CN102401727A - Method for obtaining mechanical joint stiffness - Google Patents

Abstract

The invention discloses a method for obtaining mechanical joint stiffness. The method is implemented according to the following steps: firstly, a pulse excitation method is adopted so as to obtain resonance frequency of an actual structure; secondly, an upper contact layer and a lower contact layer of a joint are regarded as a virtual material so as to build a finite element analytical model of an overall structure comprising the joint; and thirdly, a group of initial values of normal stiffness Kn and tangent stiffness Kt is firstly preset, and the preset values of the normal stiffness Kn and the tangent stiffness Kt are revised after the natural frequency which is obtained through computing and the resonance frequency which is obtained through experiment are compared with each other so as to ensure that the natural frequency which is obtained through computing continuously approaches the resonance frequency which is obtained through experiment until the natural frequency which is obtained through computing is approximate enough with the resonance frequency which is obtained through experiment, then last preset group of values of the normal stiffness Kn and the tangent stiffness Kt is the joint stiffness final fixed value which is obtained through adopting the method. In the method adopted by the invention, the iterative method is adopted so as to continuously adjust the design variable, and the finally obtained design variable is the joint stiffness data.

Description

A kind of method that obtains mechanical bond portion rigidity

Technical field

The invention belongs to the mechanical detection technical field, relate to a kind of method that obtains mechanical bond portion rigidity.

Background technology

The joint portion is meant two parts surface in contacts and accessory structure on every side thereof, and the fundamental purpose of joint portion research is to explore the Changing Pattern of contact stiffness and damping, obtains contact stiffness and damping data, realizes machine performance analysis and prediction.

All there is remarkable influence the joint portion to the static state and the dynamic perfromance of lathe.According to statistics, 30%-50% derives from the rigidity of joint portion in the quiet rigidity of lathe, and it is to be derived from the joint portion that the dynamic flexibility of lathe has more than 60%, and the damping value of lathe has especially and derives from the joint portion more than 90%.The modern machine design is the high-grade, digitally controlled machine tools design of principal character with high speed, high precision and high-level efficiency especially, need just can foresee the dynamics of lathe urgently in the pattern design phase.The joint portion The Characteristic Study is all to have crucial meaning theoretically or from practical application.But, because the joint portion is present between the parts, observe, measure and study all very difficulty, at present still immature to the research of joint portion kinetic property and mechanism, in the design phase complete machine performance is predicted still very difficulty accurately.

The research of joint portion problem is mainly carried out around machine tool structure at present, but in other physical construction, has the joint portion problem equally.The static state of single part and dynamic property can be analyzed through methods such as finite elements now exactly; But the performance evaluation of the complete machine structure that is made up of a plurality of parts can't be satisfactory; Main difficulty is that the contact stiffness of two piece surfaces and damping also can't accurately foresee in the design phase, and the joint portion problem is complete machine is moved towards in the physical construction performance evaluation by single-piece a key.

Summary of the invention

The purpose of this invention is to provide a kind of method that obtains mechanical bond portion rigidity, solved prior art and analyzed not accurate enough problem for the complete machine joint portion rigidity property that constitutes by a plurality of parts.

The technical scheme that the present invention adopted is, a kind of method that obtains mechanical bond portion rigidity, and this method is implemented according to following steps:

Step 1, employing pulse excitation method obtain the resonant frequency of practical structures

Through adopting the pulse hammer excitation structure, obtain the impulse response signal of joint portion structure, this impulse response signal is carried out Fourier transform, obtain the amplitude-frequency response of joint portion structure, confirm the resonant frequency of joint portion structure according to this amplitude-frequency response;

Step 2, the contact layer up and down of joint portion is regarded as a kind of virtual material, sets up the finite element analysis model of the complete machine structure that comprises the joint portion, obtain the differential equation of joint portion free vibration of structures:

$M\stackrel{\·\·}{\mathrm{\δ}}+\mathrm{K\δ}=0---1)$

M is the mass matrix of structure;

is vector acceleration; K is a structural stiffness matrix; δ is a motion vector, has comprised the rigidity of part and the rigidity of contact layer among the stiffness matrix K, writes accepted way of doing sth 1-1):

