WO2023124900A1 - 连续弹性体敲击运动副等效模型及其建模方法 - Google Patents
连续弹性体敲击运动副等效模型及其建模方法 Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 30
- 239000000463 material Substances 0.000 claims abstract description 25
- 238000005316 response function Methods 0.000 claims abstract description 9
- 238000012546 transfer Methods 0.000 claims abstract description 9
- 238000009527 percussion Methods 0.000 claims description 116
- 238000010079 rubber tapping Methods 0.000 claims description 7
- 238000013507 mapping Methods 0.000 claims description 5
- 238000004422 calculation algorithm Methods 0.000 claims description 3
- 230000004044 response Effects 0.000 abstract description 6
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- 238000012360 testing method Methods 0.000 description 4
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- 238000011160 research Methods 0.000 description 3
- VRAIHTAYLFXSJJ-UHFFFAOYSA-N alumane Chemical compound [AlH3].[AlH3] VRAIHTAYLFXSJJ-UHFFFAOYSA-N 0.000 description 2
- 229910052782 aluminium Inorganic materials 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 238000002474 experimental method Methods 0.000 description 2
- 238000005259 measurement Methods 0.000 description 2
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- 230000009286 beneficial effect Effects 0.000 description 1
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- 238000006243 chemical reaction Methods 0.000 description 1
- 238000004891 communication Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 229920001971 elastomer Polymers 0.000 description 1
- 239000000806 elastomer Substances 0.000 description 1
- 239000013536 elastomeric material Substances 0.000 description 1
- 238000009434 installation Methods 0.000 description 1
- 238000011089 mechanical engineering Methods 0.000 description 1
- 238000012821 model calculation Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
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- G—PHYSICS
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
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- the invention belongs to the field of mechanical engineering, and in particular relates to an equivalent model of a continuous elastic body percussion motion pair and a modeling method thereof.
- a feasible idea is to make full use of the local nonlinear characteristics of the system, isolate the percussion motion pair and treat it separately, and regard the percussion force as the secondary excitation force of the continuous elastic mechanical structure, so that the complex mechanical structure can still be Treat it as a linear system, which provides an effective way to quickly solve the local nonlinear system (the patent will be applied for separately).
- the key to realize this idea is to be able to establish an equivalent model of the knocking motion pair.
- the mass-spring model only contains It is difficult to describe the continuous collision of elastic systems with single or two modal information of the system, so it is generally used for single collision impact problems.
- the dynamic substructure method uses modal coordinates to describe the system. Some literature results show that the modal coordinates are difficult to be accurate It reflects the actual collision process, and this method can only be used for simple collision problems without slip and friction.
- the multivariable method is a method for accurately calculating the impact force proposed by combining the finite element method and the modal synthesis method. However, the solution efficiency of this method is low, and it is difficult to apply it in the actual analysis of the knock vibration response of complex mechanical structures. Therefore, the present invention proposes a new equivalent model and its modeling method in an attempt to solve the problem of rapid prediction of percussion force pulses of continuous elastic mechanical structures.
- the purpose of the present invention is to provide an equivalent model of a continuous elastic body knocking motion pair and a modeling method thereof, so as to solve the problem of rapid prediction of a continuous elastic body mechanical structure knocking force pulse.
- the present invention provides the equivalent model of the continuous elastic body knocking motion pair and its modeling method, and establishes an equivalent model for the knocking motion pair in the continuous elastic body mechanical structure or system, that is, the knocking pulse force and the knocking motion pair
- the nonlinear mapping relationship of the initial impact velocity, and the percussion secondary material is expressed by assuming that the percussion force pulse is a half-period sine wave, and using the Hertzian contact model and the origin transfer function or impulse response function of the mechanical structure at the percussion contact point, respectively
- the contact mechanical properties and the impedance properties of the mechanical structure at the percussion site are used to derive the relationship between the output and input of the nonlinear equivalent model, that is, the percussion pulse force and the initial velocity of percussion.
- the percussion force pulse of the percussion motion pair between continuous elastic bodies is determined by the sine wave amplitude F 0 and frequency ⁇ b
- V 1 +V 2 is the initial percussion force of the percussion motion pair between continuous elastic bodies
- Velocity k H and ⁇ are the contact stiffness and Hertz contact constant of the percussion pair respectively
- n1 and n2 are positive integers
- ⁇ n1 and ⁇ n2 respectively represent the n1 and n2 order natural frequencies of the two continuous elastic bodies of the percussion pair
- a n1 and a n2 respectively denote the components of the normal mode shape of the corresponding order at the knocking point.
- the sum in the formula should theoretically take an infinite number of orders, but in fact, only the sum of the first finite order can obtain a sufficient precision Analyze the results.
