CN110427730B - Gear box global equivalent statistical energy analysis modeling method - Google Patents
Gear box global equivalent statistical energy analysis modeling method Download PDFInfo
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Abstract
The invention discloses a global equivalent statistical energy analysis modeling method for a gearbox, which comprises the following steps of: step 1: establishing a reference body size model of the gearbox; step 2: dividing a solid model of the gearbox into a plurality of subsystems, and respectively obtaining the modal density and the internal loss factor of each subsystem; and step 3: merging the subsystems onto a basic equivalent surface of a reference body size model of the gearbox respectively, and calculating parameters of each subsystem model equivalent to the basic equivalent surface; and 4, step 4: determining the lower limit frequency of each basic equivalent surface based on the parameters of each subsystem model equivalent to the basic equivalent surface; and 5: calculating the thickness of each basic equivalent surface based on the lower limit frequency of each basic equivalent surface; step 6: and implanting the parameters of each subsystem model equivalent to the basic equivalent surfaces and the thickness of each basic equivalent surface into a reference body size model of the gearbox to obtain a hexahedron equivalent model. The method has high modeling analysis speed and accuracy, and is worthy of popularization.
Description
Technical Field
The invention belongs to the technical field of radiation noise, and particularly relates to a global equivalent statistical energy analysis modeling method for a gearbox.
Background
The frequency distribution of the gearbox noise is closely related to the gear rotating speed, for the common working rotating speed, the main frequency component of the gearbox radiation noise is generally in a low frequency band, but with the increase of the gear rotating speed, the fundamental frequency, the double frequency and other important frequencies of the gear meshing frequency gradually enter a high frequency band area of the gearbox. For the simulation estimation of the high-frequency noise of the gearbox, a statistical energy method is particularly suitable, and in the statistical energy analysis, a single-board system is defined as a single subsystem structure. At present, some researches on high-frequency vibration noise of a gearbox are carried out at home and abroad, but the researches have some defects which are mainly reflected in the following aspects:
(1) the structural characteristics of the gear box have obvious influence on vibration noise, the gear box body comprises relatively thick and complex structures, and when a statistical energy analysis model is established by adopting a statistical energy method, the structures cannot be accurately modeled in VAone software.
(2) Due to the fact that the box wall of the gear box body is relatively thick and the structure is complex, a large number of small-sized subsystems can be divided when the subsystems are divided by adopting a statistical energy analysis method, the small-sized subsystems cannot meet the requirement of modal density, and errors which cannot be estimated can be brought by the subsystems which do not meet the condition by using the statistical energy analysis method.
(3) In the process of establishing a statistical energy analysis model of the gearbox, modeling is generally carried out by experience, the model is too simplified and cannot reflect the real characteristics of the structure, and too thinning reduces the modal density of a subsystem, so that the model cannot meet the requirements of statistical energy analysis and calculation.
Disclosure of Invention
In view of the above, the present invention provides a modeling method for global equivalent statistical energy analysis of a gearbox, so as to solve the technical problems in the prior art.
The technical scheme of the invention is as follows:
a global equivalent statistical energy analysis modeling method for a gearbox comprises the following steps:
step 1: establishing a reference body size model of the gearbox;
step 2: dividing a solid model of the gearbox into a plurality of subsystems, and respectively obtaining the modal density and the internal loss factor of each subsystem;
and step 3: merging the subsystems onto a basic equivalent surface of a reference body size model of the gearbox respectively, and calculating parameters of each subsystem model equivalent to the basic equivalent surface;
and 4, step 4: determining the lower limit frequency of each basic equivalent surface based on the parameters of each subsystem model equivalent to the basic equivalent surface;
and 5: calculating the thickness of each basic equivalent surface based on the lower limit frequency of each basic equivalent surface;
step 6: and implanting the parameters of each subsystem model equivalent to the basic equivalent surfaces and the thickness of each basic equivalent surface into a reference body size model of the gearbox to obtain a hexahedron equivalent model.
Preferably, in the step 1, a reference body size model of the gearbox is established based on the ISO 3744:1994 standard, and the reference body size model of the gearbox is the smallest shell of the envelope gearbox.
Preferably, the division principle of the gear box solid model into a plurality of subsystems in the step 2 is that the established subsystems must be capable of clearly showing the characteristics of input, storage, loss and transmission of vibration energy.
Preferably, the principle of the sub-systems respectively combined in the step 3 is to combine the sub-systems with the same direction.
Preferably, the parameters of each subsystem model equivalent to the substantially equivalent surface in step 3 include modal density and internal loss factor, and when the parameters of each subsystem model equivalent to the substantially equivalent surface are calculated, the modal densities of the subsystems with the same direction are superposed, and the internal loss factor is subjected to average operation to serve as the parameters of each subsystem model equivalent to the substantially equivalent surface.
Preferably, the method for determining the lower limit frequency of the basic equivalent surface in step 4 is to perform modal analysis on the basic equivalent surface, and when the number of modes is greater than or equal to 5, the corresponding center frequency is determined as the lower limit frequency of the basic equivalent surface.
Preferably, in the step 5, the thickness of each substantially equivalent surface is calculated by using formula (1)
Wherein f iscrIs the lower limit frequency of the substantially equivalent plane, and D is the substantially equivalent planeBending stiffness, h is the thickness of the substantially equivalent plane, D ═ EI/(1-. mu.2) I is the wide moment of inertia of the plate, I ═ h3G is shear modulus, μ is poisson's ratio, E is elastic modulus, G ═ E/2(1+ μ), ρ is material density of the structure, c0Is the speed of sound propagation in the medium.
Compared with the prior art, the overall equivalent statistical energy analysis modeling method for the gearbox, provided by the invention, comprises the steps of calculating the modal density and the internal loss factor of the subsystems in each direction, determining the statistical energy analysis parameter of the equivalent model by means of superposition of the modal density and average of the internal loss factor, determining the lower limit frequency of the equivalent model based on the modal density of each equivalent model, calculating the equivalent thickness of each equivalent model, calculating the material density of the equivalent model on the premise of keeping the quality of the front equivalent model and the quality of the rear equivalent model unchanged, establishing the hexahedral equivalent model, and implanting the volume attribute and the material attribute into the equivalent model.
By adopting the global equivalent statistical energy analysis modeling method of the gear box, the gear box model which does not meet the calculation of the statistical energy analysis method can be suitable for statistical energy analysis calculation, and when the radiation noise is analyzed, the result of the radiation noise can be extracted only by applying the same excitation on the equivalent model obtained in the front and measuring the radiation noise at the same field point position.
Drawings
FIG. 1 is a flow chart of a gearbox global equivalent statistical energy analysis modeling method;
FIG. 2 is a view of an original model of a gear housing;
FIG. 3 is a gear housing ribbed plate structural model;
FIG. 4 is a gearbox bearing block model;
FIG. 5 is a schematic diagram of an equivalent statistical energy analysis model of a gearbox housing;
FIG. 6 is a diagram of a gearbox equivalent statistical energy analysis model radiation noise calculation model;
FIG. 7 is a plot of the gearbox case equivalent model radiated noise spectrum at 6000 rpm.
Detailed Description
The invention provides a global equivalent statistical energy analysis modeling method for a gearbox, which is described with reference to the figures 1 to 7.
As shown in fig. 1, the technical solution of the present invention is:
a global equivalent statistical energy analysis modeling method for a gearbox comprises the following steps:
step 1: establishing a reference body size model of the gearbox;
step 2: dividing a solid model of the gearbox into a plurality of subsystems, and respectively obtaining the modal density and the internal loss factor of each subsystem;
and step 3: merging the subsystems onto a basic equivalent surface of a reference body size model of the gearbox respectively, and calculating parameters of each subsystem model equivalent to the basic equivalent surface;
and 4, step 4: determining the lower limit frequency of each basic equivalent surface based on the parameters of each subsystem model equivalent to the basic equivalent surface;
and 5: calculating the thickness of each basic equivalent surface based on the lower limit frequency of each basic equivalent surface;
step 6: and implanting the parameters of each subsystem model equivalent to the basic equivalent surfaces and the thickness of each basic equivalent surface into a reference body size model of the gearbox to obtain a hexahedron equivalent model.
Further, in the step 1, a reference body size model of the gearbox is established based on the ISO 3744:1994 standard, and the reference body size model of the gearbox is the smallest shell of the envelope gearbox.
Further, the division principle of the gear box solid model into a plurality of subsystems in step 2 is that the established subsystems must be capable of clearly showing the characteristics of input, storage, loss and transmission of vibration energy.
Further, the principle of the respective merging of the subsystems in step 3 is to merge subsystems having the same direction.
