CN111506979A - Complete vibration isolation design method for automobile suspension system - Google Patents

Complete vibration isolation design method for automobile suspension system Download PDF

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CN111506979A
CN111506979A CN202010046032.0A CN202010046032A CN111506979A CN 111506979 A CN111506979 A CN 111506979A CN 202010046032 A CN202010046032 A CN 202010046032A CN 111506979 A CN111506979 A CN 111506979A
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suspension system
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王继强
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a complete vibration isolation design method for an automobile suspension system, which comprises the steps of establishing a model of the suspension system; carrying out performance limit analysis on the suspension system; calculating to obtain an optimal parameter value of the suspension system; the optimal design is confirmed to meet the performance requirements. The invention can obtain the optimal performance of the suspension system under the condition of performance limit. The design method is suitable for both passive optimization and active control design.

Description

Complete vibration isolation design method for automobile suspension system
Technical Field
The invention belongs to the field of vibration reduction of an automobile suspension system, and particularly relates to a complete vibration isolation and performance limit optimization design method for a suspension system.
Background
The suspension system of automobile is elastic device for connecting frame and axle, and has the main task of relaxing the impact transmitted from road to frame to raise the comfort of riding. Typical suspension systems mainly include elastic elements, guiding mechanisms, shock absorbers and the like, and common suspensions include macpherson suspensions, double wishbone suspensions, multi-link suspensions and the like. Depending on the control force, the suspension system can be divided into a passive suspension, a semi-active suspension and an active suspension. At present, passive suspensions are most widely applied, but for some high-performance requirements, along with the application of novel intelligent materials, active and semi-active suspensions are more and more valued. From the modeling and analysis perspective, the suspension system can be simplified into 1/4 automobile two-degree-of-freedom models, and the optimal design of the suspension system is the optimization of mass, elastic rigidity and damping coefficient in the two-degree-of-freedom models. Considering that mass and spring stiffness are more limited and required by the vehicle for weight, size, space, etc. of the suspension system, the performance of the suspension system is generally improved by optimizing the damping coefficient. For example, the patent JPH04368211A of toyota is a design method of a semi-active suspension system that optimizes damping coefficient to obtain optimal control force; the patent CN1749048A of Shanghai fuel cell automobile power system company Limited also adopts a similar damping force optimization design method; the patent CN103204043B discloses a frequency domain control method for semi-active suspension system of automobile, which is also to improve the suspension performance by optimizing the damping force.
In the optimization method, the design of the optimization method depends on an optimization numerical algorithm, such as optimization of quadratic performance index (CN103522862B), utilization of model predictive control algorithm (CN105974821B) and the like. The design based on the optimization algorithm can enable the system performance to reach the optimum aiming at the specified performance index, but the optimization design problem of a plurality of performance variables is difficult to guarantee. Multivariate optimization can in principle use multi-objective optimization methods, but the design process requires iteration and it is difficult to obtain the performance limits of the suspension system under the multi-performance variable requirements. The optimization design method capable of obtaining the performance limit under the requirement of multiple performance variables of the suspension system is not reported in the open.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems that the existing suspension system is difficult to analyze under the requirement of multiple performance variables and the performance limit is difficult to obtain, the invention provides and verifies an optimal design method capable of obtaining the performance limit of the suspension system, so that the designed suspension system has the optimal performance.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the technical scheme that:
an optimal design method for obtaining the performance limit of a suspension system comprises the following steps:
(1) establishing a model of a suspension system;
(2) carrying out performance limit analysis on the suspension system;
(3) calculating to obtain an optimal parameter value of the suspension system;
