A bracket design method for supporting and isolating tunnel axial flow fans

Abstract

The present invention discloses a bracket design method for supporting and isolating a tunnel axial flow fan, comprising: (a) using a double I-beam cantilever beam as a support structure installed on the tunnel side wall to support the tunnel axial flow fan; (b) obtaining parameters related to the axial flow fan, including mass, speed, installation position, and vibration isolation efficiency; (c) ignoring the deadweight of the cantilever beam, and calculating the moment of inertia I of the cross section of the cantilever beam according to the parameters in step (2) z (d) Based on the vibration isolation efficiency and the moment of inertia of the cantilever beam cross section I z , using the I-beam model table to determine the I-beam model; and (e) analyzing the maximum normal stress and maximum shear stress of the double I-beam cantilever beam, and comparing the maximum normal stress with the tensile proportional limit and yield limit of the cantilever beam material to ensure that the maximum normal stress does not exceed the tensile proportional limit and yield limit of the cantilever beam material.

Description

Technical Field

[0001] The present invention relates to the technical field of traffic design, and in particular to a bracket design method for supporting and isolating an axial flow fan in a tunnel. Background Art

[0002] In tunnels of highways, railways and subways, tunnel axial flow fans are usually installed to enhance tunnel air circulation and improve tunnel air quality. There are two ways to install tunnel axial flow fans in tunnels: one is to suspend the fan from the tunnel ceiling; the other is to install it on the side wall triangular bracket (see Figure 1 When installing the side wall triangular bracket, first, fix a triangular steel bracket on the tunnel side wall; then, fix the vibration isolator selected according to the vibration isolation design on the horizontal beam of the triangular bracket; finally, install the fan on the vibration isolator on the horizontal beam of the bracket.

[0003] The triangular bracket installation method for tunnel axial fans on the side walls completely separates vibration isolation design from installation design. The fan installation height, the distance from the fan to the side wall, and the safety performance of the installation structure are all borne by the triangular steel bracket and are unrelated to the vibration isolation design. Since the strong vibration generated by the fan during operation not only transmits to the tunnel, reducing vehicle driving comfort, but also accelerates the wear of the fan itself and reduces its service life, the fan also needs to be vibration isolated to significantly reduce its vibration. The vibration isolation design mainly considers the selection of the vibration isolator installed between the horizontal beam of the triangular bracket and the fan, and generally does not consider the fan installation position and installation safety performance.

[0004] Therefore, new technical methods are needed to at least partially solve the deficiencies in the existing technology. Summary of the Invention

[0005] In order to overcome the problems existing in existing methods and equipment, the present invention provides a bracket design method for supporting and isolating tunnel axial flow fans, which changes the current installation and vibration isolation method of the triangular bracket on the side wall of the tunnel axial flow fan, and replaces the double triangular bracket and four vibration isolators with a double I-beam cantilever beam to perform an integrated vibration isolation and installation design for the tunnel fan cantilever beam. This method not only ensures that the fan installation position and vibration isolation efficiency remain unchanged, but also verifies that the beam required by the vibration isolation theory is linear elastic deformation. At the same time, the strength of the cantilever beam is checked to ensure the safety performance of the fan. The double cantilever beam structure in the present invention is simpler than the double triangular bracket structure, and does not require a special vibration isolator to be matched separately.

[0006] According to one aspect of the present invention, a method for designing a bracket for supporting and isolating a tunnel axial flow fan is provided, which is characterized by comprising:

[0007] (a) Double I-beam cantilever beams are used as support structures installed on the tunnel sidewalls to support the tunnel axial flow fans;

[0008] (b) Obtain parameters related to the axial flow fan, including mass, speed, installation position, and vibration isolation efficiency;

[0009] (c) Ignoring the deadweight of the cantilever beam, calculate the moment of inertia Iz of the cross section of the single I-beam cantilever beam based on the parameters in step (2);

[0010] (d) Determine the I-beam model using the I-beam model table based on the vibration isolation efficiency and the cantilever beam cross-sectional inertia moment Iz; and

[0011] (e) Analyze the maximum normal stress and maximum shear stress of the double I-beam cantilever beam and compare the maximum normal stress with the tensile proportional limit and yield limit of the cantilever beam material to ensure that the maximum normal stress does not exceed the tensile proportional limit and yield limit of the cantilever beam material.

