Design method of simply supported beam bracket with dual functions of support and vibration isolation for tunnel fan

Abstract

The present invention discloses a design method for a simply supported beam support with dual functions of support and vibration isolation for a tunnel fan, comprising: (a) using two parallel I-beam simply supported beams, both ends of which are laterally inserted into a curved tunnel wall, as a support structure for supporting the tunnel fan; (b) determining the length l of the I-beam simply supported beam based on the fan's position in the middle of the tunnel and the height H given by ventilation design; (c) simplifying the fan-simple supported beam vibration system into a single-degree-of-freedom vibration isolation system theoretical model, and performing vibration isolation calculations on the model of the I-beam to determine the I-beam model that meets the vibration isolation requirements; and (d) analyzing the maximum normal stress and maximum shear stress of the I-beam simply supported beam, and comparing the maximum normal stress with the proportional limit and yield limit of the I-beam material to ensure that the maximum normal stress does not exceed the proportional limit and yield limit of the I-beam material.

Description

Technical Field

[0001] The present invention relates to the technical field of traffic design, and in particular to a design method for a simply supported beam bracket for a tunnel fan having dual functions of support and vibration isolation. Background Art

[0002] In long tunnels, such as those on highways and railways, insufficient air circulation prevents the dispersal of exhaust gases such as CH4, CO, CO2, and H2S, as well as road dust. This deteriorates air quality, impacting the health of drivers and passengers and compromising driving safety. Therefore, tunnels are often equipped with axial flow fans or jet fans to introduce fresh air and exhaust exhaust gases and dust. These fans are typically suspended from the tunnel ceiling or mounted on the sides of the tunnel walls, eliminating the need for separate air ducts and occupying accessible areas. When the fan is turned on, air enters the fan through the inlet, is accelerated by the impeller, and is ejected at high speed from the outlet. This high-speed airflow, along with the other air it propels, flows through the tunnel in the direction of the fan's jet. When the wind speed decays to a certain level, the next fan takes over, operating in the same manner. This ensures that fresh air is drawn in from one end of the tunnel and contaminated air is expelled from the other end.

[0003] Figure 1 This is a schematic diagram of the existing tunnel fan suspension installation. There are two transverse support rods, each of which is connected to a wire rope at both ends. The wire rope is connected in series with a cylindrical coil spring and then to an embedded component buried in the tunnel ceiling. The fan is placed horizontally on the two transverse support rods, with the fan axis parallel to the tunnel axis. When the fan is suspended and installed, it needs to be placed in the middle of the tunnel at a designed height that takes into account the ventilation effect. In addition, the load-bearing capacity of the transverse support rods, wire ropes, cylindrical coil springs, and embedded components must be checked before installation to ensure the load-bearing safety of the fan installation structure. Moreover, when the fan is operating, the accompanying violent vibration not only accelerates the wear of the fan's own components and reduces their service life, but also transmits the vibration to the tunnel, significantly reducing the comfort of vehicles traveling. Figure 1 While maintaining its required load-bearing capacity, the cylindrical coil springs in the fan isolate the fan's vibration from the tunnel, significantly reducing the vibration transmitted to the tunnel and the noise radiated by the fan's vibration. To minimize the disturbance and harm to passengers caused by the fan's aerodynamic noise, mufflers are often installed at the front and rear ends of the jet fan, or the axial fan housing is designed with a double-layer structure, with sound-absorbing material added inside to create a sound-absorbing shell. This creates a relatively complex structure.