Further, the parameters of each subsystem model equivalent to the basic equivalent surface in step 3 include modal density and internal loss factor, and when the parameters of each subsystem model equivalent to the basic equivalent surface are calculated, the modal densities of the subsystems with the same direction are superposed, and the internal loss factors are averaged to serve as the parameters of each subsystem model equivalent to the basic equivalent surface.
Further, the method for determining the lower limit frequency of the basic equivalent surface in step 4 is to perform modal analysis on the basic equivalent surface, and when the number of modes is greater than or equal to 5, the corresponding center frequency is determined as the lower limit frequency of the basic equivalent surface.
Further, in the step 5, the thickness of each substantially equivalent surface is calculated by using the formula (1)
Wherein f iscrIs the lower limit frequency of the basic equivalent plane, D is the bending rigidity of the basic equivalent plane, h is the thickness of the basic equivalent plane, D is EI/(1-mu)2) I is the wide moment of inertia of the plate, I ═ h3G is shear modulus, μ is poisson's ratio, E is elastic modulus, G ═ E/2(1+ μ), ρ is material density of the structure, c0Is the speed of sound propagation in the medium.
In the above step, the dividing principle of dividing the solid model of the gearbox into a plurality of subsystems in step 2 is summarized as follows:
1) the main mode group for determining the vibration of the structure, namely the main vibration mode always exists for different structures, and plays a main role in energy transmission, consumption and storage.
2) The modal density of the subsystems must be high enough, for example, the number of modes within the analysis bandwidth exceeds 5, i.e., high frequency, and the more dominant energy transfer subsystems need to meet this requirement, which may relax the constraints on each non-dominant subsystem.
3) The connection between the structures is determined, which determines the magnitude of the vibration energy transmission.
4) The mode similarity criterion is satisfied, namely the mode shapes have the same dynamic characteristics, namely the same damping, the same mode energy, the same coupling loss factor and the like.
5) The subsystems are partitioned according to the natural geometric boundary conditions, dynamic boundary conditions, material medium properties, mission phase requirements and experience of the system.
Example 1
When the modeling method is used for vibration analysis, the concrete steps are as follows:
step 1: establishing a reference body size model of the gearbox according to ISO 3744:1994 based on the original model of the gearbox;
step 2: establishing an entity model of the gearbox in VAone software, dividing the entity model of the gearbox into a plurality of subsystems, and respectively inquiring and extracting the modal density and the internal loss factor of each subsystem;
and step 3: merging the subsystems onto a basic equivalent surface of a reference body size model of the gearbox respectively, and calculating parameters of each subsystem model equivalent to the basic equivalent surface;
and 4, step 4: determining the lower limit frequency of each basic equivalent surface based on the parameters of each subsystem model equivalent to the basic equivalent surface;
and 5: calculating the thickness of each basic equivalent surface based on the lower limit frequency of each basic equivalent surface;
step 6: implanting parameters of each subsystem model equivalent to the basic equivalent surface and the thickness of each basic equivalent surface into a reference body size model of the gearbox to obtain a hexahedron equivalent model;
and 7: and applying the same high-frequency excitation to the equivalent model, measuring the radiation noise at the same field point position, and extracting a radiation noise result.
The calculating of the modal density and the internal loss factor of the 6 equivalent surfaces of the gear box body is that for the gear box body, 6 direction surfaces are correspondingly arranged, namely a top surface, a bottom surface, a left side surface, a right side surface, a front surface and a back surface, after the modal density and the internal loss factor of each subsystem on each direction surface are calculated and extracted, the modal density of the subsystems on each corresponding direction surface is superposed, the internal loss factor is averagely calculated, the equivalent modal density and the equivalent internal loss factor on each direction surface can be obtained, and the equivalent modal density and the equivalent internal loss factor are implanted into an equivalent flat plate.
The lower limit frequency of each equivalent surface is obtained based on the modal density of each equivalent surface, the lower limit frequency of each equivalent surface is obtained through VAone software calculation, the value of the lower limit frequency is the central frequency with the modal number being more than or equal to 5, the equivalent model thickness is determined by using a formula, and the calculation formula is as follows:
in the formula (f)crFor lower limit frequency, D is the bending stiffness of the structure, h is the thickness of the structure, D ═ EI/(1-. mu.)2) Where I is the wide moment of inertia of the plate, and I ═ h312; g is shear modulus, μ is poisson's ratio, E is elastic modulus, G ═ E/2(1+ μ); ρ is the material density of the structure; c. C0Is the speed of sound propagation in the medium. And then calculating to obtain the material density of the equivalent model on the premise of ensuring that the mass before and after the equivalence is unchanged.
