and the behaviour of the additional particles coupled to it. 3The low energy gauge coupling

In this section we present our result for the one-loop scalar correction to the low energy coupling of a U(1)gauge group in the bulk.We leave to the appendix all the computational details,focusing our attention on the holographic interpretation.Once given the main formulae for di?erent boundary conditions of the scalar?eld,we will able in the next section to discuss various scenarios of GUT symmetry breaking.

In order to regulate the loop divergence we choose the dimensional regularization, which proved to be a powerful scheme also in theories with?at extra-dimensions[25]. In the speci?c case of the one-loop correction to the zero-mode gauge correlator,it is enough to extend the brane dimension to a generic(complex)value d keeping just one extra dimension.Analogously to the Minkowski case,the isometries of AdS space are

clearly preserved.The zero-mode gauge self-energy reads,for external4d momentum p:

1

k g25

+?0(μ)+?1(μ)?Π(p2,μ),(10)

whereμis the subtraction point and?0,1(μ)are the coe?cients of the gauge kinetic terms localized on the branes.Π(p2,μ)is the one-loop scalar correction

Π(p2,μ)=?μ4?d {x n} 10dx(2x?1)2 d d q[q2+x2n+c2(x)]2.(11)

Here c2(x)=x(1?x)(?p2)and x n is the mass of the n-th Kaluza-Klein mode of the scalar?eld(see appendix).Using the technique described in the appendix,it is easy to perform the integration?rst and then the sum,getting

Π(p2,μ)=(b0/2)

?

+log z0z1 +αlog μ

+3 10dy y ?p2/2

γ

3

(1+α) .

(12)

With b0=1/3we mean the beta-function of a charged4d scalar,and d=4??.The

previous formula is a completely general result,valid for a scalar with arbitrary boundary

conditions and mass;in the case of(±±),(±?)boundary conditions,one should read

α=±1,α=0respectively and choose a function f=f±±,f=f±?,whose expression

is given in appendix.In the particular case of a(++)massless scalar,eq.(12)coincides with the result of[13].

The zero-mode gauge propagator is an exclusive observable and does not make sense

above the TeV where the0mode becomes strongly coupled.This means that eq.(12)can

be really trusted only for external momenta|p| TeV[13];at these energies it matches the

Planck brane-brane correlator,therefore admitting a simple holographic interpretation.

Once the function f in eq.(12)is expanded for z1|p|?1,the logarithmic dependence on the momentum p must be the correct one for an infrared log.The logarithmic divergence,

represented by the1/?pole,is the same as in the?at limit(for the latter,see[8]).This

was expected,because in the very high energy regime the curvature can be neglected and

AdS appears locally?at[13,14].

In the following we collect the low energy limit z1|p|?1expression ofΠ(p2,μ2)for all possible choices of boundary conditions in the massless case and for a(++)scalar with AdS bulk mass https://www.360docs.net/doc/dd4905788.html,ing the asymptotic expansions of eqs.(34),we obtain(subtracting the1/?divergence and omitting irrelevant constants):

massless scalar(1/z1?|p|>z0/z21)

Π++(p2,μ)?

b0

z0

+log z0 4logμz0?1

8π2 log z14logμz0+1

8π2

3

z0

(15)

Π+?(p2,μ)?b0

4

log

z1

?p2 .(16)

massive(++)scalar(k?m?|p|,|p|?1/z1)

Π(p2,μ)?b0

z0

+log mz0?14logμz1+m2z20z

?1 8π2 3z0+1μ+1m2log z1

6Also ref.

[26]has recently pointed out the appearance of such a small eigenvalue in the similar

case of a boundary mass term on the TeV brane for the scalar?eld.

an almost massless4d scalar contributing to the running of the gauge coupling down to

very low energy7.This explains the log p term inΠ+?.

Non-analytic operators in the bulk,like

m2log z1/z0;both are calculable,as they correspond to AdS bulk operators which

depend non-analytically on the scalar curvature R(the former)or on the Lagrangian

parameter m2(the latter).The z0

7In the case of a vector?eld,Dirichlet boundary conditions on the TeV brane implies a mass~TeV.This is expected,because its coupling with the CFT is dimensionless so that the mass is only logarithmically suppressed by1/log(k/TeV).For a fermion?eld we obtain m2~TeV2·TeV/k.

8The non-analyticity is a consequence of the fact that we need a term linear in k,while the metric is a function of k2.We thank Riccardo Rattazzi for clarifying us this point.

the logμz0,logμz1terms inΠ(p2,μ)which are the counterpart of the logμR terms of

the?at case.A further source of log z0,1terms might be?nite non-local operators which

will be in general present in the5d e?ective action.Indeed,the dependence on z0,1of the

function f in eq.(12),is quite complicated before taking the limit z0?z1.Only when the is a large separation of scales z0?z1,we recover the simple expression of eqs.(13)-(16) required by the holographic interpretation.

Concerning the holographic interpretation of the brane kinetic terms in AdS,they

correspond to adding a constant term to the4d inverse coupling1/g2(p2),shifting its

Landau pole[19].In other words,it is a modi?cation of the4d theory at a scale corre-

sponding to the position of the brane in AdS.There is therefore no connection between

boundary terms in AdS and log evolution in the holographic theory.It is remarkable that

in the?at case all the logarithmic running comes from boundary operators,while the

main logarithmic running in the4d theory dual to RSI comes from the AdS bulk.

4GUT breaking:the holographic point of view

Armed with the previous results,we discuss now di?erent mechanisms of breaking the GUT symmetry in AdS,either through suitable boundary conditions for the gauge?elds, or turning on the vev of a scalar?eld in the bulk.We consider for simplicity the particular case of an SU(5)group in the bulk broken down to SU(3)×SU(2)×U(1)and we study the loop correction to the low energy couplings given by a scalar multiplet in the fundamental representation.It is understood that the results have a general validity.

4.1GUT breaking through boundary conditions

Let us consider?rst the case in which the GUT symmetry is reduced at low energy by the boundary conditions.We assume that the SU(3)×SU(2)×U(1)gauge bosons A aμhave always parity(++),while the X,Y bosons A?aμcan be(±,?)or(??):SU(5)is broken on the TeV or Planck brane,or both.The relative parities of the doublet and triplet components of the scalar5-plet?in the bulk are?xed by gauge invariance.We choose ?2=(++)for the doublet component and this forces?3=(±,?),(??)for the triplet when A?aμare(±,?),(??)respectively.

