Physical experiment method for friction force

Abstract

The invention relates to the technical field of friction force experiments, and discloses a friction force physical experiment method which comprises the following steps: S1, establishing a multi-scale friction force model; s2, introducing a nonlinear dynamic model; s3, considering the influence of environmental factors; s4, designing an experiment system; s5, data acquisition and analysis; s6, experimental verification and optimization. The step of establishing the multi-scale friction force model comprises the substeps of establishing a microscopic friction force model based on molecular dynamics simulation; a macroscopic friction force model is deduced through a Hertz contact theory, and the influence of surface roughness and friction rate on a friction coefficient is introduced for modeling; and fitting experimental data through a least square method, and adjusting parameters in the friction force model. According to the invention, by introducing adaptive gain adjustment, disturbance compensation and robust control strategies, the stability, precision and adaptability of the system are significantly improved in friction force nonlinearity and external disturbance environments, and accurate control in a high dynamic range is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of friction experiments, and specifically to a physical experiment method for friction force. Background Art

[0002] In the fields of modern industry and robotics, friction control has always been the key to ensuring the normal operation of precision equipment and mechanical systems. The change of friction force not only affects the motion accuracy of mechanical components, but may also lead to energy waste and system instability. Therefore, how to effectively adjust and compensate for the friction force, especially in complex working environments, has become an important issue in the technical field.

[0003] In the prior art, common friction compensation methods include schemes based on PID control and model predictive control (MPC). PID control is simple and easy to implement, and can provide good performance in relatively stable environments; model predictive control (MPC) can optimize the control strategy of the system and improve the control accuracy by predicting the changes of the system state and control quantity. These methods are usually used to deal with some relatively linear friction models, and can improve the dynamic response and stability of the system to a certain extent. In addition, there are also some technologies that compensate for disturbances and nonlinear friction through predefined models, and use the controller adjustment strategy to reduce errors and improve the overall performance of the system.

[0004] However, there are still some deficiencies in the prior art. Although PID control and MPC can provide relatively stable results under ideal conditions, in an environment where the friction force is highly nonlinear or there are large external disturbances, the robustness and adaptability of these technologies are not strong enough. Due to the fixed gain of PID control, it cannot adapt to environmental changes and is prone to instability in complex environments. When the friction force changes or the external disturbance is large, the fixed control gain cannot respond to these changes in a timely manner, resulting in the system being unable to maintain the desired stability or accuracy. Although MPC can make predictions, when facing unknown disturbances or dynamic changes, the prediction accuracy of the model is often limited, resulting in slow system response or large errors. Especially in the case where the disturbance intensity and system parameters are constantly changing, the control strategy of MPC may fail, thus affecting the stability of the system; more critically, the prior art relies on predefined friction models or assumption conditions for control, but in the face of constantly changing working conditions in actual applications, these models are often not accurate enough. Therefore, it cannot adapt to the changes of the friction force in real time, resulting in limited system performance. Especially in high-speed and complex working environments, traditional control strategies cannot effectively compensate for the nonlinear changes of the friction force, resulting in reduced control accuracy and even system instability. Summary of the Invention

[0005] Aiming at the deficiencies of the existing technology, the present invention provides a physical experiment method for friction force, which solves the problems of non-linear change of friction force and poor adaptability and insufficient robustness of the control system under external disturbances in the existing technology.

[0006] To achieve the above objectives, the present invention is realized through the following technical solutions: A physical experiment method for friction force, comprising the following steps:

[0007] S1. Establish a multi-scale friction force model;

[0008] S2. Introduce a non-linear dynamics model;

[0009] S3. Consider the influence of environmental factors;

[0010] S4. Design an experimental system;

[0011] S5. Data acquisition and analysis;

[0012] S6. Experimental verification and optimization.

[0013] Preferably, the establishment of the multi-scale friction force model includes:

[0014] Establish a microscopic friction force model based on molecular dynamics simulation;

[0015] Derive a macroscopic friction force model through Hertz contact theory;

[0016] Introduce the influence of surface roughness and friction rate on the friction coefficient for modeling;

[0017] Fit the experimental data by the least squares method and adjust the parameters in the friction force model.

[0018] Preferably, the introduction of the non-linear dynamics model includes:

[0019] Use the Bouc-Wen non-linear model to describe the hysteresis effect of the friction force and adopt the dynamic equation of the classical Bouc-Wen model for modeling;

[0020] Use the Duffing oscillator model to describe the dynamic behavior of the friction force under high-frequency excitation. This model solves the Duffing equation through numerical integration or analytical methods to obtain the non-linear response characteristics;

[0021] Fit the experimental data by the least squares method and genetic algorithm to obtain the key parameters in the model, including the non-linear restoring force coefficient and the damping coefficient.

[0022] Preferably, the consideration of the influence of environmental factors includes:

[0023] Design a temperature-friction force model, and use the finite difference method to simulate the generation of frictional heat during the friction process and the influence of temperature on the frictional force;

[0024] Design a humidity-friction force model, and use the response surface method to simulate the influence of humidity on the surface lubricity and frictional force of materials;

[0025] Combined with experimental data, optimize the frictional force model under the influence of temperature and humidity through a fitting algorithm, and the fitting algorithm is the least squares method.

[0026] Preferably, the designed experimental system includes:

[0027] Design a dynamic loading system, and use the PID control algorithm to accurately control the mechanical loading in the experiment, including the normal force, tangential force and speed;

[0028] Equip high-precision equipment, including a laser interferometer and a displacement sensor;

[0029] Design an environmental control system, and use the fuzzy control algorithm to adjust the temperature, humidity and atmospheric pressure in the experiment;

[0030] Equip surface analysis equipment, including a scanning electron microscope and an atomic force microscope, for high-precision surface analysis of the friction contact surface.