[0012] According to an embodiment of the present invention, step (e) further comprises analyzing the maximum shear stress of the double I-beam cantilever beam, and comparing the maximum shear stress with the allowable shear stress of the cantilever beam material to ensure that the maximum shear stress does not exceed the allowable shear stress of the cantilever beam material.

[0013] According to an embodiment of the present invention, step (e) further comprises comparing the maximum normal stress with the allowable normal stress of the cantilever beam material to ensure that the maximum normal stress does not exceed the allowable normal stress of the cantilever beam material.

[0014] According to an embodiment of the present invention, step (e) further comprises analyzing the stress, bending moment and shear force of the cantilever beam.

[0015] According to an embodiment of the present invention, in step (c), the moment of inertia of the cross section of the arm beam I is calculated according to the following formula: z :

[0016]

[0017]

[0018] Where, I is the predetermined vibration isolation efficiency, ω is the fan operating frequency, ω n is the natural frequency of the fan-double I-beam cantilever vibration isolation system, E is the elastic modulus of the steel material, m is the mass of the fan, l is the distance from the first point on the cantilever where the fan acts on it to the tunnel wall, and l0 is the distance from the second point on the cantilever where the fan acts on it to the tunnel wall.

[0019] According to an embodiment of the present invention, in step (e), the maximum normal stress 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 (e), the maximum shear stress τ is calculated using the following formula: max :

[0023]

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

[0025] According to an embodiment of the present invention, step (d) further comprises determining m' using the following formula, where m' is an equivalent mass located at the end of the cantilever beam without deadweight and equivalent to the deadweight of the beam in terms of vibration characteristics:

[0026]

[0027] Where l0 is the distance from the end of the cantilever beam to the tunnel wall, that is, the distance from the second force point on the cantilever beam to the tunnel wall, ρ l is the theoretical linear density of I-beam.

[0028] According to an embodiment of the present invention, the natural frequency ω of the fan-double I-beam cantilever beam vibration isolation system is n Use the following formula (6) instead of formula (2) to calculate:

[0029]

[0030] 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.

[0031] BRIEF DESCRIPTION OF THE DRAWINGS

[0032] 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:

[0033] Figure 1 This is a schematic diagram of the installation of a triangular bracket on the side wall of a tunnel axial flow fan according to the prior art;

[0034] Figure 2 Schematic side and cross-sectional views of a double I-beam cantilever beam structure according to an embodiment of the invention;

[0035] Figure 3 Schematic diagram of the force, bending moment and shear force of a double 22b I-beam cantilever beam according to the embodiment of the invention;

[0036] Figure 4 is a schematic diagram of stress distribution in the cross section of a double I-beam cantilever beam at the intersection of the double I-beam cantilever beam and the tunnel wall according to an embodiment of the invention; and

[0037] Figure 5 : is a static tensile stress-strain curve of low carbon steel according to an embodiment of the invention. DETAILED DESCRIPTION

[0038] 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.

[0039] Figure 1 This is a schematic diagram of a conventional tunnel axial flow fan mounted on a side wall using a triangular bracket. The fan mass is 3050 kg, the matching motor mass is 2920 kg, and the total fan mass is 5970 kg. The motor model is Y4003-8, with a speed of 750 rpm. The distances from the point on the bracket's horizontal beam receiving the fan's force to the tunnel side wall are 2.55 m and 0.55 m, respectively. The forces acting on the four isolators are approximately equal, and the isolation efficiency is no less than 81%. See Table 1 for relevant data:

[0040] Table 1 Known parameters of the installation of the triangular bracket on the side wall of the tunnel axial flow fan

[0041]

[0042] Based on the parameters of the above-mentioned existing design such as fan mass, speed, installation position and vibration isolation efficiency, and based on the method of the present invention, the double triangular steel bracket and four vibration isolators are replaced by double I-beam cantilever beams to further illustrate the present invention in the form of an embodiment.