GUT breaking on the TeV brane

?= ?2(++)?3(+?) for A?aμ(+?)A?a5(?+)

A theory with a gauge group SU(5)in pure AdS is dual to a4d CFT with a global SU(5)invariance.Putting the Planck brane and imposing+conditions for the gauge bosons corresponds,in the holographic theory,to gauge the global symmetry.Let us now insert the TeV brane demanding?parity for the X,Y(and+for the A aμ)gauge ?elds.This deformation in AdS implies in the4d picture a spontaneous breaking of SU(5)

down to the SU (3)×SU (2)×U (1)subgroup at the TeV:the X,Y bosons acquire TeV masses through the Higgs mechanism and the CFT resonances are not SU (5)invariant.At energies higher than the TeV,however,the Planck brane-brane correlator does not probe the GUT breaking on the TeV brane and the holographic theory must appear fully SU (5)invariant.As a consequence,we expect a GUT-invariant running of the SU (3)×SU (2)×U (1)gauge couplings g i ,i =1,2,3,from the TeV up to higher energies.This is indeed what we found computing the contribution of the massless 5-plet scalar

(for 1/z 1?|p |?z 0/z 21

):18π2log z 1kg 25?b 5 +?0(1/z 0)+?i 1(1/z 1)?b 5?p 2?12 ?12?82

2log 2+89

At very low energies,|p |

di?erent for the three SU (3)×SU (2)×U (1)couplings g i .

only the SU(3)×SU(2)×U(1)symmetry is gauged.In the holographic theory we thus ?nd,in addition to the CFT sector,the SU(3)×SU(2)×U(1)gauge?elds and an elementary doublet scalar.Inserting the TeV brane in AdS and demanding a?parity for the A?aμ,the global SU(5)invariance of the CFT is spontaneously broken at the TeV to the SU(3)×SU(2)×U(1)subgroup.The corresponding Goldstone bosons can be identi?ed with the zero modes of A?a5,which appear in the dual theory as scalar excitations of the CFT with the same quantum numbers of the XY bosons.From the holographic point of view,we thus expect an SU(5)-breaking running up to the Planck scale given by the scalar doublet,while the CFT does not contribute to the di?erential running.Indeed the explicit calculation gives:

1

8π2log

z1

kg25?b5

+?i0(1/z0)+?i1(1/z1)?b i2?p2

?12 ?12 ?b i33 .(20)

This equation gives a non-ambiguous test of the holographic interpretation:the4d scalar doublet gives a di?erential running up to the scale k.This e?ect cannot be falsi?ed by the SU(5)-invariant running of the CFT.

An important observation is in order at this point.From the holographic point of view,there is no reason at all why the di?erent g i couplings should unify at the Planck scale.Indeed,in the holographic theory SU(5)is just a global symmetry of the pure CFT sector,only the SU(3)×SU(2)×U(1)group is gauged.This is in sharp contrast with the case of SU(5)broken only by the TeV brane:in that case,there is a Higgs mechanism in4d reducing the GUT group at the TeV.No analogous mechanism arises here at the Planck scale.Moreover,from the5d point of view,the situation at energies around k is similar to the?at case:there is really no exact uni?cation of the gauge couplings just because there is no uni?ed symmetry on the boundaries.As in the?at limit,however,one can estimate the threshold corrections,represented in AdS by the boundary term?i0(μ), to be small if evaluated at a scaleμ~1/z0close to the strong dynamics regime.In this sense,we recover an approximate uni?cation of the couplings g i at the Planck scale.

GUT breaking on the Planck brane

?= ?2(++)?3(?+) for A?aμ(?+)A?a5(+?)

The GUT symmetry is still broken on the Planck brane but no more on the TeV,so that the holographic picture is much similar to the previous case.Inserting a TeV brane and demanding a+parity for the A?aμ,it means that SU(5)remains a global symmetry of the CFT:the CFT resonances can be arranged in exact SU(5)multiplets.As in the previous case we expect that the only source of SU(5)breaking comes from the scalar

doublet.Indeed we obtain

1

8π2

log z 1kg 25?b 5 +?i 0(1/z 0)

+?1(1/z 1)?b i 2?p 2?1

2 ?12?82log 2 .(21)

4.2GUT breaking with a bulk vev

A di?erent mechanism to break the GUT symmetry is the standard Higgs mechanism.Let us suppose that a massless scalar ?eld Σ,propagating in the bulk,acquires a vacuum expectation value Σ constant along the ?fth dimension.In the following we assume that Σand all the other bulk ?elds have (++)boundary conditions.This vev splits the masses of the GUT multiplets,giving,for example,a (bulk)mass m ~g 5 Σ to the triplet of our scalar ?,leaving the doublet massless.An interesting possibility is that k ?m ?TeV so that the one-loop correction to the low energy couplings reads:

1

8π2log z 1

k g 25?b 5?b i 3m 2z 20

8π2log m ?b 58π2 b 5?+γ

3b i 2?b i 316

.(22)In the 4d dual picture the gauge symmetry is spontaneously broken.The 4d doublet and triplet scalars take di?erent masses (the triplet has a mass ~m/

√Σ2F F .The ?rst one is absent if we impose a Σ→?Σsymmetry and

the second one shows up only in the ?at limit m ~g 5 Σ ?k ,as already said in section 3.

5Conclusions

We have studied the dynamics of gauge interactions in the Randall-Sundrum model with gauge bosons in the bulk,which is conjectured to be dual to a 4d CFT weakly coupled to the corresponding 4d gauge sector.This duality allows us to keep a perturbative control on the model up to Planck scale,if we limit our study to inclusive correlators on the Planck brane.The evolution of the gauge couplings up to high energies in the holographic

theory gives an insight of the dynamics in the5d theory.Bulk loop corrections to brane-brane correlators give both the1/N expansion of the CFT and the ordinary perturbative expansion in powers of the gauge coupling constant.

Using dimensional regularization,we have calculated the1-loop correction to the low-energy gauge couplings in5d due to a bulk scalar with various boundary conditions on the two branes and arbitrary mass.These zero-mode propagators give the4d holographic couplings at low energy with their evolution from the Planck scale.

The calculations allowed us to study di?erent GUT scenarios where the gauge sym-metry is broken either by a Higgs mechanism,or by the boundary conditions.We have checked that in any case the results are compatible with what expected from the holo-graphic dual.

Some general conclusions can be drawn for model building.We have seen that,as the CFT has a positive beta-function,strong limits are obtained if one imposes that the gauge coupling remains perturbative up to a standard GUT scale(~1016GeV):roughly speaking,the CFT has not to be dominant with respect to the other contributions,so that large values of N are forbidden.This in turn implies that subleading CFT contribution is typically negligible.

Di?erent phenomenological models are possible.If the Standard Model particles are con?ned on the Planck brane,supersymmetry is required to stabilize the hierarchy;one reobtains a standard supersymmetric uni?cation,if a spontaneous breaking occurs on the Planck brane[10].From the4d point of view,we have just added to the MSSM a GUT-invariant CFT,which just gives a common positive contribution to all the three beta-functions.

As discussed in[11],we can also imagine to put the Standard Model on the TeV brane,in order to solve the hierarchy problem.In this case,proton decay mediated by X,Y Kaluza-Klein bosons with TeV masses must be forbidden;for example by choosing Dirichlet boundary conditions for the broken gauge bosons and requiring additional sym-metries for the TeV brane interactions.This breaking of the GUT symmetry through TeV brane boundary conditions is negligible for energies above the TeV scale;additional sources of GUT breaking are therefore required,such as a Higgs mechanism in the bulk or on the Planck brane.