[0031] Preferably, the data acquisition and analysis include:

[0032] Use a high-precision data acquisition system to record experimental data in real time, including frictional force, relative speed, normal force, temperature and humidity;

[0033] Fit the frictional force model by the least squares method and the genetic algorithm, and adjust the parameters in the frictional force model;

[0034] Use the particle swarm optimization algorithm to further optimize the model parameters so that the model can accurately describe the experimental data.

[0035] Preferably, the experimental verification and optimization include:

[0036] Compare the experimental data with the frictional force model to verify the accuracy of the model;

[0037] Based on the experimental feedback, adjust the experimental parameters in real time, including the loading rate, surface roughness of the friction surface and environmental temperature;

[0038] Use the genetic algorithm to optimize the experimental parameters to improve the accuracy and reliability of frictional force measurement.

[0039] Preferably, the designed experimental system further includes:

[0040] Surface treatment method: The friction surface is treated by laser surface modification and chemical vapor deposition to change the surface microstructure, thereby exploring the influence of the surface structure on the friction coefficient;

[0041] High-precision surface measurement technology: A scanning tunneling microscope and an ultra-high-resolution microscope are used to perform high-precision surface topography measurement on the friction contact surface to quantitatively describe the relationship between surface roughness and frictional force;

[0042] Surface roughness modeling: A roughness modeling method based on surface profile data is proposed, and surface microstructure information is incorporated into the friction force model to improve the accuracy of friction force prediction.

[0043] Preferably, the consideration of the influence of environmental factors further includes:

[0044] Modeling of multi-factor coupling influence: When considering the influence of environmental factors on the frictional force, in addition to temperature and humidity, the influence of atmospheric pressure on the frictional force is also considered, and a friction force model with multi-factor coupling is established;

[0045] Multi-dimensional monitoring of the experimental environment: During the experiment, a sensor network including temperature sensors, humidity sensors, and pressure sensors is used to monitor and collect experimental environment data in real time to ensure the stability of the experimental environment conditions and provide real-time feedback on environmental fluctuations during the experiment.

[0046] The present invention provides a physical experiment method for frictional force. It has the following beneficial effects:

[0047] 1. The present invention adopts an adaptive control technical solution. By adjusting the control gain in real time, the technical effect of maintaining the stability of the system performance under different working conditions is achieved. Compared with the fixed-gain control strategy in the prior art, the present invention solves the problem that the fixed gain cannot adapt to environmental changes through gain scheduling, enabling the system to cope with complex and non-linear frictional force changes and improving the adaptability and accuracy of the system.

[0048] 2. The present invention introduces robust control and disturbance compensation technical solutions to achieve real-time compensation for external disturbances and system uncertainties. Compared with the control solutions in the prior art that do not effectively compensate for disturbances, the present invention can effectively suppress the influence of external disturbances and significantly improve the stability and reliability of the system in harsh working environments.

[0049] 3. The present invention combines sliding mode control with an adaptive feedback mechanism to achieve the technical effect of precise control under system non-linearity and disturbances. Compared with the solutions in the prior art that rely on traditional PID control, the present invention greatly improves the anti-interference ability against uncertainties and disturbances through sliding mode control and significantly enhances the robustness of the system.

[0050] 4. The present invention combines dynamic gain regulation and disturbance observation techniques to achieve efficient and precise control in the feedback loop. Compared with the simple control strategies in the prior art, through the dual optimization of gain regulation and real-time disturbance compensation, the present invention enables the system to maintain high precision in a rapidly changing working environment, solving the problem of accuracy degradation caused by interference in traditional technologies. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a flowchart of the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0052] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the specification of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0053] Please refer to the attached Figure 1 , an embodiment of the present invention provides a physical experiment method for friction force, including the following steps:

[0054] S1. Establish a multi-scale friction force model;

[0055] Step S1 "establish a multi-scale friction force model", as the theoretical basis of the technical implementation path, undertakes the modeling core of the entire experimental scheme. In practical applications, friction force exhibits typical scale dependence, being affected by both microscopic interface structures and material intrinsic properties, as well as being dominated by macroscopic contact states and slip conditions. Therefore, before carrying out the experimental system design and non-linear response modeling, it is crucial to establish a multi-scale friction force model that can connect the microscopic and macroscopic scales.

[0056] The model proposed by the present invention is not an isolated static mechanical calculation framework, but a composite model system covering the interaction mechanism from the nanoscale to the statistical analysis of macroscopic friction behavior. Its purpose is to unify the responses of each scale of the friction system under the same expression framework, providing structural support for the experimental process.

[0057] In this embodiment, first, the molecular dynamics method is used to simulate the microscopic contact behavior.

[0058] In the actual modeling process, molecular dynamics platforms such as LAMMPS are used to calculate the nanoscale interface interactions. The van der Waals interaction, Coulomb potential energy, and bond energy potential function between atoms are considered in the model. The contact interface constructs the friction unit cell model under actual working conditions by setting different crystal orientations, orientation roughness, and loading rates, etc.

[0059] At this microscale, the frictional force exhibits an obvious non-linear rigid response relationship. In this embodiment, the frictional response caused by the elastic deformation due to micro-contact follows the basic characteristics of the Hertz contact model. Therefore, without repeating the foregoing formulas, the deformation-force response relationship is obtained by displacement-controlled loading. The micro-force values used are obtained by calculating the resultant force acting on the boundary atoms in the simulation. The normal deformation δ at the microscale is generally in the picometer to nanometer range, and the contact stiffness constant k H can be inversely obtained from the bulk modulus and lattice structure parameters of the material.