[0043] First, ignoring the beam's own weight, calculate the moment of inertia of the beam cross section I z .

[0044] Figure 2This is a schematic diagram of a double I-beam cantilever beam structure according to an embodiment of the present invention. The total mass m of the wind turbine is 5970 kg. The forces at the two points of application of the wind turbine on the cantilever beam are assumed to be equal, both at m / 2, or 2985 kg. Furthermore, the distances from the two forces to the side walls are l0 = 2.55 m (note that the second point of application is near the end of the cantilever beam and can also be calculated from the end point) and l = 0.55 m, respectively. The I-beam model has not yet been determined. Calculate the moment of inertia Iz of the beam cross section, ignoring the deadweight of the I-beam.

[0045] The fan speed n is 750 r / min, that is, the operating frequency ω is 78.54 rad / s. Substitute the vibration isolation efficiency I = 81% and ω = 78.54 rad / s into the following formula (1):

[0046]

[0047] The natural frequency ω of the fan-double I-beam cantilever beam vibration isolation system is calculated n It is 31.416rad / s.

[0048] When a double cantilever beam acts on a mass of m / 2 at the end and a point in the middle of the beam, the natural frequency of the system can be expressed as the following formula (2) (Model study of continuous cantilever beam dynamic vibration absorber. Hydropower Energy Science, 2011, 29(2); Application study of cantilever beam dynamic vibration absorber in ship converter unit. China Ship Repair, 2015, 28(4)):

[0049]

[0050] Among them, hot-rolled ordinary I-beams can generally be made of Q235 material, whose elastic modulus E is 206GPa. n =31.416rad / s, fan mass m=5970kg, l0=2.55m and l=0.55m are substituted into the above formula to calculate the moment of inertia of the cross section of a single I-beam cantilever beam I z =3992cm 4 .

[0051] Next, based on the vibration isolation efficiency and the moment of inertia of the cantilever beam cross section I z , use the I-beam model table to determine the I-beam model.

[0052] More specifically, the I-beam model table is checked and it is found that z =3992cm 4 High, and the closest one is I z =5020cm 4 , corresponding to No. 25a I-steel, and at the same time, its theoretical linear density ρ is obtained l It is 38.105kg / m.

[0053] The first-order natural frequency ω0 of the vibration system formed by the cantilever beam under the action of its own weight can be obtained according to the following formula (3):

[0054]

[0055] Transform (3) into the following formula (4):

[0056]

[0057] Where m' is the equivalent mass at the end of the cantilever beam without deadweight and equivalent to the deadweight of the beam in terms of vibration characteristics. It can be calculated according to the following formula (5):

[0058]

[0059] Let l0 = 2.55m, ρ l =38.105kg / m Substituting into the above formula, we can calculate the equivalent mass m'=47.23kg.

[0060] Since the beam ends of the double 25a I-beam cantilever beam have a mass m / 2 and a mass m' equivalent to the beam's deadweight in terms of vibration characteristics, equation (2) can be modified as follows:

[0061]

[0062] Set m' = 47.23 kg, m = 5970 kg, E = 206 GPa, I z =5020cm 4 , l0=2.55m, l=0.55mSubstitute into the above formula, and calculate the natural frequency ω of the vibration isolation system under the condition of the deadweight of the 25a I-beam cantilever beam. n It is 34.957rad / s.

[0063] The fan speed ω=78.54rad / s and the natural frequency of the vibration system ω n = 34.957 rad / s Substituting this into equation (1), we obtain a vibration isolation efficiency of I = 75.3%, which is less than the existing standard of 81%. This design does not meet the vibration isolation requirements. Therefore, it is necessary to reselect the I-beam model.

