Butterfly Calculation

M-type butterfly valve design calculation 1. the minimum wall thickness of "M"-type butterfly valve body 　　Using ASME B16.34 appendix wall thickness calculation formulas to calculate. 2. Eccentric butterfly valve stem torque calculation 　　Using the following formula, torque calculation diagram shown in Figure 2. 　　　　　MD = MM + MT + Mj + Md (1) 　　in the formula　MD ———valve stem torque, unit is N•mm; 　　　　　MM ——— sealing surface friction torque, unit is N•mm.

qM ———sealing surface necessary specific pressure, unit is MPa (look-up table or calculated) 　　R ———disc sealing radius, unit is mm 　　bM ———Sealing surface contacting width, unit is mm; 　　fM ———sealing surface friction coefficient (for rubber is 018 ~ 110); 　　h ———the eccentric distance between stem and disc center, unit is mm; 　　MT ———packing sealing friction torque (it can be negligible due to the stem use "O" ring sealing); 　　Mj ———hydrostatic torque, units is N•mm (look-up table or calculated) 　　Md ———hydrodynamic torque, unit is N•mm (look-up table or calculated) 　　3. disc thickness calculation (Figure 3) 　　　　　b = 01054 D3 H (3) 　　in the formula b ———the maximum disc thickness, unit is mm 　　　　D ———butterfly valve flow diameter, unit is mm 　　　 (Look-up table, the general b / D = 0115 ~ 0125 (Figure 2) 　　　　H ———Maximum static pressure water head (water hammer boost medium), unit is m. 　　　　H = 100 ( p +Δp) (4) 　　　　p ———Design pressure (often taking p = PN), unit is MPa Δp ———Butterfly valve quick off the valve, produces water hammer step-up value in the pipeline, unit is MPa; v ———medium flow rate, (look-up table) unit is m / h; 　　 t ———the disc experienced time from fully open to fully closed (look up table for selection), unit is s. 　　4.Check the strength of cross-section 　　(1) disc A2A cross-section Strength Check

in the formula σWA ———Verify A2A section bending stress, unit is Mpa. 　　　　　MA ———A2A section bending torque, unit is N•mm 　　　　　　　　MA = 01113 pD31 (7) 　　　　　p———Design pressure (often taking p = PN), unit is Mpa. 　　　　　D1 ———disc external diameter, unit is mm. 　　 WA ———A－A cross-section anti-bending cross-section coefficient, unit is mm3; 　　 JA ———A－A cross-section inertia moment (look-up table or calculated) unit is mm4. 　　 b ———the maximum disc thickness, unit is mm. 　　If the A-A cross-section actual bending stress, that is, 　　σWA < [σWA ] the disc design is reasonable,, [σWA ] is allowable bending stress for the material. 　　(2) disc B2B cross-section strength check 　　As the valve adopts upper and lower two-section stem to support, disc deformation is very small, so not to repeat them here. 　　the key of "M"-shaped butterfly valve design is the calculation of the upper and lower stem of driving pieces, body and disc strength, and the valve body, disc, stem, and pin and other parts rational selection and heat treatment. The valve is a single eccentric butterfly valve, torque is small, the whole disc is coated with a sealing layer, with good sealing performance, do not pollute the environment, demolition and maintenance are very convenient. Driven approach has handle type, worm gear type, electric and pneumatic, etc., is a valve that widely used.

1.preface simple butterfly valve structure, small size, light weight, and has a certain degree of flow control features. The butterfly valve heart parts- disc plays the role of cutting off medium when the valve is closed, and affected by media pressure differential of both ends before and after the valve to occur deformation, the deformation size of the valve has a greater impact to sealing performance, sealing surface itself wear and switching operating torque. Therefore, the more accurate estimates and research of disc deflection, it is reasonable to choose and design the structure size of the valve, and takes this as the basis for selection, designing transmission mechanism and adjusting the implementing devices.