(4) numerical simulation to confirm that the optimal design meets performance requirements; and (3) otherwise, returning to the steps (2) and (3), reselecting the optimized parameter values, and confirming the optimal performance of the suspension system under the condition of performance limit (if the requirements are still not met, the performance index requirement is over high, or the index requirement is reduced, or the structural parameters of the suspension system are redesigned).
Further, the model of the suspension system established in step (1) is:
Figure BDA0002369419400000021
wherein m is1、m2The mass of the lower mass block and the mass of the upper mass block in the two-degree-of-freedom model are respectively; k is a radical of1And c1Is a mass block m1Stiffness and damping coefficient, k, of the connection structure2And c2Is the mass block m2Stiffness and damping coefficient of the connection structure. x is the number of1(t) is a mass m1Displacement relative to the equilibrium position, x (t) being the relative displacement of the two masses;
Figure BDA0002369419400000022
and
Figure BDA0002369419400000023
respectively the speeds of the above two variables, and
Figure BDA0002369419400000024
and
Figure BDA0002369419400000025
its acceleration is the acceleration; y (t) is the vibration transmitted from the ground to the suspension system model,
Figure BDA0002369419400000026
then its vibration acceleration; u (t) is the optimum force to be designed, and is usually expressed as:
u(t)＝kx(t)；
where k is an optimal design parameter. Note that the model may include both passive and active design, for example, when k is used as the optimization parameter koptTo k is paired2Correction of, i.e. kopt＝k2When + k, it represents passive design; and when k is used as a feedback controller parameter, the design is an active control design. The above model is therefore a generic model, and corresponding active and passive designs are intended to be included in the patent claims.
Further, the step (2) is specifically as follows:
the above model is first expressed as a frequency domain representation:
Figure BDA0002369419400000027
wherein: x (j ω), X1(j ω) and U (j ω) are the corresponding variables x (t), x1(t) Fourier transform of u (t); d (j ω) is defined as D (j ω) ═ ω2Y (j ω), where Y (j ω) is the Fourier transform of Y (t); ω is the vibration frequency or the operating frequency of the suspension system. det (G) is defined as follows:
det(G)＝(k1-m1ω2+jc1ω)(k2-m2ω2+jc2ω)-(k2+jc2ω)m2ω2。
next, a new parameter α (j ω) is further defined, and has the following relationship with the optimal parameter k to be designed:
Figure BDA0002369419400000031
again, the following variables are defined:
Figure BDA0002369419400000032
finally, the following determinations are made regarding the damping limits of the suspension system:
(1) if R (j omega) -1 is less than or equal to 1, the suspension system can obtain complete vibration isolation with the limit performance;
(2) if | R (j ω) -1| >1, the maximum damping amplitude of the suspension system is
Figure BDA0002369419400000033
Further, the step (3) is specifically as follows:
the optimal parameter value of the suspension system is designed as follows:
(3) if | R (j ω) -1| ≦ 1, taking α (j ω) ═ R (j ω);
(4) if R (j ω) -1| is > 1, α (j ω) is taken as the solution of the joint equation
Figure BDA0002369419400000034
α (j ω) was obtained;
the corresponding optimal design yields the optimal parameter k by substituting α (j ω) into the above equation.
Further, in the step (4), numerical simulation is carried out on the optimal parameter values obtained in the step (3) to confirm that the performance requirements are met; otherwise, the suspension system parameters need to be redesigned or the performance index requirements need to be reduced.
Has the advantages that: compared with the prior art, the design method capable of obtaining the limit performance is provided aiming at the vibration reduction design of the suspension system. The design method is universal and is suitable for both passive optimization and active control design.
Drawings
FIG. 1 is a flow chart of a suspension system vibration isolation design;
FIG. 2 is a comparison of a suspension system before and after optimization, and FIG. 2-a shows x1(t) full isolation is achieved and figure 2-b shows x (t) vibration performance degradation.
Detailed Description
The present invention is further illustrated by the following description in conjunction with the accompanying drawings and the specific embodiments, it is to be understood that these examples are given solely for the purpose of illustration and are not intended as a definition of the limits of the invention, since various equivalent modifications will occur to those skilled in the art upon reading the present invention and fall within the limits of the appended claims.
The complete vibration isolation design method of the automobile suspension system comprises the following steps according to the flow shown in figure 1:
step 1: establishing a model of a suspension system:
suspension system analysis and design is generally modeled as follows in a simplified 1/4 two-degree-of-freedom automobile model:
Figure BDA0002369419400000041