If the only source of symmetry breaking is the choice of boundary conditions on the TeV brane,the uni?cation scale should be at the TeV scale.This could?t well in the framework of SU(3)W uni?cation[28],recently readdressed in extra-dimensional inspired models[29],in which the SU(2)and U(1)groups of the Standard Model are embedded into a weak SU(3)around the TeV scale.However,it is likely that this kind of model requires a scale of conformal symmetry breaking too low to be compatible with the strong limits coming from electroweak precision observables[30].

A further possibility is the breaking through Planck brane boundary conditions.In this case,there is no uni?cation in the usual sense,as only the SM gauge bosons exist in the holographic dual.Nevertheless,as in the?at case,an approximate uni?cation at high energies can be justi?ed from a5d point of view,relying on a strong coupling assumption for the boundary couplings on the Planck brane.

Using both the AdS picture and the 4d dual counterpart,uni?cation of gauge couplings in these warped spaces can be discussed.Only further work will tell us if a viable and compelling model is achievable.

Acknowledgments

We would like to thank R.Sundrum for useful discussions.We are especially grateful to R.Rattazzi who has followed this work from the beginning with many important discussions and suggestions.R.C.and E.T.thank the CERN Theory Division,where part of this work was done,for its hospitality.R.C.also acknowledges the hospitality and the ?nancial support of the Department of Physics at the University of Geneve.This work was partially supported by the EC under TMR contract HPRN-CT-2000-00148.Appendix

A Sums in AdS

We present here the method used to sum the series of eq.(11)on the AdS Kaluza-Klein

masses.Performing ?rst the integral in eq.(11),one ?nd the series

S (d )= {x n }

x 2n +c 2(x ) d/2?2,(23)

where the summation runs over the entire KK spectrum of the scalar ?eld.Depending on its boundary conditions,the KK masses x n of a massive scalar ?eld in AdS satisfy the following eigenvalue equations:

(++):

j ν(x n z 0)y ν(x n z 1);(+?):j ν(x n z 0)

Y ν(x n z 1);

(??):J ν(x n z 0)Y ν(x n z 1)(?+):J ν(x n z 0)

y ν(x n z 1)(24)

Here J ν,Y νare Bessel functions,ν=

z Y ν(z );j ν(z )=J ν?1(z )+(2?ν)

Figure3:ContourΓin the complex plane.The crosses along the real axis correspond to the real positive zeros x n of the function f.

whose zeros are the x n s,one can rewrite the sum in eq.(23)as a complex integral over the contourΓwith R→∞(see?g.3):

S(d)=1

f(z)

(27)

with f one of the functions in eq.(26)10.What follows applies for a generic parity,and therefore we will specify the function f only when necessary.The asymptotic expansion of f(z)when Im z→±∞,the same for all the parities,

f′(z)

z +O(1/z2)(28) tells us that the integral,like the original series,converges at in?nity(R→∞)if d<3. In order to?nd the expression of S(d)for d→4,we?rst take d<3and extract the limit R→∞.The contribution of the integration around the semi-circle of radius R goes to zero and we are left with the vertical contour.Let us call for convenienceΓ+,Γ?the part of this vertical contour respectively above,below the real axis.We now subtract the asymptotic behaviour of f′/f and evaluate it separately deformingΓ+andΓ?to coincide with the real axis.De?ning

F(z)=f′(z)

z

+i(z1?z0)(29)

and using the parity properties f±±(?z)=f±±(z),f±?(?z)=?f±?(z),we obtain: S(d)=

1

2

√2

2πi

Γ+dz F(z)? Γ?dz F(?z) =α

2πi Γ+dz log z2+c2 F(z)? Γ?dz log z2+c2 F(?z)

=log f(ic)+log cπ√

2

+(d/2?2) log f(ic)+log cπ√

πν z1z2z20+2+ν

πν z1

πν z1zz0?zz0zz0

z0

πν z1zz1.

(34)

References [1]Y.Kawamura,

“Gauge symmetry reduction from the extra space S(1)/Z(2)”,Prog.Theor.

Phys.103(2000)613[hep-ph/9902423];“Triplet-doublet splitting,proton stability and extra dimension”,Prog.Theor.Phys.105(2001)999[hep-ph/0012125].

化工行业标准规范

化工行业标准目录 序号化工行业标准名称标准代号单价 1 带压密封技术规范HG/T20201-2007 60.00 2 工程建设安装工程起重施工规范HG20201-200012.00 3脱脂工程施工及验收规范HG20202-2000 6.00 4化工机器安装工程施工及验收规范HG20203-200018.00 5化工金属管道工程施工及验收规范HG20225-199540.00 6工业设备、管道防腐蚀工程施工及验收规范HGJ229-199140.00 7《化工机器安装工程施工及验收规范》 (离心式压缩机) HGJ205-199230.00 8《化工机器安装工程施工及验收规范》 (中小型活塞式压缩机) HGJ206-199230.00 9铝及铝合金焊接技术规程HGJ222-199228.00 10《铜及铜合金焊接钎焊技术规程》HGJ223-199228.00 11《化学工业大、中型装置试车工作规范》HGJ231-199130.00 12《化学工业大、中型装置生产准备工作规范》HGJ232-199230.00 13《化工建设项目进口设备、材料检验大纲》HG20234-199335.00 14《化工建设项目施工设计标准》HG20235-199330.00 15《化工设备安装工程质量检验评定标准》HG20236-199340.00 16《化学工业工程建设交工技术文件规定》HG20237-199460.00 17钢筋混凝土独立式管架通用图HG21539-1992260.00 18钢筋混凝土纵粱式管架通用图HG21540-1992250.00 19焊接H型钢标准节点通用图HG21541-1992260.00 20单轨悬挂吊车梁通用图HG21542-199280.00 21圆形塔平台通用图HG21543-1992150.00 22预埋件通用图HG21544-2006100.00 23 地脚螺栓通用图HG21545-2006 50.00 24钢筋混凝土桁架式管架通用图HG21552-1993320.00 25钢铺板通用图HG21553-199370.00 26《钢制管法兰、垫片紧固件》HG20592-20635-1997150.00 27《钢制人孔和手孔》HG21514-21535-2005148.00 28《钢筋混凝土带式输送机栈桥通用图》HG/T21611.1-1996160.00

TSG 21-2015固定压力容器安全技术监察规程 3

TSG特种设备安全技术规范TSG 21—2015 固定式压力容器安全技术 监察规程 Supervision Regulation on Safety Technology for Stationary Pressure Vessel 中华人民共和国国家质量监督检验检疫总局颁布 2015年月日

