WO2022073152A1 - 一种惯性比自适应调节惯容器的设计方法 - Google Patents

一种惯性比自适应调节惯容器的设计方法 Download PDF

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WO2022073152A1
WO2022073152A1 PCT/CN2020/119818 CN2020119818W WO2022073152A1 WO 2022073152 A1 WO2022073152 A1 WO 2022073152A1 CN 2020119818 W CN2020119818 W CN 2020119818W WO 2022073152 A1 WO2022073152 A1 WO 2022073152A1
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flywheel
inertia
inertial
mass
mass block
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PCT/CN2020/119818
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English (en)
French (fr)
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孙希明
段楠
吴玉虎
仲崇权
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大连理工大学
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Priority to US17/430,548 priority Critical patent/US11965578B2/en
Priority to PCT/CN2020/119818 priority patent/WO2022073152A1/zh
Publication of WO2022073152A1 publication Critical patent/WO2022073152A1/zh

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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F15/00—Suppression of vibrations in systems; Means or arrangements for avoiding or reducing out-of-balance forces, e.g. due to motion
    • F16F15/30—Flywheels
    • F16F15/31—Flywheels characterised by means for varying the moment of inertia
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F15/00—Suppression of vibrations in systems; Means or arrangements for avoiding or reducing out-of-balance forces, e.g. due to motion
    • F16F15/10—Suppression of vibrations in rotating systems by making use of members moving with the system
    • F16F15/12—Suppression of vibrations in rotating systems by making use of members moving with the system using elastic members or friction-damping members, e.g. between a rotating shaft and a gyratory mass mounted thereon
    • F16F15/131—Suppression of vibrations in rotating systems by making use of members moving with the system using elastic members or friction-damping members, e.g. between a rotating shaft and a gyratory mass mounted thereon the rotating system comprising two or more gyratory masses
    • F16F15/133—Suppression of vibrations in rotating systems by making use of members moving with the system using elastic members or friction-damping members, e.g. between a rotating shaft and a gyratory mass mounted thereon the rotating system comprising two or more gyratory masses using springs as elastic members, e.g. metallic springs
    • F16F15/1333—Spiral springs, e.g. lying in one plane, around axis of rotation
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F15/00—Suppression of vibrations in systems; Means or arrangements for avoiding or reducing out-of-balance forces, e.g. due to motion
    • F16F15/10—Suppression of vibrations in rotating systems by making use of members moving with the system
    • F16F15/12—Suppression of vibrations in rotating systems by making use of members moving with the system using elastic members or friction-damping members, e.g. between a rotating shaft and a gyratory mass mounted thereon
    • F16F15/131—Suppression of vibrations in rotating systems by making use of members moving with the system using elastic members or friction-damping members, e.g. between a rotating shaft and a gyratory mass mounted thereon the rotating system comprising two or more gyratory masses
    • F16F15/133—Suppression of vibrations in rotating systems by making use of members moving with the system using elastic members or friction-damping members, e.g. between a rotating shaft and a gyratory mass mounted thereon the rotating system comprising two or more gyratory masses using springs as elastic members, e.g. metallic springs
    • F16F15/134—Wound springs
    • F16F15/13469—Combinations of dampers, e.g. with multiple plates, multiple spring sets, i.e. complex configurations
    • F16F15/13476—Combinations of dampers, e.g. with multiple plates, multiple spring sets, i.e. complex configurations resulting in a staged spring characteristic, e.g. with multiple intermediate plates
    • F16F15/13484—Combinations of dampers, e.g. with multiple plates, multiple spring sets, i.e. complex configurations resulting in a staged spring characteristic, e.g. with multiple intermediate plates acting on multiple sets of springs
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F15/00—Suppression of vibrations in systems; Means or arrangements for avoiding or reducing out-of-balance forces, e.g. due to motion
    • F16F15/10—Suppression of vibrations in rotating systems by making use of members moving with the system
    • F16F15/12—Suppression of vibrations in rotating systems by making use of members moving with the system using elastic members or friction-damping members, e.g. between a rotating shaft and a gyratory mass mounted thereon
    • F16F15/131—Suppression of vibrations in rotating systems by making use of members moving with the system using elastic members or friction-damping members, e.g. between a rotating shaft and a gyratory mass mounted thereon the rotating system comprising two or more gyratory masses
    • F16F15/139—Suppression of vibrations in rotating systems by making use of members moving with the system using elastic members or friction-damping members, e.g. between a rotating shaft and a gyratory mass mounted thereon the rotating system comprising two or more gyratory masses characterised by friction-damping means
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design

Definitions

  • the invention belongs to the technical field of controller structure design and analysis in a control system, and relates to the design of an inertial ratio self-adaptive adjustment inertial container, and the simulation verification of the inertial container is carried out.