$K=\left[\begin{array}{cc}{K}_c& \\ & K_j\end{array}\right]---1-1)$

K wherein _cBe the rigidity of part part,, confirm K through Finite Element Method according to the geometric configuration of part and elastic modulus, Poisson ratio and the density of material _cK _jBe the rigidity of contact layer, comprise normal stiffness K _nWith the tangential stiffness K _τ, write accepted way of doing sth 1-2):

$K_j=\left[\begin{array}{cc}{K}_n& \\ & K_{\mathrm{\τ}}\end{array}\right]---1-2)$

The normal stiffness K in likes 1-2) _nWith the tangential stiffness K _τBe unknown,

The differential equation 1 by free vibration) obtain the free vibration frequencies equation:

|K-ω ²M|＝0 2)

Following formula 2) mass matrix M is known in, and vectorial ω is the natural frequency of structure, has only the contact layer stiffness K among the stiffness matrix K _jThe unknown is if know the contact layer stiffness K _j, then according to formula 2) and formula can try to achieve the natural frequency ω of structure;

Step 3, confirm the joint portion parameter, i.e. the normal stiffness K of contact layer through process of iteration _nWith the tangential stiffness K _τ

At first preset one group of normal stiffness K _nWith the tangential stiffness K _τInitial value, according to formula 2) calculate the natural frequency ω of complete machine structure, the resonant frequency that the natural frequency ω that calculates and experiment are obtained relatively after, revised law is to stiffness K _nWith the tangential stiffness K _τPreset value; Make and calculate the resonant frequency that the natural frequency ω that obtains constantly approaches the experiment acquisition; The natural frequency ω that obtains is enough approaching with the resonant frequency that experiment obtains up to calculating, and this is confirmed according to concrete technical requirement near amplitude, then last one group of preset normal stiffness K _nWith the tangential stiffness K _τNumerical value, be exactly the final determined value of joint portion rigidity that this method obtains.

The invention has the beneficial effects as follows; Setting up the system model comprise the joint portion based on Finite Element Method, is design variable with the normal stiffness and the tangential rigidity of part surface of contact, behind the design variable initialize; The natural frequency of computing system and the system resonance frequency ratio that obtains with experiment are; Adopt process of iteration constantly to adjust design variable, make the natural frequency of calculating progressively approach resonant frequency, the final design variable that obtains is exactly the joint portion rigidity data.

Description of drawings

Fig. 1 is the structural representation of the joint portion Rigidity Experiment object of the embodiment of the invention;

Fig. 2 is the finite element model of setting up according to the experimental provision in the embodiment of the invention;

Fig. 3 is when centre plane is pressed to 0.06MPa, is the Mode Shape figure that obtains according to the embodiment of the invention;

Fig. 4 is when centre plane is pressed to 0.06MPa, is to adopt experimental modal analysis method to calculate the Mode Shape figure that obtains.

Embodiment

Below in conjunction with accompanying drawing and embodiment the present invention is elaborated.

The present invention is a kind of method that obtains mechanical bond portion rigidity, and this method is implemented according to following steps:

Step 1, employing pulse excitation method obtain the resonant frequency of practical structures

Through adopting the pulse hammer excitation structure; Obtain the impulse response signal of joint portion structure; This impulse response signal is carried out Fourier transform; Obtain the amplitude-frequency response of joint portion structure, confirm the resonant frequency of joint portion structure according to this amplitude-frequency response, principle and implementation process are referring to document [1];

Step 2, the contact layer up and down of joint portion is regarded as a kind of virtual material, sets up the finite element analysis model of the complete machine structure that comprises the joint portion, obtain the differential equation of joint portion free vibration of structures:

$M\stackrel{\·\·}{\mathrm{\δ}}+\mathrm{K\δ}=0---1)$

M is the mass matrix of structure;

is vector acceleration; K is a structural stiffness matrix; δ is a motion vector, has comprised the rigidity of part and the rigidity of contact layer among the stiffness matrix K, writes accepted way of doing sth 1-1):