[0064] Moment of inertia of the cantilever beam I z The larger the cantilever beam is, the greater its stiffness is and the smaller the vibration isolation efficiency of the vibration system is. On the contrary, the moment of inertia of the cantilever beam I z The smaller it is, the smaller its stiffness is, and the higher the vibration isolation efficiency of the vibration system is. In order to improve the vibration isolation efficiency of the vibration system I, the I-beam model table is rechecked and it is found that z =3992cm 4 Low, and the closest is I z =3570cm 4, corresponding to 22b I-beam, at the same time, the theoretical linear density ρ of a single 22b I-beam is obtained l =36.524kg / m. l = 36.524 kg / m substituted into (5) to calculate the equivalent mass m' = 45.27 kg. Then, m' = 45.27 kg, m = 5970 kg, E = 206 GPa, I z =3570cm 4 , l0=2.55m, l=0.55m are substituted into formula (6) to calculate the natural frequency ω of the vibration isolation system under the condition of taking into account the deadweight of the double 22b I-beam cantilever beam. n = 29.49 rad / s. The fan speed ω = 78.54 rad / s and the natural frequency ω n = 29.49 rad / s Substituting into formula (1), the vibration isolation efficiency I is calculated to be 83.54%, which is greater than the existing standard of 81%. The design meets the vibration isolation requirements.

[0065] After selecting the I-beam model, the cantilever beam can be subjected to force, bending moment, and shear analysis.

[0066] Figure 3 (a) is a force diagram of a double 22b I-beam cantilever beam. The total weight of the wind turbine is 5970 × 9.8 = 58506 N. The two forces acting on the cantilever beam are considered equal, both 29253 N. The distances from the two force application points to the side walls are 2.55 m and 0.55 m, respectively. The linear density of a single 22b I-beam is ρ l =36.524kg / m, then the uniformly distributed deadweight load of the two beams is 716N / m.

[0067] based on Figure 3 (a), draw the bending moment diagram for the double I-beam cantilever beam shown in 3(b). The bending moment curve is divided into two sections: one section extends from the beam end to the left to a point 2m from the beam end, where the bending moment starts at 0 at the beam end and follows a continuous, slightly upward-convex quadratic parabola to a maximum value of 59,938 Nm at 2m from the beam end; the other section extends from 0.55m from the side wall to the left to the side wall, where the bending moment starts at 59,938 Nm at 0.55m from the side wall and follows a continuous, slightly upward-convex quadratic parabola to a maximum value of 93,012 Nm at the side wall. The maximum bending moment in both sections is 93,012 Nm, located at the cross section of the beam where it intersects the tunnel wall.

[0068] according to Figure 3 (a) The force condition, draw Figure 3(c) shows the shear force diagram for the double I-beam cantilever beam. The shear force line is divided into two segments: one segment runs from the beam end to the left to a point 2 m from the beam end. The shear force starts at 29,253 N at the beam end and reaches a maximum of 30,685 N 2 m from the beam end via an inclined straight line. The other segment runs from 0.55 m from the side wall to the left to the side wall. The shear force starts at 59,938 N m 0.55 m from the side wall and reaches a maximum of 60,332 N at the side wall via an inclined straight line. The maximum shear force along both inclined straight lines is 60,332 N, located at the cross section of the beam where it intersects the tunnel wall.

[0069] Then the distribution and maximum values ​​of the bending moment and shear force of the cantilever beam are further analyzed.

[0070] Figure 4 Schematic diagram of stress distribution in the cross section of a double I-beam cantilever beam at the intersection of the beam and the tunnel wall according to an embodiment. The maximum bending moment and maximum shear force of the cantilever beam are both located at this cross section. Figure 4 The right side is a schematic diagram of the normal stress distribution. The tensile and compressive normal stresses are perpendicular to the cross section of the beam and in opposite directions. The tensile stress changes linearly from the upper end of the cross section to the neutral axis. The maximum tensile stress at the upper end of the cross section is set as σ tmax , the minimum value at the neutral axis is 0; the compressive stress changes linearly from large to small from the lower end of the cross section to the neutral axis, and the maximum compressive stress at the lower end of the cross section is set to σ cmax , the minimum value at the neutral axis is 0. Maximum tensile stress σ tmax and maximum compressive stress σ cmax are numerically equal.

