JP6645169B2 - Design method of vibration control structure - Google Patents

Description

  The present invention relates to a method for designing a structure damped by a passive dynamic vibration absorber.

  2. Description of the Related Art Conventionally, as one of dynamic vibration absorbers, there has been known an object provided with an additional object connected to an object to which vibration is input (hereinafter, referred to as a “vibration damping object”) via an elastic body or a damper. I have. As the dynamic vibration absorber, a passive type that damps without applying external power and an active type that dampens by applying external power have been developed. The active type dynamic vibration absorber requires an actuator for generating power, and also needs to control the magnitude (gain) and timing (phase) of the output of the actuator, so that the device configuration and the control configuration are complicated. . On the other hand, in a passive dynamic vibration absorber, the vibration input to the vibration damping target is absorbed by an elastic body, a damper, or an additional object. That is, since the main system is damped by the additional dynamic damper, there is no need to apply damping power from the outside, and the device configuration and control configuration are simplified.

  In general, when designing a passive dynamic vibration absorber, the mass and rigidity of the vibration damping target in the main system are measured, and then the fixed point theory (see Non-Patent Documents 1 and 2) and the minimum dispersion standard ( By calculating a transfer function based on a conventional method such as Non-Patent Documents 3 and 4, the parameters relating to the behavior of the main system and the additional system at the time of vibration input are determined. Specifically, parameters such as the mass, elastic modulus, and damping coefficient of the additive in the additional system are determined. In this method, the mass of the additional object is uniquely determined on the assumption that the mass of the vibration damping object does not fluctuate, so that the mass ratio between the vibration damping object and the additional object becomes a constant value. Therefore, when the mass of the main system or the mass of the additional system changes, a new transfer function must be calculated again, and the design of the vibration damping structure is restricted.

  Therefore, a design method of a dynamic vibration absorber in consideration of the fluctuation of the mass ratio has been proposed. For example, two additional systems are connected in series via a damper (dash pod), one additional system has a higher natural frequency than the main system, and the other additional system has a lower natural frequency than the main system. A damping structure is under consideration. In this vibration damping structure, it is said that by setting the mass ratio between the two additional systems and the main system within a predetermined range, the vibration damping effect can be secured while suppressing the mass of the additional system (Patent Document 1). reference).

JP 06-313378 A

Brock, J.E.A note on the Damped Vibration Absorber. Trans. ASME, J. Appl. Mech., 1948, A-284. Den Hartog, J.P.Mechanical Vibrations (4th edition) .McGraw-Hill, 1956. Crandall, S.H.Mark, W.D.Random Vibration in Mechanical Systems.Academic Press, 1963. Toshihiko Asami, Toshimi Wakazono, Koichi Kameoka, Motoyoshi Hasegawa, Kumi Sekiguchi. Design theory of dynamic vibration absorber attached to a structure subject to random excitation. Transactions of the Japan Society of Mechanical Engineers (C) 56-523, 1990, 619-627.

By the way, in a vibration damping structure to which a dynamic vibration absorber is applied, an object to be damped or an additional object may be changed or exchanged (hereinafter, simply referred to as “change”). In this case, the mass of the object to be damped or the mass of the additional object may also vary. In the technique in which the mass ratio is determined within the predetermined range as described above, the change of the vibration damping target or the additional object once set is not considered, and the fluctuated mass ratio may deviate from the predetermined range. . Therefore, the parameters of the vibration damping structure are not appropriately set, and there is a possibility that the vibration damping performance is reduced.
On the other hand, even if the mass ratio fluctuates, it is possible to derive an appropriate parameter by a transfer function for each of the vibration damping object and the additional object. However, it is troublesome to set parameters from a new transfer function each time the object to be damped or the additional object is changed.

  The design method of the vibration damping structure of the present invention has been devised in view of the above-described problem, and one of the objects is to suppress a decrease in vibration damping performance by a simple method. In addition, the present invention is not limited to this object, and it is possible to obtain the functions and effects derived from the respective configurations shown in “Embodiments for Carrying Out the Invention” which will not be obtained by the conventional technology. It can be positioned for other purposes.

(1) The method for designing a vibration damping structure disclosed herein includes a construction step, a setting step, and a calculation step.
In the construction step, a model of a passive vibration damping structure is constructed in which an additional system provided with a second mass body is connected to a main system provided with the first mass body via an elastic body and an attenuator.
In the setting step, a phase margin is set in advance as a phase shift of an actual vibration phenomenon allowed for a designed vibration phenomenon with respect to the vibration input to the main system or the additional system.
In the calculation step, parameters relating to the behavior of the main system and the additional system when vibration is input are calculated based on the phase margin set in the setting step.