$K=\left[\begin{array}{cc}{K}_c& \\ & K_j\end{array}\right]---1-1)$

K wherein _cBe the rigidity of part part,, confirm K through Finite Element Method according to the geometric configuration of part and elastic modulus, Poisson ratio and the density of material _c, concrete derivation and computation process are referring to document [2]; K _jBe the rigidity of contact layer, comprise normal stiffness K _nWith the tangential stiffness K _τ, write accepted way of doing sth 1-2):

$K_j=\left[\begin{array}{cc}{K}_n& \\ & K_{\mathrm{\τ}}\end{array}\right]---1-2)$

The normal stiffness K in likes 1-2) _nWith the tangential stiffness K _τBe unknown, the object of the invention will be confirmed normal stiffness K exactly _nWith the tangential stiffness K _τNear the numerical value of actual (error is minimum).

The differential equation 1 by free vibration) obtains the free vibration frequencies equation: (concrete derivation is referring to document [2])

|K-ω ²M|＝0 2)

Following formula 2) mass matrix M is known in, and vectorial ω is the natural frequency of structure, has only the contact layer stiffness K among the stiffness matrix K _jThe unknown is if know the contact layer stiffness K _j, then according to formula 2) and formula can try to achieve the natural frequency ω of structure.

Step 3, confirm the joint portion parameter, i.e. the normal stiffness K of contact layer through process of iteration _nWith the tangential stiffness K _τAt first preset one group of normal stiffness K _nWith the tangential stiffness K _τInitial value, according to formula 2) calculate the natural frequency ω of complete machine structure, the resonant frequency that the natural frequency ω that calculates and experiment are obtained relatively after, revised law is to stiffness K _nWith the tangential stiffness K _τPreset value; Make and calculate the resonant frequency that the natural frequency ω that obtains constantly approaches the experiment acquisition; The natural frequency ω that obtains is enough approaching with the resonant frequency that experiment obtains up to calculating, and this is confirmed according to concrete technical requirement near amplitude, then last one group of preset normal stiffness K _nWith the tangential stiffness K _τNumerical value, be exactly the final determined value of joint portion rigidity that the present invention obtains.

Embodiment

Fig. 1 is the structural representation of experimental subjects, and upper plate 1 wherein is of a size of 300mm * 400mm * 25mm, and the density of upper plate 1 is 8100Kg/m ³, elastic modulus is 2.07 * 10 ¹¹Pa, Poisson ratio is 0.28.Lower plate 2 is of a size of 300mm * 400mm * 40mm, and the density of lower plate 2 is 6980Kg/m ³, elastic modulus is 1.01 * 10 ¹¹Pa, Poisson ratio is 0.245.Contact force between two plates is applied by four same bolts 3.Be lined with rubber, pad and thrust bearing between bolt 3 and two plates.Contact stiffness between two plates is big more a lot of than rubber, so just can guiding rail joint portion be isolated out the faying face that the data that record in the experiment are only being pressed to upper and lower plates each other.The centre plane that between upper and lower plate, loads is pressed and is 0.06MPa, through ram hammer experimental provision is carried out pulse excitation, and it is as shown in table 1 that response signal is carried out behind the Fourier transform before the acquisition system 3 rank resonant frequencies.

Fig. 2 is at 11.0 li finite element models of being set up of general finite element analysis software ANSYS to experimental subjects.Upper and lower plate unit number is set to 11140 in this model, and the unit number of contact layer is set to 852 between the upper and lower plate.Consider that four bolts 3 are connected with upper and lower plates through rubber blanket and the bolt quality much smaller than the upper and lower plates quality, omitted the existence of bolt and rubber, pad and thrust bearing in this finite element model, total system is done imaginary Free Modal analysis.Because the normal stiffness K of contact layer _nWith the tangential stiffness K _τPrior and uncertain, need could begin model analysis behind the initial value of preset rigidity, then according to model analysis preceding 3 rank natural frequencys that obtain and the difference of testing the preceding 3 rank resonant frequencies that obtain, constantly adjust the normal stiffness K of contact layer _nWith the tangential stiffness K _τPreset value, enough hour of the difference amplitude (when suppose) of the preceding 3 rank resonant frequencies that obtain when above-mentioned preceding 3 rank natural frequencys and experiment, the normal stiffness K of contact layer in the model at this moment less than 2% error span _nWith the tangential stiffness K _τPreset value, the contact stiffness that is exactly two plates in the experimental subjects that obtains of the inventive method is near actual final numerical value.

