The bending machine presents errors in bending, so how to eliminate the work error of the bending machine? The formula is derived from the error caused by differential pressure transmitter, and the primary reason is the existence of the difference in height, i.e. h ≠ 0. To eliminate the existence of H, it is required that the two pressure points of the elbow sensor be in the same horizontal plane. That is, in principle, horizontal layout plan may be selected. However, when horizontal plan is not available, the length of differential pressure pipeline should be shortened and online real-time compensation plan should be adopted. It can be seen from the discussion on the formula of curvature radius ratio caused by thermal expansion: when L1 = L2, the length of R 'and R is the smallest, that is, the straight pipe length on both sides of the bend should be kept as much as possible. In addition, in order to reduce the convergence of stress at the pipe flowmeter, the method of elongation diversion can be adopted, namely, the expansion joint or π device mode shall be set apart from the length required by the pipe flowmeter device on both sides of the elbow flowmeter. The fluid flowing through the bend will be accelerated to the center due to the centripetal force effect imposed by the pipe wall, Form a total space rotation activity（ The intensity of the acceleration is characterized by the centripetal acceleration of the fluid, and it can be determined by measuring the differential pressure signals of the inner and outer sides of the bend. When the bending diameter ratio (degree of curvature) and the density of fluid medium are known, the flow rate can be calculated by formula when the differential pressure between the inner and outer diameter is measured.
The elbow flowmeter adopts 90 ° standard elbow sensor as flow sensor, and the differential pressure signal is measured at 45 ° points inside and outside the sensor to measure the flow rate. The flow rate is generally determined by the following formula
V= α[（ R/D） ×Δ P/ ρ 1）][1/2]
Where V is the uniform velocity; α Is the velocity coefficient; R/d is the bending diameter ratio of the bend; ρ 1 is the fluid density in the pipe; Δ P is the differential pressure signal that causes the fluid to move toward the center.
Differential pressure signal Δ P is:
Δ P= Δ P1- Δ P2
Δ P1=P1-P10， Δ P2=P2-P20，
Where, Δ P1 is the pressure increment of the fluid at point a on the outside bend side of 45 ° point of the elbow sensor; Δ P2 is the pressure increment of the fluid at point B of the bend sensor at 45 ° point; P1 is the pressure at point a when the fluid is moving at velocity V; P10 is the static pressure at point a when the fluid is still; P2 is the pressure at point B when the fluid is moving at velocity V; P20 is the static pressure at point B when the fluid is stationary.
The static pressure difference (p10-p20) of a and B points is determined by the height difference h of two points and the density of the fluid. That is, there are: Δ P=P1-P2- ρ 1gH
In practice, the elbow flowmeter is often used in other environments such as hot water pipes which have temperature difference compared with the design conditions. Because of the change of environment, there will be errors in measurement.
The following first analyzes the causes of the errors in the bending machine.
(1) Error caused by differential pressure transmitter
In the calculation formula of the flowmeter for bend, P is the differential pressure signal of the point taken on the inner and outer wall of the elbow. Now measure the differential pressure signal Δ P generally, various differential pressure transmitters are selected, and the typical measurement system is shown in Figure 2. The pressure P1 is taken out from point a, and pressure P2 is taken out from point B, and connected to a 'and B' ends of differential pressure transmitter g through pressure guide pipes L1 and L2. The height difference between a and a ', B and B' is h and H ', and the differential pressure signal measured directly by differential pressure transmitter Δ P 'is:
Δ P'=P'1-P'2=（P'1+H1 ρ 0g）-（P2+H2 ρ 0g）
Δ P'=- Δ P+（ ρ 0- ρ 1）gH
Where, ρ 0 is the density of water in the pressure pipe, which is a function of temperature at atmospheric pressure. Under normal temperature, the water temperature in the main pipe is the same, that is, the same density, that is, the water temperature in the guide pipe is the same
ρ 0= ρ one
When the water temperature in the main pipeline is higher than the ambient temperature, the water density in the main pipeline is different from that in the pressure pipe because of the existence of heat conduction.
The experiment shows that the heat radiation is the primary conduction mode of water in the pressure pipe, and the temperature of water in the pressure pipe decreases rapidly with the length of the pressure pipe. When the length of the catheter reaches a certain length l0, the temperature of the water temperature in the conduit is the same, that is, the density is not changed after l0, and it is within the range of l0, ρ 0 is a function of temperature and a function of length.
The above formula shows that the differential pressure signal measured directly by the differential pressure transmitter contains the differential pressure signal which causes the acceleration of the hot water to the center Δ Besides, there are also the signal items of differential pressure error due to the difference of height difference h between two pressure points and the difference between the density of hot water in the main pipeline and the water density in the pressure guide pipe.
(2) Curvature error caused by thermal expansion
Because the bend itself is a flexible component, the heat elongation of the heating pipe will converge to the bend, so that the bend will be bent and distorted, which will cause the curvature radius of the bend to be different from the radius of curvature in design.
To further understand the error of the attack, we calculated the following assumptions according to the practical network system (as shown in Figure 3): (1) ignoring the bending resistance, that is, the elongation of L1 and L2 segments is 0 when bending force resists bending deformation（ 2) It is assumed that the bend is still arc shaped after deformation, and it is still tangent to the pipelines on both sides（ 3) L1 and L2 pipelines are treated as members, and all deformation is in small deformation range. Set L1 and L2 variables to be separated as Δ L1 and Δ L2。 According to the assumed conditions, L1 and L2 can be regarded as cantilever beams separated from fixed points a and B, and the deflection due to temperature change is YC and YD; Available Δ L1= η L1 Δ t； Δ L2= η 2L2 Δ t；
Where η Coefficient of line expansion for pipe material
The continuity of the pipeline is approximately as follows:
YC= Δ L2； YD= Δ L1
From several relations, the angle separation of points c and D can be obtained by using the common sense of material mechanics
θ C=PDL12/2EI； θ D=PCL22/2EI
C. The deflection of point D is separated as follows: