Let Q1 be the minimum total axial force that meets the bolting requirements under certain temperature conditions. Q0 is the actual axial force when the bolt starts to work. Q2 is the actual working time after the stress relaxation. The axial force, R1 is the total stress generated by Q, R0 is the stress generated by Q0, and R2 is the stress generated by Q2. Considering the stress relaxation of material creep during the working process, there are Q0>Q1, R0>R1.
During the specified working time, due to the stress relaxation, the axial force of the bolt is reduced from Q0 to Q2, and the working stress is reduced from R0 to R2. To maintain normal operation, Q2>Q1, R2>R1.
Therefore, in the case of high temperature operation, the bolt connection design should be based on the material stress relaxation law, and determine the R0 at the beginning of the work and the preload of the bolt according to R1 under the working condition. The following describes a calculation method for determining R0 based on R1.
The stress relaxation occurs under the condition that the total deformation E is constant, and the elastic deformation Ee is converted into the plastic deformation Ep, which is loaded in the elastic range, and the stress relaxation process can be expressed as E=Ee+Ep=constant.
(1) Hooke's law R=EEe (E is the elastic modulus) (2) ie E=R/E+Ep. Deriving it to time t, then there is 0=dR/Edt+dEp/dt.
Where dEp/dt is the creep velocity v of the stable creep phase of the material, ie v=dEp/dt=-dR/Edt.
(3) The empirical formula between creep velocity and stress is v=kRm.
(4) m refers to the coefficient related to material properties and temperature. In the creep stabilization phase, k is a constant and can be found in the steel performance manual.
Then, v=kRm=-dR/Edt, dR/Rm=-kEdt.
Integrate the above formula. At the beginning of the work, t=0, R=R0. At normal working time t, R=R1, then ∫R1R0dR/Rm=-Ek∫t0dt=-Ekt, then 1/(1-m)(R11-m- R01-m)=-Ekt, finishing R0/R1=<1-(m-1)R11-m
Ekt>1/(1-m),(5)t=(R11-m-R01-m)/(m-1)kE.
(6) It can be known from equation (5) that R1 is determined by the minimum axial force required by the work, and the R0 value that can satisfy the failure of the connection within the entire working period is obtained. The bolt material and the section size can be determined according to the design. The size of the tightness.
It can be seen from equation (6) that if it is known that the initial stress R0 is relaxed to the minimum axial force, the time t required for the joint to fail is determined, so that measures can be taken to prevent the bolt joint from failing.
The calculation ideas and methods for stress relaxation of tight bolt joints under high temperature conditions are discussed above. In the actual project, in order to ensure the working performance of the bolt connection under high temperature conditions, the bolt should be tightened again when the stress relaxation is close to t time, that is, the elastic stress of the bolt is increased again, and the stress relaxation resistance is improved. It should be pointed out here that in actual engineering, the number of times of re-tightening is usually only one time, because multiple times of fastening will increase the plastic deformation of the material and damage the material. For a period of time after tightening, the bolts should be replaced to ensure the safe operation of the equipment.
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