技术领域technical field
本发明涉及应变测量领域，具体涉及一种基于切应力传递特性的应变测量方法和柔性传感器。The invention relates to the field of strain measurement, in particular to a strain measurement method and a flexible sensor based on shear stress transfer characteristics.
背景技术Background technique
传统的应变传递模型中，由于敏感层材料一般为光纤、导电金属等，其弹性模量较大，相比其它层材料大几个数量级，常常将其他各层的弹性模量忽略不计；但对于柔性传感器，各层材料均具有良好的柔性和相容性，其弹性模量往往处于同一数量级，因此无法忽略。In the traditional strain transfer model, since the material of the sensitive layer is generally optical fiber, conductive metal, etc., its elastic modulus is larger, which is several orders of magnitude larger than that of other layer materials, and the elastic modulus of other layers is often ignored; but for For flexible sensors, each layer of material has good flexibility and compatibility, and its elastic modulus is often in the same order of magnitude, so it cannot be ignored.
另外，传统的应变传递模型在建立的过程中，会假设切应力在传感器各层中以线性传递；但由于柔性材料的特性，切应力在各层中以二次曲线的方式传递，因此传统应变模型计算的应变传递率往往偏大。In addition, in the process of establishing the traditional strain transfer model, it is assumed that the shear stress is transmitted linearly in each layer of the sensor; but due to the characteristics of flexible materials, the shear stress is transmitted in the form of a quadratic curve in each layer, so the traditional strain The strain transfer rate calculated by the model is often too large.
近年来，国内外学者尝试通过添加边界条件、考虑层间结合等方式，增加应变传递模型在实际应用中可能遇到的问题，从而提高位移结果的精度，但这些方法没有改变模型本身精度不足的问题。In recent years, scholars at home and abroad have tried to increase the problems that the strain transfer model may encounter in practical applications by adding boundary conditions and considering interlayer bonding, so as to improve the accuracy of displacement results. However, these methods have not changed the lack of accuracy of the model itself. question.
因此，目前柔性传感器大多用于定性地测量结构的某些动力特征，精度不足是无法将其应用至实际工程应变测量的主要问题之一。Therefore, at present, flexible sensors are mostly used to qualitatively measure some dynamic characteristics of structures, and the lack of accuracy is one of the main problems that cannot be applied to actual engineering strain measurement.
发明内容Contents of the invention
为了解决以上问题，本发明提供一种基于切应力传递特性的应变测量方法和柔性传感器装置，通过将柔性材料切应力二次曲线传递的特性和应力应变关系结合得到改进的应变传递模型，提高了应变传递模型的精度，将柔性传感器应变传递过程量化和可视化，提高了柔性传感器的测量精度。In order to solve the above problems, the present invention provides a strain measurement method and a flexible sensor device based on the shear stress transfer characteristics, by combining the characteristics of the shear stress quadratic curve transfer of flexible materials and the stress-strain relationship to obtain an improved strain transfer model, which improves the The accuracy of the strain transfer model quantifies and visualizes the strain transfer process of the flexible sensor and improves the measurement accuracy of the flexible sensor.
为了实现上述目的，本发明采用以下技术方案予以实现：In order to achieve the above object, the present invention adopts the following technical solutions to achieve:
第一方面，本申请实施例提供了一种基于切应力传递特性的应变测量方法，包括：In the first aspect, the embodiment of the present application provides a strain measurement method based on shear stress transfer characteristics, including:
基于柔性传感器各层结构的应力关系，结合各层结构受力状态建立柔性传感器各层结构的轴向拉力/压力与剪力平衡方程；Based on the stress relationship of each layer structure of the flexible sensor, combined with the stress state of each layer structure, the axial tension/compression and shear force balance equations of each layer structure of the flexible sensor are established;
由所述轴向拉力/压力与剪力平衡方程得到正应力和切应力的映射关系；Obtain the mapping relation of normal stress and shear stress by described axial tension/pressure and shear force balance equation;
由所述正应力和切应力的映射关系，结合胡克定理，得到所述柔性传感器的切应力与敏感层应变关系方程；From the mapping relationship between the normal stress and the shear stress, combined with Hooke's theorem, the equation of the relationship between the shear stress and the strain of the sensitive layer of the flexible sensor is obtained;
根据所述柔性传感器中柔性材料的切应力在层间呈二次曲线传递的特性及位移与正应力、切应力的关系并结合所述切应力与敏感层应变方程得到所述柔性传感器中结构层与敏感层的位移平衡方程；According to the characteristic that the shear stress of the flexible material in the flexible sensor is transferred in a quadratic curve between layers and the relationship between displacement, normal stress and shear stress, and in combination with the shear stress and the strain equation of the sensitive layer, the structural layer in the flexible sensor is obtained Displacement balance equation with the sensitive layer;
由所述位移平衡方程结合所述敏感层的边界条件得到平均应变传递率；Obtaining an average strain transfer rate by combining the displacement balance equation with the boundary conditions of the sensitive layer;
将应变测量值除以所述平均应变传递率，得到修正后的应变值。The strain measurements were divided by the average strain transfer rate to obtain corrected strain values.
可选的，所述柔性传感器各层结构包括依次堆叠在结构层上的胶结层、基底层、敏感层和覆盖层；Optionally, each layer structure of the flexible sensor includes a bonding layer, a base layer, a sensitive layer and a covering layer sequentially stacked on the structural layer;
所述覆盖层三面包围所述敏感层，使得所述敏感层与空气隔绝；The covering layer surrounds the sensitive layer on three sides, so that the sensitive layer is isolated from the air;
所述敏感层，用于接收力学行为并转化为电学信号；The sensitive layer is used to receive mechanical behavior and convert it into an electrical signal;
所述基底层位于所述胶结层与所述敏感层之间，用于防止所述敏感层与所述结构层直接接触；The base layer is located between the cementing layer and the sensitive layer for preventing the sensitive layer from being in direct contact with the structural layer;
所述胶结层，用于连接所述柔性传感器与所述结构层。The adhesive layer is used to connect the flexible sensor and the structural layer.