[0060] Furthermore, to achieve the micro-macro scale modeling mapping, at the macroscale, a statistical contact theory combined with experimental measurement data is used to construct the overall frictional force expression.

[0061] Generally, the macro frictional force varies linearly with the applied normal force, but in the present invention, the dynamic effects of the surface asperity distribution state, the change in the real contact area, and the slip velocity on the frictional behavior are considered. In this embodiment, the friction coefficient is no longer treated as a constant, but is expressed as a function of the velocity v and the roughness R q .

[0062] To achieve such an expression, the following semi-empirical model is used for fitting calculation:

[0063]

[0064] where: μ(v, R q ) is the dynamic friction coefficient (dimensionless) affected by velocity and roughness; μ0 represents the initial friction coefficient under standard conditions (such as low velocity, standard roughness), usually determined by experiments (dimensionless); β is the adjustment coefficient of the influence degree of velocity on the friction coefficient, and a positive value indicates that the friction increases with the increase of velocity (dimensionless); v is the relative slip velocity, with the unit of meters per second (m / s); v0 is the velocity normalization constant, used to adjust the sensitivity of the logarithmic function in the low-velocity section (unit: m / s); γ is the adjustment coefficient of the influence of surface roughness on the friction coefficient (dimensionless); R q is the root mean square value of the surface roughness, representing the statistical index of the height distribution of the interface asperities, with the unit of micrometer (μm) or nanometer (nm).

[0065] The logarithmic term in this expression is used to describe the enhanced trend of intermolecular mutual slippage caused by the enhanced interface kinetic energy due to the increase in velocity, and the linear roughness term reflects the macroscopic influence of the more complex morphology structure leading to an increase in the number of frictional contact points.

[0066] In some embodiments, to achieve the rapid quantification of model parameters, the present invention uses the least squares method to perform regression fitting on the unknown parameters in the formula. Experimental data is obtained through a displacement-controlled loading device, and the normal force, friction force, and velocity are synchronously recorded by high-precision sensors, and the roughness is obtained by AFM measurement.

[0067] During the model fitting process, taking the experimentally measured friction force data as the target response, a residual function is established and iterative minimization calculations are performed. In specific operations, the friction force model is substituted into the objective function, and the form is as follows:

[0068]

[0069] Where: is the friction coefficient of the i-th data point measured experimentally; v i is the slip velocity and roughness value corresponding to the i-th experimental point; n is the total number of experimental data points; is the friction coefficient value predicted by the model; is the surface roughness of the i-th sample point, with the unit of micrometer (μm); min is the minimization operation;

[0070] The fitting process can be carried out using numerical calculation platforms such as MATLAB and Python. It is recommended to use the gradient descent method, quasi-Newton method, or conjugate gradient method for optimization. Under the condition that the number of samples is sufficient (not less than 30 groups), the model residual is stable within 3%.

[0071] As a further extended method, under some micro-load or extremely low velocity conditions, the friction behavior may be dominated by the adhesion force. In this embodiment, it is considered to introduce an adhesion term as a correction to form a compensation term model. This adhesion force term is not listed separately to avoid repetition with the subsequent environmental model, but is embedded as a linear correction term in the overall model and usually plays a dominant role when the normal force is less than 5N.

[0072] Through the above-mentioned integration of micro-mechanical modeling, macro-behavior expression, and experimental data inversion, the multi-scale friction force model established in step S1 can not only reflect the multi-scale coupling behavior of the interface, but also provide the displacement-force relationship input for the subsequent non-linear hysteresis modeling, thereby achieving continuous expression and functional interoperability at the model level.

[0073] S2. Introduce a non-linear dynamics model;

[0074] Not only is the friction force expression embedded as a dynamic input into the system equation, but also the dynamic characteristics such as non-linear stiffness, energy dissipation, and hysteresis are combined to multi-dimensionally characterize the behavior of the system under actual working conditions.

[0075] In the dynamic modeling of the present invention, a non-linear single-degree-of-freedom vibration system is adopted as the basic structure. By introducing the aforementioned friction excitation term, non-linear stiffness term, and hysteretic sub-structure, the model can be applied to non-linear response scenarios such as structural slip, contact wear, and interface jump.

[0076] In this embodiment, the non-linear response model of the friction system can be established in the following form:

[0077]

[0078] Where: x(t) is the relative displacement of the system, in meters (m), representing the slip displacement of the friction element at time t; is the system velocity, in meters per second (m / s), which is the derivative of displacement with respect to time and is used to measure the slip rate; is the system acceleration, in meters per second squared (m / s 2 ), which is the second derivative of displacement with respect to time and reflects the inertial response of the system during slip; m is the equivalent mass, in kilograms (kg), representing the mass of the structure or slip component participating in the vibration. In the experimental setup, this value can be obtained by weighting the masses of the slider, bracket, and connecting components; c is the damping coefficient, in Newton-seconds per meter (N·s / m), which is used to characterize the energy dissipation ability within the system. This parameter is jointly determined by factors such as sliding friction damping, internal friction of the structure, and interface damping in the actual system; k is the linear stiffness coefficient, in Newtons per meter (N / m), corresponding to the restoring force stiffness of the structure within the small deformation range; α is the non-linear stiffness coefficient, in Newtons per cubic meter (N / m 3 ), representing the non-linear restoring force generated by the system at large displacements. It shows a "hardening" response when positive and a "softening" response when negative; F fric (t) is the friction excitation force, in Newtons (N). Its expression has been given in step S1 and acts as an external excitation term on the right side of the system in this model, and its value depends on the friction coefficient calculated under real-time velocity and roughness conditions; Δ f (t) is the perturbation term or unmodeled dynamic error, in Newtons (N). It is used to absorb complex physical processes not explicitly represented in the model, such as microscopic adhesion and detachment, thermal expansion perturbation, non-ideal support loosening, etc. This term is an auxiliary term and can be regarded as a small-amplitude white noise perturbation or a system error function in actual calculations.