[0004] Therefore, new technologies and devices are needed to at least partially solve the deficiencies in the prior art. Summary of the Invention

[0005] In order to solve the above technical problems, this application will try to change Figure 1 The installation method of the tunnel fan is to use two parallel I-beams with their ends inserted horizontally into the curved tunnel wall to replace the transverse support rods, wire ropes, cylindrical coil springs and embedded parts to install the tunnel fan with a simple supported beam bracket. The two parallel I-beams are both supporting elements and vibration isolation elements. When designing the simple supported beam bracket, the fan needs to be installed in the predetermined position; the fan-simple supported beam vibration system needs to be calculated for vibration isolation to ensure that the expected vibration control requirements are met; at the same time, it is also necessary to explore whether the I-beam simply supported beam deforms within the linear elastic range and to check the normal stress and shear stress strength of the I-beam simply supported beam to ensure that the simply supported beam deforms within the linear elastic range and is safe to bear. This application provides a simpler new design method for the support and vibration isolation of tunnel fans.

[0006] According to one aspect of the present invention, a design method for a simply supported beam support having both support and vibration isolation functions for a tunnel fan is provided, characterized by comprising:

[0007] (a) Two parallel I-beams with their ends laterally inserted into the curved tunnel wall are used as the supporting structure for the tunnel fan;

[0008] (b) Determine the length l of the I-beam simply supported beam based on the fan height H given by the ventilation design in the middle of the tunnel;

[0009] (c) Simplify the fan-simply supported beam vibration system into a single-degree-of-freedom vibration isolation system theoretical model and perform vibration isolation calculations on it to determine the I-beam model that meets the vibration isolation requirements; and

[0010] (d) Analyze the maximum normal stress and maximum shear stress of the simply supported I-beam and compare the maximum normal stress with the proportional limit and yield limit of the I-beam material to ensure that the maximum normal stress does not exceed the proportional limit and yield limit of the I-beam material.

[0011] According to an embodiment of the present invention, step (d) further comprises analyzing the maximum shear stress of the double I-beam simply supported beam and comparing the maximum shear stress with the allowable shear stress of the I-beam material to ensure that the maximum shear stress does not exceed the allowable shear stress of the I-beam material.

[0012] According to an embodiment of the present invention, step (c) includes obtaining parameters related to the tunnel fan, including mass, number of revolutions, installation position, simply supported beam elastic modulus, and vibration isolation efficiency.

[0013] According to an embodiment of the present invention, step (c) further comprises determining the cross-sectional moment of inertia I of the simply supported I-beam using the following formula: Z :

[0014]

[0015]

[0016]

[0017]

[0018] Where, I is the predetermined vibration isolation efficiency, λ is the frequency ratio, ω is the fan operating frequency, ω n is the natural frequency of the fan-simple supported beam bracket vibration isolation system, E is the elastic modulus of the I-beam material, m is the mass of the fan, and K is the stiffness coefficient of the double I-beam simply supported beam.

[0019] According to an embodiment of the present invention, in step (d), the maximum normal stress of the simply supported beam support is calculated using the following formula:

[0020]

[0021] Among them, σ tmax is the maximum tensile stress, σ cmax is the maximum compressive stress, M max is the maximum bending moment, and h is the height of the I-beam cross section.

[0022] According to an embodiment of the present invention, in step (d), the maximum shear stress τ of the simply supported beam support is calculated using the following formula: max :

[0023]

[0024] Among them, Q max is the maximum shear force, S* zmax is the half-section static moment, d is the waist thickness of the I-beam cross section, and these parameters can be obtained by looking up the table.

[0025] Based on the following detailed description of specific implementation examples of the present invention in conjunction with the accompanying drawings, those skilled in the art will become more aware of the above and other objects, advantages and features of the present invention.

[0026] BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Hereinafter, some specific embodiments of the present invention will be described in detail in an illustrative and non-limiting manner with reference to the accompanying drawings. The same reference numerals in the drawings indicate the same or similar components or parts. It should be understood by those skilled in the art that these drawings are not necessarily drawn to scale. The objects and features of the present invention will become more apparent from the following description taken in conjunction with the accompanying drawings, in which:

[0028] Figure 1 This is a schematic diagram of a tunnel fan suspension installation according to the prior art;

[0029] Figure 2 Schematic diagram of the installation of a double I-steel simply supported beam support for a tunnel fan according to an embodiment of the invention;