Table 1 compute mode frequency and the comparison of testing frequency

Table 1 is the contrast of adopting model frequency with the resonant frequency of experiment acquisition of above-mentioned ANSYS computed in software.Fig. 3 is the formation figure corresponding with calculated rate.Fig. 4 is the preceding 3 rank Mode Shape figure that adopt experimental modal analysis method to obtain.The vibration shape corresponding among Fig. 3 and Fig. 4 has consistance preferably, shows that the joint portion rigidity acquisition methods that the present invention proposes is effective.

List of references

[1] Zheng Jianming, class China.Engineering Testing Technique and application, Electronic Industry Press,, Beijing in 2011

[2] Li Jingyong.Finite element method.Publishing house of Beijing University of Post & Telecommunication, 1999, Beijing

Claims (1)

1. a method that obtains mechanical bond portion rigidity is characterized in that, this method is implemented according to following steps:

Step 1, employing pulse excitation method obtain the resonant frequency of practical structures

Through adopting the pulse hammer excitation structure, obtain the impulse response signal of joint portion structure, this impulse response signal is carried out Fourier transform, obtain the amplitude-frequency response of joint portion structure, confirm the resonant frequency of joint portion structure according to this amplitude-frequency response;

Step 2, the contact layer up and down of joint portion is regarded as a kind of virtual material, sets up the finite element analysis model of the complete machine structure that comprises the joint portion, obtain the differential equation of joint portion free vibration of structures:

$M\stackrel{\·\·}{\mathrm{\δ}}+\mathrm{K\δ}=0---1)$

M is the mass matrix of structure;

is vector acceleration; K is a structural stiffness matrix; δ is a motion vector, has comprised the rigidity of part and the rigidity of contact layer among the stiffness matrix K, writes accepted way of doing sth 1-1):

$K=\left[\begin{array}{cc}{K}_c& \\ & K_j\end{array}\right]---1-1)$

K wherein _cBe the rigidity of part part,, confirm K through Finite Element Method according to the geometric configuration of part and elastic modulus, Poisson ratio and the density of material _cK _jBe the rigidity of contact layer, comprise normal stiffness K _nWith the tangential stiffness K _τ, write accepted way of doing sth 1-2):

$K_j=\left[\begin{array}{cc}{K}_n& \\ & K_{\mathrm{\τ}}\end{array}\right]---1-2)$

The normal stiffness K in likes 1-2) _nWith the tangential stiffness K _τBe unknown,

The differential equation 1 by free vibration) obtain the free vibration frequencies equation:

|K-ω ²M|＝0 2)

Following formula 2) mass matrix M is known in, and vectorial ω is the natural frequency of structure, has only the contact layer stiffness K among the stiffness matrix K _jThe unknown is if know the contact layer stiffness K _j, then according to formula 2) and formula can try to achieve the natural frequency ω of structure;

Step 3, confirm the joint portion parameter, i.e. the normal stiffness K of contact layer through process of iteration _nWith the tangential stiffness K _τ

At first preset one group of normal stiffness K _nWith the tangential stiffness K _τInitial value, according to formula 2) calculate the natural frequency ω of complete machine structure, the resonant frequency that the natural frequency ω that calculates and experiment are obtained relatively after, revised law is to stiffness K _nWith the tangential stiffness K _τPreset value; Make and calculate the resonant frequency that the natural frequency ω that obtains constantly approaches the experiment acquisition; The natural frequency ω that obtains is enough approaching with the resonant frequency that experiment obtains up to calculating, and this is confirmed according to concrete technical requirement near amplitude, then last one group of preset normal stiffness K _nWith the tangential stiffness K _τNumerical value, be exactly the final determined value of joint portion rigidity that this method obtains.

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