JP2017110747A - Design method of vibration-proof structure - Google Patents

Abstract

PROBLEM TO BE SOLVED: To suppress the lowering of vibration-proof performance by a simple method, related to a design method of a vibration-proof structure.SOLUTION: A design method of a vibration-proof structure has a construction process (step A10), a setting process (step A20) and a calculation process (step A30). In the construction process (step A10), a model of a receiving-type vibration-proof structure in which an additional system having a second mass body is connected to a main system having a first mass body via an elastic body and an attenuator is constructed. In the setting process (step A20), a phase surplus is set in advance as the phase displacement of an actual vibration phenomenon which is permitted to a designed vibration phenomenon with respect to vibration which is inputted to the main system or the additional system. In the calculation process (step A30), a parameter related to behaviors of the main system and the additional system at the input of the vibration is calculated on the basis of the phase surplus which is set in the setting process.SELECTED DRAWING: Figure 8

Description

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

  Conventionally, as one of the dynamic vibration absorbers, an object to which vibration is input (hereinafter referred to as “vibration object”) is provided with an additional object connected via an elastic body or a damper. Yes. As the dynamic vibration absorber, a passive type that suppresses vibration without applying power outside the system and an active type that suppresses vibration by applying power outside the system have been developed. An active dynamic vibration absorber requires an actuator that generates power, and it is necessary to control the magnitude (gain) and timing (phase) of the output of the actuator, which complicates the device configuration and control configuration. . On the other hand, in the passive type dynamic vibration absorber, the vibration input to the object to be controlled is absorbed by an elastic body, a damper, or an additional object. In other words, since the main system is damped by the additional system dynamic vibration absorber, it is not necessary to apply vibration damping power from the outside, and the apparatus configuration and control configuration are simplified.

  In general, when designing a passive dynamic vibration absorber, measure the mass and rigidity of the object to be controlled in the main system, and then determine 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, 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 adduct 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 suppression object does not vary, and therefore, the mass ratio between the vibration suppression object and the additional object becomes a constant value. Therefore, when the mass of the main system or the mass of the additional system fluctuates, a new transfer function must be recalculated, which restricts the design of the damping structure.

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

Japanese Patent Laid-Open No. 06-313378

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, Junichi Kameoka, Motoyoshi Hasegawa, Kumi Sekiguchi. Design theory for dynamic vibration absorbers attached to structures 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, there is a case where a vibration damping object or an additional object is changed or replaced (hereinafter simply referred to as “change”). In this case, the mass of the object to be damped and the mass of the appendage can also vary. As described above, in the technology in which the mass ratio is determined within the predetermined range, the change of the vibration suppression target and the appendage set once is not considered, and the changed mass ratio may be out of the predetermined range. . Therefore, the parameters of the vibration damping structure are not set appropriately, 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 from the transfer function for each vibration suppression object or additional object. However, it is complicated to set a parameter from a new transfer function each time the vibration suppression object or the additional object is changed.

  The design method of the vibration damping structure of the present case has been created in view of the above-described problems, and an object thereof is to suppress a reduction in vibration damping performance by a simple method. Note that the present invention is not limited to this purpose, and is an operation and effect derived from each configuration shown in “Mode for Carrying Out the Invention” to be described later. It can be positioned as another purpose.

(1) The design method of the damping structure disclosed here has a construction process, a setting process, and a calculation process.
In the construction step, a passive damping structure model is constructed in which the main system provided with the first mass body is connected to the additional system provided with the second mass body via the elastic body and the attenuator.
In the setting step, a phase margin is set in advance as a phase shift of an actual vibration phenomenon that is allowed with respect to a designed vibration phenomenon, with respect to vibration input to the main system or the additional system.
In the calculation step, parameters related 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 setting step, it is preferable to set 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 the 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 the mount as the attenuator. It is preferable to construct.

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

(6) In the construction step, a model in which the vehicle body as the second mass body is connected to the wheel as the first mass body via the suspension body as the elastic body and the attenuator is constructed. Is preferred.
In this case, in the setting step, the phase margin is preferably set in advance for vibration input to the wheel, and the calculation step uses the gravitational mass of the wheel and the gravitational mass of the vehicle body. It is preferable to calculate the parameters.

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

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

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 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 the procedure of the design method of the vibration damping structure.