[0030] Figure 3 Schematic diagram of a theoretical model for installing a double I-steel simply supported beam support for a tunnel fan according to an embodiment of the invention;

[0031] Figure 4 is a graph showing the relationship between the vibration transmissibility η and the frequency ratio λ according to an embodiment of the invention;

[0032] Figure 5 is a schematic cross-sectional view of an I-beam according to an embodiment of the invention;

[0033] Figure 6 Schematic diagram of the force on a double I-beam simply supported beam according to an embodiment of the invention;

[0034] Figure 7 Schematic diagram of bending moment of a double I-beam simply supported beam according to an embodiment of the invention; and

[0035] Figure 8 Schematic diagram of shear force of a double I-beam simply supported beam according to an embodiment of the invention. DETAILED DESCRIPTION

[0036] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. However, the embodiments or descriptions are not intended to limit the scope of protection of the present invention.

[0037] Figure 2 This diagram shows a tunnel fan installation using dual I-beams, according to an embodiment of the invention. The diagram shows a tunnel cross-section. An axial or jet fan is installed between two parallel I-beams, whose ends extend transversely into the curved tunnel wall. The fan axis is parallel to the tunnel axis. The fan's height (H) in the middle of the tunnel, as determined by ventilation design, determines the length (l) of the simply supported beams (excluding the portion extending into the tunnel wall).

[0038] The study found that Figure 2 The structure shown can be simplified as Figure 3The theoretical model of the single-degree-of-freedom vibration isolation system shown. If a simply supported beam deforms within the linear elastic range, it can be simplified into a linear elastic element with a constant stiffness coefficient k. The upper end of the elastic element is connected to a fan with a mass of m. Due to the rotor imbalance of the motor matching the fan, the fan is subjected to a vertical periodic disturbing external force with an amplitude of F0 and a frequency of ω. The lower end of the elastic element is connected to the rigid tunnel wall.

[0039] Then, the above model can be solved. Taking the centroid position of the fan when it is stationary as the origin O and the upward direction as the positive direction, an x-axis is established. The fan is subjected to a periodic external force and the force of the elastic element in the vertical direction. According to Newton's second law, the vibration differential equation of the fan is listed

[0040]

[0041] By solving equation (1), the vibration transmissibility η can be obtained

[0042]

[0043] where: N0 is the amplitude of the periodic force transmitted to the tunnel wall. When F0 is constant, the smaller η is, the smaller N0 is, and the better the vibration isolation effect is; in addition, the frequency ratio λ in the formula is

[0044]

[0045] where ω n is the natural frequency of the single-degree-of-freedom vibration isolation system, and its expression is

[0046]

[0047] According to formula (2), the curve of the change relationship between the vibration transmissibility η and the frequency ratio λ is obtained, as shown in Figure 4 shown. When λ < 2 0.5 η > 1, that is, N0 > F0, the system not only cannot reduce vibration, but instead causes vibration amplification; only when λ > 2 0.5 η is less than 1, that is, N0 < F0, the system is in the vibration isolation state, and as λ increases, the vibration isolation effect is better. For example: when the frequency ratio λ = 2.5, the corresponding vibration transmissibility η = 0.19; when the frequency ratio λ = 3.32, the corresponding vibration transmissibility η = 0.10.

[0048] In the implementation scheme, the fan is installed on a certain double-I-beam simply supported beam of a tunnel as shown in Figure 2 shown, and its relevant parameters are shown in Table 1.

[0049] Table 1 Relevant parameters for the installation of the tunnel fan on the simply supported beam

[0050]

[0051] The fan mass m and speed n are 1540 kg and 980 rpm, respectively. When the fan is placed in the middle of the tunnel at the height specified in the ventilation design, without occupying the tunnel's traffic area, the simply supported beam length is measured to be 7.5 m (excluding the portions inserted into the tunnel wall at both ends). The elastic modulus E of the I-beam material is 210 GPa. Furthermore, the expected vibration isolation efficiency I of the fan-simply supported beam system must be ≥ 90%.

[0052] Next, we further solve the cross-sectional inertia moment I of the I-beam simply supported beam: Z , and based on this, choose the appropriate specifications and models of I-beam steel.

[0053] The relationship between vibration isolation efficiency I and vibration transmissibility η is:

[0054] η=1-I(5)

[0055] If the expected vibration isolation efficiency I of the fan-simply supported beam vibration system is taken as 90%, the vibration transmissibility η = 0.1 is calculated according to formula (5). Substituting η = 0.1 into formula (2), the frequency ratio λ = 11 is calculated. 0.5 , see Table 1, the fan speed is 980r / min, that is, the operating frequency ω is 102.63rad / s, ω=102.63rad / s and λ=11 0.5 Substituting into formula (3), the natural frequency ω of the vibration system is calculated n =30.94rad / s. Then, the fan mass m=1540kg and the natural frequency ω in Table 1 are n =30.94rad / s Substituting into formula (4), the stiffness coefficient of the double I-beam simply supported beam k is calculated to be 1474217N / m.

[0056] The stiffness expression of a single elastic simply supported beam is:

[0057]

[0058] See Figure 2 The cross-sectional diagram of the double I-beam simply supported beam shown in the upper right shows that the cross-sectional moment of inertia of the double I-beam is the cross-sectional moment of inertia of the single I-beam. Z 2 times, or 2I Z , formula (6) can be modified as

[0059]

[0060] Substituting the elastic modulus E = 210 GPa, the simply supported beam length l = 7.5 m, and the beam stiffness k = 1474217 N / m in Table 1 into formula (7), the moment of inertia of the cross section of a single I-beam is calculated as Z 3085cm 4 .

[0061] Figure 5 This is a schematic diagram of the cross section of an I-beam. The height h, waist thickness d, and neutral axis zz of the I-beam cross section are shown in the figure.

[0062] From the previous calculation, we know that when the vibration isolation efficiency of the fan-double simply supported beam vibration system is 90%, the cross-sectional inertia moment of a single I-beam simply supported beam should be 3085cm 4 Check the I-beam model table and you can get 3085cm 4 Large, but the closest moment of inertia is 3400cm 4 , the corresponding model is 22a, the ratio of its moment of inertia to the static moment of half section is I z :S z The cross-section height h and waist thickness d are 200mm and 7.5mm respectively. 4 Small, but the closest moment of inertia is 2500cm 4 , the corresponding model is 20b, the ratio of its moment of inertia to the static moment of half section is I z :S z The cross-sectional height h and waist thickness d are 200 mm and 9.0 mm respectively. The relevant parameters are listed in Table 2.

[0063] Table 2 Related parameters of I-beam

[0064]

[0065] As shown in Table 2, if 22a I-beam is selected, the moment of inertia I Z =3400cm 4 . E=210GPa、l=7.5m and I in Table 1 Z =3400cm 4 Substituting into (7), we get k = 1624747 N / m. Substituting k = 1624747 N / m and the fan mass m = 1540 kg in Table 1 into (4), we get the natural frequency ω of the fan-simply supported beam vibration isolation system. n =32.48rad / s. Set the operating frequency ω in Table 1 to 102.63rad / s and the system natural frequency ω n =32.48rad / s into formula (3), and the calculated frequency ratio λ = 3.16. Substituting the frequency ratio λ = 3.16 into formula (2), the calculated vibration transmissibility η = 0.1113 is obtained. Substituting η = 0.1113 into formula (5), the calculated system vibration isolation efficiency I = 88.87%, which does not meet the design requirement of the expected vibration isolation efficiency I ≥ 90%.