可选的，所述正应力和切应力的映射关系为：Optionally, the mapping relationship between the normal stress and the shear stress is:
其中，Wc、Wg、Wb、Wp分别为所述覆盖层、所述敏感层、所述基底层和所述胶结层的横向宽度；hc、hg、hb、hp分别为所述覆盖层、所述敏感层、所述基底层和所述胶接层的厚度；τcg、τgb、τbp、τph分别为所述覆盖层和所述敏感层、所述敏感层和所述基底层、所述基底层和所述胶结层、所述胶结层和所述结构层的切应力，σc、σg、σb、σp为所述覆盖层、所述敏感层、所述基底层和所述胶接层的正应力，dx为沿所述敏感层长度方向任取的微元。Wherein, Wc , Wg , Wb , and Wp are the lateral widths of the covering layer, the sensitive layer, the base layer, and the cementing layer, respectively; hc , hg , hb , andhp are respectively is the thickness of the cover layer, the sensitive layer, the base layer and the adhesive layer; τcg , τgb , τbp , τph are the cover layer, the sensitive layer, the sensitive layer and the base layer, the base layer and the cementing layer, the cementing layer and the structural layer, σc , σg , σb , σp are the cover layer, the sensitive layer, the base layer and the adhesive layer, dx is a microelement randomly selected along the length direction of the sensitive layer.
可选的，所述柔性传感器的切应力与敏感层应变关系方程为：Optionally, the relationship equation between the shear stress of the flexible sensor and the strain of the sensitive layer is:
其中，in,
εg为所述敏感层的应变，Ec、Eg、Eb、Ep分别为所述覆盖层、所述敏感层、所述基底层和所述胶接层的弹性模量，εg is the strain of the sensitive layer, Ec , Eg , Eb , Ep are the elastic modulus of the covering layer, the sensitive layer, the base layer and the adhesive layer respectively,
可选的，所述得到所述柔性传感器的切应力与敏感层应变关系方程之后，所述方法还包括：Optionally, after obtaining the relationship equation between the shear stress of the flexible sensor and the strain of the sensitive layer, the method further includes:
根据所述柔性材料的切应力在层间呈二次曲线传递的特性，得到所述切应力的传递函数：According to the characteristic that the shear stress of the flexible material is transmitted in a quadratic curve between layers, the transfer function of the shear stress is obtained:
其中，τ1为各层下表面切应力，τ2为各层上表面切应力，h为各层材料厚度。Among them,τ1 is the shear stress of the lower surface of each layer,τ2 is the shear stress of the upper surface of each layer, and h is the material thickness of each layer.
可选的，所述位移与正应力、切应力的关系为：Optionally, the relationship between the displacement and normal stress and shear stress is:
其中，u为位移，σ为应力，ε为应变，E为弹性模量，Δ为该层结构相对下层结构的位移，τ为切应力，G为剪切模量。Among them, u is the displacement, σ is the stress, ε is the strain, E is the elastic modulus, Δ is the displacement of the layer structure relative to the underlying structure, τ is the shear stress, and G is the shear modulus.
可选的，所述结构层与所述敏感层的位移平衡方程为：Optionally, the displacement balance equation of the structural layer and the sensitive layer is:
其中，in,
可选的，所述敏感层的边界条件为：Optionally, the boundary conditions of the sensitive layer are:
其中，Lg为敏感层长度的一半。Among them, Lg is half of the length of the sensitive layer.
可选的，所述改进的应变传递模型及平均应变传递率为：Optionally, the improved strain transfer model and the average strain transfer rate are:
其中，L为敏感层长度。Among them, L is the length of the sensitive layer.
第二方面，本申请实施例提供了一种柔性传感器，用于采用上述任一方法测量应变值。In a second aspect, an embodiment of the present application provides a flexible sensor for measuring strain values by using any of the above methods.
可以看出，本发明实施例提供的一种基于切应力传递特性的应变测量方法和柔性传感器装置，提高了柔性传感器的测量精度，解决了柔性传感器应变测量精度低的问题。It can be seen that the strain measurement method and flexible sensor device based on the shear stress transfer characteristics provided by the embodiments of the present invention improve the measurement accuracy of the flexible sensor and solve the problem of low strain measurement accuracy of the flexible sensor.
