JP2017151866A - Method, device and program for supporting development of dynamic vibration absorber - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve vibration control performance and thereby curbing vibration.SOLUTION: For a vibration control structure formed by connecting a main system which has a first mass body and a first elastic body to an additional system which has a second mass body, a second elastic body and a damper and performs as a dynamic vibration absorber, the present invention includes a device executing design processing for designing the dynamic vibration absorber, and a method and a program making a computer execute the design processing, and has a construction process S2 executed by a construction section and a calculation process S3 executed by a calculation section. The construction process S2 constructs a model of the vibration control structure having the second mass body disposed with respect to the first mass body via the second elastic body and the damper. The calculation process S3 calculates an elastic coefficient of the second elastic body and a damping coefficient of the damper, when angular frequency ω of vibration fto be input into the main system is in a frequency band equal to or more than natural angular frequency ωof the main system, using either a first method which maximizes first vibration power Pto be consumed by the additional system or a second method which minimizes second vibration power Pto be input into the main system.SELECTED DRAWING: Figure 7

Description

  The present invention relates to a development support method, a development support apparatus, and a development support program for appropriately designing a dynamic vibration absorber applied to a vibration damping structure.

  A dynamic vibration absorber is configured by connecting an additional object to a structure (for example, a building, a machine, a vehicle, a ship, etc.) whose vibration is to be suppressed via an elastic body or a damper (for example, a patent) References 1 and 2). As one of the dynamic vibration absorbers, a passive type dynamic absorber that absorbs the force (vibration power) input to the structure (hereinafter referred to as “vibration object”) by an additional system comprising an elastic body, an attenuator, and an additional material. A vibration absorber is known. In the passive type dynamic vibration absorber, the object to be controlled (main system) is damped without applying damping power from the outside, so that the device configuration and the control configuration can be simplified.

  In general, when designing a passive type dynamic vibration absorber, the mass and rigidity of an object to be controlled in the main system are measured, and the mass of the additional object in the additional system is determined from other requirements. From the ratio of these two masses, parameters related to the behavior of the main system and the additional system at the time of vibration input are determined by calculating the transfer function based on conventional design methods (for example, fixed point theory and minimum dispersion standard). To do. The parameters determined here include the mass of the adduct in the additional system, the elastic coefficient, the damping coefficient, and the like.

JP 2011-144605 A JP 2006-077781 A

  By the way, the above-mentioned fixed point theory is such that the elastic coefficient, damping coefficient, etc. of the additional system are reduced so that the vibration generated by the force (vibration power) input to the object to be controlled is reduced in all frequency bands (angular frequency range). It is a method to determine. That is, in this method, since vibration is attenuated and suppressed after vibration is generated in the object to be controlled, it is difficult to suppress the generation of vibration itself. In addition, when the vibration is in a specific frequency band, it may be more efficient to design and develop by paying attention to the damping performance in that frequency band.

  The present case has been devised in view of such a problem, and is a dynamic vibration absorber capable of improving the vibration damping performance in a specific frequency band and suppressing the vibration of the vibration damping object (structure). One of the purposes is to provide a development support method, a development support device, and a development support program for a vessel. The present invention is not limited to this purpose, and is a function and effect derived from each configuration shown in the embodiment for carrying out the invention described later, and has another function and effect that cannot be obtained by conventional techniques. is there.

  (1) The dynamic vibration absorber development support method disclosed here is a passive dynamic vibration absorber having a main system having a first mass body and a first elastic body, a second mass body, a second elastic body, and an attenuator. A development support method for causing a computer to execute a process of designing the dynamic vibration absorber for a vibration damping structure that is connected to an additional system that constitutes a vibration device, and the second elastic body with respect to the first mass body And a construction step of constructing a model of the damping structure having the second mass body provided via the attenuator, and an angular frequency of vibration input to the main system is greater than or equal to a natural angular frequency of the main system At least one of the first method for maximizing the first vibration power consumed in the additional system and the second method for minimizing the second vibration power input to the main system. The elastic modulus of the second elastic body and the attenuation of the attenuator And a, a calculation step of calculating the number.

  (2) In the first method, the stiffness parameter and the damping parameter at which the first vibration power is maximized in the frequency band are expressed by the first mass body and the second mass as represented by the following formulas A and B: It is preferably given as a function of the mass ratio with the body.

(3) In the second method, the stiffness parameter related to the stiffness ratio between the main system and the additional system is set to a maximum value when the overall vibration of the damping structure falls within a predetermined range. Is preferred.
(4) In the second method, it is more preferable that the lower limit value of the stiffness parameter is set to a stiffness parameter that maximizes the first vibration power in the frequency band.

(5) In the second method, it is preferable that the damping parameter related to the damping performance of the additional system is set to a maximum value when the overall vibration of the damping structure falls within a predetermined range.
(6) In the second method, it is more preferable that the lower limit value of the attenuation parameter is set to an attenuation parameter that maximizes the first vibration power in the frequency band.

  (7) 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 device as the second elastic body and the attenuator is constructed. It is preferable to do. In this case, the vibration input to the main system becomes road noise transmitted from the road surface.

  (8) A dynamic vibration absorber development support device disclosed herein is a passive dynamic vibration absorber having a main system having a first mass body and a first elastic body, a second mass body, a second elastic body, and an attenuator. A development support apparatus that executes a process of designing the dynamic vibration absorber for a vibration damping structure that is connected to an additional system that constitutes a vibration device, and the second elastic body and the first mass body A construction unit for constructing a model of the vibration control structure having the second mass body provided via an attenuator, and a frequency at which an angular frequency of vibration input to the main system is greater than or equal to a natural angular frequency of the main system In the case of a belt, at least one of the first method for maximizing the first vibration power consumed in the additional system and the second method for minimizing the second vibration power input to the main system is used. Calculating the elastic coefficient of the second elastic body and the attenuation coefficient of the attenuator It has a, and.

  (9) A dynamic vibration absorber development support program disclosed herein is a passive dynamic vibration absorber having a main system having a first mass body and a first elastic body, a second mass body, a second elastic body, and an attenuator. A development support program for executing a process of designing the dynamic vibration absorber for a vibration damping structure that is connected to an additional system that constitutes a vibrator, wherein the second elastic body and the first mass body A construction step of constructing a model of the damping structure having the second mass body provided via an attenuator, and a frequency at which an angular frequency of vibration input to the main system is greater than or equal to a natural angular frequency of the main system In the case of a belt, at least one of the first method for maximizing the first vibration power consumed in the additional system and the second method for minimizing the second vibration power input to the main system is used. The elastic coefficient of the second elastic body and the attenuation coefficient of the attenuator Executing a calculation step of calculating, to a computer.

  According to the dynamic vibration absorber designed by the disclosed development support method, development support device, and development support program, vibration of the vibration control structure (vibration target) can be suppressed. That is, it is possible to design and develop a dynamic vibration absorber with improved vibration damping performance in a frequency band higher than the natural angular frequency of the main system.

It is a schematic diagram which shows the model of the damping structure provided with the dynamic vibration damper which concerns on embodiment. It is a graph which shows two vibration powers at the time of using a 1st method. It is a graph which shows the damping performance by a 1st method compared with the conventional method. It is a graph which shows two vibration powers at the time of using a 2nd method. It is a graph which shows the damping performance by the 1st and 2nd methods compared with the conventional method. It is a block diagram which shows the development assistance apparatus which concerns on embodiment. It is a flowchart which illustrates the procedure of the development support method which concerns on embodiment.

  A dynamic vibration absorber development support device, a development support method, and a development support program as embodiments will be described with reference to the drawings. 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.

[1. Overview]
The dynamic vibration absorber development support device according to the present embodiment is a device that executes a design process for appropriately designing a dynamic vibration absorber that controls various structures to which vibration is input. The development support method and the development support program according to the present embodiment are a method and a program for causing a computer to execute the design process described above. The dynamic vibration absorber of the present embodiment is a passive dynamic vibration absorber that is also called a dynamic damper or a mass damper, and is applied to, for example, a vibration damping structure provided in a vehicle.

[1-1. Damping structure model]
First, with reference to FIG. 1, a model of the vibration damping structure of the present embodiment will be described. This vibration damping structure is a passive dynamic vibration absorber having a main system 1 having a first mass body 1A and a first elastic body 1B, a second mass body 2A, a second elastic body 2B, and a damper 2C (attenuator). Are connected to the additional system 2 constituting the. Therefore, the model of this embodiment is roughly divided into two systems, that is, a main system 1 and an additional system 2 as shown in FIG. The passive dynamic vibration absorber here is a device (structure) that absorbs vibration of the main system 1 without applying an external force.

  The first elastic body 1B of the main system 1 has one end fixed to the first mass body 1A and the other end in contact with (supported by) the fixed end E. Further, the second elastic body 2B and the damper 2C of the additional system 2 are provided in parallel, each one end is fixed to the second mass body 2A, and each other end is fixed to the first mass body 1A. That is, the model of the vibration damping structure has the second mass body 2A provided via the second elastic body 2B and the damper 2C with respect to the first mass body 1A.

Hereinafter, the mass of the first mass body 1A is referred to as “first mass m ₁ ”, and the elastic coefficient of the first elastic body 1B is referred to as “first elastic coefficient k ₁ ”. Further, the mass of the second mass body 2A is “second mass m ₂ ”, the elastic coefficient of the second elastic body 2B is “second elastic coefficient k ₂ ”, and the damping coefficient of the damper 2C is “damping coefficient c ₂ ”. And In the design process of this embodiment, both the first mass body 1A and the second mass body 2A are regarded as rigid bodies, and the first elastic coefficient k ₁ of the first elastic body 1B is regarded as the rigidity of the main system 1. Further, the masses of the first elastic body 1B, the second elastic body 2B, and the damper 2C are all ignored, the first mass m ₁ of the first mass body 1A is regarded as the mass of the main system 1, and the second mass body 2A. a second mass m ₂ is regarded as the mass of the additional system 2.