(2) In the calculation step, it is preferable to calculate a mass ratio between the first mass body and the second mass body as one of the parameters.
(3) In the construction step, a model in which a power transmission device as the second mass body is connected to the suspension cross member as the first mass body via the elastic body and a mount as the attenuator. Construction is preferred.

(4) In this case, it is preferable that in the setting step, the phase margin is set in advance for the vibration input to the suspension cross member. Preferably, in the calculating step, the parameter is calculated using a gravitational mass of the suspension cross member and a gravitational mass of the power transmission device.
(5) Preferably, in the setting step, the phase margin is set in advance with respect to vibration input to the power transmission device, and in the calculation step, the inertial mass of the suspension cross member and the inertia mass of the power transmission device are set. Preferably, the parameter is calculated using the inertial mass.

(6) In the constructing step, constructing a model in which a vehicle body as the second mass body is connected to the wheel as the first mass body via the elastic body and a suspension device as the damper. Is preferred.
In this case, in the setting step, the phase margin is preferably set in advance for the vibration input to the wheel, and in the calculating step, the gravitational mass of the wheel and the gravitational mass of the vehicle body are used. Preferably, the parameters are calculated.

(7) In the calculation step, it is preferable to use a common loop transfer function before and after the first mass body or the second mass body is changed.
(8) In the setting step, the phase margin is preferably set to 60 ° or more.

  According to the design method of the vibration damping structure of the present invention, for the model of the vibration damping structure constructed in the construction process, the parameters relating to the behavior of the main system and the additional system are calculated in the computation process based on the phase margin set in the setting process. By performing the calculation, it is possible to suppress the deterioration of the vibration damping performance by a simple method without performing the calculation again each time the first mass body or the second mass body is changed and setting the parameters.

FIG. 1 is a schematic diagram showing a model of a passive vibration damping structure. FIG. 2 is a block diagram of the first model. FIG. 3 is a graph showing the vibration damping characteristics of the first model. FIG. 4 is a block diagram of the second model. FIG. 5 is a graph showing the vibration damping characteristics of the second model. FIG. 6 is a block diagram of the third model. FIG. 7 is a graph showing the vibration damping characteristics of the third model. FIG. 8 is a flowchart illustrating a procedure of a method of designing a vibration damping structure.

A design method of a vibration damping structure as an embodiment will be described with reference to the drawings. The embodiments described below are merely examples, and there is no intention to exclude various modifications and application of techniques not explicitly described in the following embodiments. Each configuration of the present embodiment can be variously modified and implemented without departing from the spirit thereof. Further, they can be selected as needed, or can be appropriately combined.
The vibration damping structure designed by the method of the present embodiment is damped by a passive dynamic vibration absorber (also called “dynamic damper” or “mass damper”). Although this vibration damping structure is applied to various structures to which vibration is input, in the following description, three vibration damping structures applied to an automobile will be described as an example.

[1. Common model]
First, a model common to the three damping structures will be described with reference to FIG.
This model is roughly divided into two systems, a main system S ₁ and an additional system S ₂ .
The main system S _1, to the first mass body 1 of the first mass m _1, first elastic first elastic member 1a of the coefficient k ₁ is connected. One end of the first elastic body 1a is fixed to the first mass body 1, and the other end of the first elastic body 1a is fixed to the fixed end E.
Here, the first mass body 1 and regarded as a rigid body, the first elastic coefficient k ₁ of the first elastic member 1a regarded as a rigidity of the main system S _1, also the mass of the first elastic member 1a Is ignored, and the first mass m ₁ of the first mass body 1 is regarded as the mass of the main system S ₁ .

The additional system S _2, relative to the second mass 2 of the second mass m _2, and a second elastic coefficient k ₂ of the second elastic member 2a and the damping coefficient c ₂ of the damper (damper) 2b is connected ing. These second elastic body 2a and damper 2b are arranged in parallel. One end of each of the second elastic body 2a and the damper 2b is fixed to the second mass body 2, and the other end of each of the second elastic body 2a and the damper 2b is fixed to the first mass body 1.
Here, the second mass member 2 and regarded as rigid, also ignored for the mass of the second elastic member 2a and the damper 2b, additional system S ₂ of the second mass m ₂ of the second mass 2 Is considered to be the mass of

This additional system S ₂ constitutes a passive dynamic vibration absorber for absorbing vibrations of the main system S ₁ without applying an external force.
In the above model, it is assumed that vibration (also referred to as “excitation force”) f having an angular frequency ω is input to one of the first mass body 1 and the second mass body 2. Specifically, the first mass body 1 is input first vibration f ₁ of the first angular frequency omega ₁ is the second mass 2 second vibration f ₂ is input in the second angular frequency omega ₂ Is done. In addition, those not paying attention to the input location are simply referred to as vibration f.