- the percussion force pulse of the percussion motion pair between the continuous elastic body and the fixed boundary is determined by the sine wave amplitude F 0 and the frequency ⁇ b
- V is the initial velocity of the percussion motion pair between the continuous elastic body and the fixed boundary
- k H is the contact stiffness and Hertz contact constant of the percussion pair respectively
- n is a positive integer
- ⁇ n a n represent the nth order natural frequency of the continuous elastic body of the percussion pair and the normal mode shape at the percussion point Components, obviously, the implicit relationship here is a special case of knocking between continuous elastic bodies.
- the percussion force pulse of the continuous elastic body percussion pair at a given percussion initial velocity can be quickly obtained, and the specific implementation steps are as follows:
- Step 1 Establish a Hertzian contact model for the knocking part or knocking motion pair of the continuous elastic body, that is, obtain the contact stiffness k H and the Hertzian contact constant ⁇ ;
- Step 2 For the continuous elastic body structure, establish the origin transfer function or impulse response function model of the knock point, that is, obtain the first finite-order natural frequency of the continuous elastic body structure and the component of the corresponding normal mode shape at the knock point;
- Step 3 If the initial velocity of the percussion pair of the continuous elastic body is known, then calculate ⁇ b and F 0 according to the two equations of the equivalent model, so as to obtain the percussion force pulse, which is determined by ⁇ b and F 0 half cycle sine wave.
- the beneficial effect of the present invention is that: the method of the present invention can solve the problem of fast prediction of the knocking force pulse of the continuous elastic body mechanical structure.
- Figure 1 is a physical photo of the test device knocked by the cantilever beam and the fixed stopper;
- Fig. 2 is a schematic diagram of a cantilever beam and a fixed stop knocking test device
- Fig. 3 is the comparison chart of the percussion force pulse prediction and the measured waveform of the aluminum-aluminum material percussion pair;
- Fig. 4 is a comparison chart of the percussion force pulse prediction and the measured waveform of the stainless steel-aluminum material percussion pair;
- Fig. 5 is a comparison chart of the percussion force pulse prediction and the measured waveform of the 45 steel-ABS material percussion pair;
- Fig. 6 is a comparison chart of the percussion force pulse prediction and the measured waveform of the stainless steel-ABS material percussion pair
- Figure 7 is a comparison chart of the equivalent model prediction curve and the measured data of the peak value of the secondary knocking force pulse of the stainless steel-aluminum material - the initial velocity of the knocking;
- Figure 8 is a comparison chart of the equivalent model prediction curve and the measured data of the peak value of the secondary knocking force pulse of the aluminum-aluminum material - the initial velocity of the knocking;
- Figure 9 is a comparison chart between the equivalent model prediction curve and the measured data of the peak value of the 45# steel-ABS material secondary percussion force pulse - percussion initial velocity;
- Figure 10 is a comparison chart of the equivalent model prediction curve and the measured data of the peak value of the secondary knock force pulse of the stainless steel-ABS material - the initial velocity of the knock.
- the present invention aims at the collision or knocking motion between continuous elastic bodies, and defines the continuous elastic body knocking motion pair, which includes two adjacent continuous elastic bodies, which vibrate or move relative to each other under external excitation, and between the two Contact knocking occurs at the smallest spacing between adjacent continuous elastomers.
- the present invention proposes a nonlinear equivalent model describing its knocking motion characteristics.
- the input of the model is the initial velocity of two continuous elastic bodies knocking, that is, the normal relative moving velocity of the knocking contact point when just starting to touch the knocking.
- the output of the model is the knocking pulse force between two continuous elastic bodies, which is a pair of action force and reaction force, equal in magnitude and opposite in direction, respectively acting on the knocking contact points of two continuous elastic bodies, along the contact surface method
- the line direction points to the interior of the continuous elastomeric structure.
- the mapping relationship between the output and input of this equivalent model must depend on the physical characteristics of the continuous elastic body's percussion motion pair itself.
- the present invention proposes to use the Hertz contact model to express the contact mechanical properties of the percussion pair of secondary materials, and to use the origin transfer function or impulse response function to characterize the mechanical impedance properties of the continuous elastic body at the percussion contact point , thus the percussion force impulse response of the continuum percussion motion pair at a given percussion initial velocity can be determined;
- the force of the tapping pulse can be expressed as
- the knocking pulse force always points to the interior of the continuous elastic body structure along the normal direction of the contact surface, and this direction is defined as the positive knocking force.
- the generalized coordinates are defined along this direction to express the continuous elasticity
- the normal displacement of the body knocking contact point, and the coordinate origin is set at the position of the knocking point just when the knocking contact starts.
- k H , ⁇ are the contact stiffness and Hertzian contact constant of the percussion material pair (ie percussion pair), respectively.
- ⁇ n1 and ⁇ n2 are the n1 and n2 order natural frequencies of the two continuous elastic bodies, respectively, and a n1 and a n2 are the components of the normal mode shapes of the corresponding orders of the two continuous elastic bodies at the knocking contact point.
- the displacement consists of two parts, the first part represents the displacement of the percussion point without the percussion force, and the second part represents the displacement of the percussion point under the percussion force.
- the amplitude F 0 and duration ⁇ / ⁇ b of the percussion force pulse can be obtained according to the initial velocity of the continuous elastic body percussion by using the two formulas (8) and (9), that is, the above equation expresses the continuous elastic body percussion Click on the input-output mapping relationship of the equivalent model.
- the continuous elastic body and boundary knocking are taken as special cases of two continuous elastic body knocking, and its equivalent model equation is derived.
- the same results as (10) and (11) can also be obtained by deriving the mechanical model of the continuous elastic body and the fixed boundary alone.
- the specific steps of setting up any continuous elastic body percussion pair equivalent model and determining the percussion force response are as follows:
- Step 1 For the knocking part or knocking motion pair of the continuous elastic body, the Hertzian contact model is established, that is, the contact stiffness k H and the Hertzian contact constant ⁇ are obtained.
- the Hertzian contact model of the percussion pair is related to factors such as material properties and local geometry.
- the contact stiffness can be determined by the following formula:
- E i , ⁇ i , and R i represent the Young's modulus, Poisson's ratio, and surface curvature radius at the knocking point of the elastomeric material, respectively.
- the Hertzian contact constant ⁇ can be determined according to the contact force-deformation test curve of the pair of percussion materials.
- Step 2 For the continuous elastic body structure, establish the origin transfer function or impulse response function model of the knock point, that is, obtain the first finite-order natural frequency of the continuous elastic body structure and the component of the corresponding normal mode shape at the knock point.
- the percussion contact point should be selected as the unit node when dividing the unit, so as to facilitate the processing.
- modal superposition is used to express the origin transfer function or impulse response function
- the modal truncation should be performed, that is, only the first few modes are selected for superposition, but attention should be paid not to select too few modal orders.
- the shorter the duration of the percussion force pulse the wider the frequency range covered, and the more structural modes will be excited. Therefore, the order of mode truncation needs to be set higher.
- any well-established method can be used to obtain the continuous elastic body mode or natural frequency and mode shape.
- the equivalent model of the percussion pair of continuous elastic bodies has been determined so far, that is, the parameters in equations (8), (9) or (10), (11) have been obtained, as long as the equivalent model is given
- the input that is, the initial tapping velocity, can obtain the tapping force output of the equivalent model.
- Step 3 If the initial velocity of the percussion pair of the continuous elastic body is known, then calculate ⁇ b and F 0 according to the two equations of the equivalent model, so as to obtain the percussion force pulse, which is determined by ⁇ b and F 0 half cycle sine wave.
- equation (9) or (11) contains only one unknown quantity ⁇ b , this equation should be solved first. This is a transcendental equation with respect to ⁇ b , and the numerical solution can only be obtained with numerical algorithms. Then substitute the solution of ⁇ b into another equation to obtain the value of F 0 directly.
- FIG. 1 a test device as shown in FIG. 1 was constructed, which can be briefly illustrated in FIG. 2 .
- This is a cantilever beam, which represents a continuous elastic body. Under the external excitation provided by the vibrator 10, a lateral forced vibration response occurs; a fixed stopper is set at the free end of the cantilever beam, and there is an adjustable stop between the cantilever beam and the cantilever beam. Reserve intervals, when the cantilever beam is forced to vibrate laterally, it can knock against the fixed stop. In fact, the pulse hammer 20 is used as the fixed stop.
- the material of the hammer head can be easily replaced, and the knocking force can be passed through its
- the force sensor 30 is used for measurement; the material of the free end of the cantilever beam and the knocking part of the block can be replaced; an acceleration sensor 40 is also arranged on the cantilever beam to observe the vibration acceleration of the cantilever beam knocking point.
- a harmonic signal was applied to the exciter 10 to excite the cantilever beam, and the acceleration signal at the free end of the cantilever beam and the knocking force signal with the fixed stopper ie the hammer 20 were recorded. Adjusting the reserved interval between the fixed stopper and the cantilever beam, adjusting the amplitude and frequency of the harmonic excitation force, replacing the material of the hammer head and the material of the cantilever beam’s knocking part, conducted many experiments, and obtained a series of knocking force pulses And the measured data of the initial speed of tapping.
- Hertzian contact model is established for the percussion pair formed by the free end of the cantilever beam and the fixed block (the hammer head of the force hammer 20).
- the hammer head of the force hammer 20 is in point contact with the free end of the cantilever beam.
- Table 2 lists the Hertzian contact constants when different materials are selected.