The method comprises the steps of establishing a global equivalent model of the gearbox, namely establishing a hexahedral square box model, calculating and extracting the modal density and the internal loss factor of each subsystem on each direction surface, superposing the modal density of the subsystems on each corresponding direction surface and carrying out average calculation on the internal loss factor to obtain the equivalent modal density and the equivalent internal loss factor on each direction surface for the gearbox body, implanting the equivalent modal density and the equivalent internal loss factor into an equivalent flat plate, and establishing the global equivalent hexahedral square box model of the gearbox by combining the volume attribute and the material density of the equivalent model obtained before.
Fig. 2 shows a gear case model of a two-stage gear transmission system used in the research and analysis of this embodiment, and the main profile dimension is 480 × 250 × 290(mm), which is the reference body dimension of the gear case.
The gearbox casing is divided into subsystems as shown in fig. 2, and part of the subsystems are marked in the figure and comprise 20 structural subsystems.
In the global equivalent SEA model of the gearbox, the subsystem in front of the gearbox comprises a ribbed plate with an irregular complex structure as shown in fig. 3 and a bearing seat structure as shown in fig. 4, modal density is calculated, and the modal density of the subsystem obtained by automatic calculation of VAone software is linearly superposed to obtain the calculated modal density of the subsystem in front of the box body of the global equivalent model.
The method for determining the modal density of other subsystems in the global equivalent model of the box body is the same as the method, and for the subsystems on the same surface of the initial model of the box body, software extracts the modal density of the subsystems and then carries out linear superposition to further obtain the calculated modal density of the subsystems of the global equivalent model.
According to the trial calculation of the structural modal density of the boxes with different sizes and containing ribbed plates and bearing seats, the modal density is mostly found to be between 0.001 and 0.01, and the larger the structural size is, the larger the value of the modal density is correspondingly, so that in the preliminary design stage of the gear box body, on the premise that the specific details and parameters of the gear body are not clear, the value can be selected in the range, and preliminary high-frequency noise estimation can be carried out on the gear box body.
After the statistical energy analysis parameters of all subsystems of the gear box body are determined, the modal density of each in-plane subsystem is superposed to obtain the total modal density of 6 planes, and then an equivalent statistical energy analysis model of the box body is established. According to the total modal density of each surface, the lower limit frequency of the statistical energy analysis frequency at the moment is 1250Hz, the minimum thickness of the box wall thickness is 8mm, so that the critical frequency of each subsystem does not need to be calculated, the maximum value of the critical frequency of each subsystem is 12/0.008 to 1500Hz, and the maximum value between 1250Hz and 1500Hz is taken, so the lower limit frequency of the equivalent analysis is 1500 Hz.
And finally, taking the thickness value of the equivalent model as 8mm, after the equivalent thickness is determined, establishing a statistical energy analysis model of the gearbox body by keeping the surface area of the structure unchanged and changing the material density, wherein specific size parameters of the equivalent model are shown in the following table 1.
TABLE 1 basic parameters of the tank equivalent model
After the box model is built, the specific values of the total modal density and the average internal loss factor are implanted into an equivalent model built in VAone software, and software defaults are adopted for the coupling loss factor due to the fact that the magnitude is small and calculation is difficult. Fig. 5 shows a schematic diagram of an equivalent statistical energy analysis model of the gearbox after equivalence, and fig. 6 shows an equivalent statistical energy analysis calculation model of the gearbox established in VAone software.
And giving the calculated statistical energy analysis parameters to a gear box body global equivalent model, applying a bearing dynamic load to the model, defining 1 semi-infinite field unit at a position 1m away from the center of the top surface of the gear box, receiving radiation energy, calculating radiation noise of the gear box, and obtaining a value at the central frequency in the bandwidth.
FIG. 7 is a graph of the calculated case radiation noise of the high-speed pinion at 6000rpm with a torque of 4000 N.m. As can be seen from fig. 7, when the rotation speed is 6000rpm, the maximum value of the radiation noise is 58.81dB at the central frequency of 3150Hz, and the peak value of the radiation noise occurs here because when the rotation speed is 6000rpm, the corresponding meshing frequency of the high-speed gear is 2900Hz, the meshing frequency of the low-speed gear is 3100Hz, and both the frequencies are within the frequency band range of 2820 to 3550Hz, and since the statistical energy analysis method cannot calculate the result at any frequency, only the average value in a certain frequency band can be calculated as the value at the central frequency of the frequency band, so the peak value occurs at 3550 Hz.
