A method suitable for synchronous measurement of meshing temperature and meshing stress of a marine heavy load gear in service state

Abstract

The application discloses a kind of synchronous measurement method suitable for meshing temperature and meshing stress under the service state of marine heavy load gear, it is related to heavy load transmission gear parameter on-line measurement technical field, including constructing state vector and initializing error covariance matrix;Form real-time attitude angle sequence with time stamp;Generate phase correction yaw angle, finally generate the meshing time sequence containing tooth number, meshing start time stamp, meshing end time stamp, and dynamic torque inversion value;The meshing temperature and meshing stress synchronous data packet corresponding to each meshing period are synchronously transmitted, and the quantity twin model construction is completed.The application obtains real-time attitude angle based on extended Kalman filter, divides basic meshing phase interval in combination with gear tooth profile geometric parameter, and removes attitude calculation jitter interference through three standard deviation dead zone determination logic, and the meshing start and end time of each gear tooth can be accurately identified.

Description

Technical Field

[0001] This invention relates to the field of online measurement technology for heavy-duty transmission gear parameters, specifically a method for synchronously measuring meshing temperature and meshing stress of marine heavy-duty gears under service conditions. Background Technology

[0002] Marine heavy-duty gears are widely used in ship propulsion systems, power transmission systems, and large marine equipment. They operate in complex environments, under heavy loads, and for extended periods of continuous operation. During long-term high-load service, the meshing area of ​​the gear teeth is prone to significant contact stress and frictional heat, leading to failures such as tooth wear, pitting, scuffing, and even tooth breakage. Meshing temperature and meshing stress are key parameters characterizing the service condition and health level of marine heavy-duty gears.

[0003] In existing technologies, the measurement of gear stress and temperature mostly adopts offline testing or test bench testing methods, which usually need to be carried out under shutdown or non-realistic operating conditions, making it difficult to reflect the actual load conditions of gears under actual service conditions. Some online monitoring methods can only measure external vibration or oil temperature parameters of the gearbox, and cannot directly obtain the actual temperature and stress information of the gear meshing point. At the same time, due to the high-speed rotation of gears and the periodic change of meshing position, existing measurement technologies cannot accurately determine the gear meshing moment, resulting in a low proportion of effective information in high-frequency sampling data, low utilization of wireless transmission bandwidth, and difficulty in effectively compensating for the impact of temperature changes on the tooth surface stress measurement results.

[0004] Therefore, there is an urgent need for an online monitoring device and method that can accurately identify the gear meshing moment under the actual service conditions of marine heavy-duty gears, and simultaneously perform high-precision measurement and efficient transmission of meshing temperature and meshing stress. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for simultaneously measuring meshing temperature and meshing stress of marine heavy-duty gears under service conditions, comprising the following specific steps: S1. Based on the follow-up measurement unit installed on the gear body under test and / or the follow-up structure that rotates synchronously with the gear under test, the follow-up measurement unit adopts a modular integrated structure, including an attitude measurement module, a temperature measurement module, a stress measurement module, a data acquisition and processing module, a data storage and communication module, and a power supply module, etc., as the measurement data source of this application, to obtain the static acceleration vector and the axis gyroscope drift vector, and based on the static acceleration vector and the geographic coordinate system, to obtain the initial attitude quaternion of the carrier coordinate system relative to the geographic reference coordinate system, and to construct the state vector and the initial error covariance matrix; S2. Based on each sampling time, calculate the angular velocity vector after drift compensation, and obtain the predicted attitude quaternion based on the angular velocity vector. Starting from the initial attitude quaternion, the initial three-axis gyroscope drift vector, and the error covariance matrix, perform time prediction and measurement update, extract the real-time attitude angle information, and form a real-time attitude angle sequence with timestamps. S3. Based on the number of gear teeth, the gear is divided into several sectors. Basic geometric phase interval mapping is performed. The tooth backlash influence factor is calibrated and introduced by the idle travel angle of the driving wheel. After the dynamic torque is inverted in real time by the synchronous data package of meshing temperature and meshing stress, the obtained dynamic torque value is used to calculate the dynamic torsional elastic deformation angle and generate the phase correction yaw angle. Finally, a meshing time sequence containing tooth number, meshing start time stamp, meshing end time stamp, and dynamic torque inversion value are generated. S4. The generated meshing time sequence is converted into a hardware interrupt control signal, which drives the analog-to-digital converter, including the temperature measurement module and the stress measurement module, to perform analog-to-digital conversion within a single meshing window period. All the converted binary temperature digital codes and all the binary strain digital codes are paired by timestamp, packaged into metadata segments, and after forming the original temperature-strain synchronous time sequence data segment, temperature-strain nonlinear decoupling compensation is performed. After the meshing temperature and meshing stress synchronous data packets corresponding to each meshing cycle are synchronously transmitted, the quantitative twin model is completed.

[0006] Preferably, in step S1, under the static condition when the gear stops, the time series output by the triaxial accelerometer of the follow-up measurement unit is accumulated according to each channel and divided by the number of sampling points to obtain a three-dimensional static acceleration vector, and the spatial direction of the three-dimensional static acceleration vector is used as the projection direction of the gravity acceleration vector in the carrier coordinate system under the current gear posture. Based on the geometric relationship between the unit direction vector of static acceleration and the known vertical downward gravity unit direction vector in the geographic reference coordinate system, a rotational quaternion is constructed using the angular axis transformation method to obtain the initial attitude quaternion describing the transition from the geographic coordinate system to the carrier coordinate system. Specifically, the process is as follows: First, the dot product of the two unit direction vectors is calculated to obtain the cosine of the angle between them, and the unit direction vector of the rotation axis is obtained through the cross product. Then, the cosine of half of this angle is used as the scalar part of the quaternion, and the unit direction vector of the rotation axis multiplied by the sine of half of this angle is used as the three vector parts of the quaternion. Finally, the quaternion is normalized to make its modulus equal to one. Based on the static condition of the gears stopping, the long-term angular velocity data sequence of each axis of the three-axis gyroscope is collected, the arithmetic mean of the long-term angular velocity data sequence of each axis is calculated, and all arithmetic means are integrated into an initial three-axis gyroscope drift vector, which reflects the zero-position bias of the gyroscope itself when there is no angular motion input. S1 constructs a state vector based on the initial attitude quaternion and the initial three-axis gyroscope drift vector, and constructs a seven-row, seven-column diagonal matrix based on the uncertainty of the initial attitude quaternion and the estimated variance of the initial three-axis gyroscope drift vector in the state vector, which serves as the initial error covariance matrix.

