CN112231916A - Modal quality measuring method - Google Patents
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- CN112231916A CN112231916A CN202011121954.XA CN202011121954A CN112231916A CN 112231916 A CN112231916 A CN 112231916A CN 202011121954 A CN202011121954 A CN 202011121954A CN 112231916 A CN112231916 A CN 112231916A
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Abstract
The invention provides a method for measuring modal quality, which comprises the following steps: establishing resonance of a structural part to be tested in an N-order mode; sequentially placing counterweight components on the structural part to be tested in N-order modal resonance, respectively establishing the resonance of the structural part to be tested in N-order modal after the counterweight components are placed each time, and acquiring the N-order resonance frequency of the structural part to be tested after the counterweight components are placed each time; acquiring the N-order modal mass variation of the structural part to be measured after the counterweight part is placed each time; acquiring a fitting curve of the N-order resonance frequency and the N-order modal mass variation; obtaining the slope of the fitting curve; and acquiring the N-order modal quality of the structural part to be tested based on the slope of the fitting curve and the N-order resonance frequency of the structural part to be tested after the counterweight part is placed for the first time. The invention can solve the technical problem that the existing modal quality measuring method cannot ensure the measuring precision of a complex structure or a dense modal structure.
Description
Technical Field
The invention relates to the technical field of aerospace structure dynamics testing, in particular to a modal mass measuring method.
Background
A complete vibration system must include a mass matrix, a stiffness matrix and a damping matrix, wherein the mass matrix stores kinetic energy of the system, the stiffness matrix stores potential energy of the system, and the damping matrix represents energy transfer between different systems (e.g., mechanical energy is converted into thermal energy), and the energy is continuously converted into each other through organic combination of the three, thereby constituting the motion (vibration) of the system. The form of the system after vibration is called mode.
A mode is a definition in a physical sense that corresponds to a characteristic value problem that mathematically reflects as a non-homogeneous differential equation. In a physical coordinate system, the mass matrix and the stiffness matrix are inevitably coupled, which brings great difficulty to equation solution. In a modal coordinate system, a mass matrix and a stiffness matrix are converted into a diagonal matrix by means of the orthogonal characteristic of a modal base, and a multi-degree-of-freedom system is decoupled into n single-degree-of-freedom systems, so that equation solution is greatly simplified. The diagonal matrix (mass matrix and stiffness matrix) obtained in this way is called a modal mass matrix and a modal stiffness matrix, and is referred to as modal mass and modal stiffness for short.
The modal mass, the modal stiffness and the like are defined in a modal coordinate system, and the modal mass, the modal stiffness and the like only have a mathematical calculation function and do not have actual physical meanings and dimensions. However, the mathematical parameters obtained in the modal system can be converted into the mechanical parameters in the physical system through the generalized inverse transformation. For example, the modal mass and the modal shape are used for calculating the motion equation coefficient and the dynamic load of the vibration system under a specific working condition, and an important basis is provided for aircraft control design and load design. In view of the above, dynamic characteristic parameters of the vibration system, such as modal mass and modal stiffness, occupy an important position in the design of the dynamics of the aircraft structure. Since the modal mass and the modal stiffness can be mutually derived through the natural frequency of the structure, the modal mass is generally obtained in engineering.
The methods currently available for measuring modal quality are mainly: a formula method based on a finite element model, a formula method based on a finite element model and test data, a test method based on a frequency response function and the like. The following briefly describes the above-described methods.
(1) Formula method based on finite element model
According to the definition of modal quality, a modal quality matrix is equal to the transposition of a system real quality matrix multiplied by a modal shape matrix, and the right multiplication of the modal shape matrix needs to know the system real quality matrix in a formula method, so that for a complex structure, a finite element model needs to be established at first, and the quality matrix and the modal shape are extracted through the finite element model. Since the modal shape calculated by the finite element model has a certain difference from the real shape, the accuracy of the method depends greatly on the precision of the finite element model, but the precision of the finite element model with a complex structure is difficult to guarantee, and the finite element model with the complex structure can not be established even under some conditions.