The invention provides a global equivalent statistical energy analysis modeling method for a gearbox, which comprises the steps of calculating modal densities and internal loss factors of subsystems in all directions, determining statistical energy analysis parameters of equivalent models in a mode of superposing the modal densities and averaging the internal loss factors, determining the lower limit frequency of the equivalent models based on the modal densities of the equivalent models, calculating the equivalent thickness of the equivalent models, calculating the material density of the equivalent models on the premise of keeping the quality of the equivalent models before and after unchanged, establishing a hexahedral equivalent model, and implanting volume attributes and material attributes into the equivalent models.
By adopting the global equivalent statistical energy analysis modeling method of the gear box, the gear box model which does not meet the calculation of the statistical energy analysis method can be suitable for statistical energy analysis calculation, and when the radiation noise is analyzed, the result of the radiation noise can be extracted only by applying the same excitation on the equivalent model obtained in the front and measuring the radiation noise at the same field point position.
The above disclosure is only for the preferred embodiments of the present invention, but the embodiments of the present invention are not limited thereto, and any variations that can be made by those skilled in the art are intended to fall within the scope of the present invention.
Claims (7)
1. A global equivalent statistical energy analysis modeling method for a gearbox is characterized by comprising the following steps:
step 1: establishing a reference body size model of the gearbox;
step 2: dividing a solid model of the gearbox into a plurality of subsystems, and respectively obtaining the modal density and the internal loss factor of each subsystem;
and step 3: merging the subsystems onto a basic equivalent surface of a reference body size model of the gearbox respectively, and calculating parameters of each subsystem model equivalent to the basic equivalent surface;
and 4, step 4: determining the lower limit frequency of each basic equivalent surface based on the parameters of each subsystem model equivalent to the basic equivalent surface;
and 5: calculating the thickness of each basic equivalent surface based on the lower limit frequency of each basic equivalent surface;
step 6: and implanting the parameters of each subsystem model equivalent to the basic equivalent surfaces and the thickness of each basic equivalent surface into a reference body size model of the gearbox to obtain a hexahedron equivalent model.
2. The modeling method for the global equivalent statistical energy analysis of the gearbox according to claim 1, wherein in the step 1, a reference body size model of the gearbox is established based on ISO 3744:1994 standard, and the reference body size model of the gearbox is a minimum shell of the envelope gearbox.
3. The modeling method for global equivalent statistical energy analysis of gearbox according to claim 1, wherein the division principle of dividing the solid model of gearbox into a plurality of subsystems in step 2 is that the established subsystems must be able to clearly show the characteristics of input, storage, loss and transmission of vibration energy.
4. The modeling method for gearbox global equivalent statistical energy analysis according to claim 1, wherein the principle of subsystem combination in step 3 is to combine subsystems with the same direction.
5. The modeling method for the global equivalent statistical energy analysis of the gearbox according to claim 1, wherein the parameters of the subsystem models equivalent to the substantially equivalent surface in step 3 include modal density and internal loss factor, and when the parameters of the subsystem models equivalent to the substantially equivalent surface are calculated, the modal densities of the subsystems with the same direction are superimposed, and the internal loss factor is averaged to be used as the parameters of the subsystem models equivalent to the substantially equivalent surface.
6. The modeling method for the global equivalent statistical energy analysis of the gearbox according to claim 1, wherein the method for determining the lower limit frequency of the substantially equivalent surface in the step 4 is to perform modal analysis on the substantially equivalent surface, and the corresponding center frequency when the number of modes is greater than or equal to 5 is determined as the lower limit frequency of the substantially equivalent surface.
7. The modeling method for global equivalent statistical energy analysis of gearbox according to claim 1, wherein in said step 5, the thickness of each substantially equivalent surface is calculated by formula (1)
Wherein f iscrIs the lower limit frequency of the basic equivalent plane, D is the bending rigidity of the basic equivalent plane, h is the thickness of the basic equivalent plane, D is EI/(1-mu)2) I is the wide moment of inertia of the plate, I ═ h3G is shear modulus, μ is poisson's ratio, E is elastic modulus, G ═ E/2(1+ μ), ρ is material density of the structure, c0Is the speed of sound propagation in the medium.
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| CN106407617A (en) * | 2016-11-16 | 2017-02-15 | 中国船舶重工集团公司第七0三研究所 | Full frequency-domain calculation method of vibration noise of gear case |
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