CN105574341B - A kind of bolt room temperature pretightning force computational methods to work under worst cold case - Google Patents
A kind of bolt room temperature pretightning force computational methods to work under worst cold case Download PDFInfo
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- CN105574341B CN105574341B CN201510955118.4A CN201510955118A CN105574341B CN 105574341 B CN105574341 B CN 105574341B CN 201510955118 A CN201510955118 A CN 201510955118A CN 105574341 B CN105574341 B CN 105574341B
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Abstract
The invention discloses the bolt room temperature pretightning force computational methods to work under a kind of worst cold case, are calculated available for the room temperature Prestress design for being operated in less than 40 DEG C bolts.Its design procedure, which includes, calculates bolt, nut, bolt head, gasket axial rigidity；Calculate connected piece axial rigidity；Calculate pressure containing part overall stiffness and deformation distribution coefficient；Calculate bolt and recommend assembly pretightening power；By above flow, bolt pretightening can be made to be in moderate level at low temperature, the thermal stress that will not be produced because of temperature change makes bolt pretightening too low or excessive.
Description
【Technical field】
The invention belongs to bolt technical field, and in particular to the bolt room temperature pretightning force to work under a kind of worst cold case calculates
Method.
【Background technology】
Bolt can gradually produce pretension tension in assembling process in its cross section, and appropriate pretightning force value is to bolt
The safety of connection and effectively it is particularly significant.The equipment (such as ultralow temperature BOG compressors) of worst cold case, its bolt are in for some
Operating temperature is different from fitting temperature, and bolt connection piece is often made of different materials, at this time due to the different heat of connector
Deform, the pretightning force at a temperature of working bolt can change.According to the combination of bolt connection piece material, its low temperature pretightning force phase
Pretightning force than room temperature may both rise, it is also possible to decline.When bolt material coefficient of thermal expansion is higher than connected piece, spiral shell under low temperature
The higher contraction of bolt can rise pretightning force, and then pretightning force on the contrary declines.And the value of pretightning force needs to ensure that it is working
At a temperature of be in moderate level, it is impossible to make connection loosen can not make bolt occur tension surrender or destroy.It is therefore desirable to
The value of adjustment bolt room temperature pretightning force accordingly.
【The content of the invention】
It is contemplated that being based on analytic method, the side that a kind of bolt room temperature pretightning force to work under worst cold case calculates is proposed
Method, calculates available for the room temperature Prestress design for being operated in less than -40 DEG C bolts.Utilize this method, it is known that bolt arrangement size,
Material parameter, operating temperature and the requirement to pretension level can calculate the pretightning force under room temperature.And can basis
Particular job characteristic residing for bolt, such as stress concentration, external applied load, temperature change, are adjusted pretightning force.
To reach above-mentioned purpose, the present invention is achieved by the following scheme：
The bolt room temperature pretightning force computational methods to work under a kind of worst cold case, comprise the following steps：
1) axial rigidity of each component is calculated
The axial rigidity of bolt, nut, bolt head and gasket 1-1) is calculated respectively；
Wherein, kbFor the axial rigidity of bolt, knFor the axial rigidity of nut, khFor the axial rigidity of bolt head, kwFor pad
The axial rigidity of piece, EbFor the elasticity modulus of materials of bolt, EnFor the elasticity modulus of materials of nut, EhFor the material bullet of bolt head
Property modulus, EwFor the elasticity modulus of materials of gasket, AbAccumulated for the axial cross section of bolt, AnAccumulated for the axial cross section of nut, AhFor spiral shell
The axial cross section product of bolt head, AwAccumulated for the axial cross section of gasket, LbFor the axial length of bolt, LnFor the axial length of nut, Lh
For the axial length of bolt head, LwFor the axial length of gasket；
1-2) when the outside diameter d of connected pieceaDuring≤β d, the axial rigidity k of connected piece is calculated using formula (5)c：
When the outside diameter d of connected pieceaDuring >=β d+L, the axial rigidity k of connected piece is calculated using formula (6)cmax：
As outside diameter β d≤d of connected pieceaDuring≤β d+L, the axial rigidity k of connected piece is calculated using formula (7)c：
Wherein, β represents the proportionality coefficient of bolt head outside diameter；D represents the diameter of bolt；The proportionality coefficient of α connected piece internal diameters；
