CN111062143B - Method for identifying inertial parameters of automobile engine - Google Patents

Method for identifying inertial parameters of automobile engine Download PDF

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CN111062143B
CN111062143B CN201911393175.2A CN201911393175A CN111062143B CN 111062143 B CN111062143 B CN 111062143B CN 201911393175 A CN201911393175 A CN 201911393175A CN 111062143 B CN111062143 B CN 111062143B
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罗渊
刘玉英
冯峰
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Chongqing Changan Automobile Co Ltd
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Abstract

The invention relates to an automobile engine inertia parameter identification method, which comprises the following steps: s1: establishing a six-degree-of-freedom vibration model of the engine; s2: determining the relation between the origin acceleration response and the response point acceleration response, and determining the relation between the origin excitation force and the excitation point excitation force; s3: separating a system damping matrix; s4: separating a system stiffness matrix; s5: an engine mass matrix is identified using a least squares method. The method for identifying the inertial parameters of the automobile engine separates the suspension parameters of the engine from the inertial parameters, eliminates the influence of the suspension parameters, and identifies the inertial parameters of the engine by using modal test data; the method for identifying the inertial parameters of the automobile engine is not influenced by the stiffness and the damping of the engine suspension, has high identification precision, simple identification process and high identification efficiency, and can meet the requirement of identifying the inertial parameters of the engine under the actual automobile installation condition of the engine.

