Flexible three-dimensional force sensor and preparation and self-decoupling method thereof
By using a flexible three-dimensional force sensor with nested anisotropic structures and an orthogonal nested conductive network to achieve independent three-dimensional force sensing, the problem of complex interdimensional coupling and decoupling algorithms in traditional sensors is solved, thereby improving the sensor's sensitivity and anti-interference capability.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHONGQING UNIV OF POSTS & TELECOMM
- Filing Date
- 2026-04-24
- Publication Date
- 2026-07-21
Smart Images

Figure CN122429974A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of flexible electronics and intelligent sensing technology, specifically relating to a flexible three-dimensional force sensor and its fabrication and self-decoupling method. Background Technology
[0002] Three-dimensional force sensors are key components in fields such as robotics, precision assembly, automotive electronics, and biomechanics. Traditional three-dimensional force sensors mostly use strain gauges as sensing elements, indirectly calculating force values by measuring the strain generated in an elastic body under stress. However, strain gauges are susceptible to temperature influences and exhibit zero-point drift. Furthermore, the structural design of the elastic body makes it difficult to completely eliminate interdimensional coupling, leading to mutual interference in force measurements in different directions. Decoupling algorithms are complex and have limited accuracy. Existing technologies mainly face two major challenges: first, at the material level, most flexible force-sensitive materials are isotropic or quasi-isotropic, exhibiting similar stress responses in different directions, resulting in severe interdimensional signal coupling; second, at the structural level, reliance on planar two-dimensional structural design or complex post-decoupling algorithms fails to achieve decoupling of three-dimensional forces from a physical structural perspective.
[0003] With the development of smart materials, functional materials with self-sensing properties have provided new ideas for the design of force sensors. Among them, magnetorheological elastomers (MREs) and carbon nanotube composites have attracted attention due to their unique magnetic and electrical properties, respectively. Magnetorheological elastomers (MREs) can form anisotropic chain structures induced by magnetic fields, making it possible to achieve direction-specific sensing, while carbon nanotube composites exhibit a significant piezoresistive effect. Although some studies have attempted to combine multiple functional fillers to achieve synergistic effects, simple mixing often leads to mutual constraints rather than enhancement of performance. In particular, how to make composite materials exhibit controllable anisotropic sensing characteristics in three-dimensional space through material and structural design remains a technical challenge. Existing MRE-based sensors are mostly single-layered structures, and their magnetic flux is usually arranged in a single direction, making them sensitive only to strain in a specific direction and unable to independently sense normal and shear forces in three-dimensional space. In addition, the orientation of non-magnetic high-performance fillers (such as carbon nanotubes) requires high-intensity magnetic fields, resulting in high energy consumption and complex processes. How to integrate the anisotropy of materials with the three-dimensional structural design of macroscopic devices to form a sensing unit with inherent decoupling capability is a technical problem that urgently needs to be solved in this field.
[0004] Therefore, there is an urgent need to develop a flexible three-dimensional force sensor based on anisotropic structures that can distinguish and perceive three-dimensional forces from the structural origin, reduce interdimensional coupling, and have high sensitivity and anti-interference capabilities. Summary of the Invention
[0005] To address the problems existing in the prior art, this invention proposes a flexible three-dimensional force sensor. This flexible three-dimensional force sensor incorporates anisotropic structures, specifically including: multiple three-dimensional elastic skeletons, multiple anisotropic composite elastomers, and an electrode array; each three-dimensional elastic skeleton has at least one elastic deformation region for sensing normal forces, and its interior is provided with a cavity; the three-dimensional elastic skeletons are arranged vertically; the number of anisotropic composite elastomers is the same as the number of three-dimensional elastic skeletons, and the anisotropic composite elastomers fill the cavities of the three-dimensional elastic skeletons, with their internal functional fillers oriented in a specific direction for sensing in-plane two-dimensional forces; the electrode array is disposed outside the sequentially arranged three-dimensional elastic skeletons, and each electrode is electrically connected to the anisotropic composite elastomer.