[0066] As shown in Table 2, 20b I-beam is selected, and the moment of inertia I Z =2500cm4 . E=210GPa,l=7.5m and I in Table 1 Z =2500cm 4 Substituting into (7), we get k = 1194667 N / m. Substituting k = 1194667 N / m and the fan mass m = 1540 kg in Table 1 into (4), we get the natural frequency ω of the fan-simply supported beam vibration isolation system. n =27.85rad / s. Set the operating frequency ω=102.63rad / s and the system natural frequency ω in Table 1 n Substituting λ = 27.85 rad / s into equation (3) yields a frequency ratio of λ = 3.69. Substituting λ = 3.69 into equation (2) yields a vibration transmissibility of η = 0.0793. Substituting η = 0.0793 into equation (5) yields a system vibration isolation efficiency of I = 92.07%, meeting the design requirement of an expected vibration isolation efficiency of I ≥ 90%. This indicates that the smaller the I-beam's moment of inertia and the smaller the beam's stiffness, the higher the system's vibration isolation efficiency and the better the vibration isolation effect.

[0067] After selecting the I-beam type, the stress conditions of the I-beam simply supported beam are further analyzed to complete the support design.

[0068] Figure 6 This diagram illustrates the loads on a model 20b double I-beam simply supported beam. The two I-beams are considered a single unit. The beam is 7.5 meters long and is subjected to a 15,092 N wind force in the middle of the beam. Both ends of the beam experience an upward support reaction force of 7,546 N.

[0069] Figure 7 is based on Figure 6 Schematic diagram of the bending moment of a double I-beam simply supported beam based on the stress conditions. From the cross sections at both ends of the beam to the cross section in the middle of the beam, the bending moment starts from 0 and increases linearly to the same maximum value of 28297.5Nm. The maximum tensile stress σ t,max At the bottom of the cross section in the middle of the beam, the maximum compressive stress σ c,max At the top of the cross section in the middle of the beam, the maximum tensile stress σ t,max and maximum compressive stress σ c,max Equal in size and opposite in direction.

[0070] The calculation formulas for the maximum tensile and compressive stresses of a single simply supported beam are

[0071]

[0072] Since the cross-sectional inertia moment of the two I-beams is the cross-sectional inertia moment of the single I-beam Z 2 times, formula (8) can be modified as

[0073]

[0074] M max = 28297.5Nm and the cross-sectional height h of the 20b I-beam in Table 2 = 200mm and the moment of inertia I z =2500cm 4 Substituting into formula (9), the maximum tensile and compressive stresses σ of two 20b I-beam simply supported beams are calculated as max It is 56.60MPa.

[0075] The proportional limit is the maximum tensile stress of a metal material that maintains linear elastic deformation. The I-beam is usually made of Q235 or Q345, and its proportional limits are approximately 200 MPa and 294 MPa, respectively. The maximum tensile and compressive stresses of a 20b I-beam simply supported beam after the fan is installed in the tunnel are σ max It is 56.60MPa, which is significantly smaller than the proportional limit of Q235 and Q345, indicating that the beam material is within the range of linear elastic deformation, which is consistent with Figure 3 The simply supported beam is simplified to a linear elastic element with a constant stiffness coefficient k. Furthermore, the yield strengths of Q235 and Q345 are approximately 235 MPa and 345 MPa, respectively. The maximum tensile and compressive stresses of the 20b I-beam simply supported beam are significantly lower than those of Q235 and Q345, indicating that the simply supported beam support for wind turbine installation fully meets the normal stress strength requirements. In fact, when the beam material deforms within the linear elastic range of lower normal stresses, it will not cross the proportional limit and approach the yield limit of higher normal stresses.

[0076] Figure 8 is based on Figure 6 The shear force diagram of the double I-beam simply supported beam is made based on the stress conditions. The shear force is 7546N at any cross section along the entire length of the beam. However, with the middle cross section of the beam as the boundary, the shear force directions on the left and right sections of the beam are opposite, and the maximum shear stress is located on the neutral axis of any cross section of the beam (see Figure 5 zz axis in the figure) and is parallel to the cross section.