- the initial velocity of each percussion can be determined quite accurately when each percussion occurs. Based on these initial velocities, use the built equivalent model to calculate the percussion force pulse of each percussion; self-programmed numerical calculation programs for equations (10) and (11), first solve equation (11) based on the 0.618 method Obtain ⁇ b , and then substitute into equation (10) to obtain F 0 .
- Figures 3 to 6 show the comparison between the calculated and measured values of the typical percussion force pulse waveforms of different materials at the free end of the cantilever beam. It can be seen that the predicted waveforms are basically consistent with the measured waveforms.
- Figures 7 to 10 show the comparison between the calculated value and the measured value of the amplitude of the percussion force pulse at the free end of the cantilever beam with different materials for the percussion pair.
- the amplitude of the percussion force pulse calculated according to the equivalent model increases monotonously with the initial velocity of the percussion, showing a nonlinear relationship, but close to a linear increase;
- ⁇ b corresponding to the duration of the percussion force pulse
- F 0 is related to It is directly proportional to the initial velocity of tapping.
- Fig. 7 to Fig. 10 that, no matter what kind of material pairs, they are always near the prediction curve of the equivalent model, which shows that the equivalent model of the present invention truly reflects the mechanics of the knocking pair. characteristic.
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Abstract
连续弹性体敲击运动副等效模型的建模方法，针对连续弹性体机械结构中的敲击运动副建立等效模型，采用赫兹接触模型来表达敲击副材料的接触力学性质，采用原点传递函数或脉冲响应函数来表征连续弹性体在敲击接触点处的机械阻抗性质，由此确定连续体敲击运动副在给定敲击初速度下的敲击力脉冲响应。
Description
本申请要求于2021年12月27日提交中国专利局、申请号为202111614142.3、发明名称为“连续弹性体敲击运动副等效模型及其建模方法”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
本发明属于机械工程领域，具体涉及连续弹性体敲击运动副等效模型及其建模方法。