(2) Formula method based on finite element model and test data
Considering that the modal shape calculated by the finite element model has a certain difference from the real shape, the method generally given in the current aerospace standard is to calculate by utilizing the actually measured shape data of the test and the mass matrix extracted by the finite element model, so that the modal shape matrix is obtained by the test, the real mass matrix is given by the polycondensation model which is condensed to the test point position by the complete finite element model, thus greatly reducing the calculated amount, ensuring the accuracy of the result, but still needing to establish the finite element calculation model of the structure, therefore, the method has certain difficulty for the complex structure.
(3) Frequency response function-based test method
According to the modal analysis theory and the proportional viscosity small damping condition, under the conditions that the modal density is not high and the influence of adjacent modes is not large, the relation between the modal mass and the amplitude of the imaginary part of the acceleration frequency response function and the modal damping ratio obtained by a test method of a hammering method or a vibration exciter method can be deduced through the acceleration frequency response function of an n-degree-of-freedom system, so that the modal mass can be calculated through the amplitude of the imaginary part of the frequency response function and the modal damping ratio, and the test accuracy of the modal mass depends on the damping ratio and the measurement accuracy of the transfer function. Factors influencing the damping ratio precision mainly include the separation degree of dense modes, the correction of a window function and the frequency resolution of an instrument, and the modes of all orders are separated as much as possible in a test, so that a single mode is formed in an analyzed frequency band, and the accuracy of a mode result can be improved to a certain extent. The measurement accuracy of the transfer function depends on the measurement accuracy of the acceleration and the excitation force, the existing acceleration test method is not difficult to guarantee, the core is the accuracy of the excitation force, and the used test system needs to be subjected to combined dynamic calibration before the test. Therefore, the precision of the dense modal structure is difficult to guarantee, and the combined dynamic calibration of the test system is complicated to implement.
Disclosure of Invention
The invention provides a modal quality measuring method, which can solve the technical problem that the existing modal quality measuring method cannot ensure the measuring precision of a complex structure or a dense modal structure.
The invention provides a method for measuring modal quality, which comprises the following steps:
establishing resonance of a structural part to be tested in an N-order mode, wherein N is not less than 1 and is an integer;
sequentially placing counterweight components on the structural part to be tested in the N-order modal resonance, respectively establishing the resonance of the structural part to be tested in the N-order modal after the counterweight components are placed each time, and acquiring the N-order resonance frequency of the structural part to be tested after the counterweight components are placed each time, wherein the sum of the masses of all the counterweight components placed in sequence is less than one percent of the mass of the structural part to be tested;
acquiring N-order modal mass variation of the structural part to be tested after the counterweight component is placed each time based on the mass of the counterweight component placed each time and the N-order normalized vibration mode corresponding to the position of the counterweight component placed each time;
fitting the N-order resonance frequency of the structural part to be tested after the counterweight component is placed each time and the N-order modal mass variation of the structural part to be tested after the counterweight component is placed each time to obtain a fitting curve of the N-order resonance frequency and the N-order modal mass variation;
acquiring the slope of a fitting curve based on the fitting curve of the N-order resonance frequency and the N-order modal mass variation;
and acquiring the N-order modal quality of the structural part to be tested based on the slope of the fitting curve and the N-order resonance frequency of the structural part to be tested after the counterweight part is placed for the first time.
Preferably, the N-order modal mass variation of the structural member to be measured after the counterweight member is placed each time is obtained by the following formula:
in the formula,. DELTA.MiThe N-order modal mass variation, m, of the structural member to be measured after the counterweight component is placed for the ith timepIs the sum of the masses, phi, of all counterweight members placed at a certain position p of the structural member to be measuredpFor the N-order normalized mode shape corresponding to position p.
Preferably, the N-order modal quality of the structural member to be measured is obtained by the following formula:
wherein M is the N-order modal mass, omega, of the structural member to be tested1And k is the slope of the fitting curve, and is the N-order resonance frequency of the structural part to be measured after the counterweight part is placed for the first time.
Preferably, placing the counterweight component on the structural member to be measured in the N-order modal resonance in sequence includes: and sequentially placing counterweight components at the same position or different positions on the structural part to be tested in the N-order modal resonance.
