CN105136359A - Method for calculating work load based on beam surface strain values measured by optical fiber sensors - Google Patents
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Abstract
本发明公开了一种基于光纤传感器测得的梁表面应变值计算工作载荷的方法,目的是利用光纤布拉格光栅(FBG)技术测得梁表面内应变值,然后通过理论方法获得实时的、平面外加弯曲或扭转工作载荷数据。本发明利用FBG应变传感器,按照一定间隔粘贴在梁结构上,因此梁被分成多个区域。本发明能够计算出光纤传感器处截面的扭矩、弯矩及剪切力,然后利用相邻两个截面的剪切力计算出该区域的工作载荷值,本发明提出具体实施方案用来验证本发明的精确度。本发明与目前其他测量梁工作载荷的方法相比,具有抗干扰、节省时间与成本,效率高等优点。
The invention discloses a method for calculating the working load based on the strain value of the beam surface measured by an optical fiber sensor. Bending or torsional working load data. The present invention utilizes FBG strain sensors, which are pasted on the beam structure at certain intervals, so the beam is divided into multiple regions. The present invention can calculate the torque, bending moment and shear force of the section at the optical fiber sensor, and then use the shear force of two adjacent sections to calculate the working load value of this area. The present invention proposes a specific implementation plan to verify the present invention the accuracy. Compared with other current methods for measuring the working load of beams, the present invention has the advantages of anti-interference, time and cost saving, high efficiency and the like.
Description
技术领域technical field
本发明涉及一种基于光纤传感器测得的梁表面应变值计算工作载荷的方法,属于光纤传感技术领域。The invention relates to a method for calculating a working load based on beam surface strain values measured by an optical fiber sensor, and belongs to the technical field of optical fiber sensing.
背景技术Background technique
目前,为获得梁结构件上的工作载荷,工业上采用一种严格却又耗时的设计方法,这种设计方法很大程度上依赖计算的方法,比如有限元建模(FEM)。但是有限元建模是耗费大量人力以及经济成本的方法。Currently, the industry employs a rigorous but time-consuming design approach that relies heavily on computational methods, such as finite element modeling (FEM), to obtain the operating loads on beam structures. But finite element modeling is a method that consumes a lot of manpower and economic cost.
更进一步,对于与飞行器机翼相关的实时载荷,使用的方法是二十世纪五十年代发展起来的一种相对广泛的“应变片/载荷标定”法。首先,在机翼结构的里面安装一系列离散的传统应变片,在机翼表面作用一系列集中载荷标定在这些载荷下应变片的响应,称之为影响系数。然后将应变片测量值输入软件,实时运行载荷公式得到结果。其中这种方法安装传感器时耗时耗力,而且成本较高。Further, for real-time loads associated with aircraft wings, the method used is a relatively extensive "strain gauge/load calibration" method developed in the 1950s. First, a series of discrete traditional strain gauges are installed inside the wing structure, and a series of concentrated loads are applied to the wing surface to calibrate the response of the strain gauges under these loads, which is called the influence coefficient. Then input the measured value of the strain gauge into the software, and run the load formula in real time to get the result. Wherein this method is time-consuming and labor-intensive when installing the sensor, and the cost is relatively high.
发明内容Contents of the invention
本发明技术解决问题:克服现有技术的不足,提供一种基于光纤传感器测得的梁表面应变值计算工作载荷的方法,本发明的目的是使用光纤传感器测得的梁表面应变值实时获得工作载荷。The technical problem of the present invention is to overcome the deficiencies in the prior art and provide a method for calculating the working load based on the beam surface strain value measured by the optical fiber sensor. load.
本发明的另一个目的是减少实时获取作用于梁上的工作载荷的时间。Another object of the invention is to reduce the time to acquire the working loads acting on the beam in real time.
本发明的更进一步的目的是减少与实时获取梁上的工作载荷相关的经济成本。A still further object of the present invention is to reduce the economic costs associated with acquiring the working load on the beam in real time.