[0006] A method for fabricating a flexible three-dimensional force sensor, the method comprising:
[0007] S1: Fabrication of a three-dimensional elastic framework;
[0008] S2: Prepare magnetically functionalized one-dimensional nanomaterials and disperse them in polymer prepolymers to form a magnetorheological precursor solution;
[0009] S3: Inject the magnetorheological precursor fluid into the cavity of the three-dimensional elastic skeleton and apply a directional magnetic field to orient the functional fillers along the planar direction;
[0010] S4: Curing composite slurry to form an anisotropic composite elastomer;
[0011] S5: Arrange an electrode array on the composite elastomer, integrate the signal processing unit, and complete the device packaging.
[0012] The present invention also provides a three-dimensional force self-decoupling method for a flexible three-dimensional force sensor, the method comprising: acquiring three-dimensional force components through a flexible three-dimensional force sensor; calculating the resistance changes in three orthogonal directions; constructing a linear mapping relationship between the three-dimensional force components and the resistance changes in the three orthogonal directions; and calculating the three-dimensional force components by measuring the resistance changes.
[0013] The beneficial effects of this invention are:
[0014] This invention achieves anisotropy from the microscopic distribution of materials to the macroscopic structure of the device through an orthogonal nested design of "skeleton-magnetic linkage," transforming three-dimensional forces into independent electrical signals that do not interfere with each other at the physical level, fundamentally solving the coupling problem. The resistance variation trend (positive / negative piezoresistive resistance) and magnitude of change in the orthogonal directions of this invention show significant differences, resulting in a directional sensitivity ratio far exceeding that of traditional strain gauge sensors, greatly reducing the complexity and error of the decoupling algorithm. This invention combines additive manufacturing and magnetic field induction technologies to achieve controllable construction of structures with micron-level precision. By adjusting skeleton parameters (porosity, layer thickness) and magnetic field sequences, the sensitivity, range, and other performance characteristics of the device can be precisely controlled. The ANF and polymer matrix of this invention endow the device with good flexibility and durability, making it suitable for complex curved surfaces and dynamic scenarios. This invention achieves high orientation of non-magnetic materials at lower magnetic field strengths through magnetic field induction technology, greatly reducing energy consumption. Attached Figure Description
[0015] Figure 1 This is a schematic diagram of the internal structure of the device of the present invention;
[0016] Figure 2 This is a three-dimensional elastic skeleton structure diagram of the present invention;
[0017] Figure 3 This is a structural diagram of the anisotropic composite elastomer of the present invention;
[0018] Figure 4 This is a flowchart illustrating the fabrication process of the three-dimensional force sensor of the present invention.
[0019] Figure 5 This is a schematic diagram of the anisotropic structure inside the device under stress according to the present invention;
[0020] Figure 6 This is a schematic diagram illustrating the changes in the anisotropic conductive network inside the device before and after being subjected to force, and the principle of force decoupling.
[0021] Figure 7 This is a schematic diagram of the force transmission path of the present invention. Detailed Implementation
[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0023] A flexible three-dimensional force sensor, such as Figures 1-3As shown, a flexible three-dimensional force sensor is nested with an anisotropic structure. The device includes: multiple three-dimensional elastic skeletons, multiple anisotropic composite elastomers, and an electrode array; the three-dimensional elastic skeletons have at least one elastic deformation region for sensing normal forces, and a cavity is provided inside; the three-dimensional elastic skeletons are arranged vertically; the number of anisotropic composite elastomers is the same as the number of three-dimensional elastic skeletons, and the anisotropic composite elastomers fill the cavities of the three-dimensional elastic skeletons, with their internal functional fillers oriented in a specific direction for sensing two-dimensional forces in the in-plane; the electrode array is disposed outside the three-dimensional elastic skeletons arranged vertically, and each electrode is electrically connected to the anisotropic composite elastomer.
[0024] In this embodiment, a three-dimensional elastic framework 1 serves as the structural matrix and the first conductive pathway of the device. This framework is constructed from a high-performance nanocomposite material using additive manufacturing technology, and its interior features a pre-defined, ordered hierarchical stacked structure and microchannels. Its multi-layered structure is specifically designed to sense normal (tensile and compressive) force components. Preferably, the framework material comprises a photosensitive resin, and aramid nanofibers (ANF) and MXene nanosheets dispersed therein. ANF provides mechanical toughness and support, while MXene provides high conductivity.
[0025] In this embodiment, the anisotropic composite elastomer 2 serves as the second conductive path and direction-sensitive unit of the device. It contains anisotropically oriented magnetic chains 2-1, which are formed by inducing a multidirectional sequential magnetic field within a polymer matrix (such as silicone rubber) using magnetically functionalized one-dimensional nanomaterials (preferably nickel nanoparticle-modified multi-walled carbon nanotubes, i.e., MWCNT@Ni). These magnetic chains are in situ filling the pores and channels of the three-dimensional multilayer framework. Crucially, the orientation of these magnetic chains is designed to be orthogonal to or at a specific angle to the stacking direction of the framework, thereby forming a nested and anisotropic three-dimensional conductive network within the device. When the elastic framework deforms under stress, it compresses or stretches the magnetorheological elastomer, causing changes in the arrangement and spacing of the internal magnetic particle chains, resulting in significant changes in its local resistivity and permeability.
[0026] In this embodiment, electrode array 3 is an electrode array with a specific pattern arranged on the surface or inside of the composite elastomer. By measuring the impedance change between different electrode pairs and combining it with the constitutive relationship of the anisotropic material, the direction and magnitude of the in-plane two-dimensional force can be decoupled and obtained.
[0027] The normal force electrodes (Z-direction sensing) 3-1 are distributed on the upper and lower principal planes of the sensing element. When a Z-direction normal force is applied to the sensor, the distance between the upper and lower surfaces changes, causing a dramatic change in the conductive network in the thickness direction (Z-direction) of the sensing element sandwiched in between. By measuring the impedance change between these interdigitated electrodes on the upper and lower surfaces, the impedance can be decoupled. Components. Differential measurement using paired upper and lower electrodes can suppress common-mode interference.
[0028] Tangential force electrodes (X-direction sensing) 3-2 are distributed at corresponding positions on the left and upper right of the sensing surface of the sensing unit. When When activated, the magnetic flux network arranged in the X direction inside the sensing unit changes, resulting in a change in the volume resistance along the X direction. This change is captured by the pair of side electrodes.
[0029] Tangential force electrodes (Y-direction sensing) 3-3 are distributed at corresponding positions in front of and behind the sensing surface of the sensing unit. Similar to the X-direction electrodes, when... During operation, the resistance between corresponding electrodes at the front and rear upper positions of the side is measured. Using symmetrical side electrode pairs for measurement can counteract the symmetry effect caused by the pure normal force, thereby specifically extracting the shear force signal.
[0030] Electrode lead-out and interface design: To ensure reliable signal extraction and meet practical application requirements, the sensor employs a flexible printed circuit board as the interface for electrode integration. Specifically, the endpoints of the upper and lower surface interdigitated electrodes and the strip electrodes on each side are electrically connected to corresponding pads on a custom-designed flexible printed circuit board via conductive silver paste or anisotropic conductive adhesive film, and are uniformly led out through a high-reliability board-to-board connector (e.g., a 16-pin connector with a 0.4mm pitch). This design integrates all the fine wiring into one unit, greatly reducing the number of external wiring harnesses and effectively avoiding signal crosstalk, mechanical fatigue, and assembly difficulties caused by multiple independent wires. This ensures the sensor of this invention has high three-dimensional force self-decoupling accuracy, long-term operational reliability, and mass production feasibility.
[0031] Example 1: A flexible three-dimensional force sensor with a nested anisotropic structure.
[0032] The sensor has a layered structure, consisting of a flexible encapsulation layer, an electrode layer, and a sensing element, from the outside in. For example... Figures 5-7As shown, the sensitive unit is the core of this invention, employing an orthogonal nested design of "skeleton-magnetic linkage". Specifically, the skeleton is a three-dimensional multilayer structure prepared by surface projection microscale photopolymerization 3D printing technology, composed of 2% by mass of aramid nanofibers, 5% by mass of MXene nanosheets, and a photosensitive resin matrix. The skeleton has a multilayer structure with dimensions of 15mm × 15mm × 1mm, with microchannels approximately 20μm wide between layers. Within the layers of the skeleton, a magnetostrictive anisotropic conductive network is filled. This network uses silicone rubber as a matrix, in which magnetically functionalized one-dimensional nanomaterials are dispersed and oriented, such as magnetic carbon nanotubes (MWCNT@Ni) with nickel nanoparticles loaded on their surface, synthesized by electrostatic adsorption and chemical reduction. The MWCNT@Ni filler is not randomly distributed. Instead, during the fabrication process, a magnetic field induces the MWCNT@Ni to overcome rotational resistance and align in an ordered manner within the layered stacked framework structure. This forms an anisotropic magnetic flux structure nested within the multi-layered framework, ensuring that its overall orientation is spatially parallel to the stacking direction of the three-dimensional framework. This creates a nested, anisotropic three-dimensional conductive network. This structure allows the sensor to undergo differentiated evolution of its internal conductive pathways when subjected to external forces in different directions, providing the physical basis for achieving three-dimensional force self-decoupling.
[0033] In this embodiment, the device fabrication method includes the following steps:
[0034] S1: Precise construction of the skeleton utilizes surface projection microscale photopolymerization 3D printing technology to print ANF / MXene / photosensitive resin composite slurry into a pre-defined three-dimensional multilayer skeleton structure. By adjusting printing parameters (such as dynamic mask patterns), the layer thickness, porosity, and microchannel dimensions of the skeleton are precisely controlled.
[0035] S2: Preparation of magnetorheological precursor liquid: MWCNT@Ni composite nanomaterials were synthesized by electrostatic adsorption and chemical reduction method, and then uniformly dispersed in silicone rubber prepolymer to form magnetorheological precursor liquid.
[0036] S3: Magnetic field-induced nested structure formation: The three-dimensional skeleton prepared in step S1 is completely immersed in the precursor solution prepared in step S2. A directional magnetic field (e.g., a 0.3 T magnetic field parallel to the X direction) is applied to induce MWCNT@Ni to oriented and align within the pores of the skeleton, forming a magnetic flux network orthogonal to the skeleton structure space.
[0037] S4: Curing composite slurry, which permanently fixes the orthogonal nested structure by heating or curing the silicone rubber matrix under magnetic field.
[0038] S5: Device integration and packaging. Flexible electrodes are prepared on the surface of the cured composite material, and signal processing units are integrated, wires are led out, and device packaging is completed.
[0039] Example 2: Method for fabricating the flexible three-dimensional force sensor
[0040] This embodiment details the controllable fabrication process of the sensor described in Embodiment 1.
[0041] The preparation method includes the following steps, such as: Figure 4 As shown:
[0042] (1) Construction of a three-dimensional multilayer skeleton: 1g of aramid nanofiber dispersion (1wt%), 0.5g of MXene nanosheets, 8.5g of photosensitive resin, 0.1g of photoinitiator, and 0.05g of lithium chloride viscosity modifier were mixed. After high-speed shear emulsification and ultrasonic dispersion, a uniform composite slurry was obtained (S101). Using a surface projection microscale photopolymerization 3D printer, with a layer thickness of 100μm and an exposure time of 2.5 seconds, a three-dimensional multilayer skeleton with a preset mesh structure was printed. After printing, it was ultrasonically cleaned with isopropanol and dried (S102).
[0043] (2) Synthesis of magnetic filler and preparation of precursor solution: First, multi-walled carbon nanotubes (MWCNTs) were carboxylated with concentrated acid. Then, nickel nanoparticles were grown in situ on the surface of the treated MWCNTs by chemical reduction to obtain MWCNT@Ni composite material (S201). 20 mg of this material was diluted and mixed with 100 mg of two-component silicone rubber prepolymer (A:B=10:1) and dispersant, and a uniform magnetorheological precursor solution (S202) was obtained by planetary stirring.
[0044] (3) Magnetic field-induced nested structure formation:
[0045] Method 1: The skeleton obtained in step (1) is completely immersed in the precursor solution prepared in step (2). The sample is placed in a magnetic field device to induce the magnetic filler to arrange in an orderly manner along a set direction, and vacuum-assisted infiltration is performed (S301). For example, a uniform magnetic field perpendicular to the X direction is applied, and the magnetic induction intensity can be set to 0.2 T-0.8 T. The sample is heated and cured in a magnetic field environment for 2 hours, and the temperature is controlled at 60°C-80°C to fix the nested structure (S302).