  • the inertial container is a mechanical structure that can provide an inertia ratio far exceeding its structural mass. It has been widely studied in vibration control in the fields of vehicle suspension systems, bridges, buildings, and machinery. Due to its large inertia ratio and small structural mass, the inertial container has unparalleled advantages in reducing the structural mass of the vibration controller. At present, the inertial container mainly uses the effect that the moment of inertia of the structure is greater than the inertia caused by its mass, and then further increases its inertia ratio by using structures such as gears or ball screws. However, the inertia ratio of this type of inertial container is a fixed value, and it is difficult to make necessary adjustments to follow the change of the vibration of the main structure.
  • the invention designs an inertial container whose rotational inertia can adaptively adjust the inertia ratio according to the change of the vibration response of the main structure.
  • the invention is based on the ball screw-flywheel inertia container, by reducing the basic moment of inertia of the flywheel, and adding a spring-mass block structure with high density and radial movement of the flywheel on the disk surface of the flywheel, using the mass block when the flywheel rotates
  • the force balance between the centrifugal force and the spring restoring force changes the radial distance between the mass center of the mass block and the rotation center, so as to realize the adaptive adjustment of the flywheel rotational inertia according to the vibration of the main structure, and then achieve the purpose of automatically adjusting the inertia ratio of the inertial container.
  • the feasibility and effectiveness of the present invention are verified by the simulation method. So far, no patent discloses the design of the inertial ratio adaptively adjusting
  • the present invention designs an inertial container with an adaptively adjusted inertia ratio.
  • the present invention changes the flywheel of the original lead screw-flywheel inertial container into two parts, the basic moment of inertia and the adjustable moment of inertia, through the analysis of the inertia demand in the vibration control process and the understanding of the principle of the inertia container.
  • the basic moment of inertia part is a general flywheel, on which a mounting mechanism for installing the adjustable moment of inertia part is processed.
  • the basic moment of inertia part uses low density and sufficient strength. Made of aluminum alloy.
  • the adjustable moment of inertia is partly based on the design of the spring-mass block structure, and the distance between the mass center of the mass block and the rotation center of the flywheel is automatically adjusted by using the force balance between the centrifugal force received by the mass block when the flywheel rotates and the spring restoring force, so as to realize the rotation of the flywheel. Automatic adjustment of inertia.
  • the material of the mass block is made of copper or copper alloy with high density and good self-lubricating properties.
  • the change of inertia ratio with external force load is simulated by numerical method to verify the feasibility and effectiveness of the present invention.
  • a design method for an inertial ratio adaptively adjusting inertial container comprising the following steps:
  • Step 1 Basic theoretical design of inertial ratio adaptive adjustment inertial container
  • the left side of the equal sign is the inertial force on the mass block;
  • the first item on the right side of the equal sign is the centrifugal force on the mass block, and the second item on the right side of the equal sign is the restoring force of the spring;
  • m is the mass of the mass block,
  • ⁇ (t) is the angular velocity of the flywheel,
  • R(t) is the distance from the center of mass of the mass block to the center of rotation of the flywheel (that is, the radius of rotation),
  • k is the stiffness coefficient of the spring,
  • R 0 is the minimum distance between the center of mass of the mass block and the center of rotation of the flywheel, and
  • t is the time variable.
  • p is the pitch of the lead screw
  • F l (t) is the load on the lead screw
  • J (t) is the moment of inertia of the flywheel, expressed as:
  • J 0 is the fixed moment of inertia of the flywheel;
  • the second term on the right side of the equation represents the adjustable moment of inertia of the flywheel, where n is the number of spring-mass structures, considering the symmetry and rotational balance, n is taken as 2 integer multiples.
  • Step 2 Structural theoretical design of the flywheel with adjustable moment of inertia of inertial ratio adaptive adjustment inertia container
  • the purpose of the present invention is to adjust the inertia ratio of the inertial container within a large range. It can be seen from formula (4) that to achieve this purpose, it is necessary to make the fixed moment of inertia J 0 of the flywheel as small as possible, and to increase the mass m of the mass block. Considering the flywheel as a homogeneous disk rotating around the center with a fixed axis, its fixed moment of inertia is expressed by the following formula:
  • the main part of the flywheel of the present invention is made of aluminum alloy with lower density, and a part of the material of the flywheel disk surface is removed to further reduce the fixed moment of inertia of the flywheel.