With reference to the drawings, a design method of a vibration damping structure as an embodiment will be described. The embodiment described below is merely an example, and there is no intention to exclude various modifications and technical applications that are not explicitly described in the following embodiment. Each configuration of the present embodiment can be implemented with various modifications without departing from the spirit thereof. Further, they can be selected as necessary, or can be appropriately combined.
The vibration control structure designed by the method of the present embodiment is controlled by a passive dynamic vibration absorber (also referred to as “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 vibration 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 .
A first elastic body 1a having a first elastic modulus k ₁ is coupled to the main system S ₁ with respect to a first mass _{1 having} a first mass m ₁ . 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 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. The second elastic body 2a and the damper 2b are arranged in parallel. Each one end of the second elastic body 2a and the damper 2b is fixed to the second mass body 2, and each other end of the second elastic body 2a and the damper 2b is fixed to the first mass body 1.
Here, the second mass body 2 is regarded as a rigid body, and the masses of the second elastic body 2a and the damper 2b are ignored, and the second mass m ₂ of the second mass body ₂ is added to the additional system S _2. And the mass of

The additional system S ₂ constitutes a passive dynamic vibration absorber that absorbs the vibration 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 ₁ is inputted with the first vibration f ₁ having the first angular frequency ω ₁ , and the second mass ₂ is inputted with the second vibration f ₂ having the second angular frequency ω ₂ . Is done. In addition, what does not pay attention to the input location is 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 1 is displaced by the distance x _{1 with} respect to the position x _{0 in the} stationary state (equilibrium state). Similarly, the second mass 2 is moved to the position x ₀ in the stationary state. 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, 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 the vehicle body (fixed end E) via a bush (first elastic body 1a). Vibration (first vibration f ₁ ) is input to the suspension cross member. Specifically, vibration from a suspension device connected to the suspension cross member is input. A power transmission device is coupled to the suspension cross member via mounts (second elastic body 2a, damper 2b).

The power transmission device is a device (device unit constituting a power train) that transmits traveling power in an automobile. Examples of the power transmission device include a front differential and a rear differential.
Further, in the first model, gravitational mass (first mass m ₁ , second mass m ₂ ) is 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 with which an object is attracted by gravity. Put simply, the actual weight of a stationary object is gravitational mass.

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

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

However, the functions such as the mass ratio μ, the damping capability 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 Laplace transformed and expressed in matrix form, the following equation (6) is obtained. Solving this equation (6) with respect to 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 whose frequency is expressed in a complex manner.

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

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

Next, the setting of the phase margin based on the mathematical model described above will be described.
Here, the background for setting the phase margin in this design method will be described.
Some active dynamic vibration absorbers have been studied in which a phase margin is set in order to prevent the amplitude of the input vibration from being diverged and output. On the other hand, in the vibration damping structure in which a passive dynamic vibration absorber is used, the 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 mass m 1 of the first mass ₁ and the mass m ₂ of the second mass ₂ vary, and the mass ratio μ between the main system S ₁ and the additional system S ₂ can also vary. The vibration phenomenon v generated by the vibration f input before the change of the mass ratio μ is defined as the designed vibration phenomenon v _d, and the vibration phenomenon v generated by the vibration f input after the change of the mass ratio μ is the actual vibration phenomenon. v if _a, the mass ratio μ is varied, the actual vibration phenomena v _a phase relative to the phase of the oscillation phenomenon v _d that has been designed is shifted. Therefore, in the conventional design method, a new transfer function is recalculated every time the mass ratio μ changes. As a result, the calculation load of the transfer function may increase.
The vibration phenomenon v means a behavior (physical phenomenon) of a vibration suppression target caused by the vibration f. The behavior here is a behavior of physical or temporal vibration such as amplitude or vibration angular frequency.

Therefore, in this design method, in order to take into account fluctuations in the mass ratio μ, the concept of phase margin is introduced in the design method of the damping structure in which a passive dynamic vibration absorber is used, and the phase margin is set in advance. Yes.
The phase margin here means a phase shift of the actual vibration phenomena v _a allowed for designed vibration phenomena 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, specific setting of the phase margin will be described in detail.
In order to make the phase margin equal to or larger than β, the above equation (10) when “s = λi” needs to satisfy the following inequality (11). However, i is an imaginary unit.

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

  When the phase margin is 60 ° or more, β = π / 3 is substituted in the inequality (11). Therefore, the above inequality (11) is expressed by the following inequality (12). Further, from the inequality (12), the following inequality (13) is obtained. Regarding this inequality (13), the following inequality (14) is satisfied. The following discriminant (15) is obtained from the above inequality (13) that satisfies the inequality (14).

Since the rigidity ratio p ² and the mass ratio μ are positive (> 0), the 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 the two solutions L ₁ and L ₂ of equation (16) are obtained, the following equation (17) is obtained. However, functions a, b, and c in equation (17) are as shown in equation (18) below.