本发明技术解决方案:一种基于光纤传感器测得的梁表面应变值计算工作载荷的方法,所述的梁为等截面悬臂梁或截面渐变悬臂梁,工作载荷是弯曲载荷、扭转载荷,或者两者均有。实现步骤如下:The technical solution of the present invention: a method for calculating the working load based on the strain value of the beam surface measured by the optical fiber sensor. Both. The implementation steps are as follows:
(1)在梁结构件上安装多个光纤传感器,测量弯曲载荷时,光纤传感器沿着梁的轴向粘贴;测量扭转载荷时,光纤传感器要与梁的轴线呈45°;(1) Install multiple optical fiber sensors on the beam structure. When measuring the bending load, the optical fiber sensor is pasted along the axial direction of the beam; when measuring the torsional load, the optical fiber sensor should be 45° to the axis of the beam;
(2)光纤传感器布置完后,施加弯曲载荷或扭转载荷,在梁的自由端施加一个已知单点载荷或一个力偶,获得在每一个光纤传感器处的应变值;(2) After the fiber optic sensor is arranged, apply a bending load or torsional load, apply a known single point load or a force couple at the free end of the beam, and obtain the strain value at each fiber optic sensor;
(3)布置完善光纤传感器并施加了已知载荷后,对梁进行标定测试,得到每个光纤传感器处的梁的结构性能,所述结构性能包括弯曲刚度与扭转刚度;并在此定义一个截面系数si,使其中Ii是第i个传感器处截面的惯性矩,ci是第i个传感器与中性轴的距离。根据第i个传感器处弯矩Mi与应变εi关系公式(Ei为第i个传感器处的杨氏模量),变形后带入截面系数,得到公式Mi=(ES)iεi,则(ES)i为弯矩与应变值的比例系数,标定后确定弯矩与应变之间的关系;(3) After arranging the optical fiber sensor and applying a known load, the beam is calibrated and tested to obtain the structural performance of the beam at each optical fiber sensor. The structural performance includes bending stiffness and torsional stiffness; and a section is defined here Coefficient s i , so that where I i is the moment of inertia of the section at the i-th sensor, and c i is the distance of the i-th sensor from the neutral axis. According to the relationship formula between bending moment M i and strain ε i at the i-th sensor (E i is the Young's modulus at the i-th sensor), after deformation, it is brought into the section coefficient, and the formula M i = (ES) i ε i is obtained, then (ES) i is the proportional coefficient of the bending moment and the strain value, Determine the relationship between bending moment and strain after calibration;
(4)利用标定的结构特性及光纤传感器测得的应变值计算扭矩、弯矩;(4) Calculate the torque and bending moment by using the calibrated structural characteristics and the strain value measured by the optical fiber sensor;
(5)利用相邻两个光纤传感器之间的弯矩得到剪切力,再利用剪切力计算梁实时的工作载荷。(5) The shear force is obtained by using the bending moment between two adjacent optical fiber sensors, and then the real-time working load of the beam is calculated by using the shear force.
所述的光纤传感器为光纤布拉格光栅(FBG)传感器。The optical fiber sensor is a Fiber Bragg Grating (FBG) sensor.
所述标定方法如下所述,标定的悬臂梁的长度为l,标定前已在梁上布置好光纤传感器,在梁的自由端上作用一个已知单点载荷P,则梁会发生弯曲,梁被光纤传感器离散成多个区域,每个区域长度为Δl,截面x=xi处的弯矩为M=P(l-i△l),将其带入公式中,得到公式梁的弯曲刚度在每个测量位置处就被确定;在每个光纤传感器处测得应变值,根据标定公式获得每一个光纤传感器处的弯曲刚度。The calibration method is as follows, the length of the calibrated cantilever beam is l, the fiber optic sensor has been arranged on the beam before calibration, and a known single point load P is applied to the free end of the beam, then the beam will bend, and the beam will It is discretized into multiple regions by the fiber optic sensor, the length of each region is Δl, and the bending moment at the section x= xi is M=P(li△l), which is brought into the formula , get the formula The bending stiffness of the beam is determined at each measurement location; the strain value is measured at each fiber optic sensor, according to the calibration formula Obtain the bending stiffness at each fiber optic sensor.