In the design process of the present embodiment, as shown in FIG. 1, a model is constructed in which vibration f ₁ (also referred to as “excitation force”) is input to the main system 1 (first mass body 1A). When the vibration f ₁ is input, the two mass bodies 1A and 2A are both displaced. Specifically, when the vibration f ₁ is input, the first mass body 1A is displaced by the distance x _{1 with} respect to the position x _{0 in the} stationary state (equilibrium state). Similarly, the second mass body 2A is in the stationary state. The position x _{0 is} displaced by a distance x ₂ . Thus, in this design process, a model of a two-degree-of-freedom system with a damper in which the first mass 1A of the main system 1 and the second mass 2A of the additional system 2 are displaced is constructed.

In this design process, the second elastic coefficient k ₂ and the damping coefficient c ₂ of the additional system 2 that can suppress both the vibrations of the main system 1 and the additional system ₂ are designed. Incidentally, the first mass m ₁ of the main system 1, the second mass m ₂ of the first elastic coefficient k ₁ and additional system 2 is set in a previous stage of the design process. Further, in the present design process, the case where the angular frequency ω of the vibration f ₁ input to the main system 1 is in a high frequency band (ω ≧ ω ₀ ) that is equal to or higher than the natural angular frequency ω ₀ of the main system 1 will be considered.

[1-2. Equation of motion for a system of degrees of freedom]
Here, mathematical modeling of the model shown in FIG. 1 will be described. First, the equations of motion of the two-degree-of-freedom system of FIG.

When these equations are made dimensionless, equations 3 and 4 are obtained. However, functions such as μ, z, and p ² in these equations are as shown in Equation 5. Here, μ is a parameter representing the mass ratio between the first mass body 1A and the second mass body 2A, z is a parameter relating to the damping performance of the additional system 2, and p is the rigidity between the main system 1 and the additional system 2. It is a parameter related to the ratio. Hereinafter, these will be referred to as “mass ratio μ”, “damping parameter z”, and “rigidity parameter p”, respectively.

  Expression 6 represents a result obtained by performing Laplace transform on both sides of the above expressions 3 and 4 and expressing them in a matrix form. Further, Equation 7 is obtained by solving Equation 6. Where Delta Δ in Equation 7 is as shown in Equation 8.

  From Equation 7, the transfer functions (mobility) shown in Equations 9 and 10 are obtained. These transfer functions are complex s response functions whose frequencies are expressed in a complex manner.

[1-3. Derivation of vibration power]
Next, derivation of the vibration power P will be described. The vibration power P is a force (energy) that causes the structure to vibrate, and is expressed by, for example, power [W]. If the vibration power P is a positive value, the vibration of the structure is increased. If the vibration power P is a negative value, the vibration of the structure is suppressed (absorbed). The vibration power P is given by the following equation 11 where F is the input and M is the mobility. Note that Re (M) in Equation 11 means the real part of M.

Therefore, in the two-degree-of-freedom system shown in FIG. 1, the vibration power P ₂₁ consumed in the additional system 2 (first vibration power, hereinafter referred to as “damper power P ₂₁ ”) It becomes. Further, the vibration power P ₁₁ (second vibration power, hereinafter referred to as “input power P ₁₁ ”) input to the main system 1 is represented by the following Expression 13 from Expressions 5 and 7. The damper power P ₂₁ is a vibration power that is mainly absorbed and consumed by the second elastic body 2B, and therefore has a value of 0 or less (P ₂₁ ≦ 0), and the input power P ₁₁ is a vibration input to the main system 1. Since it is power, the value is 0 or more (P ₁₁ ≧ 0).

In the design process of this embodiment, when vibration f ₁ (ω ≧ ω ₀ ) is input to the main system 1, the main system 1 and the additional system 2 are set using at least one of the following two methods. The purpose is to control both. The first method is a method for maximizing the damper power P ₂₁ consumed in the additional system 2. That is, in this way, to maximize the absolute value of the damper power P ₂₁ is a negative value. On the other hand, the second method is a method for minimizing the input power P ₁₁ input to the main system 1. That is, in this method, the absolute value of the input power P ₁₁ that is a positive value is made as small as possible.

[1-4. The first technique: maximization of the damper power P _21]
First, the first method will be described. From the above equation 12, when the damper power P ₂₁ is determined as s = λi (where i is an imaginary unit), the following equation 14 is obtained. However, λ and ω ₀ in Equation 14 are as shown in Equation 15 below. Note that λ is a frequency ratio indicating the ratio of the angular frequency ω of the input vibration f ₁ to the natural angular frequency ω ₀ of the main system 1.

  Further, when Equation 14 is transformed using the equations shown in Equation 17, Equation 16 below is obtained.