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

In order to satisfy this 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 contradicts with “a <0”. That is, there is a contradiction when trying to fill all the regions regardless of whether “a> 0” or “a <0”.
Therefore, in order not to satisfy the inequality (13) in all regions but to make the region satisfying the inequality (13) as large as possible, the following conditional expression (21) is satisfied. From this conditional expression (21), the following expression (22) is obtained, and the following relational expression (23) is obtained from the expression (22) and the above inequality (13).

When the right side of the relational expression (23) is minimized, the region satisfying the inequality (13) is maximized. That is, when “p ² ” in the following relational expression (24) obtained by modifying the relational expression (23) is minimized, the region satisfying the relational expression (23) is maximized. Further, from the relational expression (24), the following expression (25) is obtained.

“P ² ” in the 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, to maximize the area which satisfies the equation (23) sets the damping performance z is set from Equation (22), to set the rigidity ratio p ² from equation (25), thus, the weight ratio μ should 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.

Thus, if parameters such as the damping performance z, the rigidity ratio p ² , and the mass ratio μ are set, even if the set mass ratio μ changes, the parameters can be used as they are without being recalculated. This is because the common transfer function GH expressed by the equation (10) is used before and after the change in 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 before the change (here, “0.3”) is indicated by a thick solid line, and the mass ratio μ _a after the change (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 controlled with respect to the magnitude of the input vibration (first vibration f ₁ ). The smaller the compliance, the higher the vibration damping performance because the displacement of the suspension cross member with respect to the magnitude of the input vibration is suppressed. Also, 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, the damping performance increases as the gravity mass of the suspension cross member decreases or the gravity mass of the power transmission device increases.
Therefore, in the first model, by increasing the mass of the suspension cross member at the initial stage of design, or by reducing the mass of the power transmission device at the initial stage of design, the designed mass ratio μ _d is reduced in advance. Even if the actual mass ratio μ _a fluctuates, it is possible to effectively suppress the deterioration of the damping performance.

<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 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 is compared to the first model. _{The difference is} that inertial mass (first mass m ₁ , second mass m ₂ ) is used for calculation of parameters relating to the behavior of ₁ and additional system S ₂ . Here, vibration in the pitching direction is input from a propeller shaft connected to the power transmission device. The inertia mass is a mass corresponding to the magnitude of resistance generated by the inertia of the object when a force is applied to the object.
Other configurations of the second model are the same as the configurations 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 derivation similar to the above equation (7). Further, from this equation (26), the following equation (27) representing the transfer function is obtained.

From this equation (27), the second model is expressed by the transfer function G and the transfer function H as shown in the block diagram of FIG.
The round transfer function GH of the second model is given by the same formula as the round trip transfer function of the first model expressed by the above formula (10). That is, the second vibration f ₂ of the second model is input to the second mass body 2, whereas the first vibration f ₁ of the first model is input to the first mass body 1, but the same round transmission The function GH is used. That is, even if the input location of the vibration f is different, the same round transfer function GH is used in the first model and the second model.

Therefore, also in the second model, the damping performance z is set by the same formula as the formula (22) used in the first model, and the stiffness ratio p is set by the same formula as the formula (25) used in the first model. ^It is sufficient to set ² and eventually set the mass ratio μ.

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 before the change (here, “1.0”) is indicated by a thick solid line, and the mass ratio μ _a after the change (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 indicating the degree of displacement of the suspension cross member (first mass body 1) to be controlled with respect to the magnitude of the input vibration (second vibration f ₂ ). The horizontal axis represents the frequency ratio (λ = ω ₂ / ω ₀ ).

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, the damping performance increases as the inertia mass of the suspension cross member increases or the inertia mass of the power transmission device decreases. The inertial mass of the mass body is increased or decreased by changing the size or shape of the mass body such as the suspension cross member or the power transmission device. For example, even if the gravitational mass is not changed, the inertial mass can be reduced by reducing the size of the mass body.

Therefore, in the second model, the set mass ratio μ _d is increased in advance by reducing the inertial mass of the suspension cross member at the initial design or by increasing the inertial mass of the power transmission device at the initial design. As a result, even if the actual mass ratio μ _a varies, the deterioration of the 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).
In the third model, as in the first model, gravitational mass (first mass m ₁ , second mass is used for calculation of parameters related to the behavior of main system S ₁ and additional system S ₂ when vibration is input. m ₂ ) is used.

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 above equations (9) and (27).