  • the mass m and the number n of the mass block is to increase the adjustable inertia ratio of the inertial container. reasonable way.
  • the material of the mass block is determined as copper.
  • Step 3 Structural Design of Inertial Vessel Adaptive Adjustable Flywheel Based on The Above Theory
  • the inertial container designed by the present invention mainly includes the following core components: a casing 3 , a lead screw 4 , a flywheel 5 and a nut 6 .
  • the nut 6 is fixedly connected with the flywheel 5 and the axis of the nut is coaxial with the rotation center of the flywheel; the top end of the lead screw 4 is the end point B2 of the inertial container, the lead screw 4 is connected with the nut 6, and the lead screw 4 and the nut 6 are composed of
  • the screw-nut motion pair converts the linear motion received by the end point B2 of the inertial container into the rotational motion of the flywheel.
  • Said flywheel 5 includes a basic part 9 of the flywheel, a spring 7 and a mass 8 .
  • the basic part 9 of the flywheel is formed by removing a part of the material of the disk surface of the flywheel 5; the flywheel 5 is provided with a plurality of guide grooves in the radial direction, and the mass block 8 is installed in the guide groove and can move linearly along the radial direction of the flywheel.
  • One end of the spring 7 is connected to the mass block 8, and the other end is connected to the side of the guide groove close to the rotation center of the flywheel, which provides the mass block with a pulling force directed to the rotation center of the flywheel.
  • the casing 3 is a hollow structure, which encloses the structure composed of the flywheel 5, the nut 6 and the lead screw 4, so as to provide a relatively sealed and clean environment for the flywheel part of the inertial container, and reduce the work of the inertial container. of external interference.
  • the present invention designs the basic structure of the lead screw-flywheel inertia container with self-adaptive and adjustable inertia ratio, which can provide reference and guidance for subsequent similar inventions and applications;
  • the inertial container is simulated accordingly.
  • the results show that the inertial container designed by the present invention can automatically adjust the inertia ratio of the inertial container according to the change of the load. This performance is exactly what some passive vibration controllers need. .
  • FIG. 1 is a schematic diagram of the structure of an inertial ratio adaptively adjusting inertial container.
  • FIG. 2 is a schematic structural diagram of the self-adaptive adjustment flywheel of the moment of inertia.
  • Figure 3 is the harmonic signal of the simulated external load in the simulation.
  • Fig. 4 is the change of the moment of inertia of the inertial container designed by the present invention under the simulated external load.
  • Fig. 5 is the change of inertia ratio of the inertial container designed by the present invention under simulated external load.
  • Step 1 Establish the mathematical model of the adaptive adjustable structure of the inertial ratio of the adaptive inertial container.
  • the physical structure of the adaptive inertial container is shown in Figure 1.
  • the external force load is converted into the torque received by the flywheel, which in turn drives the flywheel to rotate.
  • the flywheel rotates at an angular velocity ⁇ (t)
  • the centrifugal force F c (t) on the mass m is expressed as
  • a is the acceleration of mass m in the radial direction of the flywheel.
  • N(t) is the total external torque
  • Equation (6) is the external force load on the screw.
  • Equation (6) is the motion equation of the flywheel under the action of external force.
  • the moment of inertia J(t) of the flywheel in formula (6) is composed of the fixed moment of inertia and the adjustable moment of inertia of the flywheel, namely
  • Equations (4), (7) and (8) are the basic principle and theoretical basis for the self-adaptive adjustment of the rotational inertia of the inertial vessel designed in the present invention, and then the inertia ratio of the inertial vessel can be obtained as:
  • Step 2 Considering that the main purpose of the present invention is to realize the self-adaptive adjustment of the inertia ratio of the inertial vessel in a relatively large range, that is, to realize the self-adaptive adjustment of the rotational inertia of the flywheel.
  • the flywheel rotating around the center can be regarded as a disk rotating around the center with a uniform density distribution, then the moment of inertia of its fixed moment of inertia part (the basic part 9 of the flywheel in Figure 2) can be expressed as
  • the material used for the basic part 9 of the flywheel in the inertial container of the present invention is aluminum alloy, and its density is 2.7 g/cm 3 .
  • Step 3 Structural Design of Inertial Vessel Adaptive Adjustable Flywheel Based on The Above Theory
  • the designed inertial container mainly includes the following core components: shell 3 , lead screw 4 , flywheel 5 and nut 6 .