上記の式１６における振動パワーＰ₂₁を負の値にするとともにその絶対値を最大化することで、付加系２で消費されるダンパパワーＰ₂₁が最大となり、主系１及び付加系２の振動を抑制することが可能となる。ω≧ω₀（すなわちＬ≧１）の周波数帯では、相加平均と相乗平均との関係に基づいて以下の式１８が得られる。ただし、ａ≧０，ｃ≧０である。

By making the vibration power P ₂₁ in the above equation 16 negative and maximizing its absolute value, the damper power P ₂₁ consumed in the additional system 2 is maximized, and the vibrations of the main system 1 and the additional system 2 are maximized. Can be suppressed. In the frequency band of ω ≧ ω ₀ (that is, L ≧ 1), the following Expression 18 is obtained based on the relationship between the arithmetic mean and the geometric mean. However, a ≧ 0 and c ≧ 0.

Accordingly, the damper power P ₂₁ is maximized when a = 0 and c = 0. The damper power P _{21 at} this time (when a = 0, c = 0) is expressed by the following equation 19.

According to this equation 19, it can be seen that the damper power P ₂₁ has a negative value in the frequency band of ω ≧ ω ₀ (that is, L ≧ 1). This means that there exists a frequency ratio λ that maximizes the damper power P ₂₁ in this frequency band (ω ≧ ω ₀ ). That is, the damper power P ₂₁ is maximized in the frequency band of ω ≧ ω ₀ when a = 0 and c = 0. At this time (when a = 0, c = 0), the stiffness parameter p ₂₁ and the damping parameter z ₂₁ are given by the following equations 20 and 21 from the equations related to a and c in equation 17.

Therefore, in the first method, the stiffness parameter p ₂₁ and the damping parameter z _{21 at} which the damper power P ₂₁ is maximized in the frequency band of ω ≧ ω ₀ are expressed as a function of the mass ratio μ as shown in the above equations 20 and 21. Given. That is, when both the main system 1 and the additional system 2 are damped using the first method, the mass ratio μ of the first mass body 1A and the second mass body 2A is substituted into the equations 20 and 21, respectively. A stiffness parameter p ₂₁ and a damping parameter z ₂₁ that maximize the damper power P ₂₁ are calculated. Then, by substituting the calculated parameters p ₂₁ and z ₂₁ into equations relating to p and z shown in Equation 5, the second elastic coefficient k ₂ and the damping coefficient c ₂ of the additional system ₂ are calculated and designed.

Here, with reference to FIGS. 2 and 3, the damping performance of a model in which the additional system 2 (k ₂ , c ₂ ) designed by the first method is provided for the main system 1 is evaluated. FIG. 2 is a graph in which the horizontal axis represents the frequency ratio λ and the vertical axis represents the vibration power. The damper power P ₂₁ and the input power P ₁₁ when the first method is used are indicated by a solid line and a broken line, respectively. On the other hand, FIG. 3 is a graph in which the horizontal axis represents the frequency ratio λ and the vertical axis represents the compliance (damping performance, overall vibration), and the vibration damping when the additional system 2 is designed by the first method. The performance is shown by a solid line, and the damping performance when an additional system is designed by the conventional fixed point theory is shown by a broken line. In these figures, the calculation is made assuming that the mass ratio μ is 0.5.

According to FIG. 2, by using the first method, the damper power P ₂₁ becomes a negative value and the minimum value (the absolute value is the maximum) in the frequency band where the frequency ratio λ is 1 or more (that is, ω ≧ ω ₀ ). Value). Along with this, the input power P ₁₁ also decreases. Furthermore, according to FIG. 3, in the frequency band where the frequency ratio λ is 1 or more (ω ≧ ω ₀ ), the damping performance is improved when the first method is designed compared to the conventional method. I understand. That is, by designing the additional system 2 from the above equations 20 and ₂₁ , the damper power P ₂₁ can be maximized, and vibrations of the main system 1 and the additional system 2 can be suppressed.

[1-5. Second method: minimization of input power P ₁₁ ]
Next, the second method will be described. From the above Equation 13, when s = λi and the input power P ₁₁ is obtained, the following Equation 22 is given. Note that Equation 23 is obtained by transforming Equation 22 using Equation 17 above.

According to the above equations 22 and 23, the input power P ₁₁ is a positive value.
Here, when the stiffness parameter p is set to infinity (p → ∞) in Expression 9, the mobility M ₁₁ is expressed by Expression 24 below.

Therefore, when s = λi, the real part of Expression 24 is 0 according to Expression 13, and therefore the input power P ₁₁ is “P ₁₁ → 0”.
Similarly, when the attenuation parameter z is set to infinity (z → ∞) in Expression 9, the mobility M ₁₁ is expressed by Expression 25 below.