[0046] Method 2: The skeleton obtained in step (1) is completely immersed in the precursor solution prepared in step (2), and vacuum-assisted infiltration is performed. Subsequently, the sample is placed in a triaxial Helmholtz coil magnetic field device, and magnetic fields are applied sequentially in different directions, for example, a sequence of magnetic fields of 0.3 T in the X direction, 0.2 T in the Y direction, and 0.1 T in the Z direction are applied, each for 20 minutes, to induce the magnetic filler to align in an orderly manner along the set direction. Finally, while maintaining a 0.1 T perpendicular to the X direction, it is heated at 80°C for 2 hours to solidify the nested structure.
[0047] (4) Electrode fabrication and device packaging: Liquid metal interdigitated electrodes are screen-printed onto the surface of the cured sensitive unit and lead-out wires are formed (S501). Finally, a PDMS film with a thickness of about 100 μm is used as a flexible packaging layer for packaging (S502).
[0048] Working principle and innovation of this invention:
[0049] The three-dimensional force decoupling capability of this device stems from the differentiated piezoresistive effect generated by its unique "skeleton-magnetic linkage" orthogonal nested structure under stress:
[0050] Force applied in the X direction (perpendicular to most of the magnetic flux): The magnetic flux structure is stretched or destroyed, the tunneling resistance increases, which manifests as an increase in resistance (positive piezoresistive effect).
[0051] Force applied in the Y direction (parallel to part of the magnetic flux): The magnetic flux is compacted, the conductive path increases, resulting in a significant decrease in resistance (negative piezoresistive effect).
[0052] Force applied in the Z direction (perpendicular to the skeleton layer): The contact area of the magnetic flux planar network between the skeleton layers increases dramatically, forming a new conductive path, which manifests as a significant decrease in resistance (negative piezoresistive effect), and its range of change does not overlap with the X direction.
[0053] Example 3: Three-dimensional force self-decoupling method based on the sensor
[0054] This embodiment illustrates how to use the characteristics of the sensor described in Embodiment 1 to achieve decoupling of three-dimensional force signals.
[0055] The decoupling method includes: acquiring three-dimensional force components through a flexible three-dimensional force sensor; calculating the resistance changes in three orthogonal directions; constructing a linear mapping relationship between the three-dimensional force components and the resistance changes in three orthogonal directions; and calculating the three-dimensional force components by measuring the resistance changes.
[0056] The decoupling method is based on the differential piezoresistive effect generated by the orthogonal nested structure of the sensor. Specifically, when subjected to a force along the X-axis, the vertically oriented magnetic flux network is stretched or destroyed, increasing the tunneling resistance and thus exhibiting a positive piezoresistive effect. When the sensor is subjected to a force along the Y-axis, the parallel magnetic flux inside is compacted, increasing the conductive path and decreasing the resistance, thus exhibiting a negative piezoresistive effect. When subjected to a force along the Z-axis, the contact area of the magnetic flux network between the skeleton layers increases, forming a new conductive path, and the resistance also decreases, exhibiting a negative piezoresistive effect, and its range of variation does not overlap with that of the X-axis.
[0057] The decoupling method includes the following steps: first, obtaining the reference resistance value and sensitivity coefficient of the sensor in three orthogonal directions through calibration experiments; then, acquiring the resistance change value of the sensor under stress in real time; and finally, performing decoupling calculations based on a pre-established linear mapping model.
[0058] The mapping model is as follows:
[0059]
[0060] in, , , For the three-dimensional force components to be determined, , , This represents the measured rate of change of resistance. , , These are the sensitivity coefficients in each direction. , , To calibrate the constants, this model is used to achieve real-time solutions for the three-dimensional force components.