[0077] The maximum shear stress expression on the cross section of a single beam is:

[0078]

[0079] The moment of inertia of the cross section of two parallel beams is the moment of inertia of the cross section of a single beam I Z 2 times, formula (10) is modified to

[0080]

[0081] The shear force Q max=7546N and the waist thickness d of the cross section of the 20b I-beam in Table 2 = 9.0mm, the ratio of the moment of inertia to the static moment of the half section I z :S z =16.9cm Substitute into formula (11) and calculate the maximum shear stress τ max =2.48MPa. The allowable shear stress [τ] of Q235 and Q345 is approximately 100MPa and 133MPa, respectively. The maximum shear stress of the beam is much smaller than the allowable shear stress of the material, indicating that the double 20b I-beam simply supported beam is sufficient to meet the shear stress strength requirements.

[0082] It can be seen from this that the use of double 20b I-beam simply supported beams not only deforms within the linear elastic range, but also meets the normal stress and shear stress strength requirements. It is fully capable of serving as a support for tunnel fans and can meet vibration isolation and safety requirements.

[0083] The present invention has been described above using specific embodiments, but the present invention is not limited to these specific embodiments. Those skilled in the art will appreciate that various modifications, equivalent substitutions, and variations may be made to the present invention, and that such modifications, as long as they do not depart from the spirit of the present invention, are within the scope of protection of the present invention. Furthermore, the term "one embodiment" used in various places above refers to different embodiments, and of course, all or part of these embodiments may be combined in a single embodiment.

Claims

1. A design method for a simply supported beam support with dual functions of support and vibration isolation for a tunnel fan, characterized in that: include: (a) Two parallel I-beams with their ends laterally inserted into the curved tunnel wall are used as the supporting structure for the tunnel fan; (b) Determine the length l of the I-beam simply supported beam based on the fan height H given by the ventilation design in the middle of the tunnel; (c) Simplify the fan-simply supported beam vibration system into a single-degree-of-freedom vibration isolation system theoretical model and perform vibration isolation calculations on it to determine the I-beam model that meets the vibration isolation requirements; and (d) Analyze the maximum normal stress and maximum shear stress of the simply supported I-beam and compare the maximum normal stress with the proportional limit and yield limit of the I-beam material to ensure that the maximum normal stress does not exceed the proportional limit and yield limit of the I-beam material; Wherein, step (c) includes obtaining parameters related to the tunnel fan, including mass, speed, installation position, simply supported beam elastic modulus, and vibration isolation efficiency; Wherein, step (c) further comprises determining the cross-sectional moment of inertia I of the simply supported I-beam using the following formula: Z : Where, I is the predetermined vibration isolation efficiency, λ is the frequency ratio, ω is the fan operating frequency, ω n is the natural frequency of the fan-simple supported beam bracket vibration isolation system, E is the elastic modulus of the I-beam material, m is the mass of the fan, and K is the stiffness coefficient of the double I-beam simply supported beam.

2. The design method of a simply supported beam support with dual functions of support and vibration isolation for a tunnel fan according to claim 1, characterized in that: Step (d) further includes analyzing the maximum shear stress of the double I-beam simply supported beam and comparing the maximum shear stress with the allowable shear stress of the I-beam material to ensure that the maximum shear stress does not exceed the allowable shear stress of the I-beam material.

3. The design method of a simply supported beam support with dual functions of support and vibration isolation for a tunnel fan according to claim 1, characterized in that: In step (d), the maximum normal stress of the simply supported beam is calculated using the following formula: Among them, σ tmax is the maximum tensile stress, σ cmax is the maximum compressive stress, M max is the maximum bending moment, and h is the height of the I-beam cross section.

4. The design method of a simply supported beam support with dual support and vibration isolation functions for a tunnel fan according to claim 1, wherein in step (d), the maximum shear stress τ of the simply supported beam support is calculated using the following formula: max : in, Q max is the maximum shear force, S* zmax is the half-section static moment, and d is the waist thickness of the I-beam cross section.

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