[0071] The maximum normal stress can be calculated according to the following formula:

[0072]

[0073] The maximum bending moment M max =93012Nm, moment of inertia of the cross section of No. 22b I-beam z =3570cm 4 , and the cross-sectional height h = 0.22m of the No. 22b I-beam obtained from the table are substituted into formula (7) to calculate the maximum tensile stress σ tmax and maximum compressive stress σ cmax Both are 143.3MPa.

[0074] Shear stress exists across the entire cross-section of an I-beam. The shear stress on the flanges is complex and small, so it is usually ignored. The shear stress on the web is parallel to the cross-section and directed vertically downward. Figure 4 On the left is a schematic diagram of the shear stress of the web. The shear stress along the web height is distributed according to a parabolic law. The vertex of the parabola is located at the neutral axis, which is the maximum shear stress τ max At the minimum shear stress τmin Located at the intersection of the web and flange.

[0075] The maximum shear stress can be calculated according to the following formula:

[0076]

[0077] The maximum shear force Q max =60332N, and the web thickness b of No. 22b I-beam obtained from the I-beam model table = 9.5mm, and the ratio of the moment of inertia of the cross section to the static moment of half section, that is, Substituting into formula (8), the maximum shear stress τ is calculated max =16.98MPa.

[0078] Finally, the linear elastic deformation and strength of the cantilever beam are checked.

[0079] Figure 5 This is the static tensile stress-strain curve for a low-carbon steel specimen (GB228-87, Metal Tensile Test Methods). The abscissa represents the strain ε, which is the change in specimen length divided by the original specimen length; the ordinate represents the normal stress σ, which is the tensile force applied to the specimen divided by the original cross-sectional area. Hot-rolled ordinary I-beam Q235, a low-carbon steel, exhibits the five classic deformation stages of the tensile stress-strain curve: oa; ab; bc; cd; de.

[0080] The oa segment is a linear elastic deformation segment. In this segment, stress and strain are in direct proportion. The deformation of the material satisfies Hooke's law. The normal stress at point a is defined as the proportional limit σ. p , the proportional limit σ of Q235 p About 200MPa. When the maximum normal stress σ max Less than the proportional limit σ p When , it can be considered that the material only undergoes linear elastic deformation. The maximum tensile stress σ of the 22b I-beam cantilever beam tmax and maximum compressive stress σ cmax Both are 143.3MPa, which are less than the proportional limit σ of the beam material. p , indicating that the beam material deforms within the linear elastic range, which satisfies the assumption in the previous vibration isolation design that the double I-beam cantilever beam needs to be considered as linear elastic deformation.

[0081] The ab section is the elastic deformation section. In this section, after the load is removed, the deformation of the specimen can be completely recovered, but the stress and strain no longer change in direct proportion and no longer follow Hooke's law.

[0082] The bc segment is the yield deformation segment. In this segment, the stress fluctuates slightly, while the strain increases significantly. After the load is removed, some deformation cannot disappear. The deformation that cannot disappear will affect the normal operation of the machine. Therefore, the minimum stress in this segment is usually used as an important indicator to measure the strength of the material, which is called the yield limit σ. s The yield strength of Q235 material is σ s The maximum tensile and compressive normal stresses of the 22b I-beam cantilever beam are 143.3 MPa, which are both less than the yield limit σ s , indicating that the cantilever beam meets the strength requirements. In engineering practice, in order to ensure the safety of the structure, the yield limit σ is often used. s Divide by a safety factor n greater than 1 s , we get the allowable stress [σ], when designing, the maximum working normal stress σ max It is not allowed to exceed the allowable stress [σ]. Here let n s Taking 1.5, the allowable normal stress [σ] is 156.6MPa. The maximum tensile and compressive normal stresses of the I-beam, 143.3MPa, are also less than the allowable normal stress [σ]. In fact, the tensile deformation of a material first undergoes a linear elastic deformation stage, followed by a yield deformation stage. If the material deforms only within the linear elastic range, it will not rise to the yield deformation stage.