Preferably, the number of weight components placed at a time is one or more.
Preferably, in the case where the number of weight members to be placed is plural at a time, each weight member is placed at the same position or different positions on the structural member to be measured.
By applying the technical scheme of the invention, the counterweight component is sequentially placed on the structural part to be tested in the N-order modal resonance, the N-order resonance frequency of the structural part to be tested after the counterweight component is placed each time is obtained, and a fitting curve of the N-order resonance frequency and the N-order modal mass variation is obtained according to the N-order resonance frequency of the structural part to be tested after the counterweight component is placed each time and the N-order modal mass variation of the structural part to be tested after the counterweight component is placed each time, so that the slope of the fitting curve is obtained, and the N-order modal mass of the structural part to be tested is further obtained. The method can measure the modal quality of each order of the structural part to be measured, does not need to carry out modeling, is simple and easy to implement, and improves the modal quality measurement precision of complex structural parts and dense modal structural parts.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.
Fig. 1 shows a flow chart of a method of measuring modal quality provided according to an embodiment of the invention;
FIG. 2 illustrates a schematic view of a beam structure provided in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of a bonded weight on a beam structure provided according to an embodiment of the present invention;
FIG. 4 shows a first order resonance frequency versus first order modal mass variation fitted to a curve provided in accordance with an embodiment of the present invention;
FIG. 5 illustrates a fitted graph of second order resonant frequency versus second order modal mass variation provided in accordance with an embodiment of the present invention;
fig. 6 shows a fitting graph of the third-order resonance frequency and the third-order modal mass variation, provided according to an embodiment of the present invention.
Detailed Description
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The relative arrangement of the components and steps, the numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless specifically stated otherwise. Meanwhile, it should be understood that the sizes of the respective portions shown in the drawings are not drawn in an actual proportional relationship for the convenience of description. Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate. In all examples shown and discussed herein, any particular value should be construed as merely illustrative, and not limiting. Thus, other examples of the exemplary embodiments may have different values. It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof is not required in subsequent figures.
Fig. 1 shows a flowchart of a method for measuring modal quality according to an embodiment of the present invention.
As shown in fig. 1, the present invention provides a method for measuring modal quality, the method comprising:
s1, establishing resonance of the structural part to be tested in an N-order mode, wherein N is not less than 1 and is an integer;
s2, sequentially placing counterweight components on the structural part to be tested in the N-order modal resonance, respectively establishing the resonance of the structural part to be tested in the N-order modal resonance after the counterweight components are placed each time, and acquiring the N-order resonance frequency of the structural part to be tested after the counterweight components are placed each time, wherein the sum of the masses of all the counterweight components placed sequentially is less than one percent of the mass of the structural part to be tested;
s3, acquiring N-order modal mass variation of the structural part to be measured after the counterweight part is placed each time based on the mass of the counterweight part placed each time and the N-order normalized vibration mode corresponding to the position of the counterweight part placed each time;
s4, fitting the N-order resonance frequency of the structural part to be tested after the counterweight component is placed each time and the N-order modal mass variation of the structural part to be tested after the counterweight component is placed each time to obtain a fitting curve of the N-order resonance frequency and the N-order modal mass variation;
s5, acquiring the slope of a fitting curve based on the fitting curve of the N-order resonance frequency and the N-order modal quality variation;
and S6, acquiring the N-order modal quality of the structural part to be measured based on the slope of the fitting curve and the N-order resonance frequency of the structural part to be measured after the counterweight part is placed for the first time.
By applying the technical scheme of the invention, the counterweight component is sequentially placed on the structural part to be tested in the N-order modal resonance, the N-order resonance frequency of the structural part to be tested after the counterweight component is placed each time is obtained, and a fitting curve of the N-order resonance frequency and the N-order modal mass variation is obtained according to the N-order resonance frequency of the structural part to be tested after the counterweight component is placed each time and the N-order modal mass variation of the structural part to be tested after the counterweight component is placed each time, so that the slope of the fitting curve is obtained, and the N-order modal mass of the structural part to be tested is further obtained. The method can measure the modal quality of each order of the structural part to be measured, does not need to carry out modeling, is simple and easy to implement, and improves the modal quality measurement precision of complex structural parts and dense modal structural parts.