[0007] Preferably, S2 performs prior estimation based on extended Kalman filtering, including: using the initial attitude quaternion and the initial three-axis gyroscope drift vector as the posterior state in the first cycle of the filter, and using the posterior state output in the previous step in subsequent cycles. The angular velocity vector after zero-point compensation is obtained by subtracting the posterior three-axis gyroscope drift vector from the original angular velocity measurement vector output by the three-axis gyroscope at the current moment. Based on the zero-point compensated angular velocity vector, an incremental rotation quaternion describing the rotational changes of the carrier coordinate system within the sampling period is generated. The scalar part of the incremental quaternion disclosed in this application is the cosine of half the product of the magnitude of the angular velocity vector and the sampling period, and the vector part is the sine of half the product of the unit angular velocity vector and the sampling period. The posterior attitude quaternion of the previous moment and the obtained incremental rotation quaternion are multiplied on the right according to the quaternion multiplication rule to obtain the attitude quaternion predicted in one step and the corresponding predicted state vector. The predicted value of the three-axis gyroscope drift vector is directly set to the posterior drift vector of the previous moment, which means that the drift remains unchanged when there is no new measurement information. The first-order partial derivative of the current predicted state vector with respect to the state vector at the previous moment is derived analytically. Thus, this application constructs a seven-row, seven-column state transition Jacobian matrix. The specific values ​​of each element of the matrix depend on the current quaternion and angular velocity measurement. Multiply the calculated state transition Jacobian matrix on the left by the posterior error covariance matrix of the previous time step, and then multiply it on the right by the transpose of the state transition Jacobian matrix. Add the resulting matrix to the pre-defined noise covariance matrix to obtain the prediction error covariance matrix. The noise covariance matrix is ​​determined by the statistical characteristics of the gyroscope angular velocity white noise and drift random walk noise. Fill in the noise variance values ​​at the corresponding positions on the main diagonal to complete the prior estimation.

[0008] Preferably, it also includes posterior estimation based on extended Kalman filtering: Based on the predicted attitude quaternion, the known unit gravity vector pointing to the Earth's center in the geographic reference coordinate system is spatially rotated and transformed to the carrier coordinate system to obtain the theoretical acceleration vector that the accelerometer should measure under non-motorized motion. The difference between the actual three-dimensional measurement vector output by the triaxial accelerometer at the current moment and the theoretical acceleration vector is used to obtain the three-dimensional measurement residual vector. Based on the first-order partial derivative of the theoretical acceleration vector with respect to the current seven-dimensional state vector, a three-row, seven-column measurement Jacobian matrix is ​​obtained. The measurement Jacobian matrix is ​​then multiplied on the left by the prediction error covariance matrix, and then on the right by the transpose of the measurement Jacobian matrix. Finally, the measurement noise covariance matrix of the triaxial accelerometer is added. The measurement noise covariance matrix is ​​a three-row, three-column diagonal matrix that has been calibrated in advance through static experiments. This gives us the innovation covariance matrix. The gain matrix is ​​obtained by left-multiplying the prediction error covariance matrix by the transpose of the measurement Jacobian matrix and then right-multiplying it by the inverse of the innovation covariance matrix. The state correction is obtained by left-multiplying the gain matrix by the three-dimensional measurement residual vector. The state correction is then added to the prediction state vector item by item to obtain the updated posterior state vector and the posterior error covariance matrix. Based on the quaternion components in the posterior state vector, the square root of the sum of squares is calculated as the modulus. Each component is then divided by the modulus to obtain the normalized unit posterior attitude quaternion. Based on the conversion relationship between the normalized quaternion and Euler angles, the real-time roll angle, pitch angle, and yaw angle of the servo measurement unit are extracted through trigonometric function operations such as arctangent and arcsine. The yaw angle is used to characterize the rotational angle position of the gear. The S2 outputs a real-time attitude angle sequence with timestamps, a real-time updated three-axis gyroscope drift vector, and a posterior error covariance matrix.

[0009] Preferably, S3 divides the gear into several sectors based on the number of gear teeth according to the circumference of 360 degrees, and calculates the range of the central angle that each gear tooth traverses from the start point to the end point of double tooth meshing under no load and no backlash conditions, based on the involute tooth profile geometric parameters such as the gear module, pressure angle, helix angle and tooth tip trimming amount. Based on the center angle range, it is converted into the corresponding ideal meshing start critical yaw angle and ideal meshing end critical yaw angle, and each tooth number is assigned a fixed yaw angle range; Based on manually and / or through the drive device rotating the driving tooth until it just contacts the driven tooth when the gearbox is unloaded and stationary, and measuring the idle travel angle of the driving wheel during the rotation of the driving tooth, and converting the idle travel angle into the tooth flank clearance yaw angle, the tooth flank clearance influence factor is calibrated and introduced. Based on the compensated meshing temperature and meshing stress synchronization data package generated in the previous one and / or multiple meshing cycles, the maximum meshing stress value of the corresponding tooth number at the end of the previous meshing is extracted. Based on the stress value, the Hertz contact half-width of the tooth surface and the pitch circle radius of the gear, the dynamic torque value transmitted by the gear during this meshing is deduced by multiplying force by lever arm, thus completing the real-time inversion.

[0010] Preferably, S3 establishes a linear relationship model between torsional elastic deformation and torque based on the shear elastic modulus of the gear shaft material, the polar moment of inertia of the shaft segment, and the effective length. The polar moment of inertia of the shaft segment is calculated from the shaft diameter. The obtained dynamic torque value is used to calculate the dynamic torsional elastic deformation angle of the gear body relative to the ideal rigid position caused by the elastic torsion of the shaft system based on the linear relationship model. The obtained tooth flank clearance yaw angle and dynamic torsional elastic deformation angle are algebraically added to generate the total phase correction yaw angle. Based on each tooth, the corresponding ideal meshing start critical yaw angle and ideal meshing end critical yaw angle are respectively added to the phase correction yaw angle to obtain the corrected meshing start dynamic critical angle and corrected meshing end dynamic critical angle. Based on the posterior error covariance matrix, the diagonal element values ​​of the corresponding phase correction yaw angle are extracted. The standard deviation of the yaw angle estimate is obtained by taking the square root. The decision dead zone width is set to three times this standard deviation. If the real-time yaw angle value in the real-time attitude angle crosses the decision dead zone width for several consecutive samplings, it is determined as the occurrence and / or termination of the engagement event, so as to eliminate false triggering caused by attitude calculation jitter.

[0011] Preferably, in step S3, the yaw angle sequence of the real-time attitude angle sequence is continuously compared with the corrected dynamic critical angle of each tooth. When the real-time yaw angle enters the dead zone width upwards, the current time is recorded as the meshing start event timestamp. When the real-time yaw angle exceeds the dead zone width upwards, the current time is recorded as the meshing end event timestamp. All record entries generated in chronological order, consisting of tooth number, meshing start event timestamp, and meshing end event timestamp, constitute a complete meshing time sequence, including the meshing time sequence of tooth number, meshing start timestamp, and meshing end timestamp, as well as the dynamic torque inversion value.