kc0Represent to work as d in formula (5)aValue during=β d；The elasticity modulus of materials of E ' expression connected pieces；The axis of L ' expression connected pieces
To length
2) pressure containing part overall stiffness k is calculatedc' and deformation distribution coefficient m：
3) bolt pretightening F is calculatednValue
3-1) calculate bolt pretightening FnValue recommendation：
Fn=x σsAb+m(αb-αc)ΔT·Lb·kb (10)
Wherein, x is the requirement to tools for bolts ' pretension stress level, σ under operating temperaturesFor bolt material yield stress, Δ T is
The difference of operating temperature and pretension temperature, αbFor the coefficient of thermal expansion of bolt material, αcFor the coefficient of thermal expansion of connected piece material；
When 3-2) need to such as ensure the intensity at bolt stress concentration, pretightning force FnValue range calculate according to the following formula：
bσsAb+m(αb-αc)ΔT·Lb·kb≤Fn≤σsAb/a+m(αb-αc)ΔT·Lb·kb (11)
In formula, b is the proportionality coefficient that pretension performance is kept under operating temperature, and a concentrates for bolt fastening structure maximum stress
Coefficient；
When 3-3) need to such as consider pretightning force change of the bolt in operating temperature range, pretightning force FnValue according to the following formula
Calculate：
In formula, Δ T1With Δ T2Respectively operating temperature bound and the difference of room temperature；
3-4) when there is external applied load superposition, formula (11) can be further improved as with formula (12)：
bσsAb+m(αb-αc)ΔT·Lb·kb≤Fn≤σsAb/a+m(αb-αc)ΔT·Lb·kb-P (13)
Wherein, P is the axial component of external applied load.
Compared with prior art, the invention has the advantages that：
1) change of bolt low temperature pretightning force can be more accurately predicted in the present invention.Existing calculating bolt pretightening change
Document do not consider that bolt connection piece intraware rigidity so that the influence of pretightning force, or only considered bolt to deformation distribution
With the rigidity and deformation relationship of connected piece.And the present invention equally examines the rigidity of the pressure containing parts such as bolt head, nut and gasket
Consider into, calculate pressure containing part overall stiffness and deformation distribution coefficient.Improved deformation distribution coefficient calculation formula can be more
Thermal deformation difference under low temperature is calculated exactly and is assigned to the ratio on bolt, so as to more accurately calculate bolt pretightening under low temperature
Change.
2) present invention can be directed to the room temperature assembling recommendation of various condition calculating bolt pretightenings.Bolt at work can
In face of various different operating modes and mechanical state.In the present invention, various operating modes and mechanical state can be examined according to design requirement
Consider into.Including：It can ensure that the intensity of bolt arrangement stress raiser under operating temperature is qualified；It can ensure that bolt exists
Its pretightning force is in moderate level in larger operating temperature range；Can ensure bolt external applied load with the superposition of pretightning force
Its intensity is still qualified；Multifactor synergy above；
【Brief description of the drawings】
Fig. 1 is the flow diagram of the present invention；
Fig. 2 is the structure diagram of bolt connection piece of the present invention.
【Embodiment】
The present invention is described in further detail below in conjunction with the accompanying drawings：
Bolt connection piece is generally made of bolt, nut, connected piece, gasket.Bolt is cut during pretension in bolt
Axial pre tightening force is produced on face, and at low temperature since bolt is different from the material of connected piece, the two possesses different heat receipts
Contracting amount, thus pretightning force can produce change.Pretightning force moderate at normal temperatures is horizontal, at low temperature may be too high or too low,
Therefore need according to the pretightning force value under low temperature during the change adjustment room temperature bolts assemblies of pretightning force.Calculate bolt pretightening
Change, it is necessary first to calculate the axial rigidity of each component.Axial rigidity is the ratio between axial force and axial deformation suffered by each component,
Its value depends on each component material and shape etc..Afterwards, the entirety of pressure containing part is obtained by each component contact relation and loading characteristic
Rigidity and deformation allocation proportion, the ratio determine pretightning force variable quantity caused by thermal shrinking quantity difference.Finally, it is necessary to calculate heat
The difference of deformation, this can be drawn by the coefficient of thermal expansion difference and the temperature difference of each assembly material, axial by heat distortion amount difference, bolt
Rigidity and the product of deformation coefficient are that can obtain the changing value of bolt pretightening under low temperature.