wherein m is1、m2The mass of the lower mass block and the mass of the upper mass block in the two-degree-of-freedom model are respectively; k is a radical of1And c1Is a mass block m1Stiffness and damping coefficient, k, of the connection structure2And c2Is the mass block m2Stiffness and damping coefficient of the connection structure. x is the number of1(t) is a mass m1Displacement relative to the equilibrium position, x (t) being the relative displacement of the two masses;
Figure BDA0002369419400000042
and
Figure BDA0002369419400000043
respectively the speeds of the above two variables, and
Figure BDA0002369419400000044
and
Figure BDA0002369419400000045
its acceleration is the acceleration; y (t) is the vibration transmitted from the ground to the suspension system model,
Figure BDA0002369419400000046
then its vibration acceleration; u (t) is the optimum force to be designed, and is usually expressed as:
u(t)＝kx(t)；
where k is the optimal design parameter. The model may contain both passive and active design, e.g. when k is used as the optimization parameter koptTo k is paired2Correction of, i.e. kopt＝k2When + k, it represents passive design; and when k is used as a feedback controller parameter, the design is an active control design. Due to the fact thatThe above model is a generic model and corresponding active and passive designs are intended to be encompassed by the patent claims.
In the following examples, the following parameters will be used: m is1＝1kg，c12N · s/m, and k1＝10N/m；m2＝1kg，c2＝1N·s/m，k21N/m. The goal of the optimization design is to design the optimization parameter k such that kopt＝k2+ k at harmonic frequency
Figure BDA0002369419400000047
The ultimate performance is obtained.
Step 2: carrying out performance limit analysis on the suspension system;
the above model is first expressed as a frequency domain representation:
Figure BDA0002369419400000051
wherein: x (j ω), X1(j ω) and U (j ω) are the corresponding variables x (t), x1(t) Fourier transform of u (t); d (j ω) is defined as D (j ω) ═ ω2Y (j ω), where Y (j ω) is the Fourier transform of Y (t); ω is the vibration frequency or the operating frequency of the suspension system. det (G) is defined as follows:
det(G)＝(k1-m1ω2+jc1ω)(k2-m2ω2+jc2ω)-(k2+jc2ω)m2ω2(3)
next, a new parameter α (j ω) is defined, and has the following relationship with the optimal parameter k to be designed:
Figure BDA0002369419400000052
again, the following variables are defined:
Figure BDA0002369419400000053
the performance limit of the suspension system can be determined as follows:
(1) if R (j omega) -1 is less than or equal to 1, the suspension system can obtain complete vibration isolation with the limit performance;
(2) if R (j ω) -1 > 1, the maximum damping amplitude of the suspension system is
Figure BDA0002369419400000054
Now, for the above embodiment, the following is calculated:
R(jω)＝0.25+j (6)
thus:
|R(jω)-1|＝1.25＞1 (7)
it can be concluded that the suspension system is not capable of fully isolating vibration, and the maximum damping amplitude is | α (j ω) + R (j ω) |/| R (j ω) |. this limit can be obtained by the optimal design α (j ω) determined in step 3 below.
And step 3: calculating to obtain an optimal parameter value of the suspension system;
the optimal parameters for the suspension system are designed as follows:
(1) if | R (j ω) -1| ≦ 1, taking α (j ω) ═ R (j ω);
(2) if R (j ω) -1| is > 1, α (j ω) is taken as the solution of the joint equation
Figure BDA0002369419400000061
α (j ω) was obtained.
For the present embodiment, since | R (j ω) -1| ═ 1.25 > 1, the corresponding optimal parameter α (j ω) is the solution of the following joint equation:
Figure BDA0002369419400000062
i.e., α (j ω) — 0.4-0.8 j-the maximum damping amplitude of the suspension system is therefore | α (j ω) + R (j ω) |/| R (j ω) | 0.24, i.e., 12 dB.
And 4, step 4: numerical simulation to confirm that the optimal design meets performance requirements;
if the design requirements are met, the above design is implemented(ii) a And otherwise, returning to the steps (2) and (3) to confirm the optimal performance of the suspension system under the condition of performance limit. If the requirements are still not met, the performance index requirements are over-high, or the index requirements are reduced, or the structural parameters of the suspension system are redesigned. For the above embodiment, if the index requirement is a 12dB reduction and below, the design can be confirmed; whereas if the specification requirement is above 12dB, for example at least 20dB of damping, the specification requirement is too high due to the 12dB performance limit of the suspension system. At this time, the suspension system parameters need to be redesigned or performance index requirements need to be reduced. And if the adherence index is not changed, the situation that other performance variables of the suspension are deteriorated inevitably occurs. As shown in figure 2 of the numerical simulation result, the mass m1Displacement x relative to equilibrium position1After the vibration at (t) is completely isolated, the vibration at the relative displacement x (t) of the two masses is remarkably enhanced. This will affect ride comfort.
In a word, the optimal design method of the automobile suspension system can obtain the limit performance of the suspension system; the design method facing the performance limit can judge whether the performance index requirement is feasible or not, and has important guidance for actual engineering.