附图说明Description of drawings
图1是本发明实施例提供的一种柔性传感器及结构层示意图；Fig. 1 is a schematic diagram of a flexible sensor and a structural layer provided by an embodiment of the present invention;
图2是本发明实施例提供的一种基于切应力传递特性的应变测量方法建立的流程图；Fig. 2 is a flow chart of establishing a strain measurement method based on shear stress transfer characteristics provided by an embodiment of the present invention;
图3(a)是本发明实施例提供的一种柔性传感器各层应力分布图；Figure 3(a) is a stress distribution diagram of each layer of a flexible sensor provided by an embodiment of the present invention;
图3(b)是本发明实施例提供的一种柔性传感器各层位移分析图；Fig. 3 (b) is the displacement analysis diagram of each layer of a kind of flexible sensor provided by the embodiment of the present invention;
图4是本发明实施例提供的一种基于切应力传递特性的切应力二次曲线传递分析图；Fig. 4 is a kind of shear stress quadratic curve transfer analysis diagram based on the shear stress transfer characteristic provided by the embodiment of the present invention;
图5是传统模型、本发明实施例模型和仿真结果应变传递系数对比图；Fig. 5 is a comparison chart of the strain transfer coefficient of the traditional model, the model of the embodiment of the present invention and the simulation result;
图6是传统模型、本发明实施例模型和仿真结果平均应变传递系数对比图；Fig. 6 is a comparison chart of the average strain transfer coefficient of the traditional model, the model of the embodiment of the present invention and the simulation result;
图7(a)是基底厚度为0mm时传统模型、本发明实施例模型和仿真结果应变传递系数对比图；Fig. 7 (a) is a comparison chart of the strain transfer coefficient of the traditional model, the model of the embodiment of the present invention and the simulation results when the substrate thickness is 0mm;
图7(b)是基底厚度0.25mm时传统模型、本发明实施例模型和仿真结果应变传递系数对比图；Fig. 7 (b) is a comparison chart of the strain transfer coefficient of the traditional model, the model of the embodiment of the present invention and the simulation results when the base thickness is 0.25 mm;
图7(c)是基底厚度2mm时传统模型、本发明实施例模型和仿真结果应变传递系数对比图；Fig. 7 (c) is a comparison chart of the strain transfer coefficient of the traditional model, the model of the embodiment of the present invention and the simulation results when the base thickness is 2 mm;
图7(d)是基底厚度4mm时传统模型、本发明实施例模型和仿真结果应变传递系数对比图；Fig. 7 (d) is a comparison chart of the strain transfer coefficient of the traditional model, the model of the embodiment of the present invention and the simulation results when the base thickness is 4 mm;
具体实施方式Detailed ways
下面将结合附图，对本公开实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本公开的一部分实施例，而不是全部的实施例。基于本公开所提供的实施例，本领域普通技术人员所获得的所有其它实施例，都属于本公开保护的范围。The technical solutions in the embodiments of the present disclosure will be clearly and completely described below in conjunction with the accompanying drawings. Apparently, the described embodiments are only part of the embodiments of the present disclosure, not all of them. All other embodiments obtained by persons of ordinary skill in the art based on the embodiments provided in the present disclosure belong to the protection scope of the present disclosure.
在本公开的描述中，需要理解的是，术语“中心”、“上”、“下”“前”、“后”、“左”、“右”、“竖直”、“水平”、“顶”、“底”、“内”、“外”等指示的方位或位置关系为基于附图所示的方位或位置关系，仅是为了便于描述本公开和简化描述，而不是指示或暗示所指的装置或元件必须具有特定的方位，以特定的方位构造和操作，因此不能理解为对本公开的限制。In describing the present disclosure, it is to be understood that the terms "center", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", " The orientations or positional relationships indicated by "top", "bottom", "inner" and "outer" are based on the orientations or positional relationships shown in the drawings, and are only for the convenience of describing the present disclosure and simplifying the description, rather than indicating or implying the It should not be construed as limiting the present disclosure that a device or element must have a particular orientation, be constructed and operate in a particular orientation.
除非上下文另有要求，否则，在整个说明书和权利要求书中，术语“包括”被解释为开放、包含的意思，即为“包含，但不限于”。例如包含了一系列步骤或单元的过程、方法、系统、产品或设备没有限定于已列出的步骤或单元，而是可选地还包括没有列出的步骤或单元，或可选地还包括对于这些过程、方法、产品或设备固有的其它步骤或单元。Unless the context requires otherwise, throughout the specification and claims, the term "comprising" is interpreted in an open and inclusive sense, ie "including, but not limited to". For example, a process, method, system, product or device comprising a series of steps or units is not limited to the listed steps or units, but optionally also includes unlisted steps or units, or optionally further includes For other steps or units inherent in these processes, methods, products or apparatuses.
在本公开的内容中，“在……上”、“上方”、和“之上”的含义应当以最宽泛的方式解释，使得“在...上”不仅意味着“直接在某物上”，而且还包括其间具有中间特征或层的“在某物上”的含义，并且“上方”或“之上”不仅意味着在某物“上方”或“之上”，还包括其间没有中间特征或层的在某物“上方”或“之上”的含义(即，直接在某物上)。In the context of this disclosure, the meanings of "on", "above", and "over" should be interpreted in the broadest possible way, so that "on" does not only mean "directly on something ", but also includes the meaning of "on something" with an intermediate feature or layer in between, and "above" or "over" means not only "above" or "above" something, but also without intervening The meaning of a feature or layer being "on" or "over" something (ie, directly on something).
本文参照作为理想化示例性附图的剖视图和/或平面图描述了示例性实施方式。在附图中，为了清楚，放大了层和区域的厚度。因此，可设想到由于例如制造技术和/或公差引起的相对于附图的形状的变动。因此，示例性实施方式不应解释为局限于本文示出的区域的形状，而是包括因例如制造而引起的形状偏差。因此，附图中所示的区域本质上是示意性的，且它们的形状并非旨在示出设备的区域的实际形状，并且并非旨在限制示例性实施方式的范围。Exemplary embodiments are described herein with reference to cross-sectional and/or plan views that are idealized exemplary drawings. In the drawings, the thickness of layers and regions are exaggerated for clarity. Accordingly, variations in shape from the drawings as a result, for example, of manufacturing techniques and/or tolerances are contemplated. Thus, example embodiments should not be construed as limited to the shapes of regions illustrated herein but are to include deviations in shapes that result, for example, from manufacturing. Thus, the regions illustrated in the figures are schematic in nature and their shapes are not intended to illustrate the actual shape of a region of a device and are not intended to limit the scope of example embodiments.
