Bolt fastening torque estimation and control method without torque sensor

Abstract

The invention discloses a bolt fastening torque estimation and control method without a torque sensor, which relates to the technical field of motor control and comprises the following steps of: modeling a bolt fastening system under an uncertain condition, and establishing a dynamic model containing time-varying parameters; based on motor current and rotating speed information which can be obtained in a bolt fastening system, a non-smooth torque observer is designed in combination with a kinetic model and is used for estimating the fastening torque of a bolt, and reliable feedback is provided for subsequent control; according to the fastening torque estimation value, a finite time control algorithm is designed in combination with a homogeneous technology and a power integration technology, and the finite time control algorithm is used for adjusting the estimated fastening torque in real time; carrying out stability analysis by utilizing a Lyapunov theory; and the gain parameter of the finite time control algorithm is adjusted, so that the obvious advantages in the aspects of control precision and anti-interference capability are ensured. According to the invention, the hardware dependence is reduced, the stability and reliability of the system are improved, the complexity and hardware cost of the system can be obviously reduced while the measurement precision is maintained, and the application requirements in a high-altitude or severe environment are met.

Description

Technical Field

[0001] The present invention relates to the technical field of motor estimation and control, and particularly to a method for estimating and controlling the bolt tightening torque without a torque sensor. Background Art

[0002] In engineering applications, bolt tightening is a crucial step to ensure the structural safety and stability, and is widely used in multiple fields, especially in high-altitude or special environment operation scenarios such as high-voltage transmission towers, construction sites, wind power generation facilities, bridge construction, and the installation and maintenance of large-scale mechanical equipment. These scenarios usually involve operations in high altitudes or complex environments, which pose extremely high requirements for the safety, efficiency, and accuracy of the operations. Therefore, the torque control during the bolt tightening process becomes the core link to ensure the structural connection strength and stability.

[0003] Traditional bolt tightening torque control methods usually rely on torque sensors for real-time measurement and feedback to ensure that the tightening torque reaches a predetermined value. Although this method can provide high measurement accuracy, there are several main problems in practical applications: 1) Increased system complexity: The installation and maintenance of torque sensors are very complex in high altitudes and harsh environments. Especially in high-altitude operations of transmission towers or wind power generation facilities, the arrangement and maintenance of sensors are very difficult. This not only increases the system complexity, but also may bring additional workload and safety risks. 2) High hardware cost: As a precision instrument, the torque sensor has a high cost. If a large number of sensors are used in large-scale structures or complex environments, it will not only increase the hardware cost of the system, but also reduce the overall economic benefits, and is not suitable for large-scale popularization and application. 3) Stability and reliability issues: Torque sensors are easily affected by external interference in high altitudes and harsh environments (such as strong winds, high temperatures, humidity, or vibration-prone environments), resulting in inaccurate measurement data. For example, vibration, temperature fluctuations, and electromagnetic interference, etc. Summary of the Invention

[0004] In order to overcome the above defects in the prior art, the present invention provides a method for estimating and controlling the bolt tightening torque without a torque sensor, so as to reduce the hardware dependence and improve the stability and reliability of the system, and be able to significantly reduce the system complexity and hardware cost while maintaining the measurement accuracy, and meet the application requirements in high altitudes or harsh environments.

[0005] To achieve the above object, the present invention adopts the following technical solutions, including:

[0006] A method for estimating and controlling the bolt tightening torque without a torque sensor, which estimates and controls the bolt tightening torque based on a finite-time control algorithm and a non-smooth extended state observer, specifically including the following steps:

[0007] S1. Under the condition of considering external disturbances and internal parameter uncertainties, model the bolt tightening system to obtain a dynamic model containing time-varying parameters. The bolt tightening system includes an end effector for tightening the bolt and a motor for driving the end effector.

[0008] S2. Based on the dynamic model, design a non-smooth extended state observer. The non-smooth extended state observer is used to dynamically estimate the tightening torque during the bolt tightening process according to the real-time measured speed and current of the motor.

[0009] S3. Design a finite-time control algorithm based on the power integral technique. For the external disturbances and internal parameter uncertainties of the system, by introducing a non-linear feedback term, adjust the estimated tightening torque in real time, so that the actual torque tracks the preset target torque within a finite time.

[0010] The target torque refers to the expected torque value preset according to the bolt tightening requirements.