When the vibration f is input, the mass bodies 1 and 2 are displaced. For example, when the vibration f is input, the first mass body 1 is displaced by a distance x _{1 with} respect to the stationary state (equilibrium state) position x ₀ , and similarly, the second mass body 2 is moved to the stationary state position x ₀ . It is displaced by a distance x ₂ for.
Thus, two-degree-of-freedom system model with a damper 2b which is displaced the respective main system second mass 2 of the first mass body 1 and the additional system S ₂ S ₁ is constructed.

[2. Each model]
Next, each of the three models will be described with reference to Table 1 below.

<First model>
The first model aims at damping the suspension cross member (first mass body 1) connected to the power transmission device (second mass body 2).
In this first model, a suspension cross member is connected to a vehicle body (fixed end E) via a bush (first elastic body 1a). Vibration (first vibration f ₁ ) is input to this suspension cross member. Specifically, vibration from a suspension device connected to the suspension cross member is input. A power transmission device is connected to the suspension cross member via a mount (second elastic body 2a, damper 2b).

The power transmission device is a device (a device unit constituting a power train) for transmitting running power in an automobile. The power transmission device includes a front differential, a rear differential, and the like.
In the first model, gravitational masses (first mass m ₁ , second mass m ₂ ) are used to calculate parameters relating to the behavior of the main system S ₁ and the additional system S ₂ when vibration is input. The gravitational mass is a mass corresponding to the strength of the force exerted on the object by gravity. Put simply, the actual weight of a stationary object is the gravitational mass.

Hereinafter, mathematical modeling of the first model will be described.
First, basic mathematical modeling is described.
Equations of motion of the first model are expressed by the following equations (1) and (2).

  When the above equations (1) and (2) are dimensionless, the following equations (3) and (4) are obtained.

However, functions such as the mass ratio μ, the damping ability z, and the rigidity ratio p ² in the above equations (3) and (4) are as shown in the following equation (5).

When both sides of the above equations (3) and (4) are subjected to Laplace transform and expressed in a matrix format, the following equation (6) is obtained. When this equation (6) is solved for X ~ ₁ (s) and X ~ ₂ (s), the following equation (7) is obtained. Where delta Δ in equation (7) is as shown in equation (8) below. Therefore, from the above equation (7), the following equation (9) representing the transfer function is obtained. This transfer function is a response function of a complex number s in which the frequency is represented in a complex manner.

From the equation (9), as shown in the block diagram of FIG. 2, the first model is represented by the transfer function G and the transfer function H.
The loop transfer function GH of the first model is represented by the following equation (10).

  Here, the loop transfer function GH means a transfer function that makes one round (one round) of the transfer function G and a loop of the transfer function H.

Next, the setting of the phase margin based on the above mathematical model will be described.
Here, the background of setting the phase margin in the present design method will be described.
Some active-type dynamic vibration absorbers having a phase margin set are being studied in order to prevent the amplitude of the input vibration from diverging and being output. On the other hand, in a vibration damping structure using a passive dynamic vibration absorber, a phase margin is generally not set because the amplitude of the input vibration does not diverge.

Further, the first mass body 1 and the second mass body 2 may be changed or exchanged (hereinafter, simply referred to as “change”). In this case, the first mass body 1 of the mass m ₂ of the mass m ₁ and the second mass member 2 varies, can vary even mass ratio μ of the main system S ₁ and the additional system S _2. The actual oscillation phenomenon vibration phenomena v to mass ratio and vibration phenomena v _d designed vibration phenomena v generated by the vibration f inputted before variation of mu, generated by the vibration f which is inputted after the variation of the mass ratio mu Assuming that v _a , when the mass ratio μ changes, the phase of the actual vibration phenomenon v _a deviates from the designed phase of the vibration phenomenon v _d . Therefore, in the conventional design method, a new transfer function is calculated again each time the mass ratio μ changes. Therefore, there is a possibility that the calculation load of the transfer function increases.
Note that the vibration phenomenon v means the behavior (physical phenomenon) of the vibration damping target caused by the vibration f. The behavior referred to here is physical or temporal vibration behavior such as amplitude and vibration angular frequency.