TSG R1—2015 特种设备安全技术规范 —2—修订说明 1.以《固定式压力容器安全技术监察规程》、《非金属压力容器安全技术监察规程》、《简单压力容器安全技术监察规程》、《超高压容器安全技术监察规程》(及其2013年修订稿)、《压力容器定期检验规则》、《压力容器使用规则》、《压力容器监督检验规则》等七个规范为基础,内容上不作过大的技术改动,进行上述规程内容的合并以及逻辑关系上理顺,统一并且进一步明确基本安全要求,形成关于固定式压力容器的综合规范(大规范); 2.整理国家质检总局近年来针对压力容器安全监察的有关文件,汇总《固定式压力容器安全技术监察规程》宣贯、实施中存在的具体问题,收集网上咨询意见,增补相应内容,重点解决当前存在的突出问题; 3.开展相关的调研工作,重点解决铸钢、铸铁压力容器材料技术要求(安全系数、化学成分、力学性能和适用范围),增加非焊接结构容器高强钢材料技术要求;完善超高压容器技术要求,完善非金属压力容器,如石墨、玻璃钢的基本安全要求,简化塑料压力容器监管方式;完善安全附件的基本要求,包括安全附件的种类、范围界定、型式试验要求及产品性能要求;推广压力容器设计风险评估报告;统一固定式压力容器分类的方法; 4.按照固定式压力容器各环节分章进行描述,每个环节的边界尽可能清晰,明确相应的主体责任(如耐压试验介质、压力、温度,无损检测方法、比例,热处理等技术要求明确由设计提出并且放到相应设计章节); 5.理顺法规与标准的关系,建立满足法规安全基本要求的协调标准概念; 6.进一步明确基本安全要求的内容,尽量不采用引用标准的方式描述,而是直接阐述其内容;对介质特性、产品结构、试验方法的限定要求,引用相应标准。

各种单位换算及公式

各种单位换算及公式 长度单位面积单位 1 in = 25.4 mm 1 in 2 = 6.45 cm2 1 ft = 0.3048 m 1 ft2 = 0.09 3 m2 1 micron = 0.001 mm 体积单位 1 litre = 0.001 m3 1 cu.ft. = 0.0283 m3 1 cu.in. = 16.39 cm3 1 fluid oz.(imp) = 28.41 mL 1 fluid oz.(us) = 29.57 mL 1 gal(imp) = 4.546 L 1 gal(us) = 3.79 L 温度单位 (°F-32)X5/9=℃K-273.15 = ℃ 功及能量单位 1 Nm = 1 J 1 kgm = 9.807 J 1 kW/hr = 3.6 MJ 1 lbft = 1.356 J 功率单位 1 Nm/sec = 1 W 1 lbft/sec = 1.356 W 1 kgm/sec = 9.807 W 1 Joule/sec = 1 W 1 H.P.(imp) = 745.7 W 质量单位 1 lb = 453.6 g 1 tonne = 1000 kg 1 ton(imp) = 1016 kg 1 ton(us) = 907. 2 kg

流量计算公式 Q = Cv值X 984 = Kv值X 1100 Cv = So ÷ 18 力单位 1 kgf = 9.81 N 1 lbf = 4.45 N 1 kp(kilopound) = 9.81 N 1 poundal = 138.3 mN 1 ton force = 9.964 kM 力矩单位 1 kgm = 9.807 Nm 1 ft. poundal = 0.0421 Nm 1 in lb = 0.113 Nm 1 ft lb = 1.356 Nm 压力单位 1 psi = 6.89 kPa 1 kgf/cm 2 = 98.07 kPa 1 bar = 100 kPa 1 bar = 14.5 psi 1 mm mercury = 133.3 Pa 1 in mercury = 3.39 kPa 1 Torr = 133.3 Pa 1 ft water = 0.0298 bar 1 bar = 3.33 ft water 1 atmosphere = 101.3 kPa 1 cm water = 97.89 Pa 1 in water = 248.64 Pa 换算表 1psi=6.895kPa=0.07kg/cm2=0.06895bar=0.0703atm 1standard atmosphere=14.7psi=101.3kPa=1.01325bar 1kgf/cm2 = 98.07kPa=14.22psi = 28.96ins mercury 1m3 = 1000000cm3 1cu ft/min = 28.3 l/min

承压设备带压密封技术规范

GB/T*****—2008 承压设备带压密封技术规范 编制说明 前言 《承压设备带压密封技术规范》标准由全口锅炉压力容器标准化技术委员会提出并归口。于2007年经国家标准化管理委员会在第五批国家标准制修订计划中批准。 在全国锅炉压力容器标准化技术委员会的指导下,该标准主要起草单位翔悦密封材料有限公司,于2005年起进行标准起草准备工作,于2006年上报该标准立项申报稿。为完善充实该标准,全国锅炉压力容器标准化技术委员会于2007年元月在北京召开了有带压密封技术研究和应用单位参加的会议并成立标准编制组。 为了保证该标准的编制质量,组织召开多次会议,确定编制原则和编写大纲。在编制组内成立了《承压设备带压密封技术规范》编制组。完成初稿后经多次修改,并在天津市翔悦密封材料有限公司网站上广泛征求意见。于2008年8月由全国锅炉压力容器标准化技术委员会固定式压力容器分会将征求意见稿在网上向全国征求意见。对提出的建议经认真研究贯彻到该标准中,力求完善准确。 1、编制目的和意义 带压密封技术在我国于1984年通过省部级技术鉴定,填补了国内空白,属于新型检维修技术。带压密封综合技术包括:包容泄漏部位的夹具、填充密封空腔形成新的密封比压的密封剂、注入密封剂的专用工具和为建立新的密封结构实施的封堵操作技术等四部分。 通过国内外查新未见同类国家标准,该标准是以多年应用实践为基础,结合已进行的科学实验和检测数据作为依据编制的。 带压密封技术应用有以下特点: (1)带压密封技术施工,是在泄漏介质,带温带压喷射工况下封堵,多数介质带有不同的毒性,而且泄漏部位,大部分属于压力容器压力管道,故施工有一定的风险性。因此执行相应安全规范成为必要的因素。 (2)由于带压密封技术适应性广泛,对连续化流程企业的长周期运行,具有显著的企业经济效益和社会效益,因此,目前在石油、化工、冶金、核电、热电、医药等行业广泛应用。(3)带压密封技术必须将四个组成部分协调才能收到好的效果,尤其是泄漏介质的复杂性,使技术成为需多门学科结合起来的边缘技术,带压密封的动态过程,使得经验性非常突出。 为规范带压密封施工应用操作,提高作业的安全性和成功率,特编制该标准。 2、标准编制的指导原则 在编写过程中我们主要基于标准的内容应要点突出,溯源有科学依据,便于和方便使用,(1)带压密封技术基础理论是指导带压密封操作的依据。对泄漏部位进行包容或覆盖、形成一定容积容纳密封剂的空腔,用专用工具将密封剂注入到密封空腔并形成高于泄漏介质压力的密封比压、终止泄漏,建立新的密封结构。 (2)控制密封空腔内的密封剂挤压力,既保持包容或覆盖泄漏部位的包容物(固定夹具、钢带)的稳定,同时又必须保证泄漏法兰螺栓和原泄漏结构不致超载,又能实现密封空腔内的密封剂致密。都是以合理控制密封剂挤压力为基本条件。

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设备润滑技术规范(试行) 定期按照标准对使用设备进行润滑油加注、换油是设备运行过程中减缓磨损,提高使用效率,延长使用寿命,保障安全运行,使之处于完好状态的重要保证,为了更好使用设备,确保有效完成生产任务,特制订本规范。 1、各部门要严格执行本规范内相关的加油、换油规范,认真检查设备相关润滑部位的油质、油量,及时处理润滑缺陷,详细做好加换油记录。 2、维护好润滑用具,做到专油专具,即每一品类润滑油都要有专门的加油油具并都贴上标识,不得混用。 3、加油、换油时润滑油必须严格注意油的品质,严禁杂质进入设备,必要时对润滑油先进行过滤。 4、机修工在对设备进行定期维护,小、大、中修后必须按本规范对设备进行清洗、换油。 5、加油、换油过程中各设备的油位控制必须符合该机器油位标准。