Referring to Fig. 1, the present invention comprises the following steps：
1) axial rigidity of bolt, nut, bolt head and gasket is calculated respectively；
Wherein, kbFor the axial rigidity of bolt, knFor the axial rigidity of nut, khFor the axial rigidity of bolt head, kwFor pad
The axial rigidity of piece, EbFor the elasticity modulus of materials of bolt, EnFor the elasticity modulus of materials of nut, EhFor the material bullet of bolt head
Property modulus, EwFor the elasticity modulus of materials of gasket, AbAccumulated for the axial cross section of bolt, AnAccumulated for the axial cross section of nut, AhFor spiral shell
The axial cross section product of bolt head, AwAccumulated for the axial cross section of gasket, LbFor the axial length of bolt, LnFor the axial length of nut, Lh
For the axial length of bolt head, LwFor the axial length of gasket；
Several components above, it is considered that its global sections is uniformly tension or in compression under Pre strained state, therefore can make
Its axial rigidity is calculated with mechanics of materials classical formulas.
2) axial rigidity of connected piece is calculated.Its connected piece of different bolt connection pieces is different, and it is pre-
The partial compression that connected piece only has and nut and bolt head contacts under tight state, therefore its axis cannot be calculated using classical formulas
To rigidity.Connected piece axial rigidity there is no unified formula at present, be disc shaped for connected piece shape, available
Following formula calculate.For other shapes, it may be referred to other documents or utilize Finite element arithmetic.
As shown in Fig. 2, the outside diameter d according to connected pieceaAnd select different calculation formula.Work as daVery little, its gross section
When being pressurized, equally axial rigidity is calculated using above formula：
And work as daWhen very big, it is assumed that connected piece rigidity does not continue to change with its outside diameter：
Work as daWhen placed in the middle, its axial rigidity is calculated using exponential association formula：
Wherein, kc0For d in formula (5)aValue during=β d.
3) pressure containing part coupling stiffness k is calculatedc' and deformation distribution coefficient m：
Under tools for bolts ' pretension state, bolt head, nut, connected piece and gasket belong to pressured state, and bolt then belongs to
Tension state.Therefore the overall stiffness k of pressure containing part can be drawn according to Stiffness formulac'.And pressure containing part overall stiffness and spiral shell
Proportionate relationship between bolt rigidity is known as deforming distribution coefficient, its value represents the ratio that thermal deformation difference causes bolt pretightening to change
Example.Illustrate below and the physical significance of the coefficient is illustrated：Assuming that pressure containing part belongs to plastic material, its rigidity is approximately 0, such as
Connected piece thermal shrinking quantity is more than bolt, there is the tendency for producing gap therebetween, at this time since pressure containing part is pure plasticity, all
Deformation is assigned on pressure containing part, m=0, and bolt pretightening will not change at this time.And assume that pressure containing part is pure rigid body, by
It will not be deformed during power, its axial rigidity is+∞, m=1, and whole thermal deformation differences are undertaken by bolt, and pretightning force change at this time is most
Greatly.For actual bolt connection piece, each component has certain rigidity, and the value of m is determined by each component ratio of rigidity example.
4) conventional stud pretightning force value recommendation is calculated：
Fn=x σsA+m(αb-αc)ΔT·L·kb (10)
This formula is formed by two additions, the consequent pretightning force difference for representing temperature change and bringing, and Δ T is for operating temperature and in advance
The difference of tight temperature.αbαcThe respectively coefficient of thermal expansion of bolt material and connected piece material, (αb-αc) Δ TL be low temperature under
The thermal deformation difference of bolt entirety.m(αb-αc)ΔT·L·kbFor the variable quantity of bolt pretightening.X is to spiral shell under operating temperature
The requirement of bolt pre-tight stress, σsFor bolt material yield stress.Such as requiring at a temperature of working bolt pre-tight stress to reach surrender should
The 60% of power, then x=0.6.
Two are added the assembly pretightening power recommendation that can obtain under room temperature.Such as：When bolt coefficient of thermal expansion is higher,
Bolt amount of contraction is higher than connected piece under low temperature, and bolt pretightening can increase under low temperature, therefore must reduce pretightning force under room temperature and take
Value.Δ T is negative value during low temperature in formula, (αb-αc) it is on the occasion of consequent generally negative, i.e., room temperature pretightning force value should reduce.