所述步骤(4)中利用标定的结构特性及光纤传感器测得的应变值计算弯矩的过程为:所述步骤(3)标定结果获得每一个光纤传感器处弯曲刚度,根据公式:即确定了弯矩与应变之间的关系,而应变值由每个光纤传感器测得,所以确定了每一个光纤传感器所处梁截面上的弯矩。In the step (4), the process of calculating the bending moment by utilizing the structural characteristics of the calibration and the strain value recorded by the optical fiber sensor is: the calibration result of the step (3) obtains the bending stiffness at each optical fiber sensor, according to the formula: That is, the relationship between the bending moment and the strain is determined, and the strain value is measured by each optical fiber sensor, so the bending moment on the beam section where each optical fiber sensor is located is determined.
所述步骤(5)中利用相邻两个光纤传感器之间的弯矩得到剪切力,再利用剪切力获取工作载荷的过程和公式为:In the step (5), the bending moment between two adjacent optical fiber sensors is used to obtain the shear force, and then the process and formula for obtaining the working load by the shear force are:
根据力矩的平衡原理,在截面x=xi处的剪切力Vi可以确定,计算公式为根据力的平衡原理,在截面x=xi处工作载荷Pi可以被确定,计算公式为Pi=-△Vi。According to the principle of moment balance, the shear force V i at the section x= xi can be determined, and the calculation formula is According to the force balance principle, the working load P i at the section x= xi can be determined, and the calculation formula is P i =-△V i .
本发明与现有技术相比的优点在于:The advantage of the present invention compared with prior art is:
(1)本发明减少有限元建模的复杂度,即与有限元建模相比,本发明简单,计算效率高。(1) The present invention reduces the complexity of finite element modeling, that is, compared with finite element modeling, the present invention is simple and has high calculation efficiency.
(2)本发明采用的光纤传感器质量轻,尺寸小,易组网、抗电磁干扰等优点克服了传统应变片的不足之处,具有省时省力的优点。(2) The optical fiber sensor adopted in the present invention has the advantages of light weight, small size, easy networking, and anti-electromagnetic interference, which overcomes the shortcomings of traditional strain gauges and has the advantages of saving time and effort.
(3)本发明很大程度上减少了完成结构分析、增加精确度等过程所需的时间和成本。(3) The present invention greatly reduces the time and cost required for completing structural analysis, increasing accuracy and the like.
附图说明Description of drawings
图1为等截面梁上传感器的布置图;Fig. 1 is the arrangement diagram of the sensor on the constant section beam;
图中,1-梁;2-FBG传感器(测扭转应变);3-梁的轴线;4-FBG传感器(测弯曲应变);5-传感器间隔;6-c(传感器到中性轴或中性面的距离);7-梁的长度。沿着梁的轴向方向贴装弯曲应变光纤传感器,沿着梁的轴向方向与轴呈45°贴装测扭转应变光纤传感器。In the figure, 1-beam; 2-FBG sensor (to measure torsional strain); 3-axis of beam; 4-FBG sensor (to measure bending strain); 5-sensor interval; 6-c (sensor to neutral axis or neutral axis face distance); 7-beam length. The bending strain optical fiber sensor is mounted along the axial direction of the beam, and the torsional strain optical fiber sensor is mounted along the axial direction of the beam at an angle of 45° to the axis.
具体实施方式Detailed ways
实施对象为如图1所示的悬臂梁结构件,左端固支,右端为梁的自由端,在图1中,1-梁;2-FBG传感器(测扭转应变);3-梁的轴线;4-FBG传感器(测弯曲应变);5-传感器间隔△l;6-c(传感器到中性轴或中性面的距离);7-梁的长度l。沿着梁的轴向方向贴装弯曲应变光纤传感器,沿着梁的轴向方向与轴向呈45°贴装扭转应变光纤传感器。The implementation object is a cantilever beam structure as shown in Figure 1, the left end is fixedly supported, and the right end is the free end of the beam, in Figure 1, 1-beam; 2-FBG sensor (measuring torsional strain); 3-axis of the beam; 4-FBG sensor (measuring bending strain); 5-sensor interval △l; 6-c (distance from sensor to neutral axis or neutral plane); 7-beam length l. The bending strain optical fiber sensor is mounted along the axial direction of the beam, and the torsional strain optical fiber sensor is mounted along the axial direction of the beam at an angle of 45° to the axial direction.