[0012] Preferably, in step S4, the output engagement time sequence is loaded into the controller in chronological order, and the analog-to-digital converters connected to the temperature measurement module and the stress measurement module are both set to external trigger start and continuous conversion mode. The temperature measurement module consists of a miniature thin-film platinum resistance temperature sensor and its signal conditioning circuit, while the stress measurement module consists of a metal foil full-bridge strain sensor, a Wheatstone bridge, and a programmable gain instrumentation amplifier. A level transition signal is generated based on the meshing start timestamp in the meshing time sequence. The sample-and-hold circuit inside each analog-to-digital converter captures and holds the analog input voltage at the current moment, and generates comparison voltages sequentially from the most significant bit to the least significant bit. The voltages are compared with the held voltages one by one to determine whether each bit of the binary code is zero or one. The binary digital code obtained from the comparison is stored, and a stop command is generated based on the meshing end timestamp in the meshing time sequence. All binary temperature digital codes output by the temperature analog-to-digital converter and all binary strain digital codes output by the stress analog-to-digital converter are paired one by one according to the timestamps attached during generation, packaged into raw data segments, and metadata information including the corresponding tooth number, the timestamp of the meshing start event, the timestamp of the meshing end event, and the dynamic torque inversion value is written into them to form a raw temperature-strain synchronous time series data segment bound to a single meshing event.

[0013] Preferably, step S4 is based on a specimen identical to that used in marine heavy-duty gears. Temperature sensors and strain sensors of the same batch and model are attached to the surface of the specimen according to the actual installation process. The specimen is placed on a material mechanics testing machine that can provide accurate uniaxial tensile and compressive loads and is placed in a high and low temperature environment chamber. During the entire calibration process, multiple different constant temperature levels are set sequentially. At each temperature level, a series of known mechanical loads ranging from zero to the maximum design stress value are applied and the loads are kept stable. The temperature digital output value output by the temperature sensor and the original strain digital output value output by the strain sensor are recorded under each set of working conditions. The true mechanical strain value is calculated based on the applied known load and the cross-sectional area of ​​the specimen. The system uses a radial basis function neural network to form an input vector, which consists of three features: the current temperature digital output value, the first-order time difference value of the current temperature (characterizing the rate of temperature change), and the current strain sensor raw digital output value. This vector serves as the input layer, and the predicted mechanical strain value is used as the output layer. Each neuron in the hidden layer uses a Gaussian radial basis function as its activation function. All calibrated input vectors are combined into a candidate center set. The hidden layer center vector is obtained based on orthogonal least squares. The Euclidean space distance between a selected hidden layer center vector and all other center vectors is calculated to obtain the width parameter shared by each Gaussian radial basis function. All calibrated input vectors are processed one by one through a hidden layer with predetermined center and width parameters to obtain the hidden layer output matrix. Each row of this matrix corresponds to a radial basis function activation value vector of an input sample. Using the hidden layer output matrix as the design matrix and the actual mechanical strain vector as the target vector, a linear least squares problem is solved to obtain the linear weight vector from the hidden layer to the output layer. The solution process employs singular value decomposition (SVD) to decompose the design matrix. The weights that minimize the sum of squared residuals are calculated using the decomposed orthogonal matrix and diagonal singular value matrix, thus completing network training. The model is then permanently stored.

[0014] Preferably, in step S4, the temperature digital output value and the original strain digital output value at the same moment are extracted from the binary temperature digital code and binary strain digital code to form a temperature digital output value sequence. Based on the time-aligned temperature digital output value sequence, the value of the next sampling point is subtracted from the value of the previous sampling point in chronological order, and then divided by the sampling period to obtain the temperature change rate sequence corresponding to each moment. Based on each pair of temperature change rate sequences, a three-dimensional input vector is constructed, containing the current temperature digital output value, the temperature change rate just calculated, and the current original strain digital output value. Based on the trained radial basis function neural network, the Euclidean distance between the input vector and the center vector of each hidden layer is first calculated. For each distance value, its square is calculated and divided by the square of the width parameter. The negative value is used as the exponent of the natural exponential function to obtain the activation value of the hidden layer neuron. Finally, the activation values ​​of all hidden layer neurons are multiplied by the components of the linear weight vector of the output layer at the corresponding positions and summed. The scalar value output by the network is used to obtain the predicted mechanical strain value at the corresponding sampling time. The predicted mechanical strain value is multiplied by the elastic modulus of the gear material to obtain the meshing stress value corresponding to the sampling time. The meshing stress value sequence calculated from all sampling points in the data segment is recombined with the temperature value sequence directly measured by the temperature sensor at the corresponding timestamp, and the metadata header of the original data segment is attached to form a synchronous data package of meshing temperature and meshing stress corresponding to each meshing cycle. After synchronizing and transmitting the synchronous data packets of meshing temperature and meshing stress corresponding to each meshing cycle, the quantitative twin model is constructed.

[0015] Beneficial effects This invention provides a method for simultaneously measuring meshing temperature and meshing stress of marine heavy-duty gears under service conditions, which has the following advantages: Based on the real-time attitude angle obtained by extended Kalman filter calculation, the basic meshing phase interval is divided by combining the gear tooth profile geometric parameters. At the same time, the tooth backlash calibration value and the torsional elastic deformation angle obtained by dynamic torque inversion are introduced to dynamically correct the meshing critical phase. The attitude calculation jitter interference is filtered out by the three-standard-deviation dead zone judgment logic, which can accurately identify the meshing start and end time of each tooth. A temperature-strain decoupling model is constructed using a radial basis function neural network. Temperature value, temperature change rate and original strain value are used as three-dimensional input features. The model is trained using calibration data under multiple temperature and load conditions. This model can effectively compensate for the nonlinear cross-interference of absolute temperature value and temperature fluctuation rate on strain measurement and eliminate the influence of tooth surface temperature change on stress calculation results. A temperature-strain decoupling model is constructed using a radial basis function neural network. Temperature value, temperature change rate, and original strain value are used as three-dimensional input features. The model is trained using calibration data under multiple temperature and load conditions. This model can effectively compensate for the nonlinear cross-interference of absolute temperature value and temperature fluctuation rate on strain measurement and eliminate the influence of tooth surface temperature change on stress calculation results. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0017] The present invention will now be further described with reference to the accompanying drawings.