From this equation (28), the third model is expressed by the transfer function G and the transfer function H as shown in the block diagram of FIG.
The round transfer function GH of the third model is given by the same formula as the round trip transfer function of the first model expressed by the above formula (10). That is, while the vibration suppression target of the third model is the second mass body 2, the vibration suppression target of the first model is the first mass body 1, but the same loop transfer function GH as the first model is used. It is done. Moreover, 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, but the second model The same round transfer function GH is used. That is, even if the input location and output location of the vibration f are different, the same round 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 formula as the formula (22) used in the first model, and the stiffness ratio p is set by the same formula as the formula (25) used in the first model. ^It is sufficient to set ² and eventually set the mass ratio μ.

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, with respect to the mass ratio μ, the set mass ratio μ _d before the change (here, “0.1”) is indicated by a thick solid line, and the mass ratio μ _a after the change (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 compliance indicating the degree of displacement of the body (second mass body 2) to be controlled with respect to the magnitude of the input vibration (first vibration f ₁ ) is plotted on the vertical axis. And the horizontal axis represents the frequency ratio (λ = ω ₁ / ω ₀ ).

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, the damping performance increases as the gravitational mass of the wheel decreases or the gravitational mass of the vehicle body increases.
Therefore, in the third model, the actual mass can be reduced by increasing the mass of the wheel at the initial design or reducing the mass of the vehicle body at the initial design to reduce the set mass ratio μ _d in advance. Even if the ratio μ _a fluctuates, it is possible to effectively suppress a decrease in vibration damping performance.

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

In the construction process, a passive type control system in which the additional system S ₂ provided with the second mass body 2 is connected to the main system S ₁ provided with the first mass body 1 via the second elastic body 2a and the damper 2b. Build a vibration structure model. Specifically, the first model, the second model, or the third model is constructed in the construction process.
This construction process corresponds to the calculations of the above formulas (1) to (10).

In the setting step, _a phase margin is set in advance as _a phase shift of the actual vibration phenomenon va allowed for the designed vibration phenomenon v _d for the vibration f input to the main system S ₁ or the additional system S _2. .
This setting step corresponds to the calculations of the above equations (11) and (12).
In the calculation step, parameters related 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 calculation step corresponds to the calculations of the above formulas (13) to (25).

[4. Action and effect]
Since the vibration damping structure design method of the present embodiment is configured as described above, the following operations and effects can be obtained.

(1) For the vibration damping structure model constructed in the construction process, based on the phase margin set in the setting process, the parameters relating to the behavior of the main system S ₁ and the additional system S ₂ are computed in the computation process, Even if the first mass body 1 and the second mass body 2 are changed, it is possible to suppress a decrease in the vibration damping performance using the initially calculated parameters. That is, once a parameter is calculated, it is not necessary to calculate a parameter from a new equation of motion or a new round transfer function every 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, is set such that a sufficient phase margin is obtained because, it is possible to provide a damping structure capable of allowing sufficient phase shift of the actual vibration phenomena v _a relative oscillation phenomenon v _d that has been designed, it is possible to suppress deterioration in damping performance.
(2) As described above, by setting the mass ratio μ _d in consideration of fluctuations in the setting step, even if the mass ratio μ _d fluctuates, it is possible to suppress a decrease in vibration damping performance by a simple method.

(3) In the construction process of the first model and the second model, the suspension mass member as the first mass body 1 is used as the second mass body 2 via the mount as the second elastic body 2a and the damper 2b. Build a model with connected power transmission devices.
In the vibration damping structure constructed in this way, even if the mass ratio μ between the suspension cross member at the initial design and the power transmission device at the initial design 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 the deterioration of the vibration damping performance without reworking. In other words, the suspension cross member and the power transmission device can be individually changed while suppressing a decrease in vibration damping performance by a simple method.
In addition, since the displacement of the suspension cross member can be suppressed by suppressing the deterioration of the damping performance, the vehicle body can be prevented from being pushed up by the suspension cross member. Therefore, a decrease in comfort can be suppressed.

(4) In the first model setting step, a phase margin is set in advance for the first vibration f ₁ input to the suspension cross member. In the calculation process of the first model, 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 if the actual mass ratio μ _a fluctuates, the deterioration of the damping performance can be effectively suppressed.
Specifically, by increasing the gravitational mass of the suspension cross member at 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 can be individually changed to change the mass ratio. Even if μ fluctuates, it is possible to suppress a decrease in damping performance without recalculating parameters.

(5) In the second model setting step, a phase margin is set in advance for the second vibration f ₂ input to the power transmission device. In the second model calculation step, the parameter is calculated using the inertia mass of the suspension cross member and the inertia 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 if the actual mass ratio μ _a fluctuates, the deterioration of the damping performance can be effectively suppressed.
Specifically, by reducing the inertia mass of the suspension cross member at the initial design or increasing the inertia 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 damping performance without recalculating parameters.