针对以上提到的柔性传感器测量精度不足的问题，原因为传统的应变传递模型不适用于柔性传感器中。在传感器结构中，传感器的敏感层是将结构变化转换为电信号变化的重要部分。敏感层受到覆盖层和基底的保护，传统传感器如光纤光栅传感器和应变片的敏感层材料一般为光纤、导电金属等，其弹性模量较大，相比其它层材料大几个数量级。实际应用中常常将其它各层的弹性模量忽略不计，因此，在传统模型中，会以敏感层底层的位移作为该层的整体位移；但对于柔性传感器，各层材料均具有良好的柔性和相容性，其弹性模量往往处于同一数量级。由于柔性传感器各层材料弹性模量较小，应变在从被测结构传递至传感器敏感层的过程中，会有较大的损耗，从而导致测量结果不准确。In view of the problem of insufficient measurement accuracy of flexible sensors mentioned above, the reason is that the traditional strain transfer model is not suitable for flexible sensors. In the sensor structure, the sensitive layer of the sensor is an important part that converts structural changes into electrical signal changes. The sensitive layer is protected by the covering layer and the substrate. The sensitive layer materials of traditional sensors such as fiber grating sensors and strain gauges are generally optical fibers, conductive metals, etc., and their elastic modulus is relatively large, which is several orders of magnitude larger than other layer materials. In practical applications, the elastic modulus of other layers is often ignored. Therefore, in the traditional model, the displacement of the bottom layer of the sensitive layer is used as the overall displacement of the layer; but for flexible sensors, the materials of each layer have good flexibility and Compatibility, the modulus of elasticity is often in the same order of magnitude. Due to the small elastic modulus of each layer of the flexible sensor, the strain will have a large loss in the process of transmitting from the measured structure to the sensitive layer of the sensor, resulting in inaccurate measurement results.
另外，传统的应变传递模型在建立的过程中，会假设切应力在传感器各层中以线性传递；但由于柔性材料的特性，切应力在各层中以二次曲线的方式传递，因此传统应变模型应用于柔性传感器中计算得到的应变传递率往往偏大。In addition, in the process of establishing the traditional strain transfer model, it is assumed that the shear stress is transmitted linearly in each layer of the sensor; but due to the characteristics of flexible materials, the shear stress is transmitted in the form of a quadratic curve in each layer, so the traditional strain The strain transfer rate calculated by the model applied to the flexible sensor is often too large.
本申请实施例针对以上问题提供的一种基于切应力传递特性的应变测量方法及柔性传感器装置，将柔性材料切应力二次曲线传递的特性和应力应变关系结合得到改进的应变传递模型，提高了应变传递模型的精度，将柔性传感器应变传递过程量化和可视化，提高了柔性传感器的测量精度，解决了柔性传感器应变测量精度低的问题，且本方法在传统的应变片和柔性应变传感器中均适用。计算简便且精度高，具有较强的工程适用性。The embodiment of the present application provides a strain measurement method based on the shear stress transfer characteristics and a flexible sensor device for the above problems, and combines the characteristics of the shear stress quadratic curve transfer of flexible materials with the stress-strain relationship to obtain an improved strain transfer model. The accuracy of the strain transfer model quantifies and visualizes the strain transfer process of the flexible sensor, improves the measurement accuracy of the flexible sensor, and solves the problem of low strain measurement accuracy of the flexible sensor, and this method is applicable to both traditional strain gauges and flexible strain sensors . The calculation is simple and accurate, and has strong engineering applicability.
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅用以解释本发明，并不用于限定本发明。In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.
请参阅图1，图1是本申请实施例提供的一种柔性传感器及结构层示意图，将柔性传感器简化为一个层层叠加的结构，如图1所示，柔性传感器1包括覆盖层2、敏感层3、基底层4，胶结层5，柔性传感器1通过胶结层5与结构层6进行连接，如上所述的柔性传感器1的各层材料均为线弹性材料，且各向同性。Please refer to FIG. 1. FIG. 1 is a schematic diagram of a flexible sensor and a structural layer provided by an embodiment of the present application. The flexible sensor is simplified into a layer-by-layer structure. As shown in FIG. 1, the flexible sensor 1 includes a cover layer 2, a sensitive Layer 3, base layer 4, adhesive layer 5, the flexible sensor 1 is connected to the structural layer 6 through the adhesive layer 5, and the materials of each layer of the flexible sensor 1 as described above are linear elastic materials and are isotropic.
覆盖层2位于敏感层3上方，在本申请的一个实施例中，覆盖层2位于敏感层3上方并从三面包围敏感层，即将敏感层3的顶面及侧面进行包裹，使得敏感层3与空气隔绝，防止空气中的成分与敏感层3中的材料发生反应，导致测量结果不稳定或减少传感器寿命，需要指出的是，上述覆盖层2与敏感层3的位置关系以及覆盖层2包围敏感层3的方式为本申请的一种可能的实现方式，本申请对此不作限定，任一使敏感层3与空气隔绝的方式均在本申请的保护范围内。The cover layer 2 is located above the sensitive layer 3. In one embodiment of the application, the cover layer 2 is located above the sensitive layer 3 and surrounds the sensitive layer from three sides. The air is isolated to prevent the components in the air from reacting with the materials in the sensitive layer 3, resulting in unstable measurement results or reducing the life of the sensor. It should be pointed out that the above-mentioned positional relationship between the covering layer 2 and the sensitive layer 3 and the surrounding sensitive The method of layer 3 is a possible implementation method of the application, which is not limited in the application, and any method of isolating the sensitive layer 3 from the air is within the scope of protection of the application.