5) stress concentration is considered into interior pretightning force value range：
bσsA+m(αb-αc)ΔT·L·kb≤Fn≤σsA/a+m(αb-αc)ΔT·L·kb (11)
Bolt connection piece can produce obvious stress concentration at bolt head, screw thread etc. in the operating condition, even if bolt
Section is averaged, and tension is not high, and stress raiser stress may also exceed material yield strength.(11) formula of utilization can ensure spiral shell
Stress raiser stress is still within moderate state under bolt working status.
B is the proportionality coefficient that pretension performance is kept under operating temperature in formula, can be determined according to the specific design requirement of bolt.a
For bolt fastening structure maximum stress coefficient of concentration.(11) can be kept under the bolt pretightening scope, that is, working status determined in formula
The pretightning force minimum and stress raiser of pretension performance reach the pretightning force peak of maximum permissible stress.
6) pretightning force value range when bolt works in certain temperature range：
When bolt works in certain temperature range, it is necessary to ensure that its pretightning force level in working range is moderate,
I.e. pretightning force can meet minimum pretension performance, while stress level is less than material allowable stress at proof stress concentration, its is pre-
Clamp force value refers to following formula：
Δ T in formula1With Δ T2Respectively operating temperature bound and the difference of room temperature.Fn3Value lower limit represent working
Keep the highest pretightning force of pretension performance in temperature range, the value upper limit represent make stress raiser maximum stress reach it is allowable should
The minimum pretightning force of power.
7) bolt pretightening value when external applied load is superimposed：
When bolt in the operating condition by external load function when, external applied load is superimposed with pretightning force may further improve bolt
Stress level, it is therefore desirable to consider the influence of external applied load into, pretightning force value when adjustment room temperature assembles.Formula (11) and formula
(12) can be improved as：
bσsA+m(αb-αc)ΔT·L·kb≤Fn≤σsA/a+m(αb-αc)ΔT·L·kb-P (13)
Wherein P is the axial component of external applied load.
Embodiment：
Bolt fastening structure relative dimensions can see the table below in the present embodiment：
1 bolt fastening structure dimensional parameters of table
Bolt material is SIC815 steel alloys in the present embodiment, and connected piece material is 304 stainless steels, the two related physical
Property is as shown in the table：
2 bolt connection piece material physical properties of table
At this time, bolt coefficient of thermal expansion is less than connected piece, and bolt pretightening will reduce at low temperature, i.e., bolt has generation
Loose tendency is, it is necessary to improve the value of pretightning force when room temperature assembles.
Firstly the need of calculating rigidity of bolt connecting piece and distribution coefficient m, result of calculation such as following table：
3 rigidity of table and deformation distribution coefficient calculate
Bolt strength specification presses 8.8 grades, i.e. yield stress σs=640MPa.Room temperature T0=25 DEG C, work temperature=- 100
DEG C, i.e. T=-125 DEG C of temperature difference.
As working bolt state is simple or only to bolt pretightening progress rough calculation, is simply counted using formula (10)
Calculate.X can use 0.6, and representing bolt, pre-tight stress reaches the 60% of yield stress at the working temperature.When can be calculated room temperature assembling
Recommendation pretightning force is Fn=1600kN；Pretension tension is 498MPa when room temperature assembles.
Taken into account as stress concentration phenomenon will be bolted, that is, it is excessive to be not intended to stress at bolt stress concentration, can adopt
With formula (11).The coefficient of minimum pretension is kept when b is working bolt in formula, it is bolt arrangement stress concentration to take 0.3, a herein
Coefficient, refers to handbook and determines, take 1.67 herein.Can be calculated room temperature assembly pretightening power scope is Fn=985-1600kN
, can when the fluctuation of working bolt temperature range is larger, it is necessary to keep moderate pretightning force in operating temperature range
Reference formula (12).Assuming that working bolt temperature range is arranged to -100~-50 DEG C, room temperature assembly pretightening power scope can be calculated
For Fn=985-1450kN.
Also it is superimposed when working bolt by external load, its suffered axial stress should be superimposed consideration into pretightning force value.
Bolt is by the reciprocal inertia force of maximum 300kN, i.e. P=160kN in this example.It can be calculated according to formula (13) and (14).According to formula
(13) F is calculated to obtain with (14)n=985-1300kN.