  • the nut 6 is fixedly connected with the flywheel 5 and the axis of the nut is coaxial with the rotation center of the flywheel (as shown in the position of the nut 6 in FIG. 2 ), and the nut 6 and the lead screw 4 form a lead screw-nut motion pair, the purpose is to The linear motion received by the end point B of the inertial container is converted into the rotational motion of the flywheel.
  • the flywheel 5 consists of a basic part 9 of the flywheel, a spring 7 and a mass 8 .
  • the mass block 8 is installed in the radially opened guide groove on the flywheel 5, and the mass block 8 can move linearly along the radial direction of the flywheel.
  • One end of the spring 7 is connected to the mass block 8, and the other end is connected to the side of the guide groove close to the rotation center of the flywheel, which provides the mass block with a pulling force directed to the rotation center of the flywheel.
  • the shell 3 is a hollow structure, and its purpose is to provide a relatively sealed and clean environment for the flywheel part of the inertial container, and reduce the external interference when the inertial container is working; another function of the shell 3 is to facilitate the operation of the inertial container. Therefore, the structure of the casing is not fixed, and can be designed according to the actual use requirements and installation conditions, and there is no unified style, material and other requirements. illustrate.
  • F 1 (t) and F 2 (t) are the external force loads suffered by the end point A1 of the inertial container and the end point B2 of the inertial container designed by the present invention, respectively.
  • the external force load is set to the harmonic load as shown in Figure 3, and the harmonic amplitude is 10N.
  • the inertia ratio b v of the inertial container is simulated as shown in FIG. 5 . It can be seen from Fig. 3 that with the change of the external force load, the inertia ratio of the adaptive inertial container designed by the present invention is adaptively adjusted within a large range (89.8kg ⁇ 279.6kg), indicating that the inertial container can meet the requirements of the external force