敏感层3的主要作用为将接收的力学行为转化为电学信号，以压阻应变传感器为例，敏感层3为导电层，在本申请的一个实施例中，敏感层可以为复合材料，其具有一定的电阻，当结构层6发生应变时，会引起敏感层3同时发生应变，这使得敏感层3的电阻值发生变化，且电阻值的变化量与应变大小相关，通过仪器检测敏感层3的电阻变化，即可计算得到结构层6的应变大小。在本申请的一个实施例中，敏感层为MXene/PDMS复合材料，其中PDMS(polydimethylsiloxane)为聚二甲基硅氧烷。The main function of the sensitive layer 3 is to convert the received mechanical behavior into an electrical signal. Taking the piezoresistive strain sensor as an example, the sensitive layer 3 is a conductive layer. In one embodiment of the application, the sensitive layer can be a composite material, which has A certain resistance, when the structural layer 6 is strained, it will cause the sensitive layer 3 to be strained at the same time, which makes the resistance value of the sensitive layer 3 change, and the change of the resistance value is related to the strain. By changing the resistance, the strain of the structural layer 6 can be calculated. In one embodiment of the present application, the sensitive layer is an MXene/PDMS composite material, wherein PDMS (polydimethylsiloxane) is polydimethylsiloxane.
基底层4位于敏感层3下方，基底层4材料为PDMS，但不限于此，基底层4可以防止敏感层3与结构层6直接接触，结构层6通常具备一定的导电能力，当敏感层3与结构层6直接接触时，由于敏感层3为导电层，结构层6与敏感层3会发生电性相互作用，从而影响敏感层3的电阻值，影响最终测得的结构层6的应变值大小。The base layer 4 is located below the sensitive layer 3. The material of the base layer 4 is PDMS, but not limited thereto. The base layer 4 can prevent the sensitive layer 3 from directly contacting the structural layer 6. The structural layer 6 usually has a certain conductivity. When the sensitive layer 3 When in direct contact with the structural layer 6, since the sensitive layer 3 is a conductive layer, the structural layer 6 and the sensitive layer 3 will interact electrically, thereby affecting the resistance value of the sensitive layer 3 and affecting the final measured strain value of the structural layer 6 size.
柔性传感器1通过胶结层5以胶粘的方式粘附在被测结构，即结构层6上，在本申请的一个实施例中，胶结层5为PDMS，但不限于此，结构应力应变状态通过胶结层5和基底4层传递至敏感层3。The flexible sensor 1 is adhered to the structure under test, that is, the structural layer 6, in an adhesive manner through the bonding layer 5. In one embodiment of the present application, the bonding layer 5 is PDMS, but not limited thereto. The stress and strain state of the structure is passed through The bonding layer 5 and substrate 4 layers are transferred to the sensitive layer 3 .
如上所述各材料层的各物理性能参数，例如弹性模量和泊松比如下表1所示。As mentioned above, the physical property parameters of each material layer, such as elastic modulus and Poisson's ratio, are shown in Table 1 below.
柔性应变传感器各层材料物理性能参数Physical property parameters of each layer material of flexible strain sensor
表1Table 1
下面将进一步结合实施例，对柔性传感器的应变传递机理进行具体分析，在本申请实施例中，柔性传感器的各材料层采用线弹性材料，且各向同性；弹性体仅沿轴向即图1中的X方向均匀拉伸，传感器通过胶结层使应变片产生形变，传感器不直接承受外力；覆盖层、敏感层、基底层、胶结层和结构层各层之间的交界面结合紧密，不发生相对滑移；上述各材料层分别受到上下表面切应力和该层正应力的作用；温度变化引起的各材料层的形变不在本申请实施例考虑的范围内。The following will further combine the embodiments to analyze the strain transfer mechanism of the flexible sensor in detail. In the embodiment of the present application, each material layer of the flexible sensor is made of a linear elastic material and is isotropic; the elastic body is only along the axial direction, that is, Fig. 1 The X direction in the middle is stretched uniformly, the sensor deforms the strain gauge through the bonding layer, and the sensor does not directly bear the external force; the interface between the covering layer, the sensitive layer, the base layer, the bonding layer and the structural layer is tightly bonded, and does not occur Relative slippage; the above-mentioned material layers are respectively affected by the shear stress of the upper and lower surfaces and the normal stress of the layer; the deformation of each material layer caused by temperature changes is not within the scope of consideration of the embodiments of this application.
具体地，请参阅图2，图2为一种基于切应力传递特性的应变测量方法建立的流程图，本发明将结合图2对应变模型的建立及应变的测量进行详细阐述。Specifically, please refer to FIG. 2 . FIG. 2 is a flow chart of establishing a strain measurement method based on shear stress transfer characteristics. The present invention will describe in detail the establishment of a strain model and the measurement of strain in conjunction with FIG. 2 .