Description

Method for identifying inertial parameters of automobile engine
Technical Field
The invention belongs to the field of modal testing, and particularly relates to an inertia parameter identification method for an automobile engine.
Background
The engine inertia parameters comprise mass, mass center, rotational inertia and inertia product, and the engine inertia parameters are identified, which are the preconditions and the key for researching the dynamic characteristics of the engine, optimizing the design of a suspension system and damping and isolating vibration of the engine. The existing engine inertia parameter identification method mainly comprises a three-wire torsional pendulum method, a dynamic balance method and a parameter identification method based on modal testing. The three-wire torsional pendulum method needs to change the posture of the engine at least 6 times, the identification process is complex, and the identification error is large due to the superposition of the reference. The dynamic balance method needs to build a specific test bed, is expensive in manufacturing cost and is difficult to widely apply. Therefore, the method of identifying parameters based on modal testing has become a research focus, and such methods can be classified into residual inertia method, modal model method and direct system identification method. The residual inertia method requires suspending the engine, using mass as a known parameter, and identifying the center of mass, moment of inertia, and product of inertia using the mass line between the rigid body mode and the elastomer mode of the engine. The modal model method identifies the inertia parameters of the engine by utilizing the orthogonality of the modal shape matrix and the mass matrix, however, the acquisition precision of the modal shape is low, and the identification error of the inertia parameters is large. The direct system identification method generally causes low identification precision of the inertia parameters due to the influence of engine suspension parameters.
Disclosure of Invention
The invention aims to provide an automobile engine inertia parameter identification method, which separates engine suspension parameters from inertia parameters, eliminates the influence of the suspension parameters and identifies the engine inertia parameters by using modal test data.
The invention relates to an automobile engine inertia parameter identification method, which comprises the following steps:
s1: establishing a six-degree-of-freedom vibration model of the engine;
s2: determining the relation between the origin acceleration response and the response point acceleration response, and determining the relation between the origin excitation force and the excitation point excitation force;
s3: separating the system damping matrix;
s4: separating a system stiffness matrix;
s5: an engine mass matrix is identified using a least squares method.
Further, in step S1, the engine is in a suspension state, and under the action of an excitation force, the engine generates vibration, and the engine vibration equation is as follows:
(Mω 2 -K-jCω){a(ω)}＝ω 2 {F(ω)} (1)；
in the formula (1), M is an engine mass matrix, K is a suspension stiffness matrix, C is a suspension damping matrix, { a (omega) } is coordinate origin acceleration response, { F (omega) } is coordinate origin excitation force, and omega is the frequency of engine vibration;
the engine mass matrix M expression is:
Figure GDA0003795731330000021
in the formula (2), m is the mass of the engine, x, y and z are mass center coordinates, and J xx 、J yy 、J zz To moment of inertia, J xy 、J yz 、J xz Is the product of inertia.
Further, step S2 specifically includes:
the number of the response points is more than or equal to 2, the arrangement positions of the response points reflect the approximate outline of the engine, and the relation between the acceleration response of the origin of coordinates and the acceleration response of the response points is as follows:
{a(ω)}＝(T p T T p ) -1 T p T {a p (ω)} (3)；
in formula (3) { a p (ω) } response point acceleration response, T p Transforming a matrix for the response point coordinates;
the number of the excitation points is more than or equal to 3, the excitation directions comprise 3 coordinate directions, and the relation between the excitation force of the origin of coordinates and the excitation force of the excitation points is as follows:
Figure GDA0003795731330000022
in the formula (4)
Figure GDA0003795731330000023
The matrix is an excitation point coordinate transformation matrix, theta is an excitation point direction cosine matrix, and f (omega) is an excitation force.
Further, step S3 specifically includes: within the measuring frequency band, different frequencies omega are respectively taken i ,ω j (i ≠ j) is substituted into formula (1) to obtain:
Figure GDA0003795731330000024
Figure GDA0003795731330000025
the complex conjugate of formula (5) is obtained:
Figure GDA0003795731330000026
multiplying the formula (5) by omega j {a(ω j )} T Equation (6) for left-hand multiplication of omega i {a(ω i )} T And separating the damping matrix C yields:
{a(ω i )} T (ω i ω j M+K){a(ω j )}＝λ ij (8)；
in formula (8):
Figure GDA0003795731330000031
further, step S4 specifically includes: respectively using
Figure GDA0003795731330000032
Left multiplier (6), omega j {a(ω j )} T Left-hand multiplier (7) yields:
Figure GDA0003795731330000033
in formula (10):
Figure GDA0003795731330000034
the equations (8) and (10) are extended at different frequencies, respectively, to obtain:
A T KB-R A A T MBR B ＝λ (12)
Figure GDA0003795731330000035
in formulae (12) and (13):