  • the design purpose of load adaptive adjustment of inertia ratio is

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Abstract

公开了一种惯性比自适应调节惯容器的设计方法，属于控制系统设计中的控制器结构设计与分析技术领域。本方法基于丝杠-飞轮惯容器，通过改变飞轮上质量块沿飞轮径向的位置，从而实现飞轮转动惯量的变化，进而实现惯容器惯性比的自适应调节。具体地，丝杠所受外力载荷的变化引起飞轮角速度的变化，角速度改变了弹簧-质量块结构中质量块所受的离心力，由离心力与弹簧恢复力的平衡关系确定质量块在飞轮径向的位置，从而达到了设计目的；并通过数值方法验证了本方法可以实现惯性比随外力载荷变化的自适应调节。本方法首次设计了惯性比自适应调节惯容器的结构，并首次建立了惯性比自适应调节的理论原理。

Description

一种惯性比自适应调节惯容器的设计方法 技术领域
本发明属于控制系统中的控制器结构设计与分析技术领域，涉及一种惯性比自适应调节惯容器的设计，并对该惯容器进行仿真验证。
背景技术
惯容器是一种能够提供远超其结构质量的惯性比的机械结构，已经在车辆悬挂系统、桥梁、建筑物及机械等领域的振动控制中得到了广泛地研究。惯容器以其惯性比大、结构质量小的特点，在减小振动控制器结构质量方面有着无可比拟的优势。目前，惯容器主要是通过利用结构的转动惯量大于其质量带来的惯性这一效应，再通过使用齿轮或者滚珠丝杠等结构进一步增大其惯性比。但是这类惯容器的惯性比都是定值，难以跟随主结构振动情况的变化而做出必要的调整，存在惯性比不可调等不足，难以达到最佳的振动控制效果。本发明基于振动控制对系统惯性的需求，设计了一款转动惯量可依据主结构振动响应的变化自适应调节惯性比的惯容器。本发明是在滚珠丝杠-飞轮惯容器的基础上，通过降低飞轮的基本转动惯量，并在飞轮盘面上增加了密度大、飞轮径向移动的弹簧-质量块结构，利用飞轮转动时质量块受到的离心力与弹簧恢复力之间的力平衡改变质量块质心与转动中心的径向距离，从而实现根据主结构的振动情况自适应调节飞轮转动惯量，进而达到自动调节惯容器惯性比的目的。最后利用仿真方法验证了本发明的可行性与有效性。目前为止，没有专利公开关于惯性比自适应调节惯容器的设计。
发明内容
为了更好地解决在振动控制过程中，控制器对可变惯性的需求，本发明设 计了一种惯性比自适应调节的惯容器。
本发明通过振动控制过程中对惯性的需求分析，以及对惯容器原理的理解，将原始的丝杠-飞轮惯容器的飞轮改为基础转动惯量和可调转动惯量两部分。其中，基础转动惯量部分为一般的飞轮，其上加工了用于安装可调转动惯量部分的安装机构，同时为了增大整体转动惯量的变化范围，基础转动惯量部分使用密度小且有足够强度的铝合金加工而成。所述可调转动惯量部分基于弹簧-质量块结构设计，利用质量块在飞轮旋转时受到的离心力与弹簧恢复力之间的力平衡自动调节质量块质心与飞轮转动中心的距离，实现对飞轮转动惯量的自动调节。考虑到要增大转动惯量的可调范围，质量块材料选用密度较大且具有良好的自润滑特性的铜或铜合金加工而成。最后，利用数值方法仿真了惯性比随外力载荷的变化情况以验证本发明的可行性及有效性。
本发明的技术方案为：
一种惯性比自适应调节惯容器的设计方法，包括以下步骤：
步骤1：惯性比自适应调节惯容器的基本理论设计
所述惯容器中可调转动惯量结构的理论基础为，弹簧-质量块结构在飞轮旋转时质量块所受离心力与弹簧恢复力之间的力平衡，其运动方程表示为如下形式：
Figure PCTCN2020119818-appb-000001
其中，等号左边为质量块所受惯性力；等号右边第一项为质量块所受的离心力，等号右边第二项为弹簧的恢复力；m为质量块的质量，ω(t)为飞轮的角速度，R(t)为质量块质心到飞轮转动中心的距离(即转动半径)，k为弹簧的劲度系数，R 0为质量块质心与飞轮转动中心的最小距离，t为时间变量。
基于丝杠-螺母运动副的运动原理，飞轮的角速度ω(t)与丝杠所受载荷之间运动方程表示为如下微分方程形式：
Figure PCTCN2020119818-appb-000002
其中，p为丝杠的螺距；F l(t)为丝杠所受的载荷；J(t)为飞轮的转动惯量，表示为：
J(t)＝J 0+nmR 2(t)         (3)