Therefore, in this design method, in order to consider the fluctuation of the mass ratio μ, a concept of a phase margin is introduced in the design method of the vibration damping structure using the passive type dynamic vibration absorber, and the phase margin is set in advance. I have.
Here, the phase margin means a phase shift of an actual vibration phenomenon v _a that is allowed with respect to the designed vibration phenomenon v _d . In other words, the phase margin, representing whether the actual vibration phenomenon v _a phase relative to the phase of the oscillation phenomenon v _d, which is designed to become unstable and deviate much.

Hereinafter, the specific setting of the phase margin will be described in detail.
In order to set the phase margin to β or more, the above equation (10) when “s = λi” needs to satisfy the following inequality (11). Here, i is an imaginary unit.

However, in the above inequality (11), “0 <β <π / 2” is satisfied. Re (GH) of inequality (11) is the real part of the above equation (10) when "s = λi", and Im (GH) of inequality (11) is "s = λi". This is the imaginary part of the above equation (10).
Generally, in an active-type dynamic vibration absorber, a phase margin is secured if it is 45 ° or more, and a phase margin is sufficiently secured if it is 60 ° or more. Therefore, in the following description, a case where the phase margin is 60 ° or more will be described as an example in order to secure a sufficient phase margin.

  When the phase margin is 60 ° or more, β = π / 3 is substituted in the above inequality (11). Therefore, the above inequality (11) is represented by the following inequality (12). From the inequality (12), the following inequality (13) is obtained. Regarding this inequality (13), it is assumed that the following inequality (14) is satisfied. Then, from the above inequality (13) satisfying the inequality (14), the following discriminant (15) is obtained.

Since the rigidity ratio p ² and the mass ratio μ are positive (> 0), the above discriminant (15) is always negative (<0). Therefore, the discriminant (15) is always positive. Therefore, the following equation (16) in which the left side of the above inequality (13) is equal to 0 (zero) has two real solutions. Here, when “λ ² = L” and two solutions L ₁ and L ₂ of equation (16) are obtained, the following equation (17) is obtained. However, the functions a, b, and c in Expression (17) are as shown in Expression (18) below.

In the above equation (18), if “b> 0” and “solution L ₁ <0” in equation (18), the inequality (13) is satisfied in all regions. At this time, the following inequality (19) needs to be satisfied. On the left side of this inequality (19), since “−4c> 0”, “a <0”. That is, this contradicts the assumption that “a> 0”. In the case of “a <0”, the following inequality (20) is obtained from the above inequality (13).

In order to satisfy the inequality (20), the solutions L ₁ and L ₂ need to be 0 (zero) and ∞ (infinity), and for that purpose, “a = 0” must be set. Therefore, it is inconsistent with “a <0”. That is, even if “a> 0” or “a <0”, it is inconsistent when trying to fill all the regions.
Therefore, the following conditional expression (21) is satisfied in order not to satisfy the inequality expression (13) in all the regions but to make the region satisfying the inequality expression (13) as large as possible. From the conditional expression (21), the following expression (22) is obtained, and from the expression (22) and the above inequality expression (13), the following relational expression (23) is obtained.

When the right side of the relational expression (23) is minimized, a region satisfying the inequality (13) is maximized. That is, if “p ² ” in the following relational expression (24), which is a modification of the above relational expression (23), is minimized, the region that also satisfies the relational expression (23) is maximized. From the relational expression (24), the following expression (25) is obtained.

“P ² ” in this equation (25) is called a fixed point. This fixed point, from the concept of convex optimization, the above formula (25) "p ^2" is the minimum is "p ^2". Therefore, the region satisfying the relational expression (23) is maximized.
From these, in order to maximize the region satisfying the relational expression (23), the damping performance z set from the expression (22) is set, the rigidity ratio p ² is set from the expression (25), and the mass ratio μ may be set. The damping performance z, the rigidity ratio p ² , and the mass ratio μ are parameters relating to the behavior of the main system S ₁ and the additional system S ₂ when the vibration f is input.

If parameters such as the damping performance z, the rigidity ratio p ² , and the mass ratio μ are set in this way, even if the set mass ratio μ changes, the parameters can be used without recalculation. This is because the common loop transfer function GH represented by the equation (10) is used before and after the fluctuation of the mass ratio μ.

Subsequently, referring to FIG. 3, the vibration damping performance of the first model in which the parameters are set as described above is evaluated.
In FIG. 3, for the mass ratio μ, the set mass ratio μ _d (here, “0.3”) before the fluctuation is indicated by a thick solid line, and the mass ratio μ _a after the fluctuation (here, “0.1”, “0.5”, “0.7”, “0.9”) are indicated by other line types.