油位标准以标准操作规程为准。 6、设备长时间停止使用的,使用车间应通知机修对该设备进行维修保养。机修要在检维修结束后放光设备内的润滑油,并用清洁的润滑油冲洗油箱后将油放出,并注入新的润滑油后封存设备。 7、各部门要对使用的设备加油、换油时间作出明确的时间规定,并在重新制作设备管理卡时写进此内容。 8、设备运行时严禁加注润滑油。 9、设备运行或静止时严禁带压加注润滑油。 10、设备运行时严禁换油。 11、如因停产或生产没有按时间要求进行加油、换油的则顺延到具备条件时进行加换油,但不得超过规定期限时间的50%。 12、使用部门要对使用设备设立专门的加油记录。换油记录由换油者负责在设备检修记录内以检修项目填写。

13、设备加油工作由设备使用部门自行安排相关人员负责;设备换油工作由机修工结合该设备的检维修计划时间安排换油或者在机修工的指导下由设备使用部门安排换油。 14、使用部门对加油、换油方法需要进行专门培训的,由使用部门提出申请,设备科将给予专门的培训。 15、对相关部门执行本规范不力的,视情况由设备科提出整改、限期整改、责令整改意见并使情况予以相应的处罚。 16、本规范自公布之日起试行。 附:各部门设备润滑技术规范

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神华神东电力有限责任公司神东热电公司带压堵漏技术规范书 发包人:神华神东电力有限责任公司神东热电公司 承包人: 二○一一年十一月八日

目录 1. 总则 (1) 2. 外部条件和运行环境 (2) 3. 主要技术规范 (3) 4. 带压堵漏范围 (11) 5. 服务职责 (12) 6. 质量保证和试验 (16) 7. 报价内容 (17)

1. 总则 1.1本技术规范书适用于神东电力公司上湾热电厂承压管件和大柳塔热电厂承压管件的带压堵漏。它提出了带压堵漏方面的技术要求。 1.2本技术规范书提出的是最低限度的技术要求,并未对一切技术细节做出规定,也未充分引述有关标准和规范的条文,施工单位应提供符合本规范书和工业(行业)标准的施工工艺及方案。 1.3在投标工程中投标方没有以书面形式对本规范书的条文提出异议,则意味着投标方在施工过程以及施工质量完全符合招标技术规范书的要求。 1.4本规范书所使用的标准如遇与投标方所执行的标准发生矛盾,应按较高标准执行。 1.5本技术规范书作为招标文件的技术附件,投标方要认真审阅,按照技术规范书的要求进行报价。

2. 外部条件和运行环境 2.1室外气象条件 厂址:内蒙古鄂尔多斯市伊旗上湾镇以及大柳塔镇 ?气象台站位置:北纬39°34′,东经109°44′,海拔高 度1097.50~1150m ?冬季采暖室外计算温度-18℃ ?冬季通风室外计算温度-12℃ ?夏季通风室外计算温度26℃ ?冬季空气调节室外计算温度-21℃ ?夏季空气调节室外计算温度30℃ ?夏季空调日平均室外计算温度:25℃ ?冬季空气调节室外计算相对湿度:54 % ?最热月月平均室外计算相对湿度:59 % ?夏季室外平均风速 3.6m/s ?冬季室外平均风速 3.6m/s ?夏季主导风向及频率NW—16 %;C—21 % ?冬季主导风向及频率C—11 %;S—10 % ?夏季大气压力872.1hPa ?冬季大气压力863.8hPa ?日平均温度≤+5°C的天数:163 天 ?年平均温度:18℃ ?极端最低温度:-29.6℃ ?极端最高温度:36.1℃ ? 2.2.2电源参数 2.2 所提供的电源参数为:AC 380/220V,50Hz。

压力单位换算方法

工程上常用的是兆帕(MPa):1MPa=1000000Pa。 1个标准大气压力=1.00336×0.098MPa=0.10108MPa≈0.1Mpa。 1bar=0.1MPa 压力的法定单位是帕斯卡(Pa):1Pa=1N/㎡(牛顿/平方米)。 压力单位换算: 1MPa=1000kPa 1kPa=10mbar=101.9716 mmH2O = 4.01463imH2O 10mWC=1bar=100kPa bar 巴= 0.987 大气压= 1.02 千克/平方厘米= 100 千帕= 14.5 磅/平方英寸 PSI英文全称为Pounds per square inch。P是磅pound,S是平方square,I是英寸inch。把所有的单位换成公制单位就可以算出:1bar≈14.5psi 1psi=6.895kPa=0.06895bar

1兆帕(MPa)=145磅/英寸2(psi)=10.2千克/厘米2(kg/cm2)=10巴(bar)=9.8大气压(atm) 1磅/英寸2(psi)=0.006895兆帕(MPa)=0.0703千克/厘米2(kg/cm2)=0.0689巴(bar)=0.068大气压(atm) 1巴(bar)=0.1兆帕(MPa)=14.503磅/英寸2(psi)=1.0197千克/厘米 2(kg/cm2)=0.987大气压(atm) 1大气压(atm)=0.101325兆帕(MPa)=14.696磅/英寸2(psi)=1.0333千克/厘米2(kg/cm2)=1.0133巴(bar) ------------------------------------------------------------------------------------- 压力单位换算方法 1. 1atm=0.1MPa=100KPa=1公斤=1bar=10米水柱=14.5PSI 2.1KPa=0.01公斤 =0.01bar=10mbar=7.5mmHg=0.3inHg=7.5torr=100mmH2O=4inH2O 3. 1MPa=1N/mm2 14.5psi=0.1Mpa 1bar=0.1Mpa 30psi=0.21mpa,7bar=0.7mpa 现将单位的换算转摘如下: Bar---国际标准组织定义的压力单位。 1 bar=100,000Pa 1Pa=F/A, Pa: 压力单位, 1Pa=1 N/㎡ F : 力, 单位为牛顿(N) A: 面积, 单位为㎡ 1bar=100,000Pa=100Kpa 1 atm=101,325N/㎡=101,325Pa 所以,bar是一种表压力(gauge pressure)的称呼。