[0011] S4. Use the Lyapunov theory to verify the stability of the system. By constructing a Lyapunov function and analyzing its derivative, judge the stability of the system.

[0012] S5. Approximate the optimal control effect by adjusting the gain parameters of the finite-time control algorithm.

[0013] Preferably, the specific method of step S1 is as follows:

[0014] S11. The functional relationship between the bolt tightening torque T b and the tightening angle θ b is T b = b(t)θ b ; where b(t) is a time-varying parameter.

[0015] Taking the time derivative of both sides of the equation T b = b(t)θ b yields:

[0016]

[0017] where is a continuously differentiable non-negative function representing the relative change rate of b(t); ω b is the tightening speed.

[0018] S12. The dynamic relationship between the motor and the bolt tightening torque is:

[0019]

[0020] where ω bis the fastening speed; n is the reduction ratio, representing the ratio of the motor speed to the bolt speed; J is the moment of inertia of the motor; K t is the torque constant; i q is the armature current of the motor; B is the viscous damping coefficient of the motor;

[0021] S31, the dynamic model containing time-varying parameters is obtained as follows:

[0022]

[0023] Preferably, in step S2, the non-smooth extended state observer is as follows:

[0024]

[0025] Among them, represents the estimated value of the fastening speed ω b calculated by the observer; represents the derivative of; represents the estimated value of the fastening torque T b calculated by the observer; T0 is the equivalent load torque, represents the estimated value of the equivalent load torque T0 calculated by the observer; L1 and L2 are two gain coefficients of the non-smooth extended state observer; sgn(·) is the sign function.

[0026] Preferably, in step S3, the finite-time control algorithm is as follows:

[0027]

[0028] Among them, is the first gain of the finite-time control algorithm, used to adjust the nonlinear feedback strength of the torque tracking error e1; is the second gain of the finite-time control algorithm, used to control the amplitude of the nonlinear feedback term; a2, a3, a4, a5, a6, c1 are all positive constants; is the linear feedback term, b min is the minimum value of the time-varying parameter; τ is the power adjustment parameter of the finite-time control;

[0029] By adjusting i q , the torque tracking error e1 converges within a finite time.

[0030] Preferably, in step S5, the gain parameters are adjusted by the trial-and-error method.

[0031] Preferably, in step S3, the estimated value of the bolt fastening torque is also corrected and filtered.

[0032] The present application also provides a readable storage medium, on which a computer program is stored, and when the computer program is executed, the bolt tightening torque estimation and control method of a torque-free sensor is implemented.

[0033] The present application also provides an electronic device, which includes a processor, a memory, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the bolt tightening torque estimation and control method of a torque-free sensor is implemented.

[0034] The present application also provides a computer program product, which includes a computer program / instructions. When the computer program / instructions are executed by a processor, the bolt tightening torque estimation and control method of a torque-free sensor is implemented.

[0035] The advantages of the present invention are as follows:

[0036] (1) The hardware cost of the present invention is significantly reduced. By designing a nonsmooth extended state observer (ESO), the system can use the existing motor current and speed signals for torque estimation, thus no longer relying on expensive torque sensors. This design greatly reduces the hardware investment, reduces the overall cost of the system, and improves the economic benefits, making it suitable for large-scale applications. In contrast, traditional methods rely on precise torque sensors, which are not only expensive but also require a large number of arrangements and maintenance, thus increasing the overall cost of the system.

[0037] (2) The present invention has significant advantages in terms of response speed and control accuracy. By combining homogeneous theory and power integral technology to design a finite-time controller, it can achieve fast response and precise tracking of the tightening torque within a finite time. This algorithm can still maintain a high-precision control effect under external disturbances and uncertain conditions, ensuring the reliability and efficiency of the tightening process. In contrast, although traditional torque sensors have high precision, their response speed is limited when dealing with sudden disturbances, and additional calibration is usually required to maintain accuracy.

[0038] (3) The environmental adaptability and stability of the present invention are significantly better than traditional methods. By combining a nonsmooth extended state observer (ESO) and a finite-time control algorithm, the present invention can maintain high robustness under uncertainties and external disturbances. Even under high-temperature, humid, or vibration conditions, the present invention can still estimate the torque through internal signals of the system, ensuring the accuracy of the tightening operation and the overall stability of the system. Relatively speaking, torque sensors are easily disturbed in these complex environments, resulting in inaccurate measurements and reducing the reliability of the system.