S101、首先,基于柔性传感器各材料层例如覆盖层、敏感层、基底层，胶结层的应力关系，结合各材料层受力状态建立柔性传感器各层结构的轴向拉力/压力与剪力平衡方程，轴向拉力/压力大小为正应力乘以微元长度，剪力的大小为切应力乘以微元间接触面积，具体如下：S101. First, based on the stress relationship of each material layer of the flexible sensor, such as the covering layer, sensitive layer, base layer, and cement layer, and combining the stress state of each material layer, the axial tension/compression and shear force balance equations of each layer structure of the flexible sensor are established. , the magnitude of the axial tension/compression is the normal stress multiplied by the length of the microelement, and the magnitude of the shear force is the shear stress multiplied by the contact area between microelements, as follows:
在柔性传感器沿敏感层长度方向任取微元dx，对各层进行受力分析，具体地，按照力的平衡原理，建立各材料层的轴向拉力/压力与剪力平衡方程如下：The microelement dx is randomly selected along the length direction of the sensitive layer in the flexible sensor, and the force analysis of each layer is carried out. Specifically, according to the force balance principle, the axial tension/compression and shear force balance equations of each material layer are established as follows:
(Wchc-Wghg)dσc+τcg(2hg+Wg)dx＝0 (1.1)(Wc hc -Wg hg )dσc +τcg (2hg +Wg )dx＝0 (1.1)
hgWgdσg+τgbWgdx-τcg(2hg+Wg)dx＝0 (1.2)hg Wg dσg +τgb Wg dx-τcg (2hg +Wg )dx＝0 (1.2)
hbWbdσb+τbpWbdx-τgbWgdx＝0 (1.3)hb Wb dσb +τbp Wb dx-τgb Wg dx＝0 (1.3)
hpWpdσp+τphWpdx-τbpWbdx＝0 (1.4)hp Wp dσp +τph Wp dx-τbp Wb dx＝0 (1.4)
上式中，Wc、Wg、Wb、Wp分别为覆盖层、敏感层、基底层和胶结层的横向宽度；hc、hg、hb、hp分别为覆盖层、敏感层、基底层和胶接层的厚度；τcg、τgb、τbp、τph分别为覆盖层和敏感层、敏感层和基底层、基底层和胶结层、胶结层和结构层的切应力，σc、σg、σb、σp为覆盖层、敏感层、基底层和胶接层的正应力；In the above formula, Wc , Wg , Wb , Wp are the lateral widths of the covering layer, sensitive layer, base layer and cementing layer; hc , hg , hb , hp are the covering layer, sensitive layer , the thickness of base layer and bonding layer; τcg , τgb , τbp , τph are the shear stresses of covering layer and sensitive layer, sensitive layer and base layer, base layer and bonding layer, bonding layer and structural layer, respectively, σc , σg , σb , σp are normal stresses of covering layer, sensitive layer, base layer and bonding layer;
S102、进一步地，根据上述轴向拉力/压力与剪力平衡方程得到正应力和切应力的映射关系式，具体如下：S102. Further, according to the balance equation of axial tension/compression and shear force, the mapping relationship between normal stress and shear stress is obtained, specifically as follows:
S103、进一步地，根据胡克定理，引入应力应变关系和各层材料弹性模量的关系，具体如下：S103. Further, according to Hooke's theorem, the relationship between the stress-strain relationship and the elastic modulus of each layer of material is introduced, as follows:
σ＝Eε (3)σ = Eε (3)
令：make:
上式中，σ为应力，ε为应变，E为弹性模量，Ec、Eg、Eb、Ep分别为覆盖层、敏感层、基底层和胶接层的弹性模量。In the above formula, σ is the stress, ε is the strain, E is the elastic modulus, Ec , Eg , Eb , Ep are the elastic modulus of the covering layer, sensitive layer, base layer and bonding layer, respectively.
由于覆盖层、敏感层、基底层和胶接层同步变形，三者应变梯度接近。因此，可以认为：Due to the synchronous deformation of the cover layer, sensitive layer, base layer and adhesive layer, the strain gradients of the three are close. Therefore, it can be considered that:
式中，εc、εg、εb、εp分别为覆盖层、敏感层、基底层和胶接层的应变。In the formula, εc , εg , εb , and εp are the strains of the covering layer, sensitive layer, base layer and adhesive layer, respectively.
将公式(3)-(5)带入到公式(2.1)-(2.4)中，并且为了简化表达式，令Bring formulas (3)-(5) into formulas (2.1)-(2.4), and in order to simplify the expression, let
可得各层切应力与敏感层应变关系方程如下：The relationship equation between the shear stress of each layer and the strain of the sensitive layer can be obtained as follows:
S104、由柔性材料特性可知，切应力在层间呈二次曲线传递，设其传递函数为y＝ax2。二次曲线图如图4所示，图中，h为材料层厚度，τ1为材料层下表面的切应力，τ2为材料层上表面的切应力，二者的差值τ1-τ2即为曲线末端x轴的坐标，将坐标(τ1-τ2,h)带入二次曲线方程，得到切应力的传递函数，具体如下：S104. It can be seen from the properties of the flexible material that the shear stress is transmitted between the layers in a quadratic curve, and its transfer function is set as y=ax2 . The quadratic curve is shown in Figure 4. In the figure, h is the thickness of the material layer, τ1 is the shear stress on the lower surface of the material layer, τ2 is the shear stress on the upper surface of the material layer, and the difference between the two is τ1 -τ2 is the coordinate of the x-axis at the end of the curve. Put the coordinate (τ1 -τ2 ,h) into the quadratic curve equation to obtain the transfer function of the shear stress, as follows:
根据材料力学可得位移与正应力、切应力间的关系，具体如下：According to the mechanics of materials, the relationship between displacement, normal stress and shear stress can be obtained as follows:
上述公式10-11中，u为位移，σ为应力，ε为应变，E为弹性模量，Δ为该层结构相对下层结构的位移，τ为切应力，G为剪切模量；In the above formula 10-11, u is the displacement, σ is the stress, ε is the strain, E is the modulus of elasticity, Δ is the displacement of the layer structure relative to the underlying structure, τ is the shear stress, and G is the shear modulus;
由公式(9)、(10)及公式(11)，计算得到柔性传感器各层相对下层结构的位移计算公式，具体如下：From the formulas (9), (10) and formula (11), the calculation formulas for the displacement of each layer of the flexible sensor relative to the underlying structure are obtained, as follows:
式中，Δ12为各层结构与下层结构的相对位移，u1为该层结构位移，u2为下层结构位移，G为剪切模量，h为各层材料厚度，ε为应变，τ1为各层下表面切应力，τ2为各层上表面切应力；In the formula, Δ12 is the relative displacement between each layer structure and the lower layer structure, u1 is the displacement of the layer structure, u2 is the displacement of the lower layer structure, G is the shear modulus, h is the material thickness of each layer, ε is the strain, τ1 is the shear stress on the lower surface of each layer,τ2 is the shear stress on the upper surface of each layer;
将各层对应的参数带入相对位移计算公式(12)中，得到：Put the corresponding parameters of each layer into the relative displacement calculation formula (12), and get:
柔性传感器敏感层为柔性材料，且具有一定的厚度，传统模型直接将敏感层下表面的位移代表该层位移是不准确的，因此本发明中将敏感层整体一半的相对位移引入应变传递公式中，根据图3(b)中结构层位移与敏感层位移间的关系，其中，敏感层位移取敏感层整体一半的相对位移，得到柔性传感器中结构层与敏感层的位移平衡方程，具体如下：The sensitive layer of the flexible sensor is a flexible material with a certain thickness. It is inaccurate for the traditional model to directly represent the displacement of the lower surface of the sensitive layer as the displacement of the layer. Therefore, in the present invention, the relative displacement of half of the entire sensitive layer is introduced into the strain transfer formula , according to the relationship between the displacement of the structural layer and the displacement of the sensitive layer in Figure 3(b), where the displacement of the sensitive layer takes half of the relative displacement of the whole sensitive layer, the displacement balance equation between the structural layer and the sensitive layer in the flexible sensor is obtained, as follows:
上式中：In the above formula:
S105、对位移平衡方程13.4求导，得到关于应变的常系数二阶线性非齐次微分方程，具体如下：S105. Deriving the displacement balance equation 13.4 to obtain a constant coefficient second-order linear non-homogeneous differential equation about strain, specifically as follows:
引入传感器敏感层边界条件，具体如下：Introduce the sensor sensitive layer boundary conditions, as follows:
式中，Lg为敏感层长度的一半；In the formula,Lg is half of the length of the sensitive layer;
求解得到应变的常系数二阶线性非齐次微分方程，即为改进的应变传递模型，具体如下：The constant coefficient second-order linear inhomogeneous differential equation obtained by solving the strain is the improved strain transfer model, as follows:
上式中，L为敏感层长度。In the above formula, L is the length of the sensitive layer.
通过敏感层与结构层应变之比，可得到改进的应变传递系数β，具体如下：Through the ratio of the strain of the sensitive layer to the structural layer, the improved strain transfer coefficient β can be obtained, as follows:
对式(12.8)应变传递系数求积分，得到平均应变传递率α，具体如下：Integrate the strain transfer coefficient of formula (12.8) to obtain the average strain transfer rate α, as follows:
S106、利用柔性传感器实际测量到的应变测量值除以平均应变传递率α即可得到修正后的更加精确的应变值，即，S106. Divide the measured strain value actually measured by the flexible sensor by the average strain transfer rate α to obtain a corrected and more accurate strain value, that is,
修正后的应变值＝应变测量值/αCorrected strain value = measured strain value/α
下面结合具体实施例来描述基于切应力传递特性的传感器应变传递模型改进后的效果，如图3(a)所示，以柔性传感器有限元模型为对象。在本实施例中，柔性传感器覆盖层、基底层、胶结层材料采用PDMS，敏感层材料采用MXene/PDMS复合材料，但不限于此；在本实施例中，覆盖层的尺寸为长80mm，宽30mm，高2.1mm,敏感层的尺寸为长60mm，宽10mm，高2mm,基底层的尺寸为长80mm，宽30mm，高0.5mm,胶结层的尺寸为长80mm，宽30mm，高0.05mm，但不限于此。The effect of the improved sensor strain transfer model based on the shear stress transfer characteristics will be described below in conjunction with specific embodiments, as shown in Figure 3(a), taking the finite element model of the flexible sensor as the object. In this embodiment, the flexible sensor covering layer, base layer, and bonding layer are made of PDMS, and the material of the sensitive layer is made of MXene/PDMS composite material, but not limited thereto; in this embodiment, the size of the covering layer is 80 mm in length and 80 mm in width. 30mm, height 2.1mm, the size of the sensitive layer is 60mm in length, 10mm in width, and 2mm in height, the size of the base layer is 80mm in length, 30mm in width, and 0.5mm in height, and the size of the cemented layer is 80mm in length, 30mm in width, and 0.05mm in height. But not limited to this.
如图3(a)所示，对传感器进行分层，标明各层的受力状态，通过基于切应力传递特性的传感器应变传递模型改进方法计算得到应变传递模型。在本申请的一个实施例中，可将传感器粘贴在结构中心位置，结构可以为Q235悬臂钢板，对钢板施加0.2的拉应变，测量传感器敏感层应变作为应变的传递。随后将物理性能参数输入改进的应变传递模型中，计算得到应变传递系数和平均应变传递率。As shown in Figure 3(a), the sensor is layered, and the stress state of each layer is marked, and the strain transfer model is calculated by the improved method of the sensor strain transfer model based on the shear stress transfer characteristics. In an embodiment of the present application, the sensor can be pasted at the center of the structure. The structure can be a Q235 cantilever steel plate. A tensile strain of 0.2 is applied to the steel plate, and the strain of the sensitive layer of the sensor is measured as the transmission of strain. Then the physical performance parameters were input into the improved strain transfer model, and the strain transfer coefficient and average strain transfer rate were calculated.