本发明具体实现如下:The present invention is specifically realized as follows:
(1)在梁结构件上安装多个光纤传感器,测量弯曲载荷时,沿着梁的轴向粘贴;测量扭转载荷时,光纤传感器要与梁的轴线呈45°;(1) Install multiple optical fiber sensors on the beam structure. When measuring the bending load, stick it along the axial direction of the beam; when measuring the torsional load, the optical fiber sensor should be at 45° to the axis of the beam;
(2)光纤传感器布置完后,施加弯曲载荷或扭转载荷,即作用在梁的自由端一个已知单点载荷或一个力偶,获得在每一个光纤传感器处的应变值;(2) After the fiber optic sensor is arranged, apply a bending load or torsional load, that is, act on a known single point load or a force couple at the free end of the beam, and obtain the strain value at each fiber optic sensor;
(3)布置完善光纤传感器并施加了已知载荷后,对梁进行一个简单的标定实验,得到每个光纤传感器处的梁的结构性能,所述结构性能包括弯曲刚度与扭转刚度;(3) After arranging the optical fiber sensor and applying a known load, a simple calibration experiment is carried out on the beam to obtain the structural performance of the beam at each optical fiber sensor, and the structural performance includes bending stiffness and torsional stiffness;
(4)利用标定的结构特性及光纤传感器测得的应变值计算弯矩、扭矩;(4) Calculate the bending moment and torque by using the calibrated structural characteristics and the strain value measured by the optical fiber sensor;
(5)利用相邻两个光纤传感器之间的弯矩得到剪切力,再利用剪切力计算梁实时的工作载荷。(5) The shear force is obtained by using the bending moment between two adjacent optical fiber sensors, and then the real-time working load of the beam is calculated by using the shear force.
进一步,本发明在梁上安装一套空间分辨率合理的光纤传感器网络,为了获得传感器处截面的结构特性,对于梁的弯曲情况,在梁的自由端施加一个单点载荷,用来获取梁的弯曲性能。类似的,在梁的自由端施加一个力偶,获得梁的扭转结构特性。Further, the present invention installs a set of optical fiber sensor network with reasonable spatial resolution on the beam. In order to obtain the structural characteristics of the section at the sensor, for the bending condition of the beam, a single point load is applied to the free end of the beam to obtain the beam’s bending properties. Similarly, a couple is applied at the free end of the beam to obtain the torsional structural properties of the beam.
本发明提供了一种改进的方法,该方法基于光纤传感器测得的梁表面应变值计算工作载荷。通常,多个光纤传感器布置在梁上呈现网格状、有规则的模型。光纤传感器具有尺寸小、重量轻等特点,因此使用了大量的光纤传感器。实际上这些传感器将梁分成了多个区域,这些区域为相邻两个传感器之间的部分。本发明假设这些区域有恒定的结构性能,但是不同区域的结构性能可能不同。因为在每个区域的两边缘处测得应变值,这些区域的长度可以相同也可以不同。The present invention provides an improved method for calculating operating loads based on beam surface strain values measured by fiber optic sensors. Usually, multiple fiber optic sensors are arranged on the beam in a grid-like, regular pattern. Optical fiber sensors have the characteristics of small size and light weight, so a large number of optical fiber sensors are used. These sensors actually divide the beam into zones, which are the sections between two adjacent sensors. The invention assumes that these regions have constant structural properties, but the structural properties of different regions may be different. Since strain values are measured at both edges of each zone, the zones can be the same or different in length.
本发明采用光频域反射技术,使用有相同中心波长的低反射率的光栅,及可调谐激光器。上百个FBG成一串。一种常见配置是使用480个传感器,在一条约6m长的光纤上1FBG/cm粘贴。传感器的数量依赖于梁的长度,例,对于机翼,使用者可以约1.27cm贴一个。本发明方法与当前其他方法相比具有更高的空间分辨率。The invention adopts optical frequency domain reflection technology, uses gratings with low reflectivity of the same central wavelength, and tunable lasers. Hundreds of FBGs in a string. A common configuration is to use 480 sensors, glued at 1FBG/cm on a fiber about 6m long. The number of sensors depends on the length of the beam, for example, for the wing, the user can stick one at about 1.27cm. Compared with other current methods, the method of the present invention has higher spatial resolution.