Note that the vertical axis in FIG. 3 indicates compliance indicating the degree of displacement of the suspension cross member (first mass body 1) to be damped with respect to the magnitude of the input vibration (first vibration f ₁ ). The smaller the compliance is, the more the displacement of the suspension cross member with respect to the magnitude of the input vibration is suppressed, so that the vibration damping performance is high. The horizontal axis of FIG. 3 shows the frequency ratio (λ = ω ₁ /) of the input vibration (first vibration f ₁ ) to the natural angular frequency (ω ₀ = √k ₁ / m ₁ ) of the main system S _1. ω ₀ ).

As shown in FIG. 3, the actual mass ratio mu _a becomes higher damping performance is greatly improved with respect to the set mass ratio mu _d. For example, as the gravitational mass of the suspension cross member decreases, or as the gravitational mass of the power transmission device increases, the vibration suppression performance increases.
Therefore, in the first model, increasing the mass of the original suspension cross member design, or by reducing the mass of the originally designed power transmission apparatus, by previously reducing the mass ratio mu _d designed even actual mass ratio mu _a is varied, it reduced damping performance can be effectively suppressed.

<Second model>
The second model aims at damping the suspension cross member (first mass body 1) connected to the power transmission device (second mass body 2).
In the second model, the point at which vibration (second vibration f ₂ ) is input to the power transmission device (second mass body 2) and the main system S when this vibration is input are different from the first model. _{The difference is} that inertial masses (first mass m ₁ , second mass m ₂ ) are used for calculating parameters relating to the behavior of ₁ and the additional system S ₂ . Here, vibration in the pitching direction is input from a propeller shaft connected to the power transmission device. Further, the inertial mass is a mass corresponding to the magnitude of resistance generated by inertia of the object when a force acts on the object.
Other configurations of the second model are the same as the configuration of the first model.

Hereinafter, mathematical modeling of the second model will be described.
The transfer function matrix of the second model is given by the following equation (26) by the same derivation as the above equation (7). In addition, the following equation (27) representing the transfer function is obtained from the equation (26).

From the equation (27), as shown in the block diagram of FIG. 4, the second model is represented by the transfer function G and the transfer function H.
The loop transfer function GH of the second model is given by the same equation as the loop transfer function of the first model represented by the above equation (10). That is, while the second vibration f ₂ of the second model is input to the second mass body 2, the first vibration f ₁ of the first model is input to the first mass body 1, but the same loop transmission The function GH is used. That is, the same loop transfer function GH is used in the first model and the second model even if the input point of the vibration f is different.

Therefore, also in the second model, the damping performance z is set by the same equation as the above equation (22) used in the first model, and the rigidity ratio p is set by the same equation as the above equation (25) used in the first model. ² may be set, and thus the mass ratio μ may be set.

Subsequently, referring to FIG. 5, the vibration damping performance of the second model in which the parameters are set as described above is evaluated.
In FIG. 5, for the mass ratio μ, the set mass ratio μ _d (here, “1.0”) before the fluctuation is indicated by a thick solid line, and the mass ratio μ _a after the fluctuation (here, “0.1”, “0.3”, “0.5”, “0.7”) are indicated by other line types. In FIG. 5, as in FIG. 3, the vertical axis represents compliance representing the degree of displacement of the suspension cross member (first mass body 1) to be damped with respect to the magnitude of the input vibration (second vibration f ₂ ). , The frequency ratio (λ = ω ₂ / ω ₀ ) is plotted on the horizontal axis.

As shown in FIG. 5, the actual weight ratio mu _a becomes higher damping performance is improved reduced the set mass ratio mu _d. For example, as the inertial mass of the suspension cross member increases, or as the inertial mass of the power transmission device decreases, the vibration suppression performance increases. In addition, by changing the size and shape of the mass body such as the suspension cross member and the power transmission device, the inertial mass of the mass body increases and decreases. For example, the inertial mass can be reduced by reducing the size of the mass body without changing the gravity mass.

Therefore, in the second model, reduce the inertial mass of the original suspension cross member design, or to increase the inertial mass of the originally designed power transmission device in advance large mass ratio mu _d that is set it, even as the actual mass ratio mu _a is varied, reduced damping performance can be effectively suppressed.

<Third model>
The third model aims at damping the vehicle body (second mass body 2) connected to the wheel (first mass body 1).
In the third model, a wheel is attached to a tire (first elastic body 1a) in contact with a road surface (fixed end E). Vibration (first vibration f ₁ ) is input to this wheel. Specifically, tire vibration is input. The vehicle body is connected to the wheel via a suspension device (second elastic body 2a, damper 2b).
Further, in the third model, as in the first model, the calculation of the parameters on the behavior of the main system S ₁ and additional system S ₂ when the vibration is input, gravity mass (first mass m _1, the second mass m ₂ ).