设备密封管理规定

设备密封管理规定 1、主题内容与适用范围 化工企业历来把设备密封管理与考核作为一项十分重要的工作,因为生产过程中发生泄露关系到安稳长满优生产和员工的生命安全,为此设备部把无泄漏作为设备密封管理的重要内容。为达到创建无泄漏设备、无泄漏分厂、无泄漏企业的目的,特制定本规定。 本规定适用于全公司各分厂。 2、管理内容及要求 2.1设备密封管理 2.1.1系统开车之后,要做好热紧或冷紧工作。 2.1.2化工操作人员必须经过专业培训,考试合格持证上岗。每班要进行认真巡检,发现漏点要做好记录挂漏点标示牌并及时通知专业维修人员进行处理。凡是不停车可以处理的必须在本班内进行消缺堵漏,凡是不停车不能处理的要做好准备一旦有机会立即处理。 2.1.3对运行中带有压力的漏点,所属分厂发现后要立即以书面形式报设备部,设备部要立即组织或联系外委单位在第一时间进行带压堵漏,严格防止事故扩大。堵漏前要对堵漏地点进行测厚分析,并编写堵漏方案,方案经审批后,方可实施堵漏。 2.1.4专业维修人员达到“四懂三会三好”,遵守服务承诺。(四懂:懂结构,懂性能,懂原理,懂用途;三会:会操作,会维护保养,会排除故障;三好:用好,管好,修好。) 2.1.5认真执行设备安全操作规程。

⑴、启动前严细检查。 ⑵、运行中认真巡检,各项指标符合要求,做到“四不准”(不准超温、不准超压、不准超速、不准超负荷)。 ⑶、停车后妥善处理,不把问题交给下一班。 2.1.6设备、管线、表盘、支架、基础、地面、房屋建筑要达到“五不漏”(不漏水、不漏气、不漏油、不漏液、不漏煤)。 2.1.7开展创建“完好设备”活动。 ⑴、完好设备标准 ①、主辅机零部件齐全、质量符合要求; ②、仪表、仪器、信号、连锁等各种安全装置、自动调节装置完整齐全、灵敏、准确; ③、基础机座稳固可靠,各部位连接紧固; ④、管线、阀门、支架安装牢固,标志分明; ⑤、防腐、保温、防冻设施完整有效。 ⑵、设备运转正常,性能良好,达到铭牌出力或核定能力 ①、设备润滑良好,油质符合要求,做到“五定”“三级过滤”; ②、无振动、松动、杂音等不正常现象; ③、各部位温度、压力、转速、流量、电流等运行参数符合要求; ④、生产能力达到铭牌出力或核定能力。 ⑶、技术资料齐全、准确。 ①、设备档案完整。 ②、验收及试车记录齐全; ③、运行时间记录、统计真实;

AWG-标准线径对照表

AWG 标准线径对照表 线径的粗细是以号数(xxAWG)来表示的,数目越小表示线径愈粗,所能承载的电流就越大,反之则线径越细,耐电流量越小。例如说:12号的耐电流量是20安培,最大承受功率是2200瓦,而18号线的耐电流量则是7安培,最大承受功率是770瓦。 为什么AWG号数越小直径反而越大?如这么解释你就会明白,固定的截面积下能塞相同的AWG线的数量,如11#AWG号数可塞11根而15#AWG号数可塞15根,自然的15#AWG的单位线径就较小。 美规线径值单一导体或群导体【各正值或负值】的线径值(Gauge)是以圆或平方厘米(mm2) 量测而得,平方厘米不常用在量测线径值,由于牵涉到不正确,因一般大部份的导体形体,包含长方形及其他怪异形状。因此我们拿全部的量测以圆平方厘米(c/m)为参考值 群导体计算的方法或公式: 加上单一导体的线径值总和,并比较上表求得。如果值落入两者之间,取比较少的值。 40股群导体线的线径值为,如每一芯为24 Guage = 40 x 405 c/m = 16,200 c/m = 9 AWG(得出值落入12960c/m和16440c/m之间) 快速求得线径值的方法: 两条(AWG)相加时,该单一线径值减3. ex. 2 x 18 AWG = (18-3=) 15 AWG 三条(AWG)相加时,该单一线径值减5. ex. 3 x 24 AWG = (24-5=) 19 AWG 四条(AWG)相加时,该单一线径值减6. ex. 4 x 10 AWG = (10-6=) 04 AWG 请记得“快速求得线径值的方法”一些案例也许边际会不正确,只采用此方式为大原则 AWG 标准线径规格对照表

带压密封堵漏技术国家现行标准术语

带压密封(堵漏)技术国家现行标准术语汇编 一、泄漏术语 1)泄漏leaking 高能流体经隔离物缺陷通道向低能区侵入的负面传质现象。 2)界面泄漏interface leaking 高能流体通过密封面间隙向低能区侵入的传质现象。 3)参透泄漏permeating leaking 高能流体通过密封材料毛细管向低能区侵入的传质现象。 4)破坏泄漏destroyed leaking 高能流体通过隔离体裂纹、孔洞及已失效的密封件向低能区侵入的剧烈传质现象。 5)流体fluid 泛指液体、气体、气液混合体、含有固体颗粒的气体或液体。 6)隔离物spacer 特指各种密封构件和物理隔离物;也泛指承压设备、管道、器皿等的可能发生泄漏的壁面和部位。 7)缺陷通道destroying channel 密封副间隙、毛细管、腐蚀孔洞,承压设备上的裂纹、焊接缺陷、冲刷孔洞,物品上的穿透裂纹及孔洞等。 8)负面传质negative mass transfer 不希望发生的流体介质泄漏走向。 9)泄漏介质leaking medium

经隔离物缺陷通道淌失的流体。 10)极度危害介质exceeding hazard medium GB 5044《职业性接触毒物危害程度分级》中表2所规定的介质。 二、带压xx术语 1)xxseal 隔离高能流体向低能区进行负面传质的有效措施。 2)带压密封online sealing 流体介质发生泄漏时,创建新密封结构为目的的技术手段。 3)带压密封工程online sealing engineering 以流体泄漏状态下实现再密封为研究对象,泄漏部位勘测数据为依据,应用基础科学原理及密封理论,结合工程实践活动和科学试验中所积累的理论和技术经验,创建带压密封装置为目的的一门新兴的工程技术学科。 4)带压密封工程原理online sealing engineering principle 应用流体力学的原理,以工程力学和机械科学为理论基础,通过研究流体泄漏状态下的泄漏压力与密封压力间的平衡关系,提供带压密封理论和方法。 5)注剂式带压密封online sealing for injecting sealant 向特定的封闭空腔注射密封注剂,创建新的密封结构为目的的一种技术手段。 6)密封比压sealing pressure 紧固法密封tightening leak sealing 通过紧固钢带、卡箍或缠绕带拉紧使密封材料产生有效密封比压终止泄漏的密封方法。

各种单位换算及公式

各种单位换算及公式

各种单位换算及公式 长度单位面积单位 1 in = 25.4 mm 1 in 2 = 6.45 cm2 1 ft = 0.3048 m 1 ft 2 = 0.09 3 m2 1 micro n = 0.001 mm 体积单位 1 litre = 0.001 m3 1 cu.ft. = 0.0283 m3 1 cu.i n. = 16.39 cm3 1 fluid oz. (imp) = 28.41 mL 1 fluid oz. (us) = 29.57 mL 1 gal(imp) = 4.546 L 1 gal(us) = 3.79 L 温度单位 (°-32)X5/9= C K-273.15 = C 功及能量单位 1 Nm = 1 J 1 kgm = 9.807 J 1 kW/hr = 3.6 MJ 1 Ibft = 1.356 J 功率单位 1 Nm/sec = 1 W 1 lbft/sec = 1.356 W 1 kgm/sec = 9.807 W 1 Joule/sec = 1 W 1 H.P.(imp) = 745.7 W