实际的机械系统工作在动态环境或动态工况下，连续弹性体机械结构必然产生振动，而且往往会出现其局部碰撞或敲击的情形，例如，汽车行驶中，车身、仪表总成、车门等部位容易发生敲击异响的状况，并严重影响汽车产品的品质形象和用户的感受，因此，在汽车产品开发中迫切需要预测这些异响发生几率与严重程度，并加以改进。但这种局部非线性的系统，要进行其振动响应预测分析，目前尚无准确而实用的办法。一种可行的思路是充分利用系统的局部非线性特性，将敲击运动副孤立出来单独处理，把敲击力看成连续弹性体机械结构的二次激励力，从而使复杂的机械结构仍然可以按照线性系统来对待，这为局部非线性系统的快速求解提供了一种有效的途径(将另行申报专利)，要实现这一思路的关键是能够建立敲击运动副的等效模型。
尽管碰撞问题的研究已经有很长历史，但对异响这类连续弹性体敲击问题的研究还不够成熟。对于集总元件的碰撞，仅需考虑集总元件的惯性性质及其局部的碰撞接触力学特性，相关理论已经很成熟；而连续弹性体之间的碰撞是一个更加复杂的现象，也有许多学者对其开展了大量研究。为了能快速预测碰撞力提出了不同的模型简化方法，包括质量-弹簧模型、动态子结构法和多变量法等，但都无法有效兼顾求解效率和结果精度两方面，如质量-弹簧模型仅包含系统单个或两个模态信息，难以对弹性系统的持续碰撞进行描述，所以一般用于单次碰撞冲击问题，动态子结构法则是利用模态坐标描述系统，有文献结果表明模态坐标难以准确反映实际碰撞过程，且该方法只能用于无滑移、无摩擦的简单碰撞问题。多变量法则 是结合有限元法和模态综合法所提出的用于准确计算碰撞力的方法，但是该方法求解效率偏低，难以在实际的复杂机械结构的敲击振动响应分析中应用。因此，本发明提出一种新的等效模型及其建模方法，试图解决连续弹性体机械结构敲击力脉冲的快速预测问题。
发明内容
本发明的目的在于提供连续弹性体敲击运动副等效模型及其建模方法，解决连续弹性体机械结构敲击力脉冲的快速预测问题。
为了达到上述目的，本发明提供连续弹性体敲击运动副等效模型及其建模方法，针对连续弹性体机械结构或系统中的敲击运动副建立等效模型，即敲击脉冲力与敲击初速度的非线性映射关系，并通过假设敲击力脉冲为半周期正弦波、同时分别采用赫兹接触模型和机械结构在敲击接触点的原点传递函数或脉冲响应函数来表达敲击副材料对的接触力学性质和机械结构在敲击部位的阻抗性质的方法，从而导出该非线性等效模型的输出与输入，即敲击脉冲力与敲击初速度，之间的关系式。
进一步，针对连续弹性体之间的敲击运动副，敲击力脉冲与敲击初速度之间的隐式关系，如下所示：
其中：连续弹性体之间的敲击运动副的敲击力脉冲由正弦波幅值F
0、频率ω
b确定，V
1+V
2为连续弹性体之间的敲击运动副的敲击初速度，k
H、α分别为敲击副的接触刚度、赫兹接触常数，n1、n2为正整数，ω
n1、ω
n2分别表示敲击副的两个连续弹性体的第n1、n2阶固有频率，a
n1、a
n2分别表示相应阶正则振型在敲击点处的分量，式中的和式理论上应取无限多阶，但实际上仅取前有限阶求和就可获得足够精度的分析结果。
进一步，针对连续弹性体与固定边界的敲击运动副，敲击力脉冲与敲击初速度之间的隐式关系，如下所示：
其中：连续弹性体与固定边界的敲击运动副的敲击力脉冲由正弦波幅值F
0、频率ω
b确定，V为连续弹性体与固定边界的敲击运动副的敲击初速度，k
H、α分别为敲击副的接触刚度、赫兹接触常数，n为正整数，ω
n、a
n分别表示敲击副连续弹性体的第n阶固有频率及正则振型在敲击点的分量，显然，此处的隐式关系是连续弹性体之间敲击的特例。
进一步，可快速获得连续弹性体敲击副在给定敲击初速度下的敲击力脉冲，具体实施步骤如下：
步骤一：针对连续弹性体的敲击部位或敲击运动副，建立赫兹接触模型，即获取接触刚度k
H和赫兹接触常数α；
步骤二：针对连续弹性体结构，建立敲击点的原点传递函数或脉冲响应函数模型，即获取连续弹性体结构的前有限阶固有频率及相应正则振型在敲击点的分量；
步骤三：若已知连续弹性体敲击副的敲击初速度，则根据等效模型的两个方程求出ω
b、F
0，从而获得敲击力脉冲，即由ω
b、F
0确定的半个周期正弦波。
进一步，经过步骤一、二就已经确定了敲击副的等效模型，注意等效模型的两个方程，一个是关于ω
b的超越方程，与F
0无关，因此可采用任何成熟的数值算法首先获得ω
b的解，然后再将ω
b的值代入另一个方程，容易获得F
0的解。
本发明的有益效果在于：通过本发明的方法，可解决连续弹性体机械结构敲击力脉冲的快速预测问题。
说明书附图
图1是悬臂梁与固定挡块敲击的试验装置实物照片；
图2是悬臂梁与固定挡块敲击试验装置示意图；
图3是铝-铝材料敲击副的敲击力脉冲预测与实测波形的对比图；
图4是不锈钢-铝材料敲击副的敲击力脉冲预测与实测波形的对比图；
图5是45钢-ABS材料敲击副的敲击力脉冲预测与实测波形的对比图；
图6是不锈钢-ABS材料敲击副的敲击力脉冲预测与实测波形的对比图；
图7是不锈钢-铝材料副敲击力脉冲峰值-敲击初速度的等效模型预测曲线与实测数据对比图；