The pretightning force value model under different operating modes, design condition can be obtained by formula (11), (12), (13), (14)
Enclose, feasible solution such as cannot get by above-mentioned formula, illustrate that pretightning force can not meet design condition, it is necessary to adjust under the operating mode
The value of relation number (a, b).
Above content is merely illustrative of the invention's technical idea, it is impossible to protection scope of the present invention is limited with this, it is every to press
According to technological thought proposed by the present invention, any change done on the basis of technical solution, each falls within claims of the present invention
Protection domain within.
Claims (1)
1. the bolt room temperature pretightning force computational methods to work under a kind of worst cold case, it is characterised in that comprise the following steps：
1) axial rigidity of each component is calculated
The axial rigidity of bolt, nut, bolt head and gasket 1-1) is calculated respectively；
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Wherein, kbFor the axial rigidity of bolt, knFor the axial rigidity of nut, khFor the axial rigidity of bolt head, kwFor gasket
Axial rigidity, EbFor the elasticity modulus of materials of bolt, EnFor the elasticity modulus of materials of nut, EhFor the elastic properties of materials mould of bolt head
Amount, EwFor the elasticity modulus of materials of gasket, AbAccumulated for the axial cross section of bolt, AnAccumulated for the axial cross section of nut, AhFor bolt head
Axial cross section product, AwAccumulated for the axial cross section of gasket, LbFor the axial length of bolt, LnFor the axial length of nut, LhFor spiral shell
The axial length of bolt head, LwFor the axial length of gasket；
1-2) when the outside diameter d of connected pieceaDuring≤β d, the axial rigidity k of connected piece is calculated using formula (5)c：
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As outside diameter β d≤d of connected pieceaDuring≤β d+L, the axial rigidity k of connected piece is calculated using formula (7)c：
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Wherein, β represents the proportionality coefficient of bolt head outside diameter；D represents the diameter of bolt；α represents the proportionality coefficient of connected piece internal diameter；
kc0Represent to work as d in formula (5)aValue during=β d；The elasticity modulus of materials of E ' expression connected pieces；L represents the axis of connected piece
To length；
2) pressure containing part overall stiffness k is calculatedc' and deformation distribution coefficient m：
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<mi>m</mi>
<mo>=</mo>
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3) bolt pretightening F is calculatednValue
3-1) calculate bolt pretightening FnValue recommendation：
Fn=x σsAb+m(αb-αc)ΔT·Lb·kb (10)
Wherein, x is the requirement to tools for bolts ' pretension stress level, σ under operating temperaturesFor bolt material yield stress, Δ T is work
The difference of temperature and pretension temperature, αbFor the coefficient of thermal expansion of bolt material, αcFor the coefficient of thermal expansion of connected piece material；
When 3-2) need to such as ensure the intensity at bolt stress concentration, pretightning force FnValue range calculate according to the following formula：
bσsAb+m(αb-αc)ΔT·Lb·kb≤Fn≤σsAb/a+m(αb-αc)ΔT·Lb·kb (11)
In formula, b is the proportionality coefficient that pretension performance is kept under operating temperature, and a is bolt fastening structure maximum stress coefficient of concentration；
When 3-3) need to such as consider pretightning force change of the bolt in operating temperature range, pretightning force FnValue calculate according to the following formula：
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In formula, Δ T1With Δ T2Respectively operating temperature bound and the difference of room temperature；
3-4) when there is external applied load superposition, formula (11) can be further improved as with formula (12)：
bσsAb+m(αb-αc)ΔT·Lb·kb≤Fn≤σsAb/a+m(αb-αc)ΔT·Lb·kb-P (13)
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</mrow>
Wherein, P is the axial component of external applied load.
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| CN108917997B (en) * | 2018-07-27 | 2020-08-11 | 中国核动力研究设计院 | Adapting unit stress detecting system suitable for narrow and small space |
| CN110348110B (en) * | 2019-07-08 | 2022-05-20 | 西安交通大学 | Self-adaptive identification method for rigidity of bolt-to-connector |
| CN113806881A (en) * | 2021-08-13 | 2021-12-17 | 安徽江淮汽车集团股份有限公司 | Cylinder head bolt tightening method |
| CN116702570B (en) * | 2023-08-07 | 2023-10-27 | 中国航发四川燃气涡轮研究院 | Method for calculating assembly pretightening force range of floating tile stud |
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