质量单位 1 to nne = 1000 kg 1 lb = 453.6 g

流量计算公式 Q = Cv 值X 984 = Kv 值X 1100 Cv = So 48 力单位 1 kgf = 9.81 N 1 Ibf = 4.45 N 1 kp(kilopou nd) = 9.81 N 1 pou ndal = 138.3 mN 1 ton force = 9.964 kM 力矩单位 1 kgm = 9.807 Nm 1 ft. poun dal = 0.0421 Nm 1 in lb = 0.113 Nm 1 ft lb = 1.356 Nm 压力单位 1 psi = 6.89 kPa 1 kgf/cm 2 = 98.07 kPa 1 bar = 100 kPa 1 bar = 14.5 psi 1 mm mercury =133.3 Pa 1 in mercury =3.39 kPa 1 Torr = 133.3 Pa 1 ft water = 0.0298 bar 1 bar = 3.33 ft water 1 atmosphere = 101.3 kPa 1 cm water = 97.89 Pa 1 in water = 248.64 Pa 换算表 1psi=6.895kPa=0.07kg/cm2=0.06895bar=0.0703atm 1sta ndard atmosphere=14.7psi=101.3kPa=1.01325bar 1kgf/cm2 = 98.07kPa=14.22psi = 28.96i ns mercury 1m3 = 1000000cm3

带压堵漏作业规范

带压堵漏作业规范 1、定义:带压堵漏技术是在运行状态下对管道、法兰、阀门的泄漏部位(原来封闭空腔或新建立的空腔)注入密封剂而实现消除泄漏的临时性应急措施(不包括焊接打套部分)。 2、级别划分: 2.1、为有利于带压堵漏技术应用管理,根据带压堵漏技术及封堵条件的不同,将注胶堵漏作业分为两个等级。同时具备下列条件为一类作业: 1)泄漏点温度:-20℃<T≤300℃; 2)泄漏点压力:P≤4.0MPa; 3)泄漏介质:空气、水、水蒸汽、油类、酸、碱等危害性较小的介质; 4)泄漏部位:法兰公称直径Φ≤600毫米的法兰密封面泄漏;5)管道、阀门泄漏部位在地面或有围栏的固定平台处作业。 2.2、具备下列情况之一的为二类作业: 1)泄漏点温度:300℃<T<650℃; 2)泄漏点压力:4.0MPa<P<32MPa; 3)泄漏介质:毒性危害程度为中度、高度的介质如DMF、四氯化碳、氯、氟化氢; 3、各类低温压力容器及管道应用带压堵漏无安全保障时,不采用带压堵漏,而按有关压力容器及管道规程管理。有下列情况之一

者,不能进行带压注胶堵漏作业: 1)毒性程度为极度的介质如苯、氯乙烯等; 2)设备主要受压元件及管道因裂纹而产生的泄漏部位; 3)高压、高温管道漏点; 4)管道腐蚀、冲刷减薄状况不清楚的泄漏点; 5)由于介质泄漏,使螺栓承受高于原来设计使用温度的泄漏点;6)由于介质泄漏,易使螺栓受到腐蚀的泄漏点; 7)堵漏现场安全措施不符合企业安全规定。 4、带压注胶堵漏作业的相关要求: 1)带压堵漏的施工单位必须设技术负责人,并配备必要的检测仪器及可靠的的堵漏工机具。施工过程中,现场专人负责带压堵漏技术的现场操作及安全措施的落实,并对施工质量和可靠性负责。2)带压堵漏施工前应做好准备工作。专业技术人员和施工操作人员要到泄漏现场详细调查和勘测,进行强度核算,提出具体施工方案,制定有效的操作要求和防护措施。 3)凡应用带压堵漏的作业人员必须经专业培训并持证操作。 4)凡经培训获证的作业人员中,应有取得带压密封专用夹具设计资格的人员,否则只能组织进行一类作业。 5)严格执行带压堵漏相关的国家劳动安全技术标准。高压、高温、剧毒介质管道出现泄漏情况时,要及时进行停车处理,原则上不允许带压堵漏或带压紧固。 5、专用夹具规定:

常用线规号码与线径对照表

常用线规号码与线径对照表

线规SWG BWG BG AWG 号码英寸毫米英寸毫米英寸毫米英寸毫米 7/0 6/0 5/0 4/0 3/0 2/0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 0.500 0.464 0.432 0.400 0.372 0.348 0.324 0.300 0.276 0.252 0.232 0.212 0.192 0.176 0.160 0.144 0.128 0.116 0.104 0.092 0.080 0.072 0.064 0.056 0.048 0.040 0.036 0.032 0.0280 0.0240 0.0220 0.0200 0.0180 12.700 11.786 10.973 10.160 9.449 8.839 8.230 7.620 7.010 6.401 5.893 5.385 4.877 4.470 4.046 3.658 3.251 2.946 2.642 2.337 2.032 1.829 1.626 1.422 1.219 1.016 0.914 0.813 0.711 0.610 0.559 0.508 0.457 -- -- 0.500 0.454 0.425 0.330 0.340 0.300 0.284 0.259 0.238 0.220 0.203 0.180 0.165 0.148 0.134 0.120 0.109 0.095 0.083 0.072 0.065 0.058 0.049 0.042 0.035 0.032 0.028 0.025 0.022 0.020 0.018 -- -- 12.700 11.532 10.795 9.652 8.639 7.620 7.214 6.579 6.045 5.588 5.156 4.572 4.191 3.759 3.404 3.048 2.769 2.413 2.108 1.829 1.651 1.473 1.245 1.067 0.839 0.813 0.711 0.635 0.559 0.508 0.457 0.6666 0.6250 0.5883 0.5416 0.5000 0.1152 0.3954 0.3532 0.3147 0.2804 0.2500 0.2225 0.1981 0.1764 0.1570 0.1398 0.1250 0.1313 0.0991 0.0882 0.0785 0.0699 0.0625 0.0556 0.0495 0.0440 0.0392 0.0349 0.03125 0.02782 0.02476 0.02204 0.01961 16.932 15.875 14.943 13.757 12.700 11.308 10.069 8.971 7.993 7.122 6.350 5.652 5.032 4.481 3.988 3.551 3.175 2.827 2.517 2.240 1.994 1.775 1.588 1.412 1.257 1.118 0.996 0.887 0.794 0.707 0.629 0.560 0.498 -- 0.5800 0.5165 0.4600 0.4096 0.3648 0.3249 0.2893 0.2576 0.2294 0.2043 0.1819 0.1620 0.1443 0.1285 0.1144 0.1019 0.0907 0。0808 0.0720 0.0648 0.0571 0.0508 0.0453 0.0403 0.0359 0.0320 0.0285 0.02535 0.02010 0.01790 0.01594 0.01420 -- 14.732 13.119 11.684 10.404 9.266 8.252 7.348 6.544 5.827 5.189 4.621 4.115 3.665 3.264 2.906 2.588 2.305 2.053 1.828 1.628 1.450 1.291 1.150 1.024 0.912 0.812 0.723 0.644 0.573 0.511 0.455 0.405 常用线规号码与线径对照表