Therefore, also in this case, when s = λi, the real part of Expression 25 is 0 from Expression 13, and therefore the input power P ₁₁ becomes “P ₁₁ → 0”. That is, by setting the stiffness parameter p to infinity or setting the damping parameter z to infinity, the input power P ₁₁ is minimized (ie, substantially zero).

Here, FIG. 4 shows the input power P ₁₁ and the damper power P ₂₁ when the parameters p and z are designed to be infinite. FIG. 4 is a graph corresponding to FIG. According to FIG. 4, it can be seen that the input power P ₁₁ is a value near zero. Along with this, the damper power P ₂₁ is also a value near zero. That is, it can be seen that in order to minimize the input power P ₁₁ (that is, approximately 0), at least one of the two parameters p and z may be set to infinity.

Setting the stiffness parameter p infinity, means to set the second elastic coefficient k ₂ of the additional system 2 to infinity, this means that the first mass body 1A and the second mass body 2A This is equivalent to making it vibrate together. In other words, setting the stiffness parameter p to infinity, since that would increase the first mass m ₁ of the main system 1 minute only the second mass m ₂ of additional system 2, when the vibration f ₁ is input It is possible to suppress the overall vibration. In addition, setting the attenuation parameter z to infinity means setting the attenuation coefficient c ₂ of the additional system ₂ to infinity. In other words, when the damping parameter z is set to infinity, almost all the input vibration f ₁ can be absorbed, and the overall vibration can be suppressed.

However, in an actual design, the parameters p and z cannot be infinite (that is, k ₂ and c ₂ cannot be infinite). Therefore, in practice, at least one of the parameters p and z is set as large as possible in consideration of whether or not the overall vibration of the main system 1 and the additional system 2 (damping structure) falls within a predetermined range. To do. This predetermined range is set based on somatic sensation, for example. Somatosensory sensation is a combination of surface sensation (skin sensation) such as tactile sensation and pressure sensation that humans feel, and deep sensation such as motor sensation and deep pain. This is the sense of feeling the vibration coming in and the feeling of feeling the vibration transmitted from the in-vehicle equipment such as the engine or suspension device. Examples of the predetermined range set based on the somatic sensation include “a range where the vibration felt by the driver is not uncomfortable”. Thus, when based on somatic sensation, a predetermined range can be set by performing sensory evaluation (sensory test), simulation, or the like. Further, the predetermined range may be set based on performances required for the second elastic body 2B and the damper 2C (for example, elastic performance, damping performance, safety, reliability, etc.).

That is, in the second method, at least one of the two parameters p and z reduces the overall vibration of the damping structure (vibration after being damped by the second elastic body 2B and the damper 2C) within a predetermined range. It is set to as large a value as possible. In other words, when both the main system 1 and the additional system 2 are damped using the second method, at least one of the parameters p and z is set to the maximum value when the overall vibration falls within the predetermined range. Set. The larger the parameters p and z are set, the closer the input power P ₁₁ can be to zero.

Moreover, it is also possible to include the first method described above with respect to the second method described above. Specifically, the lower limit values of the stiffness parameter p and the damping parameter z are set to the stiffness parameter p ₂₁ and the damping parameter z _{21 at} which the damper power P ₂₁ becomes maximum in the frequency band of ω ≧ ω ₀ . That is, in the second method including the first method, the stiffness parameter p is set to a value equal to or greater than the stiffness parameter p ₂₁ given by the equation 20 while considering the overall vibration, and the damping parameter z is set to the equation. 21 is set to an attenuation parameter z ₂₁ or more given by ₂₁ .

When both the main system 1 and the additional system 2 are damped using such a second method, for example, the damping parameter z is given by Equation 21 (that is, z = z ₂₁ is set), and the stiffness parameter p is set. Is set to p ≧ p ₂₁ in consideration of the overall vibration. Alternatively, the stiffness parameter p is given by Equation 20 (that is, p = p ₂₁ is set), and the damping parameter z is set to z ≧ z ₂₁ in consideration of the overall vibration. Then, the second elastic coefficient k ₂ and damping coefficient c ₂ of the additional system ₂ are calculated and designed by substituting the set parameters p and z into equations relating to p and z shown in Expression 5.

Here, the damping performance when the additional system 2 is designed by the second method including the first method is shown by a thick solid line in FIG. 5 is a graph added with a thick solid line to the graph of FIG. According to FIG. 5, in the frequency band where the frequency ratio λ is 1 or more (ω ≧ ω ₀ ), the case where the second method including the first method is set is compared to the case where only the first method is used. It can be seen that the vibration control performance is further improved. That is, while either one of the parameters p ₂₁ and z ₂₁ given by the above equations 20 and 21 is set as the lower limit value, the other parameters p and z are set in consideration of the overall vibration, and the additional system 2 Is designed, it is possible to minimize the input power P ₁₁ while maximizing the damper power P ₂₁ , and to more effectively suppress the vibration of the main system 1 and the additional system 2.

[2. Device configuration]
The development support apparatus of the present embodiment is realized by a general-purpose computer capable of executing the above-described design processing computer program 17 (development support program). FIG. 6 is a schematic configuration diagram when a development support apparatus is configured using the computer 10.