[0039] (4) The present invention has a strong anti-interference ability. The non-smooth extended state observer combines a filtering and real-time correction mechanism, effectively eliminating the influence of high-frequency noise and environmental interference. At the same time, the control algorithm is verified using Lyapunov stability theory to ensure that the system can still operate stably under complex external conditions and uncertainties. This design improves the robustness and control effect of the system, thus ensuring the safety and accuracy of the bolt tightening process. Description of the Drawings

[0040] Figure 1 It is a flowchart of a method for estimating and controlling the bolt tightening torque without a torque sensor according to the present invention.

[0041] Figure 2 It is a schematic diagram of bolt tightening. Detailed Embodiment

[0042] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments 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. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0043] The bolt tightening system based on a robot includes a robotic arm, an end effector (tightening tool), a motor, and a controller.

[0044] The robotic arm has multi-degree-of-freedom joints and can flexibly reach different bolt positions to adapt to various complex working environments. The end effector is equipped with a dedicated tightening tool to achieve automatic tightening of bolts of different specifications and sizes. The bolt tightening torque of the end effector is controlled by the motor. The controller is used to process data from various sensors and observers, and according to the real-time estimated tightening torque, precisely adjust the output of the motor drive unit using a finite-time control algorithm, and control the bolt tightening torque of the end effector through the motor.

[0045] The bolt tightening system has an adaptive ability and can still maintain a stable tightening torque at high altitudes or in harsh environments, ensuring the safety and reliability of the working process. In addition, through modular design, the bolt tightening system has an expansion ability and can be customized according to different operation requirements.

[0046] The bolt tightening system in this embodiment first collects the current and rotational speed signals of the motor as inputs. The controller inputs the collected signals into a non-smooth extended state observer (ESO) for real-time tightening torque estimation. The observer (ESO) is based on the dynamic model of the system, and uses the rotational speed and current data of the motor to calculate the tightening torque value, and compensates for the time-varying parameters and uncertainty factors therein. The entire estimation process removes high-frequency noise through filtering technology, thereby obtaining a smooth and accurate tightening torque estimation value.

[0047] During this process, it is ensured that the output tightening torque value has good stability and anti-interference ability under the premise of high precision. The design of the observer enables real-time torque monitoring during the bolt tightening process by utilizing the existing signals of the system without relying on an additional torque sensor.

[0048] As Figure 1 shown, a method for estimating and controlling the bolt tightening torque without a torque sensor according to the present invention specifically includes the following steps:

[0049] S1, analyze and model the bolt tightening system. Analyze the working principle and process of the bolt tightening system, and model the bolt tightening process under the conditions of considering external disturbances (such as environmental temperature changes, mechanical vibrations, etc.) and internal parameter uncertainties (such as motor parameter changes, friction coefficient changes, etc.) to obtain a dynamic model containing time-varying parameters.

[0050] This dynamic model covers the dynamic equation of the motor, the load torque equation, and the dynamic relationship between the bolt tightening angle and the tightening torque. Specifically, the dynamic equation of the motor describes the interaction between the motor current, voltage, rotational speed, and torque; the load torque equation considers factors such as friction and pre-tightening force involved in the bolt tightening process; and the dynamic relationship between the bolt tightening angle and the tightening torque depicts the correlation between the bolt rotation angle and the required torque during the tightening process. By constructing this system model, the mutual influence between torque, rotational speed, and current during the bolt tightening process can be comprehensively described, laying a theoretical foundation for subsequent observer design and controller design.

[0051] S2, design a non-smooth extended state observer for estimating the tightening torque.

[0052] Based on the dynamic model, using the motor current and rotational speed information available in the bolt tightening system, design a non-smooth extended state observer (ESO). This observer uses the dynamic equation of the motor and dynamically estimates the bolt tightening torque during the bolt tightening process by measuring the rotational speed and current values of the motor in real time. Measuring the actual torque through a torque sensor, that is, the true torque received by the bolt during the bolt tightening process, can verify the accuracy of the designed observer.