[0018] Please see Figure 1 This invention provides a method for simultaneously measuring meshing temperature and meshing stress of marine heavy-duty gears under service conditions, comprising the following steps: S1. Based on the follow-up measurement unit installed on the gear body under test and / or the follow-up structure that rotates synchronously with the gear under test, the follow-up measurement unit adopts a modular integrated structure, including an attitude measurement module, a temperature measurement module, a stress measurement module, a data acquisition and processing module, a data storage and communication module, and a power supply module, etc., as the measurement data source of this application, to obtain the static acceleration vector and the axis gyroscope drift vector, and based on the static acceleration vector and the geographic coordinate system, to obtain the initial attitude quaternion of the carrier coordinate system relative to the geographic reference coordinate system, and to construct the state vector and the initial error covariance matrix; S2. Based on each sampling time, calculate the angular velocity vector after drift compensation, and obtain the predicted attitude quaternion based on the angular velocity vector. Starting from the initial attitude quaternion, the initial three-axis gyroscope drift vector, and the error covariance matrix, perform time prediction and measurement update, extract the real-time attitude angle information, and form a real-time attitude angle sequence with timestamps. S3. Based on the number of gear teeth, the gear is divided into several sectors. Basic geometric phase interval mapping is performed. The tooth backlash influence factor is calibrated and introduced by the idle travel angle of the driving wheel. After the dynamic torque is inverted in real time by the synchronous data package of meshing temperature and meshing stress, the obtained dynamic torque value is used to calculate the dynamic torsional elastic deformation angle and generate the phase correction yaw angle. Finally, a meshing time sequence containing tooth number, meshing start time stamp, meshing end time stamp, and dynamic torque inversion value are generated. S4. The generated meshing time sequence is converted into a hardware interrupt control signal, which drives the analog-to-digital converter, including the temperature measurement module and the stress measurement module, to perform analog-to-digital conversion within a single meshing window period. All the converted binary temperature digital codes and all the binary strain digital codes are paired by timestamp, packaged into metadata segments, and after forming the original temperature-strain synchronous time sequence data segment, temperature-strain nonlinear decoupling compensation is performed. After the meshing temperature and meshing stress synchronous data packets corresponding to each meshing cycle are synchronously transmitted, the quantitative twin model is completed.

[0019] S1, based on the static condition when the gear stops, accumulates the time series output by the triaxial accelerometer of the follow-up measurement unit according to each channel and divides it by the number of sampling points to obtain the three-dimensional static acceleration vector. The spatial direction of the three-dimensional static acceleration vector is used as the projection direction of the gravitational acceleration vector in the carrier coordinate system under the current gear posture. Based on the geometric relationship between the unit direction vector of static acceleration and the known vertical downward gravity unit direction vector in the geographic reference coordinate system, a rotational quaternion is constructed using the angular axis transformation method to obtain the initial attitude quaternion describing the transition from the geographic coordinate system to the carrier coordinate system. Specifically, the process is as follows: First, the dot product of the two unit direction vectors is calculated to obtain the cosine of the angle between them, and the unit direction vector of the rotation axis is obtained through the cross product. Then, the cosine of half of this angle is used as the scalar part of the quaternion, and the unit direction vector of the rotation axis multiplied by the sine of half of this angle is used as the three vector parts of the quaternion. Finally, the quaternion is normalized to make its modulus equal to one. Based on the static condition of the gears stopping, the long-term angular velocity data sequence of each axis of the three-axis gyroscope is collected, the arithmetic mean of the long-term angular velocity data sequence of each axis is calculated, and all arithmetic means are integrated into an initial three-axis gyroscope drift vector, which reflects the zero-position bias of the gyroscope itself when there is no angular motion input. S1 constructs a state vector based on the initial attitude quaternion and the initial three-axis gyroscope drift vector, and constructs a seven-row, seven-column diagonal matrix based on the uncertainty of the initial attitude quaternion and the estimated variance of the initial three-axis gyroscope drift vector in the state vector, which serves as the initial error covariance matrix.

[0020] It should be noted that the state vector of this application consists of seven components. The first four components are attitude quaternions, namely their scalar part and three vector parts, respectively. The last three components are the three-axis gyroscope drift vectors. Therefore, the initial error covariance matrix constructed in this application corresponds to seven components. The first four diagonal elements are determined based on the uncertainty of the initial attitude quaternion, which is estimated from the accelerometer noise variance and the installation error angle. The last three elements are determined based on the estimated variance of the initial three-axis gyroscope drift vector, which is calculated from the sample variance of the static data in subsequent steps. Finally, all off-diagonal elements are set to zero, indicating that the initial state errors are uncorrelated.

[0021] S2 performs prior estimation based on extended Kalman filtering, including: using the initial attitude quaternion and the initial three-axis gyroscope drift vector as the posterior state in the first cycle of the filter, and using the posterior state output from the previous step in subsequent cycles. The angular velocity vector after zero-point compensation is obtained by subtracting the posterior three-axis gyroscope drift vector from the original angular velocity measurement vector output by the three-axis gyroscope at the current moment. Based on the zero-point compensated angular velocity vector, an incremental rotation quaternion describing the rotational changes of the carrier coordinate system within the sampling period is generated. The scalar part of the incremental quaternion disclosed in this application is the cosine of half the product of the magnitude of the angular velocity vector and the sampling period, and the vector part is the sine of half the product of the unit angular velocity vector and the sampling period. The posterior attitude quaternion of the previous moment and the obtained incremental rotation quaternion are multiplied on the right according to the quaternion multiplication rule to obtain the attitude quaternion predicted in one step and the corresponding predicted state vector. The predicted value of the three-axis gyroscope drift vector is directly set to the posterior drift vector of the previous moment, which means that the drift remains unchanged when there is no new measurement information. The first-order partial derivative of the current predicted state vector with respect to the state vector at the previous moment is derived analytically. Thus, this application constructs a seven-row, seven-column state transition Jacobian matrix. The specific values ​​of each element of the matrix depend on the current quaternion and angular velocity measurement. Multiply the calculated state transition Jacobian matrix on the left by the posterior error covariance matrix of the previous time step, and then multiply it on the right by the transpose of the state transition Jacobian matrix. Add the resulting matrix to the pre-defined noise covariance matrix to obtain the prediction error covariance matrix. The noise covariance matrix is ​​determined by the statistical characteristics of the gyroscope angular velocity white noise and drift random walk noise. Fill in the noise variance values ​​at the corresponding positions on the main diagonal to complete the prior estimation.