[0061] Because of its three-dimensional force self-decoupling capability, the sensor is particularly suitable for scenarios requiring the differentiation of complex force states. For example, in the field of intelligent driving, the sensor produced in this embodiment can be integrated into the steering wheel rim for driver grip detection. This system can accurately distinguish between states such as "hand off," "lightly resting," and "firmly gripping," because the sensor can independently decouple the normal grip force from the tangential friction force or steering force. This is only one exemplary application of the present invention; the sensor can also be widely used in fields requiring high-precision three-dimensional force perception, such as robotic tactile sensing, medical rehabilitation equipment, and intelligent prostheses.
[0062] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A flexible three-dimensional force sensor, characterized in that, The flexible three-dimensional force sensor is nested with anisotropic structures, specifically including: multiple three-dimensional elastic skeletons, multiple anisotropic composite elastomers, and an electrode array; the three-dimensional elastic skeletons have at least one elastic deformation region for sensing normal forces, and have cavities inside; the three-dimensional elastic skeletons are arranged vertically; the number of anisotropic composite elastomers is the same as the number of three-dimensional elastic skeletons, and the anisotropic composite elastomers fill the cavities of the three-dimensional elastic skeletons, with their internal functional fillers oriented in a specific direction for sensing two-dimensional forces in the in-plane; the electrode array is disposed outside the three-dimensional elastic skeletons arranged vertically, and each electrode is electrically connected to the anisotropic composite elastomer.
2. The flexible three-dimensional force sensor according to claim 1, characterized in that, The three-dimensional elastic framework comprises aramid nanofibers and MXene nanosheets, with interlayer microchannels having a width of 10-50 μm.
3. A flexible three-dimensional force sensor according to claim 1, characterized in that, Anisotropic composite elastomers are composed of an elastic polymer matrix, multi-walled carbon nanotubes, and soft magnetic particles. During the preparation process, the multi-walled carbon nanotubes and soft magnetic particles are oriented along the planar direction by an external magnetic field to form an anisotropic conductive / magnetic network.
4. A flexible three-dimensional force sensor according to claim 3, characterized in that, The mass fraction of multi-walled carbon nanotubes is 1%-2.5%, and the surface is coated with soft magnetic particles. The two form a synergistic piezoresistive-piezomagnetic coupling effect in the elastic polymer matrix.
5. A flexible three-dimensional force sensor according to claim 1, characterized in that, The electrode array comprises multiple independent electrode pairs arranged in a specific geometric pattern on the surface or inside of an anisotropic composite elastomer, used to detect changes in the electrical impedance of the composite elastomer in different directions.
6. A flexible three-dimensional force sensor according to claim 5, characterized in that, The electrode array includes at least two pairs of orthogonally arranged electrodes, which are used to detect the impedance changes in two orthogonal directions in the plane, and the impedance changes are mapped to the two-dimensional force components in the plane.
7. A flexible three-dimensional force sensor according to claim 1, characterized in that, The sensor's sensing structure is composed of an elastic deformation region of a three-dimensional elastic skeleton and an anisotropic composite elastic body. The sensing structure has different resistance response characteristics to force in three orthogonal directions, including positive piezoresistive effect and negative piezoresistive effect, and outputs force components in three orthogonal directions.
8. A method for fabricating a flexible three-dimensional force sensor, the method being used to fabricate a flexible three-dimensional force sensor as described in any one of claims 1 to 7, characterized in that, The method includes: S1: Fabrication of a three-dimensional elastic framework; S2: Prepare magnetically functionalized one-dimensional nanomaterials and disperse them in polymer prepolymers to form a magnetorheological precursor solution; S3: Inject the magnetorheological precursor fluid into the cavity of the three-dimensional elastic skeleton and apply a directional magnetic field to orient the functional fillers along the planar direction; S4: Curing composite slurry to form an anisotropic composite elastomer; S5: Arrange an electrode array on the composite elastomer, integrate the signal processing unit, and complete the device packaging.
9. A three-dimensional force self-decoupling method, wherein the method is used to decouple information acquired by any of the flexible three-dimensional force sensors described in claims 1-7, characterized in that, include: Three-dimensional force components are acquired using a flexible three-dimensional force sensor; Calculate the resistance changes in three orthogonal directions; A linear mapping relationship is established between the three-dimensional force components and the resistance changes in three orthogonal directions. The three-dimensional force components are calculated by measuring the resistance changes.