Life time improvement of a butterfly valve lappet by shape optimization.
The butterfly lappet valves are used as parts for adjusting components of fluid flow in hydraulic and pneumatic transportation (fig. 1).
By rotating the lappet with an angle 9 the valve decrease the fluid flow with a certain amount. It is well known that the lappet opening angle, 9, can have values till maxim 70[degrees], going over this limit, cause a dramatic grow, followed by a reduction of the momentum generated by distribution of the fluid pressure on the valve lappet (Danbon & Solliec, 2000).
Therewith, is known that in 70[degrees]-90[degrees] interval, in the butterfly lappet occur mechanical vibrations which disturb the adjusting process of fluid flow.
Due to the arguments presented above, results that function of butterfly lappet valves with angles over 70[degrees] is not recommended. Over this limit, the lappet plan is tilted with an angle between 0 and 20[degrees] with respect to the pipe axis, the lappet generate an important pressure drop (Eom, 1988).
Moreover, the forces that are taking place on the lappet can have higher values and can generate important stresses in the lappet, especially a substantial bending momentum.
The value of the bending momentum it is given by the pressure value and the way in which the pressure is distributed on the lappet surface (Leutwyler & Dalton, 2006).
Correlative with the fact that the bending momentum has a periodical variation, generated by its working condition, the butterfly lappet is loaded with fatigue bending that can lead to generation and propagation of fatigue crack.
[FIGURE 1 OMITTED]
One method to increase the life time of a butterfly lappet is to decrease the value of the bending momentum, implicit reduction of the maxim stress located in the transversal section, called critical solicitation area (Morris & Dutton, 1989).
Excepting the modification of fluid pressure and speed (both of them have great influence on the bending momentum) one method that lead to optimization of pressure distribution on the butterfly lappet, and simultaneously reduction of the bending momentum, is to optimize the lappet shape.
2. OPTIMIZATION OF THE LAPPET SHAPE
Usually, the butterfly lappets are made having a disk shape symmetric with respect to the longitudinal plan, with constant thickness and rounded edges (fig. 2.a). This lappet design do not generate a optimal fluid flow causing such a pressure distribution that the bending momentum is very high.
[FIGURE 2 OMITTED]
If the lappet shape is optimized, in such way that one section with a longitudinal plan to generate an aerodynamic profile, the fluid flow around the lappet and its pressure distribution will be optimal, resulting in a important reduction of the bending momentum value (Solliec & Danbon, 1999).
Due to complexity of the pipe flowing phenomenon, around the lappet, the optimal shape of the lappet section (profile) it was not determined by a theoretical approach, it was generated experimentally. The experimental tests have been made on butterfly lappets with diameters of , for which it was establish an optimal profile. Using this profile, the maximum bending momentum, generated in the critical section in the area of rotational axis, undergo a reduction of approximately 11.03%.
Total failure of the butterfly lappet by fatigue, is due to initiation and propagation of the fatigue crack. Generally, the crack initiate in the area with maximum load, an is generated by the bending momentum with respect to the lappet axis. Normally the crack initiation can happen in any point from that area. To determine the propagation speed of the fatigue crack, equation (1) is very often used:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
c, n, p, q--the material coefficients, determined by experimental tests;
f--the crack opening function;
R--the asymmetry coefficient for the cyclic load;
[DELTA]K = [K.sub.max] - [K.sub.min]--the stress intensity factor;
[DELTA][K.sub.th]--the threshold value of the stress intensity factor;
[K.sub.c]--the critical value of the stress intensity factor;
N--number of the loading cycles.
The bending momentum developed on the lappet varies between zero and maximal value. The maximal is determined experimentally, herby the asymmetry coefficient R = 0.
For this study case, equation (1) becomes:
da/dN = c x [DELTA][K.sup.n][[1 - [DELTA][K.sub.th]/[DELTA]K].sup.p]/ [[1 - [K.sub.max]/[K.sub.c]].sup.q] (2)
Using this equation and supposing that the crack grows with constant speed, it is possible to determine the cycles number between two different crack lengths, [a.sub.f] and [a.sub.t]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
The integration of equation (4) is the dependent equation of crack length function to the cycles number.
3. NUMERICAL RESULTS
To establish the lifetime of a butterfly lappet, have been determined the variation of crack length with respect to the loading cycles, a = f(N), and speed variation of the crack growths function to the loading cycles, da/dN = f(N).
Both butterfly lappets, disk shape (fig. 2.a) and optimized shape (fig. 2.b), were made from a material having the following mechanical properties: strength stress [[sigma].sub.r] = 310.3N/[mm.sup.2]; yield stress [[sigma].sub.c] = 172.4N/[mm.sup.2]; breaking tenacity [K.sub.c] = 2432MPa x [square root of mm]; the material coefficients for equation (1) c = 0.5762; n = 3.6; p = 0.5; q = 0.5;
For a certain fluid flow, for which experimental tests have been done, positioning the lappet in such way to obtain the maximum bending momentum, the maximal recorded stresses are: [[sigma].sub.max] = 159.7 N/[mm.sup.2] for disk shape and [[sigma].sub.max] = 142.1 N/[mm.sup.2] for optimized shape.
Considering that the crack initiate on the lappet surface, in the middle of the axis the following numerical results are obtained: fig. 3 a, b for disk shape and fig. 4 a, b for lappet optimized shape.
The numerical results have been obtained using the software NASGRO 5.01.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
The main conclusion which arises from the presented research work is that using a optimized shape of the butterfly lappet the maximal stress is considerably reduced and the durability of the lappet is increasing. Hence, for the initial lappet shape, the critical crack length [a.sub.cr] = 21.89 mm and [c.sub.cr] = 89.74 mm is reached after [N.sub.c] = 7.8 x [10.sup.6] cycles, for the optimized shape lappet the critical crack length [a.sub.cr] = 22.562 mm and [c.sub.cr] = 98.59 mm is reached after [N.sub.c] = 13.32 x [10.sup.6] cycles.
Danbon F. & Solliec C., (2000), Aerodynamic Torque of a Butterfly Valve-Influence of an Elbow on the Time-Mean and Instantaneous Aerodynamic Torque, ASME J. Fluids Eng., 122, pp.337-344
Eom K., (1988), Performance of Butterfly Valves as a Flow Controller, ASME J. Fluids Eng., 110, pp.16-19.
Leutwyler Z. & Dalton C., (2006), A Computational Study of Torque and Forces Due to Compressible Flow on a Butterfly Valve Disk in Mid-stroke Position, ASME J. Fluids Eng., 128, pp.1074-1082
Morris M. J. & Dutton J. C., (1989), Aerodynamic Torque Characteristics of Butterfly Valves in Compressible Flow, ASME J. Fluids Eng., 111, pp.392-399
Solliec C. & Danbon F., (1999), Aerodynamic Torque Acting on a Butterfly Valve. Comparison and Choice of a Torque Coefficient, ASME J. Fluids Eng., 121, pp.914-917
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|Author:||Pintilie, Gheorghe; Albut, Aurelian|
|Publication:||Annals of DAAAM & Proceedings|
|Date:||Jan 1, 2008|
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