[0022] It also includes posterior estimation based on extended Kalman filtering: Based on the predicted attitude quaternion, the known unit gravity vector pointing to the Earth's center in the geographic reference coordinate system is spatially rotated and transformed to the carrier coordinate system to obtain the theoretical acceleration vector that the accelerometer should measure under non-motorized motion. The difference between the actual three-dimensional measurement vector output by the triaxial accelerometer at the current moment and the theoretical acceleration vector is used to obtain the three-dimensional measurement residual vector. Based on the first-order partial derivative of the theoretical acceleration vector with respect to the current seven-dimensional state vector, a three-row, seven-column measurement Jacobian matrix is ​​obtained. The measurement Jacobian matrix is ​​then multiplied on the left by the prediction error covariance matrix, and then on the right by the transpose of the measurement Jacobian matrix. Finally, the measurement noise covariance matrix of the triaxial accelerometer is added. The measurement noise covariance matrix is ​​a three-row, three-column diagonal matrix that has been calibrated in advance through static experiments. This gives us the innovation covariance matrix. The gain matrix is ​​obtained by left-multiplying the prediction error covariance matrix by the transpose of the measurement Jacobian matrix and then right-multiplying it by the inverse of the innovation covariance matrix. The state correction is obtained by left-multiplying the gain matrix by the three-dimensional measurement residual vector. The state correction is then added to the prediction state vector item by item to obtain the updated posterior state vector and the posterior error covariance matrix. Based on the quaternion components in the posterior state vector, the square root of the sum of squares is calculated as the modulus. Each component is then divided by the modulus to obtain the normalized unit posterior attitude quaternion. Based on the conversion relationship between the normalized quaternion and Euler angles, the real-time roll angle, pitch angle, and yaw angle of the servo measurement unit are extracted through trigonometric function operations such as arctangent and arcsine. The yaw angle is used to characterize the rotational angle position of the gear. S2 outputs a real-time attitude angle sequence with timestamps, a real-time updated three-axis gyroscope drift vector, and a posterior error covariance matrix.

[0023] S3 divides the gear into several sectors based on the number of teeth on a circumference of 360 degrees. Based on the involute tooth profile geometric parameters such as the gear module, pressure angle, helix angle, and tooth tip trimming amount, it calculates the range of the central angle that each tooth traverses from the start point to the end point of double tooth meshing under no-load and no-backlash conditions. Based on the center angle range, it is converted into the corresponding ideal meshing start critical yaw angle and ideal meshing end critical yaw angle, and each tooth number is assigned a fixed yaw angle range; Based on manually and / or through the drive device rotating the driving tooth until it just contacts the driven tooth when the gearbox is unloaded and stationary, and measuring the idle travel angle of the driving wheel during the rotation of the driving tooth, and converting the idle travel angle into the tooth flank clearance yaw angle, the tooth flank clearance influence factor is calibrated and introduced. Based on the compensated meshing temperature and meshing stress synchronization data package generated in the previous one and / or multiple meshing cycles, the maximum meshing stress value of the corresponding tooth number at the end of the previous meshing is extracted. Based on the stress value, the Hertz contact half-width of the tooth surface and the pitch circle radius of the gear, the dynamic torque value transmitted by the gear during this meshing is deduced by multiplying force by lever arm, thus completing the real-time inversion.

[0024] S3 establishes a linear relationship model between torsional elastic deformation and torque based on the shear elastic modulus of the gear shaft material, the polar moment of inertia of the shaft segment, and the effective length. The polar moment of inertia of the shaft segment is calculated from the shaft diameter. The obtained dynamic torque value is used to calculate the dynamic torsional elastic deformation angle of the gear body relative to the ideal rigid position caused by the elastic torsion of the shaft system based on the linear relationship model. It should be noted that the linear relationship model requires the acquisition of the geometric and material parameters of the gear shaft system, including: the effective torsional length of the gear shaft, the cross-sectional diameter of the shaft, and the shear modulus of the shaft material. The effective torsional length refers to the axial distance from the center plane of the gear body to the nearest fixed constraint end or the midpoint of the high-stiffness support bearing on the shaft; the cross-sectional diameter of the shaft should be the equivalent diameter of the part of the shaft subjected to torque; the shear modulus of elasticity can be found in the material handbook or determined by torsion test of the same batch of materials as the gear.

[0025] Next, calculate the polar moment of inertia of the cross-section of the shaft segment. The polar moment of inertia is a quantity that depends only on the geometry of the cross-section. For a solid circular cross-section, its value is determined by the diameter of the shaft, specifically by multiplying the diameter value by itself four times, then multiplying by pi, and finally dividing by thirty-two. This polar moment of inertia represents the geometric ability of each point on the cross-section to resist torsional deformation.

[0026] Define the torsional elastic deformation angle under unit torque. According to the circular shaft torsion theory in mechanics of materials, for isotropic linear elastic materials, within the material shear ratio limit, there is a strict proportional relationship between the transmitted torque and the generated torsional angle. Combining the above effective torsional length, unit torque value, and a term related to the product of polar moment of inertia and shear modulus, in a physical sense, the torsional angle is directly proportional to both the transmitted torque and the shaft length, and inversely proportional to the polar moment of inertia of the shaft and the shear modulus of the material. Therefore, dividing the effective length of the shaft by the product of the shear modulus and the polar moment of inertia yields the torsional elastic deformation constant of the shaft system. Finally, a linear relationship model is established. For any real-time changing torque value, simply multiply the torque value by the pre-calculated torsional elastic deformation constant mentioned above. The resulting product is the relative torsional angle between the two ends of the shaft segment under the current torque, which is the dynamic torsional elastic deformation angle. This linear relationship only holds when the gear shaft material has not yielded and the deformation is within the elastic range. Its accuracy depends on the accuracy of the shaft's geometric dimensions measurement and the precise calibration of the material's shear elastic modulus. After the model is established, it is solidified into a mapping rule from torque to torsional angle, which can be called in real time during each meshing determination in step three. The obtained tooth flank clearance yaw angle and dynamic torsional elastic deformation angle are algebraically added to generate the total phase correction yaw angle. Based on each tooth, the corresponding ideal meshing start critical yaw angle and ideal meshing end critical yaw angle are respectively added to the phase correction yaw angle to obtain the corrected meshing start dynamic critical angle and corrected meshing end dynamic critical angle. Based on the posterior error covariance matrix, the diagonal element values ​​of the corresponding phase correction yaw angle are extracted. The standard deviation of the yaw angle estimate is obtained by taking the square root. The decision dead zone width is set to three times this standard deviation. If the real-time yaw angle value in the real-time attitude angle crosses the decision dead zone width for several consecutive samplings, it is determined as the occurrence and / or termination of the engagement event, so as to eliminate false triggering caused by attitude calculation jitter.

[0027] S3 continuously compares the yaw angle sequence of the real-time attitude angle sequence with the corrected dynamic critical angle of each tooth. When the real-time yaw angle enters the dead zone width upwards, the current time is recorded as the meshing start event timestamp. When the real-time yaw angle exceeds the dead zone width upwards, the current time is recorded as the meshing end event timestamp. All the record entries generated in chronological order, consisting of tooth number, meshing start event timestamp, and meshing end event timestamp, constitute a complete meshing time sequence, including the meshing time sequence of tooth number, meshing start timestamp, and meshing end timestamp, as well as the dynamic torque inversion value.