Figure GDA0003795731330000036
Figure GDA0003795731330000037
Figure GDA0003795731330000038
Figure GDA0003795731330000039
Figure GDA00037957313300000310
Figure GDA00037957313300000311
wherein
Figure GDA00037957313300000312
Left multiplying both sides of equation (13)
Figure GDA0003795731330000041
The following can be obtained:
Figure GDA0003795731330000042
the combined (12) and (20) split stiffness matrices:
Figure GDA0003795731330000043
further, in step S5, equation (21) may be written as:
ξMφ＝ψ (22)；
the least square method can be used for obtaining:
M＝(ξ T ξ) -1 ξ T ψφ T (φφ T ) -1 (23)。
further, after the mass matrix M is obtained, 10 inertial parameters of the engine can be calculated according to equation (2).
According to the method for identifying the inertia parameters of the automobile engine, the suspension parameters of the engine are separated from the inertia parameters, the influence of the suspension parameters is eliminated, and the inertia parameters of the engine are identified by using modal test data; the method for identifying the inertia parameters of the automobile engine is not influenced by the suspension rigidity and damping of the engine, has high identification precision, simple identification process and high identification efficiency, and can meet the requirement of identifying the inertia parameters of the engine under the actual automobile installation condition of the engine.
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FIG. 1 is a flow chart of a method for identifying inertial parameters of an automotive engine according to the present invention;
FIG. 2 is ω i ,ω j (i ≠ j) value schematic diagram.
Detailed Description
The invention will be further explained with reference to the drawings.
The method for identifying the inertia parameters of the automobile engine shown in the figure 1 comprises the following steps:
s1, establishing a six-degree-of-freedom vibration model of an engine; the engine is in a suspension state, and generates vibration under the action of excitation force, and the engine vibration equation is as follows:
(Mω 2 -K-jCω){a(ω)}＝ω 2 {F(ω)} (1)；
in the formula (1), M is an engine mass matrix, K is a suspension stiffness matrix, C is a suspension damping matrix, { a (omega) } is coordinate origin acceleration response, and { F (omega) } is coordinate origin excitation force; j is a complex symbol indicating that jC ω is a complex form, and ω is the frequency of the engine vibration.
The engine mass matrix M expression is:
Figure GDA0003795731330000051
in the formula (2), m is the mass of the engine, x, y and z are mass center coordinates, J xx 、J yy 、J zz To turn toMoment of inertia, J xy 、J yz 、J xz Is the product of inertia.
S2, determining the relation between the origin acceleration response and the response point acceleration response, and determining the relation between the origin excitation force and the excitation point excitation force; the number of the response points is more than or equal to 2, the arrangement positions of the response points reflect the approximate outline of the engine, and the relation between the acceleration response of the origin of coordinates and the acceleration response of the response points is as follows:
{a(ω)}＝(T p T T p ) -1 T p T {a p (ω)} (3)；
in formula (3) { a p (ω) } response point acceleration response, T p Transforming a matrix for the response point coordinates;
the number of the excitation points is more than or equal to 3, the excitation directions comprise 3 coordinate directions, and the relation between the excitation force of the origin of coordinates and the excitation force of the excitation points is as follows:
Figure GDA0003795731330000052
in the formula (4)
Figure GDA0003795731330000053
The matrix is an excitation point coordinate transformation matrix, theta is an excitation point direction cosine matrix, and f (omega) is an excitation force.
S3, separating a system damping matrix; within the measuring frequency band, different frequencies omega are respectively taken i ,ω j (i ≠ j) is substituted into formula (1) to obtain:
Figure GDA0003795731330000054
Figure GDA0003795731330000055
the complex conjugate of formula (5) is obtained:
Figure GDA0003795731330000056
respectively multiplying the formula (5) by omega j {a(ω j )} T Equation (6) for left-hand multiplication of omega i {a(ω i )} T And separating the damping matrix C yields:
{a(ω i )} T (ω i ω j M+K){a(ω j )}＝λ ij (8)；
in formula (8):
Figure GDA0003795731330000057
s4, separating a system stiffness matrix; are used separately
Figure GDA0003795731330000061
Left multiplier (6), omega j {a(ω j )} T Left-hand multiplier (7) yields:
Figure GDA0003795731330000062
in formula (10):
Figure GDA0003795731330000063
the equations (8) and (10) are extended at different frequencies, respectively, to obtain:
A T KB-R A A T MBR B ＝λ (12)
Figure GDA0003795731330000064
in formulae (12) and (13):
Figure GDA0003795731330000065
Figure GDA0003795731330000066
Figure GDA0003795731330000067
Figure GDA0003795731330000068
Figure GDA0003795731330000069
Figure GDA00037957313300000610
wherein
Figure GDA00037957313300000611
Left multiplying both sides of equation (13)
Figure GDA00037957313300000612
The following can be obtained:
Figure GDA00037957313300000613
combining equations (12) and (20) the split stiffness matrix:
Figure GDA00037957313300000614
s5, identifying an engine mass matrix by using a least square method; equation (21) can be written as:
ξMφ＝ψ (22)；
the least square method can be used for obtaining:
M＝(ξ T ξ) -1 ξ T ψφ T (φφ T ) -1 (23)。
after the mass matrix M is obtained, 10 inertia parameters of the engine can be calculated according to the formula (2).