[0079] In order to enhance the system's ability to characterize the friction hysteresis characteristics, in some embodiments, this embodiment further introduces a Bouc-Wen hysteretic sub-structure as an internal friction response sub-module, thereby replacing the traditional friction excitation term to form a strong hysteretic system containing dynamically evolving variables. At this time, the model expression is as follows:

[0080]

[0081] where: z(t) represents the internal hysteresis variable, dimensionless, representing the internal memory state of the hysteresis force and reflecting the non-instantaneous response of the friction system; is the time derivative of the hysteresis variable, with the unit of per second (1 / s), representing the evolution rate of the hysteresis behavior; A is the strength coefficient of the hysteresis term, with the unit of Newton (N), used to control the proportion and absolute amplitude of the hysteresis force in the overall system response; α1 is the rigid recovery factor, dimensionless, controlling the stiffness feedback part of the system's response to the input velocity; β1 is the energy dissipation term coefficient, dimensionless, used to describe the stability and energy dissipation characteristics of the hysteresis loop. The larger the value, the wider the hysteresis loop; γ1 is the dynamic asymmetry term coefficient, dimensionless, used to adjust the asymmetric behavior of the system, especially suitable for modeling the friction behavior under unbalanced excitation scenarios; n1 represents the nonlinear power control factor, unit: dimensionless. The higher the value, the more significant the nonlinear hysteresis behavior of the system.

[0082] In a possible implementation, the actual response variables of the system (such as displacement or acceleration) are measured in real time by experimental sensors (such as laser displacement meters, piezoelectric accelerometers), and then combined with this model for reverse verification, and then the model parameter identification and accuracy optimization are completed through algorithms such as least squares or Kalman filtering.

[0083] In addition, to ensure the stability of the system in frequency response analysis, eigenvalue analysis means are introduced in some embodiments to judge whether the relationship between the system damping ratio, natural frequency and response mode meets the measured response trend. By determining whether there is an imaginary part in the eigenvalues of the system matrix and controlling its numerical range, it is possible to predict in advance whether the system may have self-excited oscillation or critical instability problems.

[0084] In summary, by introducing a nonlinear dynamics model and a friction excitation coupling mechanism in step S2, not only the dynamic response structure of the mechanical system is established, but also physical support is provided for subsequent simulation prediction, parameter optimization and state reconstruction. By defining complete system parameters with clear physical meanings, it is ensured that the model has engineering applicability and research repeatability, and can achieve a complete logical connection with multi-scale friction models.

[0085] S3. Consider the influence of environmental factors;

[0086] The core objective of S3 is to reverse-identify the key physical parameters in the nonlinear system through the processing and fitting of experimental observation data, and then realize the correction, verification and optimization of the modeling results. In this process, relying on the dynamic structure and friction response expression established in the previous steps, multiple physical processes are integrated into a computable model through parameter space mapping to form a complete, data-driven parameter estimation and optimization framework.

[0087] Generally, there are many types of parameters involved in the friction system, including structural parameters (such as stiffness and damping), non-linear term parameters (such as hardening coefficient), influence factors in the friction coefficient function, and various hysteresis response control parameters in the hysteresis model. Since these parameters are difficult to obtain through direct measurement, it is necessary to inversely identify their values by combining numerical methods and experimental observation data. For this purpose, this step adopts a system parameter identification algorithm with multi-channel, nested, and regularization control, and constructs a corresponding residual minimization objective function. This method can take into account both the model prediction ability and the physical rationality of parameters, and is a key technical means to achieve system calibration and adaptive adjustment.

[0088] In this embodiment, the objective function based on the non-linear least squares method is constructed as follows:

[0089]

[0090] where: J(θ) is the value of the objective function, representing the fitting error between the model and the experimental data and the regularization control term under the current parameter set θ, with the unit of square meter (m 2 );

[0091] θ is the set of parameters to be identified, including the following multiple sub-items:

[0092] θ = {c, k, α, μ0, β, γ, A1, α1, β1, γ1, n2};

[0093] where: c is the damping coefficient, with the unit of N·s / m; k is the linear stiffness coefficient, with the unit of N / m; α is the non-linear stiffness coefficient, with the unit of N / m 3 ; μ0 is the reference friction coefficient, dimensionless; β is the adjustment coefficient of the influence degree of velocity on the friction coefficient, dimensionless; γ is the adjustment coefficient of the influence of surface roughness on the friction coefficient (dimensionless); A1 is the hysteresis amplitude factor, with the unit of N; α1 is the hysteresis rigidity control factor, dimensionless; β1 is the hysteresis energy dissipation control factor, dimensionless; γ1 is the hysteresis asymmetry adjustment factor, dimensionless; n2 is the hysteresis non-linear power control index, dimensionless.

[0094] is the experimentally collected displacement data at the i-th time node, with the unit of m; is the displacement value at the corresponding moment obtained by numerical integration of the model under the current parameter set θ, with the unit of m; n is the total number of experimental samples (i.e., the number of time sampling points), which is a positive integer; p is the number of parameters to be optimized, that is, the dimension of the vector θ; γ2 is the regularization coefficient (usually taking values such as 10 -4 ), dimensionless, and is used to prevent model overfitting or parameter drift.