In the invention, the counterweight components are sequentially placed on the structural part to be tested in the N-order modal resonance, so that the additional mass at each time is the sum of the masses of all the counterweight components including the current time, and the masses of the counterweight components placed at each time can be the same or different.
For example, the first placement of the weight component has a mass m1The mass of the second placing of the weight member is m2The mass of the third weight member is m3Then the first additional mass is m1The additional mass of the second time is m1+m2The third additional mass is m1+m2+m3。
According to an embodiment of the invention, the N-order modal mass variation of the structural member to be measured after the counterweight member is placed each time is obtained by the following formula:
in the formula,. DELTA.MiThe N-order modal mass variation, m, of the structural member to be measured after the counterweight component is placed for the ith timepIs the sum of the masses, phi, of all counterweight members placed at a certain position p of the structural member to be measuredpFor the N-order normalized mode shape corresponding to position p.
For example, three counterweight components are placed on the structural component to be measured in the N-order modal resonance for three times, and the mass of each counterweight component is mp1、mp2、mp3And the three weight components are respectively placed at three different positions p1, p2 and p3, and the N-order normalized mode shapes corresponding to the three different positions are respectively phip1、φp2、φp3Therefore, the variation Δ M of the N-order modal mass of the structural member to be measured after the counterweight member is placed for the first time1＝mp1φp1 2And the N-order modal mass variation delta M of the structural part to be detected after the counterweight part is placed for the second time2＝mp1φp1 2+mp2φp2 2And the structure to be tested after the counterweight part is placed for the third timeN-order modal mass variation Δ M of a part3＝mp1φp1 2+mp2φp2 2+mp3φp3 2。
According to an embodiment of the present invention, the N-order modal quality of the structural member to be measured is obtained by the following formula:
wherein M is the N-order modal mass, omega, of the structural member to be tested1And k is the slope of the fitting curve, and is the N-order resonance frequency of the structural part to be measured after the counterweight part is placed for the first time.
According to an embodiment of the present invention, sequentially placing the weight member on the structural member to be measured in the N-order modal resonance includes: and sequentially placing counterweight components at the same position or different positions on the structural part to be tested in the N-order modal resonance.
According to one embodiment of the invention, the number of weight parts placed at a time is one or more.
According to one embodiment of the invention, each weight part is placed at the same or different location on the structure to be tested, in case the number of weight parts to be placed at a time is multiple.
The invention is described in detail below by measuring the modal mass of each order of the beam structure. The beam structure dimensions are 1500mm long by 100mm wide by 3mm thick, as schematically shown in figure 2.
For convenient calculation, only the modal masses of the first three steps of the beam structure are calculated, and the modal mass of each step is normalized by the position of the right end part of the beam structure, namely, the counterweight component is placed at the right end part every time, and at the moment, the normalized vibration mode of the beam structure after the counterweight component is placed at every time is unchanged.