[0028] S4 loads the output engagement time sequence into the controller in chronological order, and sets the analog-to-digital converters connected to the temperature measurement module and stress measurement module to external trigger start and continuous conversion mode. The temperature measurement module consists of a miniature thin-film platinum resistance temperature sensor and its signal conditioning circuit, while the stress measurement module consists of a metal foil full-bridge strain sensor, a Wheatstone bridge, and a programmable gain instrumentation amplifier. A level transition signal is generated based on the meshing start timestamp in the meshing time sequence. The sample-and-hold circuit inside each analog-to-digital converter captures and holds the analog input voltage at the current moment, and generates comparison voltages sequentially from the most significant bit to the least significant bit. The voltages are compared with the held voltages one by one to determine whether each bit of the binary code is zero or one. The binary digital code obtained from the comparison is stored, and a stop command is generated based on the meshing end timestamp in the meshing time sequence. All binary temperature digital codes output by the temperature analog-to-digital converter and all binary strain digital codes output by the stress analog-to-digital converter are paired one by one according to the timestamps attached during generation, packaged into raw data segments, and metadata information including the corresponding tooth number, the timestamp of the meshing start event, the timestamp of the meshing end event, and the dynamic torque inversion value is written into them to form a raw temperature-strain synchronous time series data segment bound to a single meshing event.

[0029] Based on the same specimen as marine heavy-duty gears, temperature and strain sensors of the same batch and model are attached to the surface of the specimen according to the actual installation process. The specimen is placed on a material mechanics testing machine that can provide accurate uniaxial tensile and compressive loads and is placed in a high and low temperature environment chamber. During the entire calibration process, multiple different constant temperature levels are set sequentially. At each temperature level, a series of known mechanical loads from zero to the maximum design stress value are applied and the loads are kept stable. The temperature digital output value output by the temperature sensor and the original strain digital output value output by the strain sensor are recorded under each set of working conditions. The true mechanical strain value is calculated based on the applied known load and the cross-sectional area of ​​the specimen. The system uses a radial basis function neural network to form an input vector, which consists of three features: the current temperature digital output value, the first-order time difference value of the current temperature (characterizing the rate of temperature change), and the current strain sensor raw digital output value. This vector serves as the input layer, and the predicted mechanical strain value is used as the output layer. Each neuron in the hidden layer uses a Gaussian radial basis function as its activation function. All calibrated input vectors are combined into a candidate center set. The hidden layer center vector is obtained based on orthogonal least squares. The Euclidean space distance between a selected hidden layer center vector and all other center vectors is calculated to obtain the width parameter shared by each Gaussian radial basis function. Specifically, all calibrated input vectors are combined into a candidate center set. Initially, the hidden layer contains no neurons, and the network's residual vector is the target's true mechanical strain value vector. The algorithm performs the following iterative process: For each vector in the candidate center set, it is first orthogonalized with the current residual vector. Then, the proportion by which the sum of squared output errors is reduced after adding a Gaussian function centered on this vector to the network is estimated, i.e., the error reduction ratio. The candidate vector that results in the largest error reduction ratio is selected as the new hidden layer neuron center, removed from the candidate set, and formally added to the network. Subsequently, the residual vector is updated, and the portion explained by the center is subtracted from the current residual. This selection process is repeated until the cumulative error reduction ratio of all selected centers exceeds a pre-set threshold, at which point the iteration stops. Finally, the number of hidden layer neurons equals the number of selected centers. All calibrated input vectors are processed one by one through a hidden layer with predetermined center and width parameters to obtain the hidden layer output matrix. Each row of this matrix corresponds to a radial basis function activation value vector of an input sample. Using the hidden layer output matrix as the design matrix and the actual mechanical strain vector as the target vector, a linear least squares problem is solved to obtain the linear weight vector from the hidden layer to the output layer. The solution process employs singular value decomposition (SVD) to decompose the design matrix. The weights that minimize the sum of squared residuals are calculated using the decomposed orthogonal matrix and diagonal singular value matrix, thus completing network training. The model is then permanently stored.

[0030] S4 extracts the temperature digital output value and the original strain digital output value at the same moment from the binary temperature digital code and binary strain digital code to form a temperature digital output value sequence. Based on the time-aligned temperature digital output value sequence, the value of the next sampling point is subtracted from the value of the previous sampling point in time order, and then divided by the sampling period to obtain the temperature change rate sequence corresponding to each moment. Based on each pair of temperature change rate sequences, a three-dimensional input vector is constructed, containing the current temperature digital output value, the temperature change rate just calculated, and the current original strain digital output value. Based on the trained radial basis function neural network, the Euclidean distance between the input vector and the center vector of each hidden layer is first calculated. For each distance value, its square is calculated and divided by the square of the width parameter. The negative value is used as the exponent of the natural exponential function to obtain the activation value of the hidden layer neuron. Finally, the activation values ​​of all hidden layer neurons are multiplied by the components of the linear weight vector of the output layer at the corresponding positions and summed. The scalar value output by the network is used to obtain the predicted mechanical strain value at the corresponding sampling time. The predicted mechanical strain value is multiplied by the elastic modulus of the gear material to obtain the meshing stress value corresponding to the sampling time. The meshing stress value sequence calculated from all sampling points in the data segment is recombined with the temperature value sequence directly measured by the temperature sensor at the corresponding timestamp, and the metadata header of the original data segment is attached to form a synchronous data package of meshing temperature and meshing stress corresponding to each meshing cycle. After synchronously transmitting the meshing temperature and meshing stress data packets corresponding to each meshing cycle, a quantitative twin model is constructed. The meshing temperature and stress data carried in each data packet are used as known scalar values ​​at the actual sensor installation locations on the tooth surface. A spatial interpolation algorithm based on radial basis functions is used to reconstruct the field for all other unmeasured mesh nodes on the tooth surface. For each node to be interpolated, its three-dimensional Euclidean distance to all known sensor location nodes is calculated. The square of this distance is divided by the square of a spatial correlation length determined by the sensor spacing, and the result is negative, serving as the exponent of the natural exponential function to obtain the Gaussian weight of the known point to be interpolated. The temperature (or stress) values ​​of all known points are multiplied by their corresponding Gaussian weights, summed, and then normalized by the sum of all weights. The result is the estimated temperature (or stress) value of the node to be interpolated at the current moment. By traversing all mesh nodes on the tooth surface, the complete tooth surface temperature and stress field distribution under the current meshing state can be obtained. The interpolated temperature and stress field data are mapped onto the 3D gear model in real time. Temperature contour maps are rendered using thermographic chromatography, and stress contour maps are rendered using equivalent stress chromatography. The virtual gear is driven to rotate at the same angular velocity according to the real-time attitude angle sequence, and the contour maps of the corresponding teeth are dynamically switched and displayed in the meshing area. Simultaneously, the continuously transmitted, real-time updated drift vectors of the three-axis gyroscopes are plotted as time history curves in a dedicated area of ​​the interface to monitor the gyroscope's health status. The system also synchronously analyzes the changing trends of the peak temperature and peak stress of each tooth with the number of meshing cycles, presenting them as graphs and indicator dashboards, providing direct visualization for gear wear trend analysis, fatigue life assessment, and early fault warning.