Hereinafter, mathematical modeling of the third model will be described.
The transfer function of the third model is expressed by the following equation (28), similarly to the equations (9) and (27).

From the equation (28), as shown in the block diagram of FIG. 6, the third model is represented by the transfer function G and the transfer function H.
The loop transfer function GH of the third model is given by the same equation as the loop transfer function of the first model represented by the above equation (10). That is, while the vibration damping target of the third model is the second mass body 2, the vibration damping target of the first model is the first mass body 1, but the same loop transfer function GH as the first model is used. Can be Also, while the first vibration f ₁ of the third model is input to the first mass body 1, the second vibration f ₂ of the second model is input to the second mass body 2, The same loop transfer function GH is used. That is, even if the input point and the output point of the vibration f are different, the same loop transfer function GH is used in the first model, the second model, and the third model.

Therefore, also in the third model, the damping performance z is set by the same equation as the above equation (22) used in the first model, and the rigidity ratio p is set by the same equation as the above equation (25) used in the first model. ² may be set, and thus the mass ratio μ may be set.

Subsequently, referring to FIG. 7, the vibration damping performance of the third model in which the parameters are set as described above is evaluated.
In FIG. 7, for the mass ratio μ, the set mass ratio μ _d (here, “0.1”) before the fluctuation is indicated by a thick solid line, and the mass ratio μ _a after the fluctuation (here, “0.3”, “0.5”, “0.7”, “1.0”, “2.0”) are indicated by other line types. In FIG. 7, as in FIGS. 3 and 5, the vertical axis represents the compliance indicating the degree of displacement of the vehicle body (second mass body 2) to be damped with respect to the magnitude of the input vibration (first vibration f ₁ ). , The frequency ratio (λ = ω ₁ / ω ₀ ) is plotted on the horizontal axis.

As shown in FIG. 7, the actual mass ratio mu _a becomes higher damping performance is greatly improved with respect to the set mass ratio mu _d. For example, as the gravitational mass of the wheel is reduced or as the gravitational mass of the vehicle body is increased, the damping performance is improved.
Therefore, in the third model, increasing the mass of the original wheel design, or by reducing the initial body mass design, by previously reducing the set mass ratio mu _d, actual mass even the ratio mu _a is varied, reduced damping performance can be effectively suppressed.

[3. Design method of vibration control structure]
Next, a method of designing a vibration damping structure will be described.
In the present design method, as shown in FIG. 8, three steps are performed in the order of a construction step (Step A10), a setting step (Step A20), and a calculation step (Step A30).

The constructing step, the main system S ₁ to the first mass body 1 is provided, control of the second elastic member 2a and a passive type second mass 2 is coupled to additional system S ₂ provided through the damper 2b Build a model of the vibration structure. Specifically, the first model, the second model, or the third model is constructed in a construction step.
This construction step corresponds to the calculations of the above equations (1) to (10).

In the setting step, _a phase margin is preset for the vibration f input to the main system S ₁ or the additional system S ₂ as _a phase shift of the actual vibration phenomenon v _a allowed relative to the designed vibration phenomenon v _d . .
This setting step corresponds to the calculation of the above equations (11) and (12).
In the calculation step, parameters relating to the behavior of the main system S ₁ and the additional system S ₂ when the vibration f is input are calculated based on the phase margin set in the setting step.
This operation step corresponds to the operations of the above equations (13) to (25).

[4. Action and Effect]
Since the method of designing a vibration damping structure according to the present embodiment is configured as described above, the following operations and effects can be obtained.

(1) For the model of the vibration damping structure constructed in the construction step, parameters relating to the behavior of the main system S ₁ and the additional system S ₂ are computed in the computation step based on the phase margin set in the setting step. Even if the first mass body 1 and the second mass body 2 are changed, it is possible to suppress a decrease in vibration damping performance using the parameters calculated initially. That is, once the parameters are calculated, it is not necessary to calculate the parameters from a new equation of motion or a new loop transfer function each time the first mass body 1 or the second mass body 2 is changed, thereby reducing the calculation load. be able to. Also, parameters related to the behavior of the main system S ₁ and additional system S _2, based on a preset phase margin in consideration of the variation of the set mass ratio mu _d, it is set such that a sufficient phase margin is obtained Therefore, it is possible to provide a vibration damping structure capable of sufficiently allowing a phase shift of the actual vibration phenomenon v _a with respect to the designed vibration phenomenon v _{d, and} to suppress a decrease in vibration damping performance.
(2) By thus setting the variation considering mass ratio mu _d in the configuration step, it is possible to suppress deterioration in vibration damping performance in a simple manner as a mass ratio mu _d is varied.