[0095] The objective function consists of two parts: the former is the observation error term, which reflects the difference between the model prediction and the experimental data; the latter is the regularization control term, which restricts the parameters from taking too large values or oscillating, and enhances the stability of the numerical solution.

[0096] In a possible implementation, the model prediction part is numerically integrated and solved by the Runge-Kutta method. The initial conditions are set according to the experiment settings (for example, the initial displacement and initial velocity are zero), and the integration step size is set according to the experimental sampling frequency. For example, at a sampling rate of 1 kHz, Δt = 10 -3 s can be taken and dynamically adjusted within the error threshold range.

[0097] To improve the identification stability and convergence rate, one of the following numerical algorithms can be used for parameter search during the optimization process:

[0098] Levenberg–Marquardt (LM) method: used for medium-dimensional problems, combining the gradient and Newton directions;

[0099] Conjugate gradient method: suitable for large-scale parameter spaces;

[0100] Genetic algorithm: has stronger global convergence ability for non-convex objective functions and is applicable to problems with strong non-linear coupling between parameters.

[0101] As an option, to achieve the joint identification of multi-channel response data, this embodiment supports constructing a joint residual objective function, which is extended to the following form:

[0102]

[0103] Where: J total (θ) is the multi-channel objective function value, with the unit of square meter (m 2 ); w x , w v are the residual weight factors (unitless), which are used to balance the contribution degrees of different channels and can be set according to the channel noise levels; is the experimental and model prediction velocity value, with the unit of m / s, which can be obtained by differentiating the displacement data or taking the derivative of the model output.

[0104] This form simultaneously introduces the observation residuals of displacement and velocity, thereby enhancing the dynamic fitting ability of the model.

[0105] Specifically, in some embodiments, the generalization ability of parameter identification is also verified by setting strategies such as multiple initial values of the objective function, separation of the cross-validation set and the training set. Common methods include K-fold cross-validation, leave-one-out method, etc. If the multiple identification results converge within the allowable error range, it is considered that the model structure has strong stability.

[0106] In addition, to further improve the recognition credibility, a Bayesian posterior evaluation mechanism can also be introduced. As before, its basic framework is as follows:

[0107] P(θ|X) ∝ P(X|θ)·P(θ);

[0108] Where: P(θ|X) is the posterior probability distribution; P(X|θ) is the likelihood function, constructed from the residuals in the objective function; P(θ) is the prior distribution, which can usually be set as a Gaussian distribution or a uniform distribution, and is set according to engineering experience.

[0109] By analyzing the shape of the posterior distribution (such as maximum a posteriori estimation, covariance analysis, etc.), the uncertainty interval of the parameters can be obtained to assist subsequent system robustness analysis and fault tolerance boundary design.

[0110] S3 realizes the accurate identification and model calibration of the parameters of the nonlinear friction system by constructing an objective function with residuals as the core and integrating regularization, multi-channel optimization, and Bayesian analysis methods. This step not only completes the modeling closed-loop but also enables the entire modeling framework to have the ability of feedback correction, and can dynamically adapt to the variation characteristics of friction behavior under different working conditions.

[0111] S4. Design an experimental system;

[0112] S4 further constructs a system-level control closed-loop to achieve state regulation, disturbance suppression, and dynamic feedback control of the friction system. This step logically relies on the identified physical modeling parameters and state variables, and realizes the closed-loop control goal in a dynamic system with friction nonlinear characteristics by constructing a state estimation structure and a control strategy, thereby ensuring the stability, accuracy, and robustness of the experimental process or engineering system.

[0113] Generally, the nonlinear friction system has typical characteristics such as time-varying, non-stationary, and strong uncertainty. Simply relying on open-loop response or static parameter tuning cannot adapt to the continuous change of the system state with time or environmental disturbances. Therefore, in the present invention, in step S4, not only the state space expression form is designed, but also the extended state estimation and model predictive control structures are further integrated into the feedback path to form a stable, updatable, and adaptive system control framework.

[0114] In this embodiment, based on the system identification model and parameter set obtained in step S3, a state space expression form is first constructed for subsequent state estimator and controller design.

[0115] Generally, the system dynamics model can be rewritten as the following state space structure:

[0116]

[0117] Where: is the system displacement state variable, with the unit of m; is the system velocity state variable, with the unit of m / s; m is the equivalent mass, with the unit of kg; c, k, and α are the damping coefficient (N·s / m), linear stiffness (N / m), and nonlinear stiffness (N / m 3 ); F fric (t) is the friction excitation force.

[0118] This structure forms a second-order nonlinear state space model, which is the basis for the subsequent design of feedback controllers and observers.

[0119] To improve the system's perception ability of unobserved states (such as internal hysteresis terms or dynamic friction gains), an extended Kalman filter (EKF) is introduced in this embodiment to achieve joint state and parameter estimation. The state prediction process is as follows:

[0120]

[0121] Where: is the state prediction value at the k-th step; is the state estimation value updated at the k-th step; f(·) is the state transition function, corresponding to the aforementioned state space model; P k|k-1 is the covariance prediction matrix, describing the prediction uncertainty; A k is the Jacobian of the state transition matrix with respect to the state variables, reflecting the system dynamics; Q k is the process noise covariance matrix, resulting from modeling errors or disturbances; y k is the measurement vector at the k-th step, usually displacement or acceleration; h(·) is the observation model function; H k is the Jacobian matrix of the observation model; R k is the measurement noise covariance matrix; K k is the Kalman gain, used to correct the predicted state; θ is the set of parameters to be identified.