Claims

1. A method for synchronously measuring meshing temperature and meshing stress of marine heavy-duty gears under service conditions, characterized in that: The specific steps include the following: S1. Based on the follower measurement unit installed on the gear body under test and / or the follower structure that rotates synchronously with the gear under test, obtain the static acceleration vector and the axis gyroscope drift vector. Based on the static acceleration vector and the geographic coordinate system, obtain the initial attitude quaternion of the carrier coordinate system relative to the geographic reference coordinate system, and construct the state vector and the initial error covariance matrix. S2. Based on each sampling time, calculate the angular velocity vector after drift compensation, and obtain the predicted attitude quaternion based on the angular velocity vector. Starting from the initial attitude quaternion, the initial three-axis gyroscope drift vector, and the error covariance matrix, perform time prediction and measurement update, extract the real-time attitude angle information, and form a real-time attitude angle sequence with timestamps. S3. Based on the number of gear teeth, the gear is divided into several sectors. Basic geometric phase interval mapping is performed. The tooth backlash influence factor is calibrated and introduced by the idle travel angle of the driving wheel. After the dynamic torque is inverted in real time by the synchronous data package of meshing temperature and meshing stress, the obtained dynamic torque value is used to calculate the dynamic torsional elastic deformation angle and generate the phase correction yaw angle. Finally, a meshing time sequence containing tooth number, meshing start time stamp, meshing end time stamp, and dynamic torque inversion value are generated. S4. The generated meshing time sequence is converted into a hardware interrupt control signal, which drives the analog-to-digital converter, including the temperature measurement module and the stress measurement module, to perform analog-to-digital conversion within a single meshing window period. All the converted binary temperature digital codes and all the binary strain digital codes are paired by timestamp, packaged into metadata segments, and after forming the original temperature-strain synchronous time sequence data segment, temperature-strain nonlinear decoupling compensation is performed. After the meshing temperature and meshing stress synchronous data packets corresponding to each meshing cycle are synchronously transmitted, the quantitative twin model is completed.

2. The method for synchronously measuring meshing temperature and meshing stress of marine heavy-duty gears under service conditions, as described in claim 1, is characterized in that: S1, based on the static condition when the gear stops, accumulates the time series output by the triaxial accelerometer of the follow-up measurement unit according to each channel and divides it by the number of sampling points to obtain a three-dimensional static acceleration vector. Based on the geometric relationship between the unit direction vector of static acceleration vector and the known vertical downward gravity unit direction vector in the geographic reference coordinate system, a rotational quaternion is constructed using the angular axis transformation method to obtain the initial attitude quaternion describing the transition from the geographic coordinate system to the carrier coordinate system. Based on the static condition of the gears stopping, the long-term angular velocity data sequence of each axis of the three-axis gyroscope is collected, the arithmetic mean of the long-term angular velocity data sequence of each axis is calculated, and all arithmetic means are integrated into the initial three-axis gyroscope drift vector; S1 constructs a state vector based on the initial attitude quaternion and the initial three-axis gyroscope drift vector, and constructs a diagonal matrix based on the uncertainty of the initial attitude quaternion and the estimated variance of the initial three-axis gyroscope drift vector in the state vector, which is then used as the initial error covariance matrix.

3. The method for synchronously measuring meshing temperature and meshing stress of marine heavy-duty gears under service conditions, as described in claim 2, is characterized in that: The S2 is based on extended Kalman filtering for prior estimation, including: using the initial attitude quaternion and the initial three-axis gyroscope drift vector as the posterior state in the first cycle of the filter; The angular velocity vector after zero-point compensation is obtained by subtracting the posterior three-axis gyroscope drift vector from the original angular velocity measurement vector output by the three-axis gyroscope at the current moment. Based on the zero-point compensated angular velocity vector, an incremental rotation quaternion describing the rotational changes of the carrier coordinate system within the sampling period is generated. The posterior attitude quaternion of the previous moment is multiplied by the obtained incremental rotation quaternion according to the quaternion multiplication rule to obtain the attitude quaternion predicted in one step and the corresponding predicted state vector. The predicted value of the three-axis gyroscope drift vector is directly set to the posterior drift vector of the previous moment. The first-order partial derivative of the current predicted state vector with respect to the state vector at the previous moment is derived analytically, and the state transition Jacobian matrix is ​​constructed. Multiply the calculated state transition Jacobian matrix on the left by the posterior error covariance matrix of the previous time step, and then multiply it on the right by the transpose of the state transition Jacobian matrix. Add the resulting matrix to the pre-set noise covariance matrix to obtain the prediction error covariance matrix, thus completing the prior estimation.

4. A method for synchronously measuring meshing temperature and meshing stress of marine heavy-duty gears under service conditions, as described in claim 3, is characterized in that: It also includes posterior estimation based on extended Kalman filtering: Based on the predicted attitude quaternion, the known unit gravity vector pointing to the Earth's center in the geographic reference coordinate system is spatially rotated and transformed to the carrier coordinate system to obtain the theoretical acceleration vector. The difference between the actual three-dimensional measurement vector output by the triaxial accelerometer at the current moment and the theoretical acceleration vector is used to obtain the three-dimensional measurement residual vector. Based on the first-order partial derivative of the theoretical acceleration vector with respect to the current state vector, the measurement Jacobian matrix is ​​obtained. The measurement Jacobian matrix is ​​then multiplied on the left by the prediction error covariance matrix, and then on the right by the transpose of the measurement Jacobian matrix. Finally, the measurement noise covariance matrix of the triaxial accelerometer is added to obtain the innovation covariance matrix. The gain matrix is ​​obtained by left-multiplying the prediction error covariance matrix by the transpose of the measurement Jacobian matrix and then right-multiplying it by the inverse of the innovation covariance matrix. The state correction is obtained by left-multiplying the gain matrix by the three-dimensional measurement residual vector. The state correction is then added to the prediction state vector item by item to obtain the updated posterior state vector and the posterior error covariance matrix. Based on the quaternion components in the posterior state vector, the square root of the sum of squares is calculated as the modulus, and each component is divided by the modulus to obtain the normalized unit posterior attitude quaternion. Based on the conversion relationship between the normalized quaternion and Euler angles, the real-time roll angle, pitch angle and yaw angle of the servo measurement unit are extracted through trigonometric function operations such as arctangent and arcsine. The S2 outputs a real-time attitude angle sequence with timestamps, a real-time updated three-axis gyroscope drift vector, and a posterior error covariance matrix.