(3) In the construction process of the first model and the second model, the suspension cross member as the first mass body 1 is mounted on the second mass body 2 via the mount as the second elastic body 2a and the damper 2b. Build a model that connects power transmission devices.
In the vibration damping structure constructed in this way, even if the mass ratio μ between the initial design of the suspension cross member and the original design of the power transmission device fluctuates, parameters relating to the behavior of the main system S ₁ and the additional system S ₂ are calculated. It is possible to suppress a decrease in the vibration damping performance without performing again. In other words, the suspension cross member and the power transmission device can be individually changed while suppressing the deterioration of the vibration damping performance by a simple method.
In addition, since the displacement of the suspension cross member is suppressed by suppressing the deterioration of the vibration damping performance, it is possible to suppress the vehicle body from being pushed up by the suspension cross member. Therefore, a decrease in comfort can be suppressed.

(4) In the first model setting step, pre-set the phase margin for the first vibration f ₁ to be input to the suspension cross member. In the calculation process of the first model, the parameters are calculated using the gravitational weight of the suspension cross member and the gravitational weight of the power transmission device.
In the first model, since it improves as the damping performance actual mass ratio mu _a relative set mass ratio mu _d increases, by previously reducing the mass ratio mu _d designed, even actual mass ratio mu _a is varied, it reduced damping performance can be effectively suppressed.
Specifically, by increasing the gravitational mass of the suspension cross member at the time of the initial design or reducing the gravitational mass of the power transmission device at the initial design, the suspension cross member and the power transmission device are individually changed to change the mass ratio. Even if μ fluctuates, it is possible to suppress a decrease in vibration suppression performance without recalculating the parameters.

(5) In the second model setting step, pre-set the phase margin for the second vibration f ₂ inputted to the power transmission device. In the calculation process of the second model, parameters are calculated using the inertial mass of the suspension cross member and the inertial mass of the power transmission device.
In the second model, since it improves as the damping performance actual mass ratio mu _a relative set mass ratio mu _d is reduced, by previously increasing the set mass ratio mu _d, even actual mass ratio mu _a is varied, it reduced damping performance can be effectively suppressed.
Specifically, by reducing the inertial mass of the suspension cross member at the initial design or increasing the inertial mass of the power transmission device at the initial design, the suspension cross member and the power transmission device are individually changed to change the mass ratio. Even if μ fluctuates, it is possible to suppress a decrease in vibration suppression performance without recalculating the parameters.

(6) In the construction process of the third model, a model in which the vehicle body as the second mass body 2 is connected to the wheel as the first mass body 1 via the suspension device as the second elastic body 2a and the damper 2b. To build. Further, in the setting step of the third model, previously setting the phase margin for the first vibration f ₁ to be input to the wheel.
The damping structure thus constructed, as the mass ratio of the vehicle body of the original design and the original wheel design μ varies, without re-calculating the parameters relating to the behavior of the main system S ₁ and additional system S ₂ In addition, it is possible to suppress a decrease in vibration damping performance. In other words, the wheels and the vehicle body can be individually changed while suppressing the deterioration of the vibration damping performance by a simple method. In addition, the displacement of the vehicle body is suppressed by suppressing the decrease in the vibration damping performance, so that the decrease in comfort can be suppressed.

In the calculation process of the third model, parameters are calculated using the gravitational mass of the wheel and the gravitational mass of the vehicle body.
In the third model, since it improves as the damping performance actual mass ratio mu _a relative set mass ratio mu _d increases, by previously reducing the set mass ratio mu _d, even actual mass ratio mu _a is varied, it reduced damping performance can be effectively suppressed.
Specifically, by increasing the gravitational mass of the wheel at the beginning of the design or by reducing the gravitational mass of the vehicle at the beginning of the design, it is possible to suppress a decrease in vibration damping performance without recalculating the parameters. For example, if the weight of the wheel is reduced, or the gravitational mass of the vehicle body is increased due to an increase in the number of passengers or a load, the vibration damping performance is improved.

(7) By using the common loop transfer function GH expressed by the equation (10) before and after the fluctuation of the mass ratio μ in the calculation process, the damping performance z, the rigidity ratio p ² , and the mass ratio μ can be easily determined. Parameters can be set. In other words, since the once set transfer function GH is used as it is in the calculation process, the calculation load can be reduced.

