The present invention concerns a connecting element for connecting a blade, or airfoil profile, to the hub of an industrial axial fan, a blade system comprising said connecting element, and an industrial axial fan comprising such blade system.
The axial fans for industrial application typically comprise a hub and a plurality of airfoil profiles.
A blade basically comprises two parts, the airfoil profile having the function to move the air, and the connecting element or attachment having the function to link the airfoil profile to the hub.
Object of the present invention is the connecting element connecting the airfoil to the hub and the blade system comprising a blade, an hub and the connecting element according to the present invention.
It is further an object of the present invention an industrial axial fan comprising such blade system.
In the field of axial fans, many different technical solutions are known for connecting the airfoil profile to the hub of the fan.
In order to briefly discuss the prior art, it is important to reassume the static and dynamic forces acting on the blades of an industrial axial fan during its operation, in particular with respect to the effect of the centrifugal forces.
Then, we will described various solutions actually known in the field and having the purpose to decrease the steady and eventually the unsteady loads on the element connecting the airfoil profile to the hub of the axial fan.
The forces acting on the blades of an axial fan during operation can be divided in steady forces A) and unsteady forces B).
A) The steady forces, as indicated in the attached
If the blade axis in inclined of an angle α toward the air suction side with respect to the ideal rotating plane, the centrifugal force generate a bending moment into the axial plane, having direction opposed to the direction of the moment the lift and the weight generate, as shown in the
Consequently the resulting steady state bending moment transferred to the hub will be reduced, according the following formula:
M=L·x
ca
+W·x
cg
−C·y
cg (1)
Their amplitude cyclically repeats, for that reason they are also commonly called alternated forces.
These forces originate fatigue phenomena, therefore they are more dangerous for the blade life when compared to the steady forces. Furthermore, they are responsible for the vibration of the structure supporting the fan.
Actually, various solutions acting on the blade attachment to reduce the above described forces, are used to improve the final product design reducing the loads and costs of it.
It is also the aim of the present invention to provide an innovative attachment to the blades of industrial axial fans, suitable to reduce the effects of both the steady and the unsteady loads, and the costs of it.
Connecting elements actually known in the field of the industrial axial fan and used on the market to decrease the steady and/or the unsteady loads generated by the forces acting on the blades during operation, are represented in the attached
A first connecting element comprises the rigid connection shown on
The support of the connecting element on the hub is designed so that the airfoil profile axis is inclined in the vertical plane and has a fixed angle α with respect to the ideal rotation plane. This arrangement as the centrifugal force is opposing the lift, allowing to decrease the steady loads according the above mentioned formula (1), but has no effect on the unsteady loads.
Another connecting element known in the art is the hinged connection shown on
A further connecting element known in the art comprises a flexible connection comprising one single element, as shown on
A further connecting system known in the art comprises a connecting element as it is shown in
It must be underlined that during the operation the steady state forces tend to deform the blade in a shape similar to the first mode of a cantilever beam.
At the same time, the centrifugal force tends to counteract to the blade deformation. Therefore longer is the blade connecting element, larger is the center of gravity displacement, greater is the steady state resulting bending moment reduction.
The effect produced by the centrifugal force is linearly depending on the displacement of the center of gravity, which is more than linearly depending on the length of the blade attachment.
The dynamic response of a blade to the alternated loads is depending on its modal properties.
The fan blade can be schematized as follows: a cantilever beam (the attachment), restrained on one end and with a suspended rigid mass (the profile) on the free end. Without affecting the consideration, assuming the attachment has a constant cross section, the blade natural frequencies are inversely proportional to the square of the attachment length, according to the following equation:
Considering the same radial extension for the attachment, the invention presents a longer length due to the camber compared to the systems known in the art, that means, for an identical fan blade, its natural frequencies are remarkably lower.
Considering the blade of the axial fan as a mass-damping-stiffness system and assuming it similar to a multi-degrees-of-freedom (MDoF) system, when the system is dynamically excited with a time dependent forces f(t), the equation of motion is the following:
M{umlaut over (x)}(t)+C{dot over (x)}(t)+K x(t)=f(t) (3)
The system of coupled differential equations (3) can be transformed from the geometrical coordinate system into a system of N uncoupled differential equations in terms of modal coordinates, through the well-known Modal Analysis Method:
m
i
{umlaut over (q)}
i(t)+ci{dot over (q)}i(t)+kiqi(t)=pi(t) (4)
Equation (4) can be rewritten in terms of the dynamic variables w, which is the system frequency and δi which is the modal damping ratio, both defined as follows:
The Rayleigh formulation of the modal damping ratio is a good approximation of the non-linear damping, typical for the multi-body assembly:
c
i
=a
0
m
i
+a
1
k
i (7)
Substituting equation (7) in equation (6) the modal damping can be re written in terms of the natural frequency:
Where a0 and a1 are constant depending on the mass and stiffness properties of the system.
The function (8) is showed in
The blade response in terms of geometrical coordinates can be obtained from the superposition of the displacement related to each single modal contribution.
It is evident that reducing each single modal displacement contribution leads to a reduction of the blade overall response and consequently to a reduction of the load effects on the blade.
The single modal contribution is strictly depending on the two main modal parameters listed above: the frequency and the modal damping. As shown in
There is therefore a need in the field for having a connecting element which, for the same radial size and under the same loads, allows to obtain higher displacement and consequently higher counteracting effect than the blade assemblies of the prior art.