5. A method for synchronously measuring meshing temperature and meshing stress of marine heavy-duty gears under service conditions, as described in claim 1, is characterized in that: S3 is based on the number of gear teeth, which is divided into several sectors according to the circumference of 360 degrees. Based on the involute tooth profile geometric parameters such as the gear module, pressure angle, helix angle and tooth tip trimming amount, S3 calculates the range of the central angle that each tooth spans from the start point to the end point of double tooth meshing under no load and no backlash. Based on the center angle range, it is converted into the corresponding ideal meshing start critical yaw angle and ideal meshing end critical yaw angle, and each tooth number is assigned a fixed yaw angle range; Based on manually and / or through the drive device rotating the driving tooth until it just contacts the driven tooth when the gearbox is unloaded and stationary, and measuring the idle travel angle of the driving wheel during the rotation of the driving tooth, and converting the idle travel angle into the tooth flank clearance yaw angle, the tooth flank clearance influence factor is calibrated and introduced. Based on the compensated meshing temperature and meshing stress synchronization data package generated in the previous one and / or multiple meshing cycles, the maximum meshing stress value of the corresponding tooth number at the end of the previous meshing is extracted. Based on the stress value, the Hertz contact half-width of the tooth surface and the pitch circle radius of the gear, the dynamic torque value transmitted by the gear during meshing is reversed to complete the real-time inversion.

6. A method for synchronously measuring meshing temperature and meshing stress of marine heavy-duty gears under service conditions, as described in claim 5, is characterized in that: S3 establishes a linear relationship model between torsional elastic deformation and torque based on the shear elastic modulus of the gear shaft material, the polar moment of inertia of the shaft segment, and the effective length, and calculates the obtained dynamic torque value based on the linear relationship model. The obtained tooth flank clearance yaw angle and dynamic torsional elastic deformation angle are algebraically added to generate the total phase correction yaw angle. Based on each tooth, the corresponding ideal meshing start critical yaw angle and ideal meshing end critical yaw angle are respectively added to the phase correction yaw angle to obtain the corrected meshing start dynamic critical angle and corrected meshing end dynamic critical angle. Based on the posterior error covariance matrix, the diagonal element values ​​of the corresponding phase-corrected yaw angle are extracted. The standard deviation of the yaw angle estimate is obtained by taking the square root. The decision dead zone width is set to three times this standard deviation. If the real-time yaw angle value in the real-time attitude angle crosses the decision dead zone width for several consecutive samplings, it is determined that the engagement event has occurred and / or ended.

7. A method for synchronously measuring meshing temperature and meshing stress of marine heavy-duty gears under service conditions, as described in claim 6, is characterized in that: S3 continuously compares the yaw angle sequence of the real-time attitude angle sequence with the corrected dynamic critical angle of each tooth. When the real-time yaw angle enters the dead zone width upwards, the current time is recorded as the meshing start event timestamp. When the real-time yaw angle exceeds the dead zone width upwards, the current time is recorded as the meshing end event timestamp. All record entries generated in chronological order, consisting of tooth number, meshing start event timestamp, and meshing end event timestamp, constitute a complete meshing time sequence, including the meshing time sequence of tooth number, meshing start timestamp, and meshing end timestamp, as well as the dynamic torque inversion value.

8. A method for synchronously measuring meshing temperature and meshing stress of marine heavy-duty gears under service conditions, as described in claim 1, characterized in that: The S4 loads the output engagement time sequence into the controller in chronological order, and sets the analog-to-digital converters connected to the temperature measurement module and stress measurement module to external trigger start and continuous conversion mode. A level transition signal is generated based on the meshing start timestamp in the meshing time sequence. The sample-and-hold circuit inside each analog-to-digital converter captures and holds the analog input voltage at the current moment, and generates comparison voltages sequentially from the most significant bit to the least significant bit. The voltages are compared with the held voltages one by one to determine the binary code of each bit. The binary digital code obtained by the comparison is stored, and a stop command is generated based on the meshing end timestamp in the meshing time sequence. All binary temperature digital codes output by the temperature analog-to-digital converter and all binary strain digital codes output by the stress analog-to-digital converter are paired one by one according to the timestamps attached during generation, packaged into raw data segments, and metadata information including the corresponding tooth number, the timestamp of the meshing start event, the timestamp of the meshing end event, and the dynamic torque inversion value is written into them to form a raw temperature-strain synchronous time series data segment bound to a single meshing event.

9. A method for synchronously measuring meshing temperature and meshing stress of marine heavy-duty gears under service conditions, as described in claim 8, characterized in that: S4 is based on the same specimen as marine heavy-duty gears. It records the temperature digital output value output by the temperature sensor and the original strain digital output value output by the strain sensor under each set of working conditions. It also calculates the true mechanical strain value based on the applied known load and the cross-sectional area of ​​the specimen. The radial basis function neural network uses three features—the current temperature digital output value, the first-order time difference value of the current temperature (characterizing the rate of temperature change), and the current strain sensor raw digital output value—as the input vector, which serves as the input layer, and outputs the predicted mechanical strain value as the output layer. All calibrated input vectors are combined into a candidate center set. The hidden layer center vector is obtained based on orthogonal least squares. The Euclidean space distance between a selected hidden layer center vector and all other center vectors is calculated to obtain the width parameter shared by each Gaussian radial basis function. All calibrated input vectors are processed one by one through a hidden layer with predetermined center and width parameters to obtain the hidden layer output matrix. The linear weight vector from the hidden layer to the output layer is obtained by solving a linear least squares problem.

10. A method for synchronously measuring meshing temperature and meshing stress of marine heavy-duty gears under service conditions, as described in claim 1, characterized in that: S4 extracts the temperature digital output value and the original strain digital output value at the same moment from the binary temperature digital code and the binary strain digital code to form a temperature digital output value sequence. Based on the time-aligned temperature digital output value sequence, the value of the next sampling point is subtracted from the value of the previous sampling point in time order, and then divided by the sampling period to obtain the temperature change rate sequence corresponding to each moment. Based on each pair of temperature change rate sequences, a three-dimensional input vector is constructed, and based on a trained radial basis function neural network, the predicted mechanical strain value at the corresponding sampling time is obtained. Multiply the predicted mechanical strain value by the elastic modulus of the gear material to obtain the meshing stress value corresponding to the sampling time. Combine the meshing stress value sequence calculated from all sampling points in the data segment with the temperature value sequence directly measured by the temperature sensor at the corresponding timestamp, and attach the metadata header of the original data segment to form a synchronous data package of meshing temperature and meshing stress corresponding to each meshing cycle. After synchronizing and transmitting the synchronous data packets of meshing temperature and meshing stress corresponding to each meshing cycle, the quantitative twin model is constructed.

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