# Estimation method of deflection of butterfly plate

2022-09-27
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The butterfly valve has the advantages of simple structure, small volume, light weight, and certain flow regulation characteristics

when the valve is closed, the butterfly plate, the heart part of the butterfly valve, plays the role of cutting off the medium. Due to the pressure difference between the front and rear ends of the valve and optimizing the storage period, oxidation resistance and UV resistance, it will deform. The size of its deformation has a great impact on the sealing performance of the valve, the wear of the sealing surface itself and the switching operating torque. Therefore, a more accurate estimation and Research on the deflection of the butterfly plate can reasonably select and design the structural size of the valve, and use this as a basis to select and design the transmission mechanism and adjustment actuator

2. Stress analysis the main shaft of the butterfly valve is inserted into the butterfly plate and fastened by four long taper pins. The main shaft and the butterfly plate can be regarded as a whole. There is a clearance fit between the main shaft and the shaft sleeve. When calculating the deformation, the butterfly plate can be approximately regarded as a simply supported variable cross-section beam. The butterfly plate is circular, and the load along the axis of the butterfly plate is uneven, as shown in Figure 1. After the butterfly plate is subjected to the medium force, the beam will bend. If the stress is within the elastic limit, the deformation energy in the whole beam is: in formula (1), only the influence of bending moment is considered. In addition, each element will also store a certain amount of shear strain energy, which is much smaller than the bending strain energy and can be omitted. According to gastigliano's first theory: formula (2) shows that if many external forces (generalized forces, including bending moments) act on an elastomer, the partial derivative of the deformation energy U of the elastomer to any external force Pi is equal to the displacement Yi of the action point of the force along the direction of the force, as shown in Figure 2. For butterfly plate, it is very difficult to calculate integral and partial derivative. According to the principle of J. g. Maxwell -- Mohr (HO): the moment M ° (x) in formula (2) can be regarded as the moment M ° (x) caused by the action of a unit load along the direction of the force PI at the action point of the same beam, then: the integration of formula (3) is still very difficult, because the change of M0 (x) is relatively simple, m (x) is a function changing with X, the butterfly plate is circular, and its thickness along the axis X is not a fixed value, therefore, The inertia product J of the butterfly plate is actually a more complex function J (x) that varies with X

formula (3) can use the simple algorithm suggested by Saint venat. This algorithm is briefly explained as follows: let ej=cont (constant value)

If any point K is required to encourage enterprises to use the displacement of new materials, a unit virtual force Q can be applied on point K, and m (x), m ° (x) diagrams can be made, as shown in Figure 3. Equation (4) shows that only the area of the M (x) diagram needs to be calculated to calculate the displacement（ ω 1、 ω 2) And multiply by the ordinate value m ° l of the m ° (x) graph directly below the centroid of the area. If M (x) is complex and difficult to calculate, the area ω 1、 ω 2 and the center of gravity Cl, C2 can be obtained by drawing. Adopted area ω 1、 ω 2. Cl and C2 are calculated by the method of segmented moments. The finer the segments, the more accurate the results are. The center of gravity of each segment can be approximately taken as each segment ω The center of I. Then the butterfly plate studied here, J (x) is also a very complex function. Therefore, it can also be evaluated by using the Willy sargin method, that is, Graph Multiplication evaluation

as mentioned above, to calculate the deformation of the butterfly plate, the butterfly plate can be divided into many segments along the axis X direction 1,2,3 n,n+1...， And find out j, JZ, J3 of each section perpendicular to the x-axis direction Jn, Jn+1 ".. values, and then calculate the M1, M2,... Mn, mn+1... Values of each section, as shown in Figure 4. According to the series of data, draw a graph in proportion, that is, use a graph to express the complex functional relationship of M (x), J (x). 3. Deflection analysis and calculation. If the deflection YK of a certain point on the beam is required, add the unit force Q on the K point falsely, and make the M 0 (x) of the unit force 。 In this way, we can use the Graph Multiplication of Willy sargin to evaluate. At this time, equation (4) has the following form: ω x1、 ω X2-m (x)/j (x) figure area

since we consider the butterfly plate as a simply supported beam approximately, the deflection y value calculated by formula (5) or by graph multiplication is the common deflection of all points on each longitudinal section of the butterfly plate in the Z direction, and the deflection yk-k on the longitudinal section K-K is equal, as shown in Figure 4. However, the deflection in the z-axis direction is actually unequal by scanning the 1-CUT page of the station and storing the relevant information in the database. For example, the deflection YK of the k-point at the edge, which has fallen to less than 20%, should be larger than the deflection Y0 of the center point 0, that is, there should also be a deflection, which is generated by the bending moment in the z-axis direction under the action of force Q

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