  The computer 10 (development support device) includes a CPU 11 (Central Processing Unit), a memory 12 [Read Only Memory (ROM), Random Access Memory (RAM), etc.], an external storage device 13 [Hard Disk Drive (HDD), Solid State Drive (SSD), optical drive, flash memory, reader / writer, etc.], input device 14 (keyboard, mouse, etc.), output device 15 (display, printer device, etc.) and communication device 16 (wireless or wired transmission / reception device). These are connected to be communicable with each other via a bus 18 (control bus, data bus, etc.) provided in the computer 10. The computer program 17 is installed in the external storage device 13.

  The computer program 17 may be recorded in a recording medium 19 that can be read by an optical drive, a flash memory, a reader / writer, or the like. Alternatively, the computer program 17 may be recorded in an online storage on a network to which the computer 10 can be connected. In any case, it can be executed by downloading the computer program 17 to the HDD, SSD or the like of the computer 10 or by reading it into the CPU 11 or the memory 12.

The CPU 11 of this embodiment reads a program installed in the external storage device 13 on the memory 12 and executes it, and outputs a calculation result to the output device 15. Data necessary for the design process is set based on an input from the input device 14 or as a value given in advance. The data necessary for the design process includes the first mass m ₁ and the first elastic modulus k ₁ of the main system 1 and the second mass m ₂ of the additional system 2. If data such as the shape of each mass body 1A, 2A is required for modeling, data created by general-purpose three-dimensional CAD (Computer Aided Design) software can be used for the computer program 17, or It is set by input from the input device 14.

  The functions of the computer program 17 for executing the design process described above are schematically shown in FIG. The computer program 17 is provided with a construction unit 17a and a calculation unit 17b. Each of these elements may be realized by an electronic circuit (hardware), or a part of these functions may be provided as hardware and the other part may be software.

The construction unit 17a constructs a model of the above-described vibration damping structure. Further, when the angular frequency ω of the vibration f ₁ input to the main system 1 is a frequency band equal to or higher than the natural angular frequency ω ₀ , the calculation unit 17b performs at least one of the first method and the second method described above. The second elastic coefficient k ₂ and the damping coefficient c ₂ of the additional system ₂ are calculated.

In the present embodiment, a model of a vibration damping structure provided in a vehicle will be described as an example. The construction unit 17a of the present embodiment constructs a model in which the vehicle body as the second mass body 2A is connected to the wheel as the first mass body 1A via the suspension device as the second elastic body 2B and the damper 2C. To do. That is, in the model of the present embodiment, the main system 1 includes a wheel (first mass body 1A) and a tire (first elastic body 1B), and the additional system 2 includes a vehicle body (second mass body 2A), a suspension spring ( A second elastic body 2B) and a shock absorber (damper 2C). The fixed end E is a road surface, and the vibration f ₁ is road noise. The angular frequency ω of the road noise f ₁ is a high frequency band higher than the natural angular frequency ω ₀ of the main system 1 (ω> ω ₀ ).

Calculating unit 17b of the present embodiment, when the road noise f ₁ to the main system 1 which includes a wheel is inputted, a first approach to maximize the damper power P ₂₁ consumed by the suspension system, mainly An object is to both suppress the main system 1 and the additional system 2 by using the second method for minimizing the input power P ₁₁ input to the system 1. That is, the vibration of the vehicle body (the second mass body 2A of the additional system 2) is also suppressed by damping the wheel and the tire (main system 1) using the second technique in which the first technique is incorporated.

Calculation unit 17b, first, by substituting the mass ratio μ in the equation 20 and 21 of the damper power P ₂₁ in the frequency band of the omega ≧ omega ₀ is for calculating a stiffness parameter p ₂₁ and damping parameter z ₂₁ with the maximum . Next, with the calculated two parameters p ₂₁ and z ₂₁ as lower limit values, at least one of the stiffness parameter p and the damping parameter z is set to the maximum value when the overall vibration falls within a predetermined range. For example, the stiffness parameter p is set to a value as large as possible while keeping the vibration transmitted to the vehicle body within a predetermined range, and the damping parameter z is set to the calculated damping parameter z ₂₁ . Then, the second parameters of elasticity k ₂ and damping coefficient c ₂ of the additional system ₂ are calculated and designed by substituting the set parameters p and z into equations for p and z shown in Equation 5. The coefficients k ₂ and c ₂ designed by the calculation unit 17 b are stored in the external storage device 13 and output by the output device 15.

[3. flowchart]
FIG. 7 is a flowchart showing a procedure (development support method) when the computer 10 executes the computer program 17. As shown in FIG. 7, step S1 is an initial setting step. In this step S1, data necessary for the design process (first mass m ₁ , first elastic modulus k ₁ , second mass m _2, etc.) are prepared or input from the external storage device 13 or the input device 14. .