(8) In the setting step, by setting the phase margin to 60 ° or more, π / 3 is substituted for β in the above equation (11) (that is, “cosβ” is set to “0.5”). “Cosβ” can be given by a simple expression or a numerical value as compared with a case where other values such as 59 ° and 61 ° are used for the margin, and the calculation load of the parameter can be reduced.
Further, in the active type vibration damping structure, it is assumed that the phase margin is sufficiently secured if the phase margin is 60 °. Therefore, even in the passive type vibration damping structure of the present invention, the phase margin can be sufficiently ensured. .

  (9) Although the first mass body 1 and the second mass body 2 are common between the first model and the second model, the first model uses gravitational mass while the second model uses inertial mass. Therefore, the type of mass used in the calculation process is different. Therefore, by reducing the inertial mass of the suspension cross member at the initial design and increasing the gravitational mass, or increasing the inertial mass of the power transmission device at the initial design and reducing the inertial mass, the first model and the second model are reduced. It is possible to suppress the deterioration of the damping performance in both models.

Furthermore, the first model, the second model, and the third model differ in the first mass body 1 and the second mass body 2, so that the damping performance of all the first model, the second model, and the third model is reduced. Can be reduced.
In addition, since the first model, the second model, and the third model use the common loop transfer function given by the above equation (10), the calculation load can be further reduced.

[5. Modification]
Finally, a modification of the present design method will be described.
For example, the model of the damping structure to be built in the construction step, two-degree-of-freedom system with a damper 2b which is displaced each with additional system second mass 2 of S ₂ and the first mass body 1 of the main system S ₁ Is applicable to not only the first to third models but also various structures. For example, a vehicle body or a power transmission device may be applied to the first mass body 1, and a suspension cross member or a wheel may be applied to the second mass body. In this case, the mass used in the calculation step may be a gravitational mass or an inertial mass.

Further, the phase margin preset in the setting step is not limited to 60 °, but can be set to an arbitrary size such as 30 ° or 45 °. In this case, since π / 6 or π / 4 is substituted for β in the above equation (11), the secured phase margin is rather small, and “cosβ” becomes somewhat complicated. The effect can be obtained.
In addition, the model of the vibration damping structure constructed in the construction process can be applied not only to automobiles but also to other structures and structures of buildings.

DESCRIPTION OF SYMBOLS 1 1st mass body 1a 1st elastic body 2 2nd mass body 2a 2nd elastic body 2b Damper (attenuator)
E fixed end S ₁ main system S ₂ additional system c ₂ attenuation coefficient f, f _1, f ₂ vibration k _1, k ₂ modulus m _1, m ₂ mass x _1, x ₂ distance ω, ω _1, ω ₂ corners frequency

Claims (8)

A construction step of constructing a model of a passive vibration damping structure in which an additional system provided with a second mass body is connected to the main system provided with the first mass body via an elastic body and an attenuator,
For the vibration input to the main system or the additional system, a setting step of setting a phase margin in advance as a phase shift of an actual vibration phenomenon allowed for a designed vibration phenomenon,
Based on the phase margin set in the setting step, a calculating step of calculating parameters relating to the behavior of the main system and the additional system when vibration is input,
A method for designing a vibration damping structure, comprising: The method according to claim 1, wherein, in the calculating step, a mass ratio between the first mass body and the second mass body is calculated as one of the parameters. In the constructing step, constructing a model in which a power transmission device as the second mass body is connected to the suspension cross member as the first mass body via the elastic body and a mount as the damper. The method for designing a vibration damping structure according to claim 1, wherein: In the setting step, for the vibration input to the suspension cross member, the phase margin is set in advance,
4. The method according to claim 3, wherein in the calculating step, the parameter is calculated using a gravitational mass of the suspension cross member and a gravitational mass of the power transmission device. 5. In the setting step, the phase margin is set in advance for the vibration input to the power transmission device,
4. The method according to claim 3, wherein in the calculating step, the parameter is calculated using an inertial mass of the suspension cross member and an inertial mass of the power transmission device. 5. In the construction step, a model in which a vehicle body as the second mass body is connected to the wheel as the first mass body via a suspension device as the elastic body and the damper,
In the setting step, for the vibration input to the wheel, the phase margin is set in advance,
Wherein in the calculation step, a method of designing a by vibration damping structure according to claim 1 or 2, characterized in that for calculating the parameters by using the gravitational mass gravitational mass and the vehicle body of the wheel. The method according to any one of claims 1 to 6, wherein the operation step uses a common loop transfer function before and after the first mass body or the second mass body is changed. How to design a damping structure. The method of designing a vibration damping structure according to claim 1, wherein in the setting step, a phase margin is set to 60 ° or more.

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