光纤传感器安装在梁上之后,弯曲与扭转载荷可以按照下面所述方法施加。对于弯曲载荷,一个外加的平面外单点载荷,且载荷已知,作用在梁的自由端上,通常沿着机翼主轴方向。类似的,对于扭转载荷,一对已知的力偶作用在结构的自由端。接下来,使梁承受工作载荷。在加载期间,利用每一部分的结构性能信息及从传感器中测得的应变值,按照使用者自己设定的时间间隔,每个区域处的扭矩、弯矩,剪切力,载荷都可以被计算出来。After the fiber optic sensor is mounted on the beam, bending and torsional loads can be applied as described below. For bending loads, an applied out-of-plane single point load, with a known load, acts on the free end of the beam, usually along the main axis of the wing. Similarly, for torsional loading, a known couple acts on the free ends of the structure. Next, subject the beam to the working load. During the loading period, using the structural performance information of each part and the strain value measured from the sensor, according to the time interval set by the user, the torque, bending moment, shear force and load at each area can be calculated come out.
下面更细节化的描述确定弯曲载荷的理论方法,因为弯曲与扭转的推导理论及公式具有相似特征,所以类比可以得到扭转情况。The theoretical method of determining the bending load is described in more detail below, because the derivation theory and formulas of bending and torsion have similar characteristics, so the torsion situation can be obtained by analogy.
这种方法建立在均匀梁的经典弯曲方程上:This approach is based on the classical bending equations for a uniform beam:
其中y是垂直位移,x是梁轴向坐标,M(x)是弯矩,E为杨氏模量(或弹性模量),I是惯性矩公式(1)可以被写作针对非均匀梁的形式:where y is the vertical displacement, x is the axial coordinate of the beam, M(x) is the bending moment, E is Young's modulus (or modulus of elasticity), and I is the moment of inertia Equation (1) can be written as form:
其中ε(x)是应变值,c(x)是传感器到中性轴的距离,均为梁轴向x的函数。where ε(x) is the strain value and c(x) is the distance from the sensor to the neutral axis, both are functions of the beam axis x.
梁结构被传感器分成很多区域,则每一区域可定义为梁上长度为Δl的部分,公式(2)可写成针对每一个应变的方程,比如截面x=xi处方程如下The beam structure is divided into many regions by the sensor, each region can be defined as a part of the beam whose length is Δl, formula (2) can be written as an equation for each strain, for example, the equation at section x= xi is as follows
下标i是截面x=xi处传感器的编号。The subscript i is the number of the sensor at section x= xi .
如果定义截面系数:If the section coefficient is defined:
将(4)式代入公式(3)为:Substituting formula (4) into formula (3) is:
下一步是通过一个已知的单点载荷进行一个简单的标定。The next step is to perform a simple calibration with a known single point load.
标定中的梁的长度为l,被传感器离散成多个区域,每个区域长度为Δl,截面x=xi处的弯矩为M=P(l-i△l),将式带入(3)式,梁的弯曲刚度在每个测量位置处就被确定。带入后:The length of the beam being calibrated is l, which is discretized into multiple regions by the sensor, each region has a length of Δl, and the bending moment at the cross-section x= xi is M=P(li△l), and the formula is brought into (3) formula, the bending stiffness of the beam is determined at each measurement location. After bringing in:
公式(5)中的弹性模量与截面系数的乘积通过下式标定即可获得:The product of elastic modulus and section coefficient in formula (5) can be obtained by calibration with the following formula:
为了获得梁的工作载荷数据,应变值ε在实验中测得,弯曲刚度(EI)通过单点荷标定实验获得,于是在实验中任何载荷的作用下,在每一个区域处的弯矩即可确定:In order to obtain the working load data of the beam, the strain value ε is measured in the experiment, and the bending stiffness (EI) is obtained through the single-point load calibration experiment, so under any load in the experiment, the bending moment at each region can be Sure:
则公式(5)为:Then formula (5) is:
Mi=(ES)iεi(9)M i =(ES) i ε i (9)
根据力矩的平衡原理,在截面x=xi处的剪切载荷可以确定:According to the principle of moment balance, the shear load at section x= xi can be determined as:
最后,根据力的平衡原理,工作载荷可以被确定:Finally, according to the balance of forces principle, the working load can be determined:
Pi=-△Vi(11)P i =-△V i (11)
本发明利用光纤布拉格光栅(FBG)技术提供的梁表面面内应变测量值实时、超高效率的计算平面外加弯曲和扭转载荷。The invention utilizes the in-plane strain measurement value of the beam surface provided by the fiber Bragg grating (FBG) technology to calculate the plane applied bending and torsional loads in real time and with super high efficiency.