Step S2 is a step (building process) for building the above-described vibration damping structure model, and is performed by the building unit 17a described above. In step S2, a vibration damping structure model having the second mass body 2A provided via the second elastic body 2B and the damper 2C is constructed for the first mass body 1A.
Step S3 is a step (calculation step) for calculating the second elastic coefficient k ₂ and the damping coefficient c ₂ described above, and is performed by the calculation unit 17b described above. In this step S3, when the angular frequency ω of the vibration f ₁ input to the main system 1 is a frequency band equal to or higher than the natural angular frequency ω ₀ , at least one of the first method and the second method is used. A second elastic coefficient k ₂ and a damping coefficient c ₂ are calculated. In step S4, these coefficients k ₂ and c ₂ are stored and output.

[4. effect]
(1) In the development support method, the development support apparatus 10 and the development support program 17 described above, when the frequency band is ω ≧ ω ₀ , the first method for maximizing the damper power P ₂₁ and the minimum input power P ₁₁ are minimized. Since the coefficients k ₂ and c _{2 of} the additional system ₂ are calculated using at least one of the second method to be realized, the vibration damping performance in this frequency band can be improved. Thereby, the vibration of the damping structure (damping target object) can be suppressed.

Furthermore, the coefficient k ₂ of the additional system 2 can be obtained by maximizing the damper power P ₂₁ consumed in the additional system 2, minimizing the input power P ₁₁ input to the main system 1, or a combination thereof. , C ₂ are designed, vibration that may occur can be suppressed. That is, according to the present development support method, apparatus 10, and program 17, in order to deal directly with the vibration power P, as is apparent from FIGS. Compared with the conventional method (fixed point theory) of suppressing vibration, overall vibration (mechanical compliance) can be reduced, and overall vibration can be effectively suppressed.

(2) In the first method described above, the stiffness parameter p ₂₁ and the damping parameter z ₂₁ at which the damper power P ₂₁ is maximum in the frequency band of ω ≧ ω ₀ are represented by the mass ratio μ as shown in the equations 20 and 21 above. Is given as a function of Therefore, if the mass ratio μ (= m ₂ / m ₁ ) is determined, the stiffness parameter p ₂₁ and the damping parameter z _{21 at} which the damper power P ₂₁ is maximized can be determined. As a result, the coefficients k ₂ and c ₂ of the additional system 2 that maximizes the damper power P ₂₁ in the above frequency band can be easily designed, and the damping performance in this frequency band can be improved.

(3) According to the second method described above, the stiffness parameter p is set to the maximum value when the overall vibration falls within the predetermined range, so that the input power P ₁₁ can be made as small as possible. That is, in the second method, the input power P ₁₁ itself of the vibration f _{1 serving as} the vibration source can be reduced, so that the vibration of the damping structure can be suppressed. In addition, the input power P ₁₁ can be reduced as much as possible by setting the damping parameter z to the maximum value when the overall vibration falls within a predetermined range, thereby suppressing the vibration of the damping structure. Can do. In these cases, by setting the predetermined range based on the somatic sensation, the stiffness parameter p can be set in consideration of the sensation actually felt by humans.

(4) Further, in the second method described above, p ₂₁ the lower limit of the stiffness parameter p, the damper power P ₂₁ in the frequency band of the omega ≧ omega ₀ is given by the stiffness parameter p ₂₁ (i.e. formula 20, which becomes the maximum ). Thus, by including a part of the first method in the second method, it is possible to further improve the vibration damping performance, and to more effectively suppress the vibration. The damping performance can also be set by setting the lower limit value of the damping parameter z to the damping parameter z ₂₁ (that is, z ₂₁ given by Equation ₂₁ ) that maximizes the damper power P ₂₁ in the frequency band of ω ≧ ω _0. Can be further increased, and vibration can be more effectively suppressed.

(5) As illustrated in the present embodiment, the vehicle body as the second mass body 2A is connected to the wheel as the first mass body 1A via the suspension device as the second elastic body 2B and the damper 2C. When the model is constructed, even if the road noise f ₁ is input from the road surface, both the main system 1 and the additional system 2 can be controlled, so that the vibration of the vehicle body can be suppressed.

[5. Others]
Although the embodiments of the present invention have been described above, the present invention is not limited to the above-described embodiments, and various modifications can be made without departing from the spirit of the present invention.
The specific content of the development support method described above is an example, and is not limited to the above. For example, in the calculation of the coefficients k ₂ and c ₂ of the additional system 2, only the first method may be used, and when the second method is used, either one of the stiffness parameter p and the damping parameter z is used. The first method may be included only in setting the lower limit value. Alternatively, the first method may not be included in the second method. That is, the lower limit values of the parameters p and z are not particularly set, and any of the parameters p and z may be set as large as possible.