[0122] Through the EKF framework, not only can the system state be estimated, but also the unmeasurable states such as hysteresis variables and friction gain terms in the model can be dynamically updated.

[0123] After obtaining the available state estimation, a finite-time control strategy based on model predictive control (MPC) is introduced in this embodiment to achieve system response tracking and deviation adjustment.

[0124] Specifically, the following predictive control optimization problem is constructed:

[0125]

[0126] The constraint conditions are:

[0127]

[0128] u min u ≤ u(t + i) ≤ u max ;

[0129]

[0130] where: u(t) is the control input (such as active loading, friction regulator output), with the unit of N or V; x ref (t) is the desired response trajectory, with the unit of m; is the predicted displacement value at the i-th step; N p is the length of the prediction time domain window, with the unit of steps; Q and R are weight matrices that control the trade-off between response deviation and control cost; u min , u max are the upper and lower limits of the control signal; x min , x max are the displacement constraint conditions.

[0131] This optimization problem can be solved by quadratic programming or sequential quadratic programming methods to generate a control input sequence in real time for adjusting friction behavior, reducing system oscillations, and maintaining a stable operating state.

[0132] In a possible implementation, the feedback mechanism is nested and executed in the same control cycle as the Kalman filter and the model predictive controller. In each sampling period, state prediction and update are first performed, and then the optimal control input is solved based on the updated state to ensure that the system response is robust to unpredictable friction changes.

[0133] Generally, the entire control loop can be deployed in real time through LabVIEW, MATLAB / Simulink, or an embedded controller. Stable closed-loop control can be achieved when the system delay does not exceed 1 / 10 of the control cycle.

[0134] Through state-space modeling, extended Kalman filter design, and a feedback control strategy based on predictive optimization, the system realizes adaptive response regulation for nonlinear friction behavior, not only improving the stability of the system to disturbances but also providing a unified structural platform and implementation path for subsequent system expansion, online model update, and experimental feedback optimization.

[0135] S5. Data acquisition and analysis;

[0136] To systematically verify the response accuracy and stability of the foregoing model and control strategy under different working conditions, the present invention further introduces a simulation platform and a result analysis module in step S5, which are mainly used to output quantitative indicators such as the dynamic response curve, energy dissipation performance, and trajectory tracking accuracy of the system, and provide a standardized simulation tool set for comparing the performance of different controllers.

[0137] In the overall structure, step S5 serves as the "digital verification" phase of the system. It not only undertakes the response prediction function but also constructs a reference basis for the subsequent experimental platform parameter setting and controller deployment strategy, ensuring the integrity closed-loop from theoretical modeling to system implementation.

[0138] In this embodiment, the simulation process is based on the non-linear dynamic model established in step S2 and integrates the feedback control input in S4. The fixed-step numerical integration method is used for the discretization of the state variable evolution process. The adopted integration method is the classical fourth-order Runge-Kutta method, with the integration step size taken as Δt = 0.001 s and the total simulation duration being 10 seconds.

[0139] During the simulation process, to facilitate the observation of the controller's dynamic regulation ability for the non-linear friction system, generally, a representative initial perturbation or external excitation form is selected. As an option, a step reference signal x ref (t) or a sinusoidal perturbation excitation can also be set to simulate the system's response ability under sudden changes or periodic loads.

[0140] Specifically, in the case of the controller being added, the input signal u(t) of the system is generated in real-time by the MPC controller and applied to the friction system structure. The response of the simulation system to this input is manifested as the time-evolution trajectories of the state variables x1(t) (displacement) and x2(t) (velocity).

[0141] To quantify the system performance, the following energy loss index and trajectory tracking index are introduced in this embodiment:

[0142]

[0143] Where: E diss is the total friction energy consumption of the system within the total simulation duration T, with the unit of joule (J), representing the total energy loss generated by the system due to friction; μ(x2(t), R q ) is the friction coefficient function, which is a joint function of the velocity x2(t) and the surface roughness R q , dimensionless; N is the normal load applied to the friction interface, with the unit of newton (N), which is a constant value set in the simulation; x2(t) is the instantaneous velocity of the system, with the unit of meter per second (m / s); t is the simulation time variable, with the unit of second (s); |x2(t)| is the absolute value of the velocity, reflecting the energy transfer amount independent of the slip direction; T is the total simulation time, with the unit of second (s);

[0144] The integration is realized in a numerical discrete manner and is obtained by cumulative calculation for all time nodes.

[0145] This index can be used to quantify the energy dissipation ability under different control strategies or different friction surface roughness conditions, facilitating subsequent optimization design.

[0146] In some embodiments, to further evaluate the trajectory tracking ability and dynamic accuracy of the controller, the following error performance function is constructed in this embodiment:

[0147]

[0148] where: J track is the mean square error (MSE) of the trajectory tracking error, with the unit of meter; is the reference displacement value at the i-th time point, with the unit of meter (m); x1(t i ) is the actual displacement value output by the simulation system; n2 is the total number of simulation time steps; t i is the discrete time point (unit: second or other time unit), representing a certain time step in the discrete time series.

[0149] The smaller this index is, the stronger the tracking ability of the control system to the desired trajectory.

[0150] To further expand the simulation function, in some embodiments, different roughness R q conditions and speed excitation intervals are also set to perform a parameter sensitivity analysis on the friction coefficient function μ(v, R q ). For example, R q can be set as {20nm, 100 nm, 500nm}, corresponding to different surface texture treatment processes (such as mechanical polishing, sandblasting, anodizing, etc.). Combining the waveform and spectrum characteristics analysis of the system response, the nonlinear response mode of the friction structure under different friction interface conditions can be deduced.