In this embodiment, the weight member is a weight. Performing free mode test of the beam structure by hammering method, establishing resonance of the beam structure in the first-order mode, and bonding weights step by step on the right end part of the beam structure in the first-order mode resonance, as shown in the schematic diagramAs shown in fig. 3, the resonance of the beam structure after the weight is bonded at each time in the first-order mode is respectively established, the first-order resonance frequency of the beam structure after the weight is bonded at each time is obtained, and the first-order modal mass variation of the beam structure after the weight is bonded at each time is obtained based on the mass of the weight and the first-order normalized vibration mode corresponding to the right end; fitting the first-order resonance frequency of the beam structure after the weight is adhered each time and the first-order modal mass variation of the beam structure after the weight is adhered each time, and obtaining a fitting curve of the first-order resonance frequency and the first-order modal mass variation, as shown in fig. 4. Slope k from the fitted curve in FIG. 41And the first-order resonance frequency omega of the beam structure after the weight is bonded for the first time1' obtaining first-order modal masses M of a Beam Structure1：
Similarly, fig. 5 is a fitting curve of the second-order resonance frequency and the second-order modal mass variation, and the specific steps are the same as the first-order solving method, which is not described again in this embodiment. Slope k from the fitted curve in FIG. 52And the second-order resonance frequency omega of the beam structure after the weight is bonded for the first time1"obtaining second order modal masses M of Beam Structure2：
Similarly, fig. 6 is a fitting curve of the third-order resonance frequency and the third-order modal mass variation, the specific steps are the same as the first-order solving method, and the description is omitted in this embodiment. Slope k from the fitted curve in FIG. 63And the third-order resonance frequency omega of the beam structure after the first weight bonding1' obtaining third-order modal mass M of beam structure3：
According to the invention, weights are added step by step when the beam structure resonates, and the modal mass of each step of the beam structure is obtained through the slope of a fitting curve of the resonant frequency and the modal mass variation and the resonant frequency of the beam structure after the weights are bonded for the first time, so that the modal mass measurement accuracy of a complex structure and a dense modal structure is improved.
Spatially relative terms, such as "above … …," "above … …," "above … …," "above," and the like, may be used herein for ease of description to describe one device or feature's spatial relationship to another device or feature as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if a device in the figures is turned over, devices described as "above" or "on" other devices or configurations would then be oriented "below" or "under" the other devices or configurations. Thus, the exemplary term "above … …" can include both an orientation of "above … …" and "below … …". The device may be otherwise variously oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
It should be noted that the terms "first", "second", and the like are used to define the components, and are only used for convenience of distinguishing the corresponding components, and the terms have no special meanings unless otherwise stated, and therefore, the scope of the present invention should not be construed as being limited.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A method of measuring modal quality, the method comprising:
establishing resonance of a structural part to be tested in an N-order mode, wherein N is not less than 1 and is an integer;
sequentially placing counterweight components on the structural part to be tested in the N-order modal resonance, respectively establishing the resonance of the structural part to be tested in the N-order modal after the counterweight components are placed each time, and acquiring the N-order resonance frequency of the structural part to be tested after the counterweight components are placed each time, wherein the sum of the masses of all the counterweight components placed in sequence is less than one percent of the mass of the structural part to be tested;
acquiring N-order modal mass variation of the structural part to be tested after the counterweight component is placed each time based on the mass of the counterweight component placed each time and the N-order normalized vibration mode corresponding to the position of the counterweight component placed each time;
fitting the N-order resonance frequency of the structural part to be tested after the counterweight component is placed each time and the N-order modal mass variation of the structural part to be tested after the counterweight component is placed each time to obtain a fitting curve of the N-order resonance frequency and the N-order modal mass variation;
acquiring the slope of a fitting curve based on the fitting curve of the N-order resonance frequency and the N-order modal mass variation;
and acquiring the N-order modal quality of the structural part to be tested based on the slope of the fitting curve and the N-order resonance frequency of the structural part to be tested after the counterweight part is placed for the first time.
2. The method according to claim 1, wherein the N-order modal mass variation of the structural member to be tested after each placement of the weight component is obtained by:
in the formula,. DELTA.MiThe N-order modal mass variation, m, of the structural member to be measured after the counterweight component is placed for the ith timepIs the sum of the masses, phi, of all counterweight members placed at a certain position p of the structural member to be measuredpFor the N-order normalized mode shape corresponding to position p.
3. The method according to claim 1, wherein the N-order modal quality of the structural member under test is obtained by:
wherein M is the N-order modal mass, omega, of the structural member to be tested1And k is the slope of the fitting curve, and is the N-order resonance frequency of the structural part to be measured after the counterweight part is placed for the first time.
4. The method of claim 1, wherein sequentially placing the weight components on the structure under test at N-order modal resonance comprises: and sequentially placing counterweight components at the same position or different positions on the structural part to be tested in the N-order modal resonance.
5. The method according to claim 1, wherein the number of weight components placed at a time is one or more.
6. A method according to claim 5, characterized in that in the case of a plurality of weight parts being placed each time, each weight part is placed at the same or a different location on the structure to be tested.
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