带压堵漏安全管理规定(新版)

( 安全管理 ) 单位:_________________________ 姓名:_________________________ 日期:_________________________ 精品文档 / Word文档 / 文字可改 带压堵漏安全管理规定(新版) Safety management is an important part of production management. Safety and production are in the implementation process

带压堵漏安全管理规定(新版) 1目的和范围 为规范带压堵漏安全管理,降低作业风险,确保作业人员安全,特制定本规定。 本规定适用于各装置运行状态下的设备、管道、法兰、阀门等泄漏部位带压、带温堵漏的安全管理。 2管理职责 2.1设备部负责带压堵漏作业的管理。 2.2带压堵漏单位负责制定带压堵漏安全操作规程、作业方案等,负责带压堵漏作业的实施及管理。 2.3各分厂、车间负责带压堵漏作业过程中的工艺管理,提供工艺、设备相关参数及相关安全要求。 2.4HSE管理部对带压堵漏作业进行监督检查。 3管理流程

3.1总体要求 3.1.1设备部对带压堵漏单位、操作人员的资质进行审核,确保满足带压堵漏作业要求。 3.1.2带压堵漏作业专用工具和施工工具必须满足耐温、耐压、防火防爆和国家规定的其它安全要求,不允许在现场使用不合格的工具。 3.1.3带压堵漏作业防护用品必须符合标准。 3.1.4每次作业前都必须取得公司相关部门的同意后,才能按方案进行带压堵漏作业。 3.2带压堵漏作业风险分析及方案、防护措施的制定 3.2.1泄漏介质分为普通介质和危险介质,其中危险介质有:高温高压介质、有毒介质、腐蚀和烧灼介质、易燃易爆介质等。 3.2.2作业前,施工单位对现场进行检查,对泄漏部位的泄漏介质、温度、压力、孔洞大小,外部尺寸和缺陷等情况必须勘测清楚,认真记录,彻底了解现场工况,针对泄漏的介质及带压堵漏操作可能带来的风险,制定施工方案和安全措施。

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线材线号AWG与导线截面积对照表 芯线

American Wire Gauge AWG mm2 42 0.003 1/0.06 41 0.004 1/0.07 40 0.005 1/0.08 38 0.008 1/0.10 36 0.013 1/0.127 34 0.020 1/0.16 7/0.06 32 0.032 1/0.203 7/0.08 8/0.07 11/0.06 30 0.051 1/0.26 7/0.10 11/0.08 14/0.07 19/0.06 28 0.081 1/0.32 7/0.12 11/0.10 16/0.08 21/0.07 28/0.06 26 0.129 1/0.40 7/0.16 9/0.14 11/0.12 16/0.10 25/0.08 33/0.07 45/0.06 24 0.205 1/0.50 7/0.20 14/0.14 19/0.12 26/0.10 41/0.08 53/0.07 73/0.06 22 0.326 1/0.65 7/0.26 11/0.203 13/0.18 17/0.16 22/0.14 29/0.12 42/0.10 65/0.08 20 0.518 1/0.80 7/0.30 10/0.26 12/0.23 16/0.203 20/0.18 26/0.16 34/0.14 46/0.12 66/0.10 18 0.823 1/1.02 7/0.40 10/0.32 16/0.26 20/0.23 26/0.203 33/0.18 41/0.16 54/0.14 73/0.12 65/0.127 104/0.10 16 1.309 1/1.29 7/0.50 11/0.40 17/0.32 25/0.26 32/0.23 41/0.203 52/0.18 65/0.16 85/0.14 119/0.12 165/0.10 14 2.081 1/1.63 11/0.50 17/0.40 26/0.32 40/0.26 50/0.23 65/0.203 82/0.18 103/0.16 135/0.14 183/0.12 264/0.10 12 3.309 1/2.05 17/0.50 27/0.40 41/0.32 54/0.28 80/0.23 102/0.203 130/0.18 164/0.16 10 5.261 1/2.60 27/0.50 42/0.40 65/0.32 99/0.26 126/0.23 162/0.203 206/0.18 261/0.16 8 8.366 1/3.26 26/0.65 67/0.40 104/0.32 157/0.26 6 13.30 1/4.12 27/0.80 40/0.65 68/0.50 105/0.40 165/0.32 4 21.1 5 1/5.20 26/1.02 42/0.80 64/0.65 107/0.50 168/0.40 2 33.6 3 1/6.54 4 26/1.29 42/1.02 67/0.80 101/0.6 5 171/0.50 0 53.48 1/8.254 26/1.63 41/1.29 66/1.02 106/0.80 161/0.65 1. 基准线规直径:直径5 mil(0.005 inch)为36 AWG: 2. 相邻线号之间以几何级数计算:见右框图中公式。 例如:d18 = d36 × r (36-18) = 5 × 8.06053 = 40.3mils = 1.024mm d n = d 36× r (36 - n)( mil ) = 0.127 r(36 - n)( mm ) 其中,r = (460/5) 1/39 = 1.1229322

Gauge 板材 换算

Gauge 板材換算

钢材理论重量计算 钢材理论重量计算的计量单位为公斤(kg )。其基本公式为: 钢的密度为:7.85g/cm3 ,各种钢材理论重量计算公式如下: 圆钢盘条(kg/m)W= 0.006165 ×d×d d = 直径mm 直径100 mm 的圆钢,求每m 重量。每m 重量= 0.006165 ×1002=61.65kg 螺纹钢(kg/m)W= 0.00617 ×d×d d= 断面直径mm 断面直径为12 mm 的螺纹钢,求每m 重量。每m 重量=0.00617 ×12 2=0.89kg 等边角钢(kg/m)= 0.00785 ×[d (2b – d )+0.215 (R2 –2r 2 )] b= 边宽 d= 边厚R= 内弧半径r= 端弧半径求20 mm ×4mm 等边角钢的每m 重量。从冶金产品目录中查出4mm ×20 mm 等边角钢的R 为3.5 ,r 为1.2 ,则每m 重量= 0.00785 ×[4 ×(2 ×20 – 4 )+0.215 ×(3.52 – 2 ×1.2 2 )]=1.15kg 不等边角钢(kg/m)W= 0.00785 ×[d (B+b –d )+0.215 (R2 – 2 r 2 )] B= 长边宽 b= 短边宽d= 边厚R= 内弧半径r= 端弧半径求30 mm ×20mm ×4mm 不等边角钢的每m 重量。从冶金产品目录中查出30 ×20 ×4 不等边角钢的R 为3.5 ,r 为1.2 ,则每m 重量= 0.00785 ×[4 ×(30+20 –4 )+0.215 ×(3.52 –2 ×1.2 2 )]=1.46kg 钢板(kg/m2)W= 7.85 ×d d= 厚厚度4mm 的钢板,求每m2 重量。每m2 重量=7.85 ×4=31.4kg 钢管(包括无缝钢管及焊接钢管(kg/m)W= 0.02466 ×S (D –S )D= 外径 S= 壁厚外径为60 mm 壁厚4mm 的无缝钢管,求每m 重量。每m 重量= 0.02466 ×4 ×(60 –4 )=5.52kg

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