[0083] The cd section is the strengthening deformation section. In this section, the specimen recovers its ability to resist deformation. To increase deformation, the tensile force must be increased.

[0084] The de segment is a local deformation segment, in which the transverse dimension of a certain location of the specimen suddenly decreases significantly until it is broken at that location.

[0085] In addition, the maximum shear stress τ of the beam material max =16.98MPa is much smaller than the allowable shear stress [τ] = 100MPa of Q235.

[0086] The results show that the use of double 22b I-steel cantilever beams not only deforms within the linear elastic range, but also meets the strength requirements. It is fully capable of serving as a support for tunnel axial flow fans and can meet the requirements of vibration isolation and safety.

[0087] 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 method for designing a bracket for supporting and isolating a tunnel axial flow fan, characterized in that: include: (a) Double I-beam cantilever beams are used as support structures installed on the tunnel sidewalls to support the tunnel axial flow fans; (b) Obtain parameters related to the axial flow fan, including mass, speed, installation position, and vibration isolation efficiency; (c) Ignoring the deadweight of the cantilever beam, calculate the moment of inertia of the cantilever beam cross section I according to the parameters in step (2): z ; (d) Based on the vibration isolation efficiency and the moment of inertia of the cantilever beam cross section I z , use the I-beam model table to determine the I-beam model; as well as (e) Analyze the maximum normal stress and maximum shear stress of the double I-beam cantilever beam and compare the maximum normal stress with the tensile proportional limit and yield limit of the cantilever beam material to ensure that the maximum normal stress does not exceed the tensile proportional limit and yield limit of the cantilever beam material; In step (c), calculate the moment of inertia of the cross section of the arm beam I according to the following formula: z : Where, I is the predetermined vibration isolation efficiency, ω is the fan operating frequency, ω n is the natural frequency of the fan-double I-beam cantilever vibration isolation system, E is the elastic modulus of the steel material, m is the mass of the fan, l is the distance from the first point on the cantilever where the fan acts on it to the tunnel wall, and l0 is the distance from the second point on the cantilever where the fan acts on it to the tunnel wall; In step (e), the maximum normal stress 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, h is the height of the I-beam cross section; In step (e), the maximum shear stress τ is calculated using the following formula: max : Among them, Q max is the maximum shear force, S* zmax is the static moment of half section, and b is the thickness of the I-beam web.

2. The bracket design method for supporting and isolating a tunnel axial flow fan according to claim 1 is characterized in that: Step (e) further includes analyzing the maximum shear stress of the double I-beam cantilever beam and comparing the maximum shear stress with the allowable shear stress of the cantilever beam material to ensure that the maximum shear stress does not exceed the allowable shear stress of the cantilever beam material.

3. The bracket design method for supporting and isolating a tunnel axial flow fan according to claim 1 is characterized in that: Step (e) further includes comparing the maximum normal stress to an allowable normal stress of the cantilever beam material to ensure that the maximum normal stress does not exceed the allowable normal stress of the cantilever beam material.

4. The bracket design method for supporting and isolating a tunnel axial flow fan according to claim 1 is characterized in that: Step (e) also includes analyzing the forces, bending moments, and shear forces of the cantilever beam.

5. The bracket design method for supporting and isolating a tunnel axial flow fan according to claim 1 is characterized in that: Step (d) further includes determining m' using the following formula, where m' is an equivalent mass located at the end of the cantilever beam without its own weight and having vibration characteristics equivalent to the beam's own weight: Where l0 is the distance from the end of the cantilever beam to the tunnel wall, that is, the distance from the second force point on the cantilever beam to the tunnel wall, ρ l is the theoretical linear density of I-beam.

6. The bracket design method for supporting and isolating a tunnel axial flow fan according to claim 5 is characterized in that: Natural frequency ω of the fan-double I-beam cantilever beam vibration isolation system n Use the following formula (6) instead of formula (2) to calculate:

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