[0053] S3. Design a finite-time control algorithm based on the power integral technique to rapidly converge and precisely control the tightening torque. After obtaining an accurate torque estimate value, use the finite-time control algorithm based on the power integral technique to rapidly converge and precisely control the tightening torque for the uncertainties and disturbances in the bolt tightening system. This control algorithm adjusts the estimated torque in real time by introducing a non-linear feedback term, so that the actual torque tracks the preset target torque within a finite time. This algorithm ensures that the system stably performs the bolt tightening operation under the conditions of high precision and fast response.

[0054] S4. Use the Lyapunov theory to analyze the stability of the system, and prove that the system converges and reaches a stable state within a finite time.

[0055] To verify the stability of the control system, use the Lyapunov theory to strictly analyze the system. By constructing a Lyapunov function and solving its derivative, it is proved that under the combined action of the finite-time control algorithm and the ESO, the system can converge to a stable state within a finite time, that is, the tightening torque error (output torque - target torque) tends to zero or its neighborhood, ensuring that the bolt tightening torque can accurately reach the set value. In addition, through the sensitivity analysis of different parameters, the robustness and reliability of the designed system in practical applications are further verified.

[0056] S5. For the gain parameters of the finite-time control algorithm, first delimit the range of its sufficient conditions through theoretical derivation. Subsequently, use the trial-and-error method to further adjust the gain parameters to ensure their significant advantages in terms of control accuracy and anti-interference ability.

[0057] Through the theoretical derivation in S4, the sufficient conditions for the gain parameters are obtained. Then, in order to further improve the control accuracy and anti-interference ability of the system, the trial-and-error method is used to adjust the gain parameters. In practical applications, due to the existence of factors such as the dynamic characteristics of the system, external disturbances, and modeling errors, the range of gain parameters obtained by theoretical derivation may not directly achieve the optimal control performance. Therefore, the trial-and-error method adjusts the specific values of the gain parameters through multiple experiments and simulations, gradually approaching the optimal control effect. During this process, different disturbance situations and changes in the working environment are considered, and by comparing indicators such as control accuracy, response time, and anti-interference performance, the most suitable gain parameter values are finally determined.

[0058] In step S1, in order to accurately describe the dynamic behavior of the bolt tightening system, based on physical laws and dynamic analysis, the following dynamic model is established.

[0059] (1) The dynamic model of the tightening torque: The bolt tightening torque T b and the tightening angle θ b have a certain functional relationship, and its form is: Tb = b(t)θ b . Among them, b(t) is a time-varying parameter that reflects the influence of factors such as friction coefficient and temperature on the torque. To analyze its dynamic characteristics, the time derivative is taken on both sides of the above equation:

[0060]

[0061] Among them, is a continuously differentiable non-negative function representing the relative change rate of b(t). This equation shows that the change of the tightening torque is not only related to the bolt tightening speed ω b but also affected by the dynamic adjustment of the time-varying parameter b(t).

[0062] (2) The dynamic relationship between the motor and the bolt is as follows:

[0063]

[0064] Among them, ω b is the bolt tightening speed, with the unit of radians per second (rad / s); n is the reduction ratio, which is the ratio of the motor speed to the bolt speed and is dimensionless; J is the moment of inertia of the motor, with the unit of kilogram square meter (kg·m 2 ); K t is the torque constant, which reflects the relationship between the motor current and the generated electromagnetic torque, with the unit of newton meter per ampere (N·m / A); i q is the armature current, with the unit of ampere (A); B is the motor viscous damping coefficient, with the unit of newton meter per radian per second (N·m / (rad / s)).

[0065] (3) Combining the above derivations, the complete mathematical model of the bolt tightening system can be expressed as the following state equations:

[0066]

[0067] This model is a coupled non-linear differential equation system that reflects the dynamic interaction relationship between the tightening torque T b and the bolt tightening speed ω b , and at the same time incorporates the uncertainties of the time-varying parameters b(t) and c(t).

[0068] Regarding b(t) as a time-varying dynamic parameter, in practical applications, the tightening torque of the bolt is also affected by factors such as friction, environmental temperature, and deformation of the connecting parts. These factors will cause b(t) to have uncertainties under different conditions.