图8是铝-铝材料副敲击力脉冲峰值-敲击初速度的等效模型预测曲线与实测数据对比图；
图9是45#钢-ABS材料副敲击力脉冲峰值-敲击初速度的等效模型预测曲线与实测数据对比图；
图10是不锈钢-ABS材料副敲击力脉冲峰值-敲击初速度的等效模型预测曲线与实测数据对比图。
激振器—10，力锤—20，力传感器—30，加速度传感器—40。
下面通过具体实施方式进一步详细说明。
本发明针对连续弹性体之间的碰撞或敲击运动，定义连续弹性体敲击运动副，它包含两个相邻的连续弹性体，它们在外部激励下发生振动或相对运动，并在两个相邻连续弹性体的最小间距处发生接触敲击。本发明提出描述其敲击运动特性的非线性等效模型，该模型的输入为两个连续弹性体敲击初速度，即刚开始接触敲击时敲击接触点的法向相对运动速度，该模型的输出为两个连续弹性体之间的敲击脉冲力，它是一对作用力与反作用力，大小相等，方向相反，分别作用在两个连续弹性体敲击接触点，沿接触面法线方向指向连续弹性体结构内部。
显然，该等效模型输出与输入之间的映射关系必然取决于连续弹性体敲击运动副自身的物理特性。为了构建这种映射关系，本发明提出，采用赫兹接触模型来表达敲击副材料对的接触力学性质，采用原点传递函数或脉冲响应函数来表征连续弹性体在敲击接触点处的机械阻抗性质，由此便可以确定连续体敲击运动副在给定敲击初速度下的敲击力脉冲响应；为了 能够快速确定这种映射关系，本发明依据大量敲击脉冲力的实测结果，对敲击脉冲力波形提出假设，令其为半个周期的正弦波，于是仅需两个参数就可以确定敲击脉冲力波形，一个是正弦波幅值F
0，即敲击力脉冲的峰值F
0，另一个是正弦波频率ω
b，即对应确定了敲击力脉冲持续的时间ΔT＝π/ω
b。
依据本发明的上述思路，可以导出连续弹性体敲击运动副等效模型的具体方程。
根据波形假设，敲击脉冲力可以表达为
f(t)＝F
0sinω
bt 0≤t≤π/ω
b (1)
注意连续弹性体发生敲击时，敲击脉冲力始终沿接触面法线方向指向连续弹性体结构内部，定义该方向为敲击力为正，同时沿此方向定义广义坐标，用以表达连续弹性体敲击接触点的法向位移，坐标原点设定在刚好开始敲击接触时敲击点的位置。当两个连续弹性体互相敲击时，两个连续弹性体上敲击接触点的法向位移分别记为x
1、x
2，皆是时间t的函数，利用赫兹接触模型可以把敲击力表达为
式中：k
H、α分别为敲击材料对(即敲击副)的接触刚度和赫兹接触常数。
如果两个连续弹性体在敲击接触点的原点脉冲响应函数(与原点传递函数构成拉普拉斯变换对)分别记为h
1(t)、h
2(t)，利用连续弹性体的模态信息可以表达为
式中：ω
n1、ω
n2分别为两个连续弹性体的第n1、n2阶固有频率，a
n1、a
n2分别为两个连续弹性体相应阶次正则振型在敲击接触点的分量。
设若两个连续弹性体在时刻t＝0开始发生敲击，即：x
1(0)＝0，x
2(0)＝0，且两个连续弹性体上敲击点的初速度分别为V
1、V
2，在随后的敲击过程中，两个连续弹性体上敲击点的位移可分别表示为
式中：位移由两部分组成，第一部分表示敲击点在没有敲击力作用下的位移，第二部分表示敲击点在敲击力作用下的位移。
根据(1)式的敲击力脉冲波形的假设，在t＝π/2ω
b时，f(t)达到最大值F
0，且两个连续弹性体敲击接触点的相对速度为零，即有如下关系式：
式中：
分别表示两个连续弹性体敲击接触点的速度，可由(4)、(5)式求导获得。
利用(3)～(7)式，并把(1)的敲击力波形假设代入，可以导出如下关系：
显然，利用(8)、(9)两式就可根据连续弹性体敲击的初速度获得敲击力脉冲的幅值F
0与持续时间π/ω
b，即上述方程表达了连续弹性体敲击副等效模型的输入输出映射关系。
(8)、(9)两式适用于任何连续弹性体结构。假如连续弹性体在外部激励下与固定边界发生敲击，则相当于其中一个连续弹性体变为固定的刚体，在(8)、(9)式中令V
2＝0、a
n2＝0，且把n
1记为n、V
1记为V，可得出确定敲击力脉冲输出的方程为：
此处，把连续弹性体与边界敲击作为两个连续弹性体敲击的特例，导出了它的等效模型方程。事实上，单独对连续弹性体与固定边界建立力学型进行推导，也会得到与(10)、(11)式相同结果。
按照本发明的方法，建立任何连续弹性体敲击副等效模型并由此确定敲击力响应的具体步骤如下：
步骤一：针对连续弹性体的敲击部位或敲击运动副，建立赫兹接触模型，即获取接触刚度k
H和赫兹接触常数α。
敲击副的赫兹接触模型与材料特性和局部几何形状等因素有关，例如，针对点接触类型的敲击副赫兹接触模型，其接触刚度可由下式确定：
其中：
E
i、ν
i、R
i分别表示弹性体材料的杨氏模量、泊松比和敲击点处表面曲率半径。赫兹接触常数α可根据敲击副材料对的接触力-变形试验曲线来确定。
步骤二：针对连续弹性体结构，建立敲击点的原点传递函数或脉冲响应函数模型，即获取连续弹性体结构的前有限阶固有频率及相应正则振型在敲击点的分量。
