UDK 624.042.12
The influence factors of flexibility and stress concentration in the taps to the calculation
of cooling strain of radial compensators in heat supply network
V.I. Belilovets
Scientific supervisor: Doctor of Technical science, Professor Y.L. Lipovka
Language supervisor: T. V. Zhavner
Siberian Federal University
Results of the study of computational models of the radial compensators
Lets consider three computational models of the radial compensators located in the
horizontal plane and which are not pinched by the ground. Each computational model variable
by the quantity is the radius of curvature tap. There are the characteristics of computational
models below. In the calculations of rigid point of support were considered absolutely rigid
and the resistance of friction forces of free-end bearings was not taken into account.
Table 1 - Characteristics of computational models of radial compensators
Сalculated value
Dimension
External pipe diameter / nominal wall thickness of
mm
compensator number 1
Cantilever / back width of compensator number 1 (excluding
m
taps size)
Allowable slideback voltage of compensator number 1
MPa
External pipe diameter / nominal wall thickness of
compensator number 2
Cantilever / back width of compensator number 2 (excluding
taps size)
Allowable compensation voltage of compensator number 2
External pipe diameter / nominal wall thickness of
compensator number 3
Cantilever / back width of compensator number 3 (excluding
taps size)
Allowable compensation voltage of compensator number 3
Pre-stressing coefficient
Calculated coolant temperature (the pipe wall)
Installation temperature
The elastic modulus of piping material at a working
temperature
Excessive internal pressure
Linear thermal expansion of piping material at the estimated
temperature of coolant (the pipe wall)
Strength reduction factor of weld joint action at any load other
than the bending moment
Reduction factor of weld joint strength at bending moment
Rated allowable stress of piping material at the operating
temperature
Value
159/4,5
3/1,5
146
mm
219/6
m
4/2
MPa
154
mm
426/7
m
6/3
MPa
nondimensio
nal quantity
0
С
0
С
150
MPa
196000
MPa
1,6
mm/m0С
0,0125
nondimensio
nal quantity
nondimensio
nal quantity
MPa
1
130
-20
1
0,9
140
There are graphs of the stress distribution on calculated cross sections of these models of
radial compensators below.
Figure 1 – Distribution diagram of tension of the compensator number 1 at radius of
the outer diameter of tap pipe to one
Figure 2 – Distribution diagram of tension of the compensator number 1 (left) and
number 2 (right) at radius of three tap pipe outer diameters
If you pay attention, you can see that the maximum voltage with and without
consideration of the coefficients are comparable in the first two computational models within
approximately using the tap radius which is equal to three outer diameters of the pipe. For the
third calculation model similar graph is as follows
Figure 3 – Stress distribution diagram of the compensator number 3 in radius of three
tap pipe outer diameters
It is evident that a similar comparison with the first model calculations on the graph
above is not observed. Now pay attention to plots of the maximum total departure from the
adjacent compensated shoulder radius of curvature taps.
Figure 4 – Dependence diagram of the maximum total cantilever of adjacent
compensated shoulders by the radius of taps curvature for calculation model of compensator
number 1
Figure 5 – Dependence diagram of the maximum total cantilever of adjacent
compensated shoulders at the radius of taps curvature for the calculation model of
compensator number 3
If the third calculation model to increase the wall thickness from 7 to 12 mm, the point
of intersection graphs of maximum total departure of adjacent compensated shoulder radius of
curvature taps shifts to the center of coordinates.
Figure 6 – Dependency diagrams of the maximum total departure adjacent
compensated shoulders the radius of taps curvature for calculation model compensator
number 3 with a thickness of 12 mm (left) and 7 mm (right)
Conclusions
Chart analysis suggests the following conclusions:
1) The most beneficial in terms of safety margins is the use of taps, the radius of
curvature which is equal to one outer diameter of the pipe.
2) The increase of the curve radius of the taps from one to two outer diameters leads to
the increases of the maximum cantilever of the compensated shoulders twice.
3) In calculations it is necessary to take into account the coefficients of flexibility taps
and stress concentrations because the ignorance of the latter leads to the incorrect results.
4) In case of tap radius reduction and increasing the wall thickness of pipe in
calculation model there is the process of equation of the flexibility coefficients of taps and
there are stress concentrations to the unity.
References
1. A.A. Nikolaev Spravochnik of the designer. M.: Publishing house of literature on
construction, 1965
2. A.A. Lyamin, A.A. Skvortsov Proyektirovaniye and calculation of designs of
thermal networks. M.: Publishing house of literature on construction, 1965
3. A.G. Kamerstein, V. V. Rozhdestvensky, M. N. Ruchimsky Calculation of
pipelines on durability. M.: State scientific and technical publishing house of oil
and mountain and fuel literature, 1963
4. Norms of calculation on durability of pipelines of thermal networks. RD 10-40001. M.: State mining inspection of Russia, 2001