[0069] In a bolt tightening system, the main reason why the tightening torque cannot be directly obtained is that the system lacks a torque sensor and is affected by many uncertainties and external disturbances. These factors include friction, temperature changes, time-varying characteristics of the mechanical system, and changes in external loads, etc. In addition, only the current and rotational speed of the motor can be measured in the system. Although these signals can indirectly reflect the change of torque, they cannot directly correspond to the actual tightening torque. Therefore, to solve this problem, the present invention designs a non-smooth extended state observer (ESO). The ESO uses the rotational speed and current information of the motor and constructs a dynamic model containing uncertainties and time-varying parameters to estimate the torque during the bolt tightening process in real time. This observer can converge quickly, improve the estimation accuracy, and has strong anti-interference ability.

[0070] In step S2, the designed non-smooth extended state observer (ESO) is as follows:

[0071]

[0072] Wherein, represents the estimated value of the bolt angular velocity ω b calculated by the observer, represents the derivative of. T b is the tightening torque acting on the bolt, represents the estimated value of the tightening torque T b calculated by the observer, T0 represents the equivalent load torque, defined as represents the estimated value of the equivalent load torque, representing the estimation of the equivalent load torque by the ESO. L1 and L2 are two gain coefficients of the ESO, providing error correction to ensure fast convergence, is the sign function to ensure the correct direction of the disturbance estimation.

[0073] Furthermore, the estimated value of the bolt tightening torque is corrected and filtered to further reduce the estimation error and noise interference, thereby improving the stability and accuracy of the tightening torque control.

[0074] To further improve the estimation accuracy of the bolt tightening torque, a filtering technique is used to perform real-time correction and filtering on the torque estimation value output by the observer. This step removes noise and interference signals, eliminates high-frequency interference and errors that may exist in the measurement process, and improves the accuracy and stability of the torque estimated by the observer. At the same time, the estimated value is smoothed to ensure that the input signal of the subsequent control algorithm is more stable, thereby improving the overall performance of the control system.

[0075] In step S3, based on the dynamic characteristics of the system and the output of the non-smooth extended state observer, a finite-time control algorithm is designed by introducing the power integral technique, achieving finite-time precise control of the bolt tightening torque.

[0076] The finite-time control algorithm is designed as follows:

[0077]

[0078] Where, is the first gain of the finite-time control algorithm, adjusting the nonlinear feedback strength of the torque tracking error e1 to ensure the robustness of the system to disturbances. is the second gain of the finite-time control algorithm, controlling the overall amplitude of the nonlinear feedback term, which is related to the dynamic characteristics of the system. a2, a3, a4, a5, a6, c1 are positive constants. is the linear feedback term designed based on the nominal model of the system (without uncertainty assumption), used to compensate for the dynamics of the error system, b min is the minimum value of the time-varying parameter of the dynamic model of the tightening torque, τ is the power adjustment parameter of the finite-time control to achieve finite-time convergence. By adjusting i q , the torque tracking error e1 converges to a small interval within a finite time (instead of infinite asymptote). This characteristic is particularly suitable for scenarios where bolt tightening requires fast response and high precision.

[0079] In step S5, for the gain parameters of the finite-time control algorithm, theoretical derivations are first carried out to determine their reasonable value ranges. Through the system dynamics model and Lyapunov stability analysis, the relationships between the gain parameters, the system response time, the error convergence speed, and the robustness are derived. Theoretically, choosing appropriate gains can ensure the stability of the system and make the torque tracking error reach the expected goal within a finite time. The selection of parameters is not fixed, so an experimental and adjustment strategy is adopted, gradually adjusting the control gains based on the actual system performance. After the preliminary parameter setting, through experimental tests and simulation verification, the parameters are further optimized to ensure that the system can operate stably under various working conditions.

[0080] In the experiment, by testing different bolt tightening tasks, the values of the gain parameters β1 and β2 are adjusted to observe the torque tracking accuracy and response time of the system. The experimental environment simulates different load conditions and external disturbances, and the actual bolt tightening process in work is simulated through a dynamic loading device.

[0081] In each experiment, the error between the bolt tightening torque output by the controller and the target torque was recorded, and the actual bolt tightening torque was measured using a high-precision sensor. By comparing the control effects under different parameter settings, the gain configuration with the highest control accuracy and the shortest response time within a limited time was found.

[0082] After adjustment, the controller can quickly converge the torque tracking error to the predetermined allowable error range within a limited time, and the error is less than 5% in most cases. The torque tracking time of the system is significantly shortened and usually can reach the steady state within 1 second, which is much lower than the traditional PID control method.