[0151] In addition, in a specific implementation manner, the present invention also introduces a spectrum analysis and Fourier transform module to perform a frequency-domain analysis on the speed response x2(t) of the system. Its calculation formula is as follows:

[0152]

[0153] where: X2(f) is the Fourier transform result of the speed response in the frequency domain, with the unit of m / s·Hz -1 ; f is the frequency variable, with the unit of hertz (Hz); X2(t) is the time-domain signal, unit: m / s·Hz -1 , representing a physical quantity or system output that changes with time; f is the frequency (unit: hertz, Hz), representing the frequency-domain variable of the Fourier transform; t is the time (unit: second, s), representing the independent variable of the signal in the time domain; e -j2πft is the complex exponential function (unit: dimensionless), which is the core term in the Fourier transform, representing the weighted oscillation of the signal in the frequency domain; j is the imaginary unit (unit: dimensionless), representing the imaginary part in the complex number.

[0154] The Fourier spectrum can reveal the main vibration frequency, nonlinear frequency doubling response, and frequency mixing characteristics of the system, and assist in judging the modulation mode of the friction input in the frequency domain.

[0155] In a possible implementation, the spectrum analysis results are jointly evaluated with the energy consumption index in the time domain to optimize the controller bandwidth and filter design parameters.

[0156] To ensure the stability and authenticity of the simulation results, a simulation validity criterion is also defined in this embodiment, including the maximum displacement deviation limit (e.g., |x1(t)| ≤ 0.01m), the maximum control input limit (such as |u(t)| ≤ 50N), and the system response convergence time t s less than a preset value (e.g., 2s). If the above conditions are not met, the controller needs to be redesigned or the parameters need to be readjusted.

[0157] S5 realizes the multi-dimensional verification and technical closed-loop of the dynamic model and feedback control mechanism of the friction system constructed by the present invention through establishing a numerical simulation module, an energy and accuracy evaluation system, a spectrum analysis structure, and exploring the sensitivity of simulation parameters.

[0158] S6. Experimental verification and optimization;

[0159] S6 further optimizes the feedback control strategy of the system and introduces adaptive control and robust control technologies. The application of these technologies enables the system to maintain high robustness and accuracy in a complex external disturbance and friction change environment. By dynamically adjusting the control gain, compensating for disturbances in real time, and introducing advanced control methods, the core purpose of this step is to ensure that the control system has strong adaptability, can work stably in actual operation, and effectively cope with the influence of uncertain factors.

[0160] To handle the friction nonlinearity, external disturbances, and parameter uncertainties that the system may encounter in practical applications, this embodiment combines adaptive control and robust control strategies in step S6. The introduction of adaptive control enables the control gain to be adjusted in real time to adapt to changes in different working states; while robust control ensures that the system can maintain stability and accuracy even when the system parameters are uncertain or affected by external disturbances.

[0161] Adaptive control optimizes the system response by adjusting the control gain matrix. In this control structure, the control gain is adjusted according to the change of the system state to ensure that the system can still maintain good performance in a changing environment. Specifically, the adjustment rule of the control gain matrix K adjust (t) is:

[0162] K adjust (t) = K base + ΔK(t);

[0163] Where: K adjust (t) is the adjusted gain matrix at time t (unit: dimensionless), which is adjusted by an adaptive algorithm to ensure that the system can still maintain stable performance under non-linear friction and interference; K base is the reference gain matrix (unit: dimensionless), which is the initial gain value and is usually set under the condition that the system parameters are known and stable; ΔK(t) is the dynamic gain adjustment amount (unit: dimensionless), which is calculated based on the real-time state of the system and error feedback and is used to adjust the gain.

[0164] To cope with the influence of external disturbances on the system performance, a disturbance observer is further introduced in this embodiment. This observer can estimate and compensate external disturbances in real time to ensure that the system output is not affected by the disturbances.

[0165] The disturbance estimation formula is as follows:

[0166]

[0167] Where: is the disturbance estimation value at time t (unit: Newton, N), which is used to estimate the force exerted on the system by external disturbances; L is the disturbance observer gain (unit: dimensionless), which determines the response intensity of the disturbance estimator to the system output error. This gain needs to be adjusted through the control system design to ensure fast and accurate estimation of the disturbance; y(t) is the actual output value of the system (unit: meter or meter per second, depending on the specific system state). Usually, it is the displacement, velocity, etc. of the system; is the estimated output of the system (unit: meter or meter per second), which is given by the system model or filter; This embodiment combines adaptive control and robust control technologies to further improve the performance of the controller and the stability of the system. Through the combination of the two, the system can not only operate under large disturbances and parameter uncertainties, but also dynamically adjust the control strategy to adapt to the changing working environment; is the previous moment's estimation value of the external disturbance at time t - 1 (unit: Newton, N, or other appropriate units), which represents the disturbance estimation at the previous time step.

[0168] Specifically, the calculation formula for the control input u(t) is:

[0169]

[0170] Where: u(t) is the control input at time t (unit: Newton, N), which is the control signal calculated by the controller based on the system state and the disturbance estimation; K adjust(t) is an adaptive gain matrix (unit: dimensionless), which is the adjusted control gain for regulating the control input; x(t)3 is the system state variable vector (unit: meters and meters per second), which contains state information such as displacement and velocity. This state information serves as the system feedback input control signal; is the estimated value of the external disturbance (unit: Newton, N), which is given by the disturbance observer to compensate for the influence of the external disturbance on the system.