It is therefore the aim of the present invention to provide a connecting element for industrial axial fans, suitable to allow that the blade, when it is subject to unsteady loads, is forced to modify its modal properties: frequencies and deformation shapes. Within this aim, it is an object of the present invention to provide a connecting element for connecting the airfoil profile to the hub of an axial industrial fan suitable to minimize the effects of the unsteady loads on the blade system.
More in details, it is also an object of the present invention to provide a connecting element suitable to reduce the response of the blade to alternated loads in general and resonance condition in particular.
Another object of the present invention is to provide a connecting element which allows to minimize the natural frequencies of the system with respect the systems known in the art; for the first modes, the associated modal damping are higher than for the prior art solutions and for the higher modes, the associated damping is lower. In order to achieve this aim and these and other objects that will became more clear from the following detailed description of a preferred embodiment that is merely illustrative and not limitative of the present invention, the present invention provide a connecting element which has a rectangular cross section and an “L” shaped longitudinal section, being the short side of “L” connected to the hub and the long side to the profile, with a typical ratio between the two sides of 0.1.
The natural frequencies of a blade system comprising a connecting element according to the present invention are lower than the ones of the known systems; for the first modes, the associated modal damping are higher than for the prior art solutions and for the higher modes, the associated damping is lower. Due to the distribution of the exciting forces, only the first three modes give significant contribution to the blade response; therefore the response of the blade to the cyclic loads is strongly attenuated. In addition the exciting cyclic loads have a spatial (radial) distribution which amplitude is time-dependent as per the following formula:
f(x,t)=g(x)·h(t) (9)
g(x) is a function only of the radial position
h(t) is a periodic function
This means that after half of the period, the forcing function has exactly the same amplitude but with opposite sign. The deformed shape of the system has not the same symmetry, because the restraint is not symmetric as better shown in the
Therefore, with respect to a blade system of prior art which generally cannot operate in a large range of speed around the critical one due to the intensification of the response, for the blade system of the present invention comprising a connecting element according to the present invention, which system is also part of the present invention, this range of speed is drastically reduced and in many cases there will be no limitation in the operating speed range.
With respect to the prior art, the connecting element according to the present invention allows to reduce the response of the blade system to alternated loads in general and in resonance condition in particular.
Further characteristics and advantages of the present invention will become clear from the following detailed description of a preferred embodiment that is merely illustrative and not limitative and is shown in the figures that are attached hereto, in which:
With reference to the above mentioned Figures, the main task of the present invention is to provide a connecting element for connecting the airfoil profile to the hub of an industrial axial fan.
With reference to the above, the present invention concerns a connecting element 1 consisting of an extremely simple element, see for example
Said first part 1a of the L-shaped profile, which is the shorter part, is apt to be connected to the hub 20 while said second part 1b, which is the longer part, is apt to be connected to the airfoil profile 10, said link part 1c connecting said short part 1a to said long part 1b.
The blade system 100 comprising the connecting element 1 according to the present invention, is also part of the invention.
The blade system 100 for industrial axial fans is characterized by the fact that the blade, subject to unsteady loads, is forced to modify its modal properties: frequencies and deformation shapes, as described above.
The inventors have carried out functional tests to compare the blade system 100 of the present invention, comprising the connecting element 1 according to the invention, to the prior art systems. The results confirm that with the connecting element 1 of the present invention the natural frequencies of the system are 20% lower than in the prior art, the damping ratios of the first three vibration modes are respectively 24%, 15% and 3% higher than the same damping ratios of a blade system according to the prior art, only the fourth mode has 4% of lower damping.
Considering a blade system typical loading condition, the relative participation factor of the first four modes are respectively 0.43, 0.24, 0.14 and 0.09; therefore the response of the blade to that system of loads is completely described by the superposition of the response of these four modes.
Due to the differences in the damping ratio, the blade system 100 of the present invention, comprising the innovative connecting element 1, has a maximum response 22% reduced with respect to the response of a blade system of the prior art. Considering that the loads on the blade are proportional to its response, the invention involves a significant reduction in loads acting on the blade.
Additionally, the connecting element 1 according to the present invention has the further, very important characteristic to be non-symmetrical.
The influence of these factors on the behavior of the system is explained here below with reference to
During the operation the steady state forces (weight W, and lift force L) tend to deform the blade 10 in a shape similar to the first vibration mode of a cantilever beam.
At the same time, the centrifugal force C tends to counteract to the blade deformation.
The effect produced by the centrifugal force C is linearly depending on the displacement of the center of gravity, which is more than linearly depending on the length of the blade attachment.
For the same radial size and under the same loads, the blade system of the present invention comprising a connecting element which has a longer length with respect to the connecting elements of the prior art, can provide higher displacement of the blade and, consequently, higher counteracting effect than the blade known in the art.
As it is evident from
Still preserving its peculiar features, the connecting element 1 may be realized by means of several different methods, allowing to reach very low production costs when compared with those of the connecting elements currently available on the market.
Further advantages reached by the blade system of the present invention thanks to the connecting element of the invention, are the following:
It will be appreciated that such extrusion allows to easily realize different shapes, which can obtain further important advantages: for example a larger thickness may be provided when higher stresses are foreseen, i.e. in the hub-connection zone (reference is to
The L-shaped connecting element according to the present invention may be eventually combined with a prior art system to increase its effects.
Another advantage obtained by the connecting element of the present invention consists in its unsymmetrical shape: thanks to the L-shaped unsymmetrical profile, the connecting element 1 can be assembled with the linking part 1c turned either up or down (
Of course the connecting element can be fixed to the hub 20 with one or more bolts depending on the operation duty (reference is to
Filing Document | Filing Date | Country | Kind |
---|---|---|---|
PCT/EP2015/074027 | 10/16/2015 | WO | 00 |