为了说明本发明,一个具体例子如下In order to illustrate the present invention, a specific example is as follows
(1)一根长为l的等截面悬臂梁上沿着轴向按照一定间隔布置粘贴FBG应变传感器(1) FBG strain sensors are pasted on a cantilever beam with equal cross-section along the axial direction at a certain interval.
(2)在其自由端施加一个已知的单点载荷力P,然后根据公式(6)即可完成每个传感器处的弯曲刚度标定实验。(2) Apply a known single-point load force P on its free end, and then complete the bending stiffness calibration experiment at each sensor according to formula (6).
(3)标定的等截面梁性能可与下式计算结果进行对比:(3) The performance of the calibrated equal-section beam can be compared with the calculation results of the following formula:
(4)然后利用标定的弯曲刚度、应变值使用本发明中的公式(8)、(10)、(11)计算弯矩、剪切力、工作载荷等。(4) Then use the calibrated bending stiffness and strain values to calculate the bending moment, shear force, working load, etc. using formulas (8), (10), and (11) in the present invention.
(5)在上述梁上布置传感器的位置上施加等值载荷,记录梁在等间距均布载荷作用下测量应变值,然后带入本发明中的公式(8)、(10)、(11)计算弯矩、剪切力、工作载荷等。(5) apply an equivalent load on the position where the sensor is arranged on the above-mentioned beam, record the beam to measure the strain value under the action of an equidistant uniform load, then bring into the formula (8), (10), (11) in the present invention Calculate bending moments, shear forces, working loads, and more.
(6)将计算的载荷与实际施加的工作载荷做比较,计算精确度。(6) Compare the calculated load with the actual applied working load to calculate the accuracy.
(7)当梁为截面渐变梁时,类比均匀截面梁的情况,分别加载单点载荷与均布载荷情况下,传感器处梁的弯矩、剪力、及载荷的值。(7) When the beam is a beam with a gradual cross-section, analogous to the case of a beam with a uniform cross-section, the values of the bending moment, shear force, and load of the beam at the sensor are respectively loaded with a single point load and a uniform load.
通过上述具体实施方案可以验证等截面梁或截面渐变梁分别承受单点载荷与均布载荷情况下弯曲刚度的标定结果正确性。并且利用梁表面面内应变值及标定的结构性能可以实时计算平面外加弯曲工作载荷,通过与施加的已知载荷对比,确定精度误差。对于扭转载荷可类比得到。The correctness of the calibration results of the bending stiffness under the conditions of a single-point load and a uniformly distributed load can be verified through the above-mentioned specific implementation scheme. In addition, the in-plane strain value of the beam surface and the calibrated structural performance can be used to calculate the plane applied bending load in real time, and the accuracy error can be determined by comparing with the applied known load. An analogy can be obtained for torsional loads.
尽管上面对本发明说明性的具体实施方式进行了描述,以便于本技术领域的技术人员理解本发明,但应该清楚,本发明不限于具体实施方式的范围,对本技术领域的普通技术人员来讲,只要各种变化在所附的权利要求限定和确定的本发明的精神和范围内,这些变化是显而易见的,一切利用本发明构思的发明创造均在保护之列。Although the illustrative specific embodiments of the present invention have been described above, so that those skilled in the art can understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, As long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are included in the protection list.
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