[0171] In a possible implementation manner, this embodiment combines the Sliding Mode Control (SMC) technology to further enhance the robustness of the system under disturbances. The sliding mode control enables the system to maintain strong robustness against external disturbances after reaching the sliding mode surface through the design of the "sliding mode surface" of the system state. This control method can greatly reduce the sensitivity of the system to external parameter uncertainties and disturbances, thereby ensuring the stability of the system in complex environments.

[0172] During the implementation process, the design goal of the sliding mode controller is to ensure that the system state variable x(t)3 can quickly approach the expected value and maintain a good dynamic response under the influence of external disturbances.

[0173] By combining robust control and disturbance compensation, this embodiment realizes a control scheme that can not only cope with the internal uncertainties of the system but also effectively suppress external disturbances. Specifically, the robust control module provides the disturbance rejection ability for the system, enabling the system to work stably under different load conditions; while the disturbance compensation module provides the real-time perception and compensation ability for external disturbances, ensuring the high-precision performance of the system in different working environments.

[0174] Step S6 enables the friction system of the present invention to maintain high performance and stability in a dynamic working environment by introducing various technical means such as adaptive control, robust control, and disturbance compensation. The combination of specific gain adjustment, disturbance estimation and compensation, and sliding mode control strategies ensures that the system can complete precise control tasks in complex and uncertain environments.

[0175] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A physical experiment method for friction force, characterized in that, It includes the following steps: S1. Establish a multi-scale friction force model; S2. Introduce a non-linear dynamics model; S3. Consider the influence of environmental factors; S4. Design an experimental system; S5. Data acquisition and analysis; S6. Experimental verification and optimization.

2. The frictional force physical experiment method according to claim 1, characterized in that, The establishment of the multi-scale friction force model includes: Based on molecular dynamics simulation, establish a microscopic friction force model; Derive a macroscopic friction force model through Hertz contact theory; Introduce the influence of surface roughness and friction rate on the friction coefficient for modeling; Fit the experimental data by the least squares method to adjust the parameters in the friction force model.

3. A method for a physical experiment on frictional force according to claim 1, characterized in that, The introduction of the non-linear dynamics model includes: Use the Bouc-Wen non-linear model to describe the hysteresis effect of the friction force, and adopt the dynamic equation of the classical Bouc-Wen model for modeling; Use the Duffing oscillator model to describe the dynamic behavior of the friction force under high-frequency excitation. This model solves the Duffing equation by numerical integration or analytical method to obtain the non-linear response characteristics; Fit the experimental data by the least squares method and genetic algorithm to obtain the key parameters in the model, including the non-linear restoring force coefficient and damping coefficient.

4. A physical experiment method for friction force according to claim 1, characterized in that, The consideration of the influence of environmental factors includes: Design a temperature-friction force model, and use the finite difference method to simulate the generation of frictional heat during the friction process and the influence of temperature on the friction force; Design a humidity-friction force model, and use the response surface method to simulate the influence of humidity on the surface lubricity of the material and the friction force; Combined with the experimental data, optimize the friction force model under the influence of temperature and humidity through a fitting algorithm, and the fitting algorithm is the least squares method.

5. A physical experiment method for friction force according to claim 1, characterized in that, The design of the experimental system includes: Design a dynamic loading system, and use the PID control algorithm to accurately control the mechanical loading in the experiment, including the normal force, tangential force and velocity; Equip with high-precision equipment, including a laser interferometer and a displacement sensor; Design an environmental control system, and use the fuzzy control algorithm to adjust the temperature, humidity and atmospheric pressure in the experiment; Equip with surface analysis equipment, including a scanning electron microscope and an atomic force microscope, to conduct high-precision surface analysis of the friction contact surface.

6. A method for a physical experiment of frictional force according to claim 1, characterized in that, The data acquisition and analysis includes: Use a high-precision data acquisition system to record the experimental data in real time, including the friction force, relative velocity, normal force, temperature and humidity; Fit the friction force model by the least squares method and genetic algorithm to adjust the various parameters in the friction force model; Use the particle swarm optimization algorithm to further optimize the model parameters so that the model can accurately describe the experimental data.

7. A method for a physical experiment on frictional force according to claim 1, characterized in that, The experimental verification and optimization includes: Compare the experimental data with the friction force model to verify the accuracy of the model; Based on the experimental feedback, adjust the experimental parameters in real time, including the loading rate, friction surface roughness and environmental temperature; Use the genetic algorithm to optimize the experimental parameters to improve the accuracy and reliability of the friction force measurement.

8. A method for a physical experiment of frictional force according to claim 1, characterized in that, The design of the experimental system further includes: Surface treatment method: Treat the friction surface by laser surface modification and chemical vapor deposition to change the surface microstructure, so as to explore the influence of the surface structure on the friction coefficient; High-precision surface measurement technology: Use scanning tunneling microscopes and super-high-resolution microscopes to perform high-precision surface topography measurements on friction contact surfaces, and quantitatively describe the relationship between surface roughness and friction force; Surface roughness modeling: Propose a roughness modeling method based on surface profile data, and incorporate surface microstructure information into the friction force model to improve the accuracy of friction force prediction.

9. A method for a physical experiment of frictional force according to claim 1, characterized in that The consideration of the influence of environmental factors further includes: Modeling of multi-factor coupling effects: When considering the influence of environmental factors on friction force, in addition to temperature and humidity, also consider the influence of atmospheric pressure on friction force, and establish a friction force model with multi-factor coupling; Multi-dimensional monitoring of the experimental environment: During the experiment, use a sensor network, including temperature sensors, humidity sensors, and pressure sensors, to monitor and collect experimental environment data in real time, ensure the stability of the experimental environment conditions, and provide real-time feedback on environmental fluctuations during the experiment.

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