如果采用有限元来分析连续弹性体结构，注意单元划分时应把敲击接触点选择为单元节点，才方便进行处理。利用模态叠加来表达原点传递函数或脉冲响应函数时，应该进行模态截断，即仅选取前若干阶模态进行叠加，但注意模态阶次不要选取过少。一般而言，敲击力脉冲持续的时间越短，覆盖的频率范围越宽，越多的结构模态会被激起，因此，模态截断的阶次需要定得越高。此处，获取连续弹性体模态或固有频率与振型，可以采用任何成熟的方法。
事实上，至此连续弹性体敲击副的等效模型已经确定，即方程(8)、(9)或(10)、(11)中的各项参数均已求得，只要给定等效模型的输入，即敲击初速度，就能获得等效模型的敲击力输出。
步骤三：若已知连续弹性体敲击副的敲击初速度，则根据等效模型的两个方程求出ω
b、F
0，从而获得敲击力脉冲，即由ω
b、F
0确定的半个周期正弦波。
由于方程(9)或(11)仅包含一个未知量ω
b，所以应先求解该方程。这是关于ω
b的超越方程，只能用数值算法获得数值解。然后把ω
b的解代入另一个方程可直接获得F
0的值。
实施例：
为了获得实测的敲击力信号，以便验证本发明预测的敲击力，构建了图1所示的试验装置，可以用图2来简明示意。这是一个悬臂梁，代表一个连续弹性体，在激振器10提供的外部激励下，发生横向强迫振动响应；在悬臂梁的自由端设置一个固定挡块，与悬臂梁之间有可调的预留间歇，当悬臂梁受迫横向振动时，可与固定挡块发生敲击，实际上，用脉冲力锤20来作为固定挡块，锤头材料可方便更换，敲击力可通过它的力传感器30进行测量；悬臂梁自由端与挡块敲击部位的材料可更换；在悬臂梁上还设置了加速度传感器40，可观测悬臂梁敲击点部位的振动加速度。
在实验中，给激振器10施加谐波信号，对悬臂梁进行激振，记录悬臂梁自由端的加速度信号及其与固定挡块即力锤20的敲击力信号。调节固定挡块与悬臂梁的预留间歇、调节谐波激振力的幅值与频率、更换锤头材料和悬臂梁敲击部位材料，进行了多次实验，获得了一系列敲击力脉冲及其敲击初始速度的实测数据。
针对上述悬臂梁系统，建立它的有限元模型，并进行模态分析，可求出其固有频率和正则振型，表1列出了前4阶固有频率及其正则振型在敲击点处的分量。
表1悬臂梁结构模态实测和有限元模型计算值表
针对悬臂梁自由端与固定挡块(力锤20的锤头)构成的敲击副，建立赫兹接触模型。此处力锤20的锤头与悬臂梁自由端都是点接触，表2列出了选用不同材料对时的赫兹接触常数。
表2悬臂梁自由端敲击副材料及其赫兹接触常数表
至此，实际上就已确定了悬臂梁自由端敲击副的等效模型，即方程(10)、(11)中所需的各项参数，如果给定敲击初速度输入就可以由此等效模型给出敲击力输出。
根据实测的悬臂梁自由端加速度信号以及敲击力信号时间历程，经过必要的处理后，可以相当准确地确定各次敲击发生时的敲击初速度。基于这些初速度，利用所建的等效模型，求出每次敲击的敲击力脉冲；自编了方程(10)和(11)的数值计算程序，先基于0.618法求解方程(11)得到ω
b，再代入方程(10)计算得到F
0。
图3～图6给出了悬臂梁自由端敲击副不同材料对时的典型敲击力脉冲波形计算值与实测值的对比，可见，预测波形与实测波形基本一致。
图7～图10给出了悬臂梁自由端敲击副不同材料对时敲击力脉冲幅值计算值与实测值的对比。首先由图7～图10可见，按照等效模型计算的敲击力脉冲幅值随敲击初速度单调增长，呈现非线性关系，但接近线性增长；事实上，由敲击副等效模型的方程可以看出，当赫兹接触常数α＝1时，ω
b(对应于敲击力脉冲持续时间)与敲击初速度无关，而仅与材料接触刚度和结构机械阻抗性质有关，F
0则与敲击初速度成正比。其次由图7～图10可见，实测的众多敲击力脉冲幅值，无论何种材料副，它们总在等效模型预测曲线附近，说明本发明的等效模型真实反映了敲击副的力学特性。
需要提前说明的是，在本发明中，除非另有明确的规定和限定，术语“安装”、“相连”、“连接”、“固定”等术语应做广义理解，例如，可以是固定连接，也可以是可拆卸连接，或一体地连接；可以是直接相连，也可以通过中间媒介间接相连，可以是两个元件内部的连通。对于本领域的普通技术人员而言，可以根据具体情况理解上述术语在本发明中的具体含义。
以上所述的仅是本发明的实施例，方案中公知的具体结构及特性等常识在此未作过多描述。应当指出，对于本领域的技术人员来说，在不脱离本发明结构的前提下，还可以作出若干变形和改进，这些也应该视为本发明的保护范围，这些都不会影响本发明实施的效果和专利的实用性。本申请要求的保护范围应当以其权利要求的内容为准，说明书中的具体实施方 式等记载可以用于解释权利要求的内容。
Claims (5)