The above-described vibration damping structure (wheel, vehicle body, etc.) is an example, and the vibration damping structure is not limited to that applied to a vehicle. If the vibration damping structure has at least the second mass body 2A provided via the second elastic body 2B and the damper 2C with respect to the first mass body 1A, the natural angular frequency of the main system 1 is obtained by this design process. When a vibration f ₁ having an angular frequency ω equal to or higher than ω ₀ is input, vibrations of the main system 1 and the additional system 2 can be suppressed.

1 main system 1A first mass body 1B first elastic body 2 additional system, dynamic vibration absorber 2A second mass body 2B second elastic body 2C damper (attenuator)
10 Computer (Development support device)
11 CPU
12 memory 13 external storage device 14 input device 15 output device 16 communication device 17 computer program (development support program)
18 bus 19 recording medium m ₁ first mass m ₂ second mass k ₁ first elastic coefficient k ₂ second elastic coefficient c ₂ damping coefficient P vibration power P ₁₁ input power (first vibration power)
P ₂₁ damper power (second vibration power)
f ₁ vibration, road noise ω angular frequency of vibration f ₁ ω ₀ natural angular frequency of main system 1 p stiffness parameter p ₂₁ ω ≧ ω ₀ , damper parameter P ₂₁ stiffness parameter z damping parameter z ₂₁ ω ≧ ω Damping parameter that maximizes damper power P _{21 at 0} λ Frequency ratio μ Mass ratio x ₀ Position at rest x ₁ Displacement of first mass x ₂ Displacement of second mass M ₁₁ , M ₂₁ transfer function ( Mobility)

Claims (9)

A damping structure in which a main system having a first mass body and a first elastic body is connected to an additional system having a second mass body, a second elastic body, and an attenuator to form a passive dynamic vibration absorber. A development support method for causing a computer to execute a process of designing the dynamic vibration absorber,
A construction step of constructing a model of the damping structure having the second mass body provided via the second elastic body and the attenuator for the first mass body;
The first method for maximizing the first vibration power consumed in the additional system when the angular frequency of vibration input to the main system is a frequency band equal to or higher than the natural angular frequency of the main system, and the main system A calculation step of calculating an elastic coefficient of the second elastic body and a damping coefficient of the attenuator using at least one of the second method of minimizing the second vibration power input to
A development support method for a dynamic vibration absorber, comprising: In the first method, the stiffness parameter and the damping parameter at which the first vibration power is maximized in the frequency band are expressed by the first mass body and the second mass body as shown by the following formulas A and B. The dynamic vibration absorber development support method according to claim 1, wherein the dynamic vibration absorber development support method is given as a function of a mass ratio.

In the second method, the stiffness parameter relating to the stiffness ratio between the main system and the additional system is set to a maximum value when the overall vibration of the damping structure falls within a predetermined range. The method for supporting development of a dynamic vibration absorber according to claim 1 or 2. 4. The dynamic vibration absorber development according to claim 3, wherein in the second method, the lower limit value of the stiffness parameter is set to a stiffness parameter that maximizes the first vibration power in the frequency band. Support method. In the second method, the damping parameter relating to the damping performance of the additional system is set to a maximum value when the overall vibration of the damping structure falls within a predetermined range. The development support method of the dynamic vibration absorber of any one of -4. 6. The dynamic vibration absorber according to claim 5, wherein in the second method, the lower limit value of the damping parameter is set to a damping parameter that maximizes the first vibration power in the frequency band. Support method. 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 device as the second elastic body and the attenuator is constructed. The dynamic vibration absorber development support method according to claim 1, wherein the dynamic vibration absorber is developed. A damping structure in which a main system having a first mass body and a first elastic body is connected to an additional system having a second mass body, a second elastic body, and an attenuator to form a passive dynamic vibration absorber. , A development support apparatus for executing a process of designing the dynamic vibration absorber,
A construction part for constructing a model of the damping structure having the second mass body provided via the second elastic body and the attenuator with respect to the first mass body,
The first method for maximizing the first vibration power consumed in the additional system when the angular frequency of vibration input to the main system is a frequency band equal to or higher than the natural angular frequency of the main system, and the main system Using at least one of the second method for minimizing the second vibration power input to the calculation unit, calculating the elastic coefficient of the second elastic body and the attenuation coefficient of the attenuator,
A dynamic vibration absorber development support device characterized by comprising: A damping structure in which a main system having a first mass body and a first elastic body is connected to an additional system having a second mass body, a second elastic body, and an attenuator to form a passive dynamic vibration absorber. , A development support program for executing a process of designing the dynamic vibration absorber,
A construction step of constructing a model of the damping structure having the second mass body provided via the second elastic body and the attenuator for the first mass body;
The first method for maximizing the first vibration power consumed in the additional system when the angular frequency of vibration input to the main system is a frequency band equal to or higher than the natural angular frequency of the main system, and the main system A calculation step of calculating an elastic coefficient of the second elastic body and a damping coefficient of the attenuator using at least one of the second method of minimizing the second vibration power input to
A dynamic vibration absorber development support program, characterized in that a computer is executed.

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