2.stress analysis Butterfly valve spindle inserts into disc, by four long tapered fastening pin, can take spindle and disc as a whole. Between the spindle and sleeve is the gap matching, in the calculation of deformation, it can approximately take the disc seemed as the simply supported bearing type variable cross-section beams. The disc is circular, the load that along disc axial direction is uneven, as shown in Figure 1

disc that is affected by the media force, the beam will occur bending, if the stress within the elastic limit, the whole deformation within the beam as follows:

formula (1) only considers the bending moment effects. In addition, each module will also store a certain degree of shear strain energy, which is much smaller than the bending strain energy, is negligible. From Castile Lane Arnold (Gastigliano) first theorem to get:

formula (2) shows that: if a number of external forces (generalized force, including the moment) affect on one elastomer, then the elastomer deformation energy U for any external force Pi partial derivatives is equal to the force of the acting point along the the direction of force deformation yi, as shown in Figure 2

concerning the disc, quadrature and partial derivatives are very difficult. According to Maxwell (JG Marwell) - Moore (O. Moho) principle that,

in formula (2) can be seen as the same beam Pi acting point, bearing the effect of one unit load along Pi direction that causes bending moment M ° (x), that is,

formula (3) points is still very difficult, because M0 (x) change is relatively simple, M (x) is a a function that changes by x, disc is circular, and its thickness along the axis X also is not a fixed value, Therefore, the disc inertia J is actually varies with the X and more complex function J (x). formula (3) can use weilih Saint-Venat proposed simple algorithm. This algorithm is simple and described as follows: makes EJ = cont (fixed value) If you require any point K displacement, it can act a unit virtual afterburner Q on the K point, and make M (x), M ° (x) diagram, shown in Figure 3.

formula (4) shows that: knowing deflexion only need to calculate M (x) picture area (ω1, ω2), and multiplied the vertical coordinates M ° l that just below centroid area M ° (x) diagram. If M (x) is complex, and very difficult to calculate them, the area of ω1, ω2 and focus of cl, c2 can be applied to mapping derived. Using area of ω1, ω2 sub-taking moment method derived cl, c2, the section is more detailed, and with more accurate results, each center of gravity can be approximated to take snippets of each subparagraph ωi center. Then

The disc studied here, J (x) is also a very complex function and, therefore, can use weilih Saint-Venat method to calculate, namely, the picture multiplication evaluatation. As mentioned above, find disc deformation, can divide the disc along the axis X direction into many sections 1,2,3 ... n, n +1 ..., and find the Xaxis perpendicular to the direction of sections in the paragraphs J,, JZ, J3 ... Jn, Jn +1 ".. value is used, and then find the various sections of M1, M2, ... Mn, Mn +1 ... values, shown in Figure 4

According to

…series data, we make the picture of

indicate the M (x), J (x) complex function relationship with a graphics.

according to the proportion, That is to

3、Deflection Analysis and Calculation If required beam deflection YK of any point, in the K-point increase the imaginary unit force Q, and to make the M 0 (x). This allows the use of weilih Saint-Venat diagrammatic multiplication method to calculate. In this case, formula (4) has the following form:

formula ωx1, ωx2-M (x) / J (x) Graphic Area As we nearly take the disc to be considered as a simple beam, therefore, using formula (5) to calculate or derived by multiplying the deflection y values are disc in the Z direction of each vertical section that all points have the common deflection, vertical section KK's deflection yK-K are equal, Figure 4. However, Z-axis direction deflection in fact not equal, such as the edge K-point deflection should be larger than deflection y0 of center 0, that is, there should be another deflection, this deflection is uner the effect of force q, by the Z-axis direction bending moment generated. Taking A-A axis as a fixed end, taking Z-axis direction half disc D / 2 as a cantilever beam, its deflection can be approximately considered to be Zaxis direction parallel to the X-axis deflection of each section.

Z-axis direction deflection y: Similarly, according to the multiplication of weilih Saint-Venat. To calculate the disc edge K point maximum deflection yKZ is also the same that add a virtual unit force Q on the K point (see Figure 5), then are:

in the formula, ω2 --- m (z) / J (z) Graphic Area According to the superposition principle, the deflection y of any point of the disc should besum of the X-axis direction simple beam deflection y2 and Z-axis cantilever beam deflection y2, namely:

formula (7) is to use diagram multiplication to calculate the disc deflection formula

4.Conclusion Taking the disc approximately as the beam conditions to calculate the deformation, in the calculation of one position deformation, ignoring the impact of another direction, but this effect would bound the deformation of disc. Using this method, to calculate the deflection is relatively similar, the calculated result is too large, but it is safe and allowed for the engineering design.