Claims (1)

1. An inertia parameter identification method of an automobile engine is characterized by comprising the following steps:
s1: establishing a six-degree-of-freedom vibration model of the engine;
s2: determining the relation between the origin acceleration response and the response point acceleration response, and determining the relation between the origin excitation force and the excitation point excitation force;
s3: separating the system damping matrix;
s4: separating a system stiffness matrix;
s5: identifying an engine mass matrix by using a least square method;
in step S1, the engine is in a suspension state, and under the action of an excitation force, the engine generates vibration, and an engine vibration equation is as follows:
(Mω 2 -K-jCω){a(ω)}＝ω 2 {F(ω)} (1)；
in the formula (1), M is an engine mass matrix, K is a suspension stiffness matrix, C is a suspension damping matrix, { a (omega) } is coordinate origin acceleration response, { F (omega) } is coordinate origin excitation force, and omega is the frequency of engine vibration;
the engine mass matrix M expression is:
Figure FDA0003795731320000011
in the formula (2), m is the mass of the engine, x, y and z are mass center coordinates, J xx 、J yy 、J zz To moment of inertia, J xy 、J yz 、J xz Is the product of inertia;
the step S2 specifically includes:
the number of the response points is more than or equal to 2, the arrangement positions of the response points reflect the approximate outline of the engine, and the relation between the acceleration response of the origin of coordinates and the acceleration response of the response points is as follows:
{a(ω)}＝(T p T T p ) -1 T p T {a p (ω)} (3)；
in formula (3) { a p (ω) } response point acceleration response, T p Transforming a matrix for the response point coordinates;
the number of the excitation points is more than or equal to 3, the excitation directions comprise 3 coordinate directions, and the relation between the excitation force of the origin of coordinates and the excitation force of the excitation points is as follows:
Figure FDA0003795731320000021
in formula (4)
Figure FDA0003795731320000022
Is an excitation point coordinate transformation matrix, theta is an excitation point direction cosine matrix, and f (omega) is an excitation force;
step S3 specifically includes: within the measuring frequency range, different frequencies omega are respectively taken i ,ω j (i ≠ j) is substituted into formula (1) to obtain:
Figure FDA0003795731320000023
Figure FDA0003795731320000024
the complex conjugate of formula (5) can be obtained:
Figure FDA0003795731320000025
respectively multiplying the formula (5) by omega j {a(ω j )} T And formula (6) multiplies omega left i {a(ω i )} T And separating the damping matrix C yields:
{a(ω i )} T (ω i ω j M+K){a(ω j )}＝λ ij (8)；
in formula (8):
Figure FDA0003795731320000026
step S4 specifically includes: respectively using
Figure FDA0003795731320000027
Left multiplication formula (6), omega j {a(ω j )} T Left-hand multiplier (7) yields:
Figure FDA0003795731320000028
in formula (10):
Figure FDA0003795731320000029
the equations (8) and (10) are extended at different frequencies, respectively, to obtain:
A T KB-R A A T MBR B ＝λ (12)
Figure FDA00037957313200000210
in formulas (12) and (13):
Figure FDA00037957313200000211
Figure FDA00037957313200000212
Figure FDA0003795731320000031
Figure FDA0003795731320000032
Figure FDA0003795731320000033
Figure FDA0003795731320000034
wherein
Figure FDA0003795731320000035
Multiplying equation (13) on both sides
Figure FDA0003795731320000036
The following can be obtained:
Figure FDA0003795731320000037
combining equations (12) and (20) the split stiffness matrix:
Figure FDA0003795731320000038
in step S5, equation (21) may be written as:
ξMφ＝ψ (22)；
the least square method can obtain:
M＝(ξ T ξ) -1 ξ T ψφ T (φφ T ) -1 (23)；
after the mass matrix M is obtained, 10 inertia parameters of the engine can be calculated according to the formula (2).
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CN112611511B (en) * 2020-11-30 2022-03-29 桂林电子科技大学 Method for acquiring inertia parameters of complex component based on acceleration frequency response function
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