其中，J 0为飞轮的固定转动惯量；等式右边第二项表示飞轮的可调转动惯量部分，其中n为弹簧-质量块结构的数量，考虑到对称性和转动的平衡，n取2的整数倍。
联合式(1)-(3)得到本发明惯容器的自适应惯性比为：
Figure PCTCN2020119818-appb-000003
以上为所设计的惯容器惯性比自适应调节的理论原理。
步骤2：惯性比自适应调节惯容器可调转动惯量飞轮的结构理论设计
本发明的目的是在较大的范围内调节惯容器的惯性比。由式(4)可知，要实现此目的，需要使飞轮的固定转动惯量J 0尽量小，并且增大质量块的质量m。将飞轮看作是绕中心做定轴转动的匀质圆盘，则其固定转动惯量用下式表示：
Figure PCTCN2020119818-appb-000004
式中，r为飞轮的半径，ρ为飞轮的密度，V为飞轮的总体积。结合式(4)和(5)可知，在飞轮半径不变的情况下，可以通过使用密度较小的材料，并减小飞轮的体积来减小飞轮的固定转动惯量J 0。因此，本发明的飞轮主体部分采用密度较小的铝合金加工而成，并去除了飞轮盘面的一部分材料以进一步减小飞轮的 固定转动惯量。
为获得较大的惯性比可调节范围，根据式(3)，并充分考虑惯容器的尺寸限制、飞轮回转半径等约束问题，增加质量块的质量m和数量n是增加惯容器可调惯性比的合理途径。在综合考虑常用材料的密度、成本、可加工性、自润滑性等性能后，质量块的材料定为铜。
步骤3：基于上述理论的惯容器自适应可调飞轮的结构设计
本发明所设计的惯容器主要包括如下核心部件：壳体3、丝杠4、飞轮5和螺母6。
其中，螺母6与飞轮5固连且螺母的轴线与飞轮的转动中心同轴；所述丝杠4的顶端为惯容器的端点B2，丝杠4与螺母6连接，丝杠4与螺母6组成丝杠-螺母运动副，将惯容器的端点B2受到的直线运动转换为飞轮的旋转运动。
所述飞轮5包括飞轮的基本部分9、弹簧7和质量块8。其中，飞轮的基本部分9通过去除飞轮5盘面的一部分材料构成；飞轮5沿径向开有多个导向槽，质量块8安装导向槽内，并能沿飞轮的径向做直线运动。弹簧7一端与质量块8连接，另一端与导向槽靠近飞轮转动中心的一侧相连，为质量块提供指向飞轮转动中心的拉力。
所述壳体3为空心结构，其将飞轮5、螺母6及丝杠4组成的结构包裹在内，从而给惯容器的飞轮部分提供一个相对密封且干净的环境，减少惯容器工作时所受的外界干扰。
步骤4：仿真验证
由于(1)和(2)为复杂的微分方程，其解析解难以获得，为了验证本发明的可行性，搭建了自适应惯容器的MATLAB/Simulink仿真模型，并用模拟的载荷信号对本发明进行了相应的验证。仿真结果表明，本发明能够对其所受外载荷的 变化做出相应的响应，达到了设计目的。
本发明的有益效果：
1)基于离心力和弹簧恢复力的动力学特性，建立了自适应惯容器对其所受载荷变化而自适应调节惯性比的理论基础，该理论基础能够有效地支撑起自适应惯容器的设计及后续相关的适应性改进需求；
2)基于惯性比自适应调节的理论基础，本发明设计了惯性比自适应可调的丝杠-飞轮惯容器基本结构，能够对后续类似的发明及应用提供借鉴和指导；
3)基于模拟载荷信号对惯容器做了相应的仿真，结果表明本发明所设计的惯容器能够根据载荷的变化情况自动调节惯容器的惯性比，这个性能恰是一些被动振动控制器所需要的。
附图说明
图1是惯性比自适应调节惯容器的结构示意图。
图2是转动惯量自适应调节飞轮的结构示意图。
图3是仿真中模拟外载荷的谐波信号。
图4是本发明设计的惯容器在模拟外载荷下转动惯量的变化情况。
图5是本发明设计的惯容器在模拟外载荷下惯性比的变化情况。
图中：1惯容器的端点A；2惯容器的端点B；3壳体；4丝杠；5飞轮；6螺母；7弹簧；8质量块；9飞轮的基本部分。
具体实施方式
以下结合附图和自适应惯性比理论基础的推导过程，详细说明本发明的具体设计及实施方式。
本实施例的具体过程是针对图1所示自适应惯容器结构所进行，详细设计步骤如下：
步骤1：建立自适应惯容器惯性比自适应可调结构的数学模型，如图1所示自适应惯容器的物理结构，当惯容器的端点A1和惯容器的端点B2受到外力载荷时，在丝杠-螺母运动副的作用下，外力载荷转换为飞轮受到的扭矩，进而带动飞轮转动。当飞轮以角速度ω(t)转动时，质量块m受到的离心力F c(t)表示为
F c(t)＝mω 2(t)R(t)        (1)
考虑到质量块m沿飞轮径向运动时所受的弹簧恢复力F k(t)为
F k(t)＝k[R(t)-R 0]         (2)
由牛顿运动定律可以得到，质量块m在飞轮转动时所受合外力如下
Figure PCTCN2020119818-appb-000005
其中，a为质量块m在飞轮径向方向的加速度。
将式(1)和(2)代入(3)式得到飞轮在水平面内转动时的运动方程
Figure PCTCN2020119818-appb-000006