- 连续弹性体敲击运动副等效模型及其建模方法，其特征在于，针对连续弹性体机械结构或系统中的敲击运动副建立等效模型，即敲击脉冲力与敲击初速度的非线性映射关系，并通过假设敲击力脉冲为半周期正弦波、同时分别采用赫兹接触模型和机械结构在敲击接触点的原点传递函数或脉冲响应函数来表达敲击副材料对的接触力学性质和机械结构在敲击部位的阻抗性质的方法，从而导出该非线性等效模型的输出与输入，即敲击脉冲力与敲击初速度，之间的关系式。
- 根据权利要求1所述的连续弹性体敲击运动副等效模型及其建模方法，其特征在于：针对连续弹性体之间的敲击运动副，敲击力脉冲与敲击初速度之间的隐式关系，如下所示：
其中：连续弹性体之间的敲击运动副的敲击力脉冲由正弦波幅值F 0、频率ω b确定，V 1+V 2为连续弹性体之间的敲击运动副的敲击初速度，k H、α分别为敲击副的接触刚度、赫兹接触常数，n1、n2为正整数，ω n1、ω n2分别表示敲击副的两个连续弹性体的第n1、n2阶固有频率，a n1、a n2分别表示相应阶正则振型在敲击点处的分量，式中的和式理论上应取无限多阶，但实际上仅取前有限阶求和就可获得足够精度的分析结果。 - 根据权利要求1所述的连续弹性体敲击运动副等效模型及其建模方法，其特征在于，针对连续弹性体与固定边界的敲击运动副，敲击力脉冲与敲击初速度之间的隐式关系，如下所示：
其中：连续弹性体与固定边界的敲击运动副的敲击力脉冲由正弦波幅 值F 0、频率ω b确定，V为连续弹性体与固定边界的敲击运动副的敲击初速度，k H、α分别为敲击副的接触刚度、赫兹接触常数，n为正整数，ω n、a n分别表示敲击副连续弹性体的第n阶固有频率及正则振型在敲击点的分量，显然，此处的隐式关系是连续弹性体之间敲击的特例。 - 根据权利要求1所述的连续弹性体敲击运动副等效模型及其建模方法，其特征在于，可快速获得连续弹性体敲击副在给定敲击初速度下的敲击力脉冲，具体实施步骤如下：步骤一：针对连续弹性体的敲击部位或敲击运动副，建立赫兹接触模型，即获取接触刚度k H和赫兹接触常数α；步骤二：针对连续弹性体结构，建立敲击点的原点传递函数或脉冲响应函数模型，即获取连续弹性体结构的前有限阶固有频率及相应正则振型在敲击点的分量；步骤三：若已知连续弹性体敲击副的敲击初速度，则根据等效模型的两个方程求出ω b、F 0，从而获得敲击力脉冲，即由ω b、F 0确定的半个周期正弦波。
- 根据权利要求4所述的连续弹性体敲击运动副等效模型及其建模方法，其特征在于，经过步骤一、二就已经确定了敲击副的等效模型，注意等效模型的两个方程，一个是关于ω b的超越方程，与F 0无关，因此可采用任何成熟的数值算法首先获得ω b的解，然后再将ω b的值代入另一个方程，容易获得F 0的解。
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102270249A (zh) * | 2010-06-07 | 2011-12-07 | 上海通用汽车有限公司 | 识别零部件特征频率的方法 |
| CN104142219A (zh) * | 2014-07-17 | 2014-11-12 | 浙江工业大学 | 一种基于多点脉冲激励的主轴系统运行模态分析方法 |
| CN104200122A (zh) * | 2014-09-22 | 2014-12-10 | 大连交通大学 | 复杂焊接结构随机振动疲劳寿命预测方法 |
| CN114282417A (zh) * | 2021-12-27 | 2022-04-05 | 重庆大学 | 连续弹性体敲击运动副等效模型及其建模方法 |
-
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102270249A (zh) * | 2010-06-07 | 2011-12-07 | 上海通用汽车有限公司 | 识别零部件特征频率的方法 |
| CN104142219A (zh) * | 2014-07-17 | 2014-11-12 | 浙江工业大学 | 一种基于多点脉冲激励的主轴系统运行模态分析方法 |
| CN104200122A (zh) * | 2014-09-22 | 2014-12-10 | 大连交通大学 | 复杂焊接结构随机振动疲劳寿命预测方法 |
| CN114282417A (zh) * | 2021-12-27 | 2022-04-05 | 重庆大学 | 连续弹性体敲击运动副等效模型及其建模方法 |
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| CN116882247A (zh) * | 2023-07-21 | 2023-10-13 | 中国船舶科学研究中心 | 一种三维弹性体芯材的夹芯板振动计算方法 |
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