进一步地，为验证本发明适用于计算层状结构传感器的应变传递系数，另使用传统应变传递模型计算结果进行比较。图5给出了敏感层长度为60mm和100mm状态下，传统模型、优化模型和仿真结果的应变传递曲线的对比，图6给出了三者平均应变传递率随敏感层长度变化的结果对比。由图5和图6可知，本发明提出的应变传递模型改进方法误差显著小于传统应变传递模型的计算方法，这说明了本发明在提高应变传递模型精度上的有效性。Further, in order to verify that the present invention is applicable to the calculation of the strain transfer coefficient of the layered structure sensor, the calculation results of the traditional strain transfer model are used for comparison. Figure 5 shows the comparison of the strain transfer curves of the traditional model, the optimized model and the simulation results when the length of the sensitive layer is 60 mm and 100 mm, and Figure 6 shows the comparison of the average strain transfer rate of the three with the length of the sensitive layer. It can be seen from Figures 5 and 6 that the error of the improved method of the strain transfer model proposed by the present invention is significantly smaller than the calculation method of the traditional strain transfer model, which illustrates the effectiveness of the present invention in improving the accuracy of the strain transfer model.
进一步地，为验证本发明所述方法的适用性能广的特点，使用了不同厚度的基底层对结果进行对比，分别为0mm、0.25mm、2mm、4mm。图7(a)-图7(d)分别为各种基底层厚度下的应变传递系数对比，由图可知，在四种条件下，优化模型的结果都要更优于传统模型，这也说明了本发明在各种层状传感器上的适用性。Further, in order to verify the wide applicability of the method of the present invention, base layers of different thicknesses were used to compare the results, which were 0mm, 0.25mm, 2mm, and 4mm, respectively. Figure 7(a)-Figure 7(d) are the comparisons of strain transfer coefficients under various base layer thicknesses. It can be seen from the figure that under the four conditions, the results of the optimized model are better than the traditional model, which also shows that The applicability of the present invention on various layered sensors is shown.
通过上述图1-图7所示出的实施例中的一种基于切应力传递特性的改进的应变传递模型，将柔性材料切应力二次曲线传递的特性和应力应变关系结合得到改进的应变传递模型，提高了应变传递模型的精度，将柔性传感器应变传递过程量化和可视化，提高了柔性传感器的测量精度，解决了柔性传感器应变测量精度低的问题，且本方法在传统的应变片和柔性应变传感器中均适用。计算简便且精度高，具有较强的工程适用性。Through an improved strain transfer model based on the shear stress transfer characteristics in the above-mentioned embodiments shown in Figures 1 to 7, the improved strain transfer can be obtained by combining the characteristics of the shear stress quadratic curve transfer of flexible materials and the stress-strain relationship The model improves the accuracy of the strain transfer model, quantifies and visualizes the strain transfer process of the flexible sensor, improves the measurement accuracy of the flexible sensor, and solves the problem of low strain measurement accuracy of the flexible sensor. Applies to all sensors. The calculation is simple and accurate, and has strong engineering applicability.
以上所述的实施例仅仅是对本申请的优选实施方式进行描述，并非对本申请的范围进行限定，在不脱离本申请的设计精神的前提下，本领域普通技术人员对本申请的技术方案做出的各种变形及改进，均应落入本申请的权利要求书确定的保护范围内。The above-mentioned embodiment is only a description of the preferred implementation of the application, and is not intended to limit the scope of the application. On the premise of not departing from the design spirit of the application, those skilled in the art made the technical solution of the application Various modifications and improvements should fall within the scope of protection determined by the claims of the present application.
| Application Number | Priority Date | Filing Date | Title |
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| CN202310503631.4ACN116518910B (en) | 2023-05-06 | 2023-05-06 | Strain measurement method based on shear stress transfer characteristic and flexible sensor |
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| CN202310503631.4ACN116518910B (en) | 2023-05-06 | 2023-05-06 | Strain measurement method based on shear stress transfer characteristic and flexible sensor |
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| CN116518910Atrue CN116518910A (en) | 2023-08-01 |
| CN116518910B CN116518910B (en) | 2025-07-11 |
| Application Number | Title | Priority Date | Filing Date |
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| CN202310503631.4AActiveCN116518910B (en) | 2023-05-06 | 2023-05-06 | Strain measurement method based on shear stress transfer characteristic and flexible sensor |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2018113520A1 (en)* | 2016-12-21 | 2018-06-28 | 清华大学 | Flexible pressure sensor and fabricating method thereof |
| CN110987248A (en)* | 2019-11-28 | 2020-04-10 | 同济大学 | A kind of flexible tactile sensor and preparation method thereof |
| CN115270062A (en)* | 2022-09-28 | 2022-11-01 | 中国科学院武汉岩土力学研究所 | In-situ stress calculation method by stress relief method considering irregular borehole shape |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2018113520A1 (en)* | 2016-12-21 | 2018-06-28 | 清华大学 | Flexible pressure sensor and fabricating method thereof |
| CN110987248A (en)* | 2019-11-28 | 2020-04-10 | 同济大学 | A kind of flexible tactile sensor and preparation method thereof |
| CN115270062A (en)* | 2022-09-28 | 2022-11-01 | 中国科学院武汉岩土力学研究所 | In-situ stress calculation method by stress relief method considering irregular borehole shape |
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| CN116518910B (en) | 2025-07-11 |
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