为了得到飞轮的角速度ω(t)，需要得到飞轮在外力载荷下的运动方程。对于飞轮存在如下关系
J(t)β＝N(t)         (5)
式中，β为飞轮的角加速度且
Figure PCTCN2020119818-appb-000007
N(t)为合外力矩，考虑到丝杠-螺母运动副特性可得N(t)为
Figure PCTCN2020119818-appb-000008
其中，F l(t)为丝杠所受外力载荷。将式(6)及β代入式(5)得到外力作用下飞轮的运动方程为
Figure PCTCN2020119818-appb-000009
式(6)中飞轮的转动惯量J(t)由飞轮的固定转动惯量和可调转动惯量两部分组成，即
J(t)＝J 0+nmR 2(t)        (8)
式(4)、(7)和(8)即为本发明所设计惯容器的转动惯量自适应可调的基本原理和理论基础，进而可得惯容器的惯性比为
Figure PCTCN2020119818-appb-000010
至此，得到本发明所设计惯容器惯性比随载荷自适应调节的基本原理。
步骤2：考虑到本发明的主要目的是在较大的范围内实现惯容器惯性比的自适应可调，即实现飞轮的转动惯量自适应可调。绕中心转动的飞轮可以认为是一个密度均匀分布的绕中心转动的圆盘，则其固定转动惯量部分(如图2中飞轮的基本部分9)的转动惯量可以表示为
Figure PCTCN2020119818-appb-000011
结合式(8)可知，减小基础转动惯量J 0能够有利于增大飞轮整体的转动惯量J(T)可调范围。考虑式(10)，在回转半径r给定的情况下，飞轮的基本转动惯量可以通过减小飞轮体积V以及使用密度ρ更小的材料来实现降低基本转动惯量J 0的目标。
因此，本发明惯容器中飞轮的基本部分9采用的材料为铝合金，其密度为2.7g/cm 3。为了进一步的减小飞轮的基本转动惯量，并在保证飞轮结构具有足够的强度的条件下，去除了飞轮盘面上的部分材料(对比图1中的5和图2中的9)。基于上述参数和条件，确定本设计惯容器中飞轮的基本转动惯量 J 0＝2×10 -4kg·m 2。
从式(8)等号右边第二项可知，在飞轮直径固定的情况下，通过增大质量块的质量m和增加质量块的数量n是增大飞轮转动惯量可调范围的重要手段，因此质量块选择密度较大且带有自润滑性的铜加工而成，其为长宽高都为20mm的正方体，并且在质量块两端留有滑块与飞轮上滑轨配合实现质量块在离心力F c(t)和弹簧恢复力F k(t)的作用下沿飞轮径向运动。确定质量块质量为0.072kg，数量为4个。如图2所示，质量块8通过弹簧7与飞轮5相连，从而实现质量块质心与飞轮转动中心的位置R(t)＝10～96mm的变化。
步骤3：基于上述理论的惯容器自适应可调飞轮的结构设计
所设计的惯容器主要包括如下核心部件：壳体3、丝杠4、飞轮5和螺母6。
其中，螺母6与飞轮5固连且螺母的轴线与飞轮的转动中心同轴(如图2中螺母6的位置所示)，螺母6与丝杠4组成丝杠-螺母运动副，目的是将惯容器的端点B受到的直线运动转换为飞轮的旋转运动。丝杠4以及与丝杠配套的螺母6可以根据需求选用，丝杠4螺距选为p＝10mm。
所述飞轮5由飞轮的基本部分9、弹簧7及质量块8组成。质量块8安装在飞轮5上的沿径向开的导向槽内，质量块8能沿飞轮的径向做直线运动。弹簧7一端与质量块8连接，另一端与导向槽靠近飞轮转动中心的一侧相连，为质量块提供指向飞轮转动中心的拉力。
所述壳体3为空心结构，其目的是为了给惯容器的飞轮部分提供一个相对密封且干净的环境，减少惯容器工作时所受的外界干扰；壳体3另一个作用就是便于惯容器的安装，因此壳体的结构并不是固定的，可以根据实际的使用需求和安装情况进行针对性的设计，并没有统一的样式、材质等要求，本发明中暂不对壳体的设计进行过多的说明。
步骤4：仿真验证
对图1所示的惯容器在外力载荷时的响应情况进行仿真验证与分析。根据惯容器的性质，其所受外力载荷
Figure PCTCN2020119818-appb-000012
式中，F 1(t)和F 2(t)分别是本发明所设计的惯容器的端点A1和惯容器的端点B2所受的外力载荷。考虑到惯容器在应用中常将惯容器的端点A1作为固定点的实际情况，在这一步的仿真验证中将惯容器的端点A1设置为固定端，即F 1(t)＝0。根据实际情况，将所受外力载荷设置为如图3所示的谐波载荷，谐波幅值为10N。本发明所设计的惯容器的相关参数设置为n＝4，m＝0.28kg，k＝500N/m，J 0＝0.0002kg·m 2，R 0＝0.01m，p＝0.01m。再通过数值仿真的仿真来验证惯容器的转动惯量及惯性比随载荷的变化情况。