(6) In the third model construction process, 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. Build up. In the third model setting step, a phase margin is set in advance for the first vibration f ₁ input to the wheel.
In the vibration damping structure constructed in this way, even if the mass ratio μ between the original design wheel and the original design vehicle body fluctuates, parameters relating to the behavior of the main system S ₁ and the additional system S ₂ are not recalculated. , The deterioration of the damping performance can be suppressed. In other words, it is possible to individually change the wheel and the vehicle body while suppressing a decrease in the damping performance by a simple method. In addition, since the displacement of the vehicle body can be suppressed by suppressing the decrease in vibration damping performance, it is possible to suppress the decrease in comfort.

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 if the actual mass ratio μ _a fluctuates, the deterioration of the damping performance can be effectively suppressed.
Specifically, by reducing the gravitational mass of the wheel at the initial design or reducing the gravitational mass of the vehicle body at the initial design, it is possible to suppress a decrease in the damping performance without recalculating the parameters. For example, if the wheel weight is reduced, or the gravitational mass of the vehicle body increases due to an increase in the number of passengers or cargo, the vibration damping performance increases.

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

(8) In the setting step, π / 3 is substituted for β in the above equation (11) by setting the phase margin to 60 ° or more (that is, “cosβ” is set to “0.5”). Compared to the case where another value such as 59 ° or 61 ° is employed, “cosβ” can be given by a simple expression or numerical value, and the calculation load of the parameter can be reduced.
In addition, in the active vibration suppression structure, if the phase margin is 60 °, it is assumed that the phase margin is sufficiently secured. Therefore, even in the passive vibration suppression structure of the present case, the phase margin can be sufficiently secured. .

  (9) Although the first mass body 1 and the second mass body 2 are common to the first model and the second model, the first model uses gravity mass, whereas 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 by increasing the inertial mass of the power transmission device at the initial design and reducing the inertial mass, It is possible to suppress a decrease in damping performance in both models.

Furthermore, since the first mass 1 and the second model 2 are different between the first model, the second model, and the third model, the vibration damping performance is reduced in all of the first model, the second model, and the third model. Can be suppressed.
In addition, since the first model, the second model, and the third model use the common one-round transfer function given by the above equation (10), the calculation load can be further reduced.

[5. Modified example]
Finally, a modification of this design method will be described.
For example, the model of the damping structure constructed in the construction process is a two-degree-of-freedom system with a damper 2b in which the first mass ₁ of the main system S 1 and the second mass ₂ of the additional system S ₂ are displaced. If it is a model of this, it can apply not only to a 1st-3rd model but to 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 gravitational mass or inertial mass.

Further, the phase margin set in advance in the setting step is not limited to 60 °, and 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 phase margin to be secured is slightly small and “cosβ” is slightly complicated. An effect can be obtained.
In addition, the vibration suppression structure model 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 damping coefficient f, f ₁ , f ₂ vibration k ₁ , k ₂ elastic coefficient m ₁ , m ₂ mass x ₁ , x ₂ distance ω, ω ₁ , ω ₂ angle frequency

Claims (8)

A construction step of constructing a passive damping structure model in which an additional system provided with a second mass body is connected to a main system provided with a 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 for presetting a phase margin 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 calculation step for 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 for designing a damping structure according to claim 1, wherein, in the setting step, a mass ratio between the first mass body and the second mass body is set as one of the parameters. In the construction step, a model is constructed 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 the mount as the attenuator. A method for designing a vibration damping structure according to claim 1 or 2. In the setting step, the phase margin is set in advance for vibrations input to the suspension cross member,
4. The method for designing a vibration damping structure according to claim 3, wherein, in the calculation step, the parameter is calculated using a gravitational mass of the suspension cross member and a gravitational mass of the power transmission device. In the setting step, the phase margin is preset for vibration input to the power transmission device,
5. The method for designing a damping structure according to claim 3, wherein in the calculation step, the parameter is calculated using an inertial mass of the suspension cross member and an inertial mass of the power transmission device. In the construction step, a model in which a vehicle body as the second mass body is connected to a wheel as the first mass body via a suspension device as the elastic body and the attenuator,
In the setting step, for the vibration input to the wheel, the phase margin is set in advance,
The method for designing a damping structure according to any one of claims 1 to 5, wherein, in the calculation step, the parameter is calculated using a gravitational mass of the wheel and a gravitational mass of the vehicle body. . The calculation step uses a common transfer function before and after the first mass body or the second mass body is changed, and is described in any one of claims 1 to 6 Design method for damping structure. The method for designing a vibration damping structure according to any one of claims 1 to 7, wherein, in the setting step, the phase margin is set to 60 ° or more.

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