Claims (5)

1. A complete vibration isolation design method for an automobile suspension system comprises the following steps:
(1) establishing a model of a suspension system;
(2) carrying out performance limit analysis on the suspension system;
(3) calculating to obtain an optimal parameter value of the suspension system;
(4) and (4) performing numerical simulation to confirm that the optimal design meets the performance requirement, and if the optimal design does not meet the performance requirement, returning to the steps (2) - (4), and reselecting an optimal parameter value or reducing the index requirement.
2. The method for designing the complete vibration isolation of the automobile suspension system according to claim 1, wherein the model of the suspension system established in the step (1) is as follows:
Figure FDA0002369419390000011
wherein m is1、m2The mass of the lower mass block and the mass of the upper mass block in the two-degree-of-freedom model are respectively; k is a radical of1And c1Is a mass block m1Stiffness and damping coefficient, k, of the connection structure2And c2Is the mass block m2Stiffness and damping coefficient of the connection structure. x is the number of1(t) is a mass m1Displacement relative to the equilibrium position, x (t) being the relative displacement of the two masses;
Figure FDA0002369419390000012
and
Figure FDA0002369419390000013
respectively the speeds of the above two variables, and
Figure FDA0002369419390000014
and
Figure FDA0002369419390000015
its acceleration is the acceleration; y (t) is the vibration transmitted from the ground to the suspension system model,
Figure FDA0002369419390000016
then its vibration acceleration; u (t) is the optimal force to design expressed as:
u(t)＝kx(t)；
where k is the optimal design parameter.
3. The method of claim 2, wherein the model comprises both passive and active design, and k is an optimization parameter koptTo k is paired2Correction of, i.e. kopt＝k2When + k, it represents passive design; and when k is used as a feedback controller parameter, the design is an active control design.
4. The method for designing the complete vibration isolation of the automobile suspension system according to claim 2, wherein the analysis of the performance limit of the suspension system in the step (2) is specifically as follows:
the model is first expressed as a frequency domain representation:
Figure FDA0002369419390000017
wherein: x (j ω), X1(j ω) and U (j ω) are the corresponding variables x (t), x1(t) Fourier transform of u (t); d (j ω) is defined as D (j ω) ═ ω2Y (j ω), where Y (j ω) is the Fourier transform of Y (t); ω is the vibration frequency or the operating frequency of the suspension system; det (G) is defined as follows:
det(G)＝(k1-m1ω2+jc1ω)(k2-m2ω2+jc2ω)-(k2+jc2ω)m2ω2；
next, a new parameter α (j ω) is further defined, and has the following relationship with the optimal parameter k to be designed:
Figure FDA0002369419390000021
again, the following variables are defined:
Figure FDA0002369419390000022
finally, the following determinations are made regarding the damping limits of the suspension system:
(1) if R (j omega) -1 is less than or equal to 1, the suspension system can obtain complete vibration isolation with the limit performance;
(2) if R (j ω) -1 > 1, the maximum damping amplitude of the suspension system is
Figure FDA0002369419390000023
5. The method for designing the complete vibration isolation of the automobile suspension system according to claim 4, wherein the calculation in the step (3) to obtain the optimal parameter value of the suspension system specifically comprises the following steps:
the optimal parameter value of the suspension system is designed as follows:
(1) if | R (j ω) -1| ≦ 1, taking α (j ω) ═ R (j ω);
(2) if R (j ω) -1| is > 1, α (j ω) is taken as the solution of the joint equation
Figure FDA0002369419390000024
α (j ω) was obtained;
(3) the optimal parameter k is obtained from α (j ω).
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112329214A (en) * 2020-10-20 2021-02-05 南京航空航天大学 Optimization design method of energy collection type shock absorber

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108446520A (en) * 2018-04-18 2018-08-24 南京航空航天大学 The parameter matching control system and optimization method of semi-active suspension system and mechanical elastic vehicle wheel
CN110594344A (en) * 2019-08-20 2019-12-20 南京航空航天大学 Zero-damping vibration absorber optimization design method

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108446520A (en) * 2018-04-18 2018-08-24 南京航空航天大学 The parameter matching control system and optimization method of semi-active suspension system and mechanical elastic vehicle wheel
CN110594344A (en) * 2019-08-20 2019-12-20 南京航空航天大学 Zero-damping vibration absorber optimization design method

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112329214A (en) * 2020-10-20 2021-02-05 南京航空航天大学 Optimization design method of energy collection type shock absorber

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