图4为本发明所设计的惯容器的转动惯量随外力载荷的变化情况。从图中可以看出在t＝4s当外力载荷开始改变时(如图3所示)，惯容器的转动惯量也开始增加开始变大。在t＝5s时(如图3所示在外力载荷改变到半个周期时其变化率最大时)，惯容器的转动惯量迅速的增大并达到一个周期内的最大值(4.8×10 -4kg·m 2)，之后迅速减小并在t＝6s附近时惯容器的转动惯量恢复到2.8×10 -4kg·m 2(基础转动惯量加上质量块在最小位置时带来的转动惯量部分)。图4中后面周期进一步说明了本发明所设计惯容器的转动惯量能够实现根据外力载荷的变化而改变。
为了进一步验证本发明所设计的自适应惯容器，惯容器的惯性比b v被仿真如图5所示。结合图3可以看出，随着外力载荷的变化，本发明设计的自适应惯容器的惯性比在很大的范围内自适应调节(89.8kg～279.6kg)，表明该惯容器能 够满足根据外力载荷自适应调节惯性比的设计目的。
以上所述实施例仅表达本发明的实施方式，但并不能因此而理解为对本发明专利的范围的限制，应当指出，对于本领域的技术人员来说，在不脱离本发明构思的前提下，还可以做出若干变形和改进，这些均属于本发明的保护范围。

Claims (1)

  1. 一种惯性比自适应调节惯容器的设计方法，其特征在于，该方法基于丝杠-飞轮惯容器，对飞轮进行结构设计，降低飞轮的基础转动惯量，同时在飞轮盘面上增加弹簧-质量块结构；当丝杠受外力载荷致使飞轮转动，质量块在离心力和弹簧恢复力的共同作用下沿飞轮径向运动，质量块位置的变化使得飞轮的转动惯量随之改变，进而使惯容器的惯性比随外力载荷的变化而自适应调节；具体包括以下步骤：
    步骤1：惯性比自适应调节惯容器的理论设计
    飞轮的转动惯量与其质量分布有关，在飞轮盘面上设计弹簧-质量块结构，利用飞轮转动时质量块所受离心力与弹簧恢复力之间的力平衡，得到质量块在飞轮径向方向位置与飞轮角速度的关系：
    Figure PCTCN2020119818-appb-100001
    其中，等号左边为质量块所受惯性力；等号右边第一项为质量块所受的离心力，等号右边第二项为弹簧的恢复力；m为质量块的质量，ω(t)为飞轮的角速度，R(t)为质量块质心与飞轮转动中心的距离，k为弹簧的劲度系数，R 0为质量块质心与飞轮转动中心的最小距离，t为时间变量；
    基于丝杠-螺母运动副的运动原理，飞轮的角速度ω(t)与丝杠所受载荷之间的运动方程表示为如下微分方程形式：
    Figure PCTCN2020119818-appb-100002
    其中，p为丝杠的螺距；F l(t)为丝杠所受的载荷；J(t)为飞轮的转动惯量，表示为
    J(t)＝J 0+nmR 2(t)  (3)
    其中，J 0为飞轮的固定转动惯量；等式右边第二项表示飞轮的可调转动惯量部分，n为弹簧-质量块结构的数量，n取2的整数倍；
    由式(1)-(3)得到惯容器的自适应惯性比为：
    Figure PCTCN2020119818-appb-100003
    步骤2：可调转动惯量飞轮的结构理论设计
    由式(4)可知，通过减小飞轮的固定转动惯量J 0，并增大质量块的质量m，以实现在较大范围内调节惯容器的惯性比；将飞轮看作是绕中心做定轴转动的匀质圆盘，则其固定转动惯量表示为：
    Figure PCTCN2020119818-appb-100004
    式中，r为飞轮的半径，ρ为飞轮的密度，V为飞轮的总体积；结合式(4)和(5)可知，在飞轮半径不变的情况下，通过减小飞轮的密度及体积来减小飞轮的J 0；因此飞轮主体部分采用铝合金加工而成，并去除飞轮盘面的一部分材料以进一步减小飞轮的固定转动惯量；
    根据式(3)，并充分考虑惯容器的尺寸限制、飞轮回转半径约束问题，增加质量块的质量m和数量n，所述质量块的材质为铜；
    步骤3：惯容器自适应可调飞轮的结构设计
    所述惯容器包括壳体(3)、丝杠(4)、飞轮(5)和螺母(6)；
    所述螺母(6)与飞轮(5)固连且螺母(6)的轴线与飞轮(5)的转动中心同轴；所述丝杠(4)的顶端为惯容器的端点B(2)；丝杠(4)与螺母(6)连接，并与螺母(6)组成丝杠-螺母运动副，将惯容器的端点B(2)受到的直线运动转换为飞轮的旋转运动；
    所述飞轮(5)包括飞轮的基本部分(9)、弹簧(7)和质量块(8)；其中，飞轮的基本部分(9)通过去除飞轮(5)盘面的一部分材料构成；飞轮(5)沿径向开有多个导向槽，质量块(8)安装导向槽内，并能沿飞轮的径向做直线运 动；弹簧(7)一端与质量块(8)连接，另一端与导向槽靠近飞轮转动中心的一侧相连；
    所述壳体(3)为空心结构，其将飞轮(5)、螺母(6)及丝杠(4)组成的结构包裹在内；
    步骤4：仿真验证
    搭建惯性比自适应调节惯容器的MATLAB/Simulink仿真模型，并用模拟的载荷信号对所述惯容器进行验证。
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