[0083] Under the experimental conditions with external disturbances, the system can effectively resist the influence of disturbances, the tightening torque always remains within the expected range, and the error fluctuation is small. Especially in a complex working environment, the anti-interference ability is excellent, ensuring the stability and safety of high-altitude operations.

[0084] The above are only the preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for estimating and controlling bolt tightening torque without a torque sensor, characterized in that: Based on the finite time control algorithm and non-smooth extended state observer, the bolt tightening torque is estimated and controlled, which specifically includes the following steps: S1, modeling a bolt tightening system under the condition of considering external disturbance and internal parameter uncertainty to obtain a dynamic model including time-varying parameters; the bolt tightening system includes an end effector for tightening the bolt and a motor for driving the end effector; S2, based on the dynamic model, designing a non-smooth extended state observer; the non-smooth extended state observer is used to dynamically estimate the tightening torque during the bolt tightening process according to the real-time measurement of the motor speed and current; S3, a finite-time control algorithm is designed based on the power integral technique. In view of the external disturbance and internal parameter uncertainty of the system, the estimated tightening torque is adjusted in real time by introducing nonlinear feedback terms, so that the actual torque can track the preset target torque within a finite time; The target torque refers to the expected torque value preset according to the bolt tightening requirements; S4, Lyapunov theory is used to verify the stability of the system. The stability of the system is determined by constructing the Lyapunov function and analyzing its derivatives; S5, by adjusting the gain parameters of the finite time control algorithm, the optimal control effect is approached.

2. The method for estimating and controlling bolt tightening torque without a torque sensor according to claim 1, characterized in that: The specific method of step S1 is as follows: S11, bolt tightening torque T b With tightening angle θ b The functional relationship between them is T b =b(t)θ b ; Where b(t) is a time-varying parameter; Pair T b =b(t)θ b Taking the time derivative of both sides, we get: in, is a continuously differentiable non-negative function, representing the relative rate of change of b(t); ω b is the tightening speed; S12, the dynamic relationship between the motor and the bolt tightening torque is: Among them, ω b is the tightening speed; n is the reduction ratio, which means the ratio of the motor speed to the bolt speed; J is the motor moment of inertia; K t is the torque constant; i q is the armature current of the motor; B is the viscous damping coefficient of the motor; S31, the kinetic model including time-varying parameters is as follows:

3. The method for estimating and controlling bolt tightening torque without a torque sensor according to claim 2, characterized in that: In step S2, the non-smooth extended state observer is as follows: in, represents the tightening speed ω calculated by the observer b An estimated value of express The derivative of represents the tightening torque T calculated by the observer b T0 is the estimated value of the equivalent load moment, represents the estimated value of the equivalent load torque T0 calculated by the observer; L1 and L2 are the two gain coefficients of the non-smooth extended state observer; sgn(·) is the sign function.

4. The method for estimating and controlling bolt tightening torque without a torque sensor according to claim 3, characterized in that: In step S3, the finite time control algorithm is as follows: in, is the first gain of the finite time control algorithm, which is used to adjust the nonlinear feedback strength of the torque tracking error e1; is the second gain of the finite time control algorithm, used to control the amplitude of the nonlinear feedback term; a2, a3, a4, a5, a6, c1 are all positive constants; is the linear feedback term, b min is the minimum value of the time-varying parameter; τ is the power regulation parameter of finite time control; By adjusting i q , so that the torque tracking error e1 converges within a finite time.

5. The method for estimating and controlling bolt tightening torque without torque sensor according to claim 1, characterized in that: In step S5, the gain parameter is adjusted by trial and error.

6. The method for estimating and controlling bolt tightening torque without torque sensor according to claim 1, characterized in that: In step S3, the estimated value of the bolt tightening torque is also corrected and filtered.

7. A readable storage medium, characterized in that: A computer program is stored thereon, and when the computer program is executed, a method for estimating and controlling bolt tightening torque without a torque sensor as described in any one of claims 1 to 6 is implemented.

8. An electronic device, characterized in that: It includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, a method for estimating and controlling bolt tightening torque without a torque sensor as described in any one of claims 1 to 6 is implemented.

9. A computer program product, characterized in that It includes a computer program / instruction, which, when executed by a processor, implements a bolt tightening torque estimation and control method without a torque sensor as described in any one of claims 1-6.

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