A high-speed motorized spindle core temperature prediction method

Abstract

The application provides a high-speed motorized spindle shaft core temperature prediction method, relates to the technical field of mechanical transmission component performance testing, and acquires initial air gap thickness, initial bearing play and part thermal physical property parameters by collecting real-time operation parameters of the spindle and temperatures of multiple-position external measuring points, and constructs iterative initial boundary conditions; then, centrifugal expansion and thermal deformation are coupled to solve transient actual air gap, bearing real-time working play and actual contact load, according to which, air gap equivalent heat exchange coefficient, bearing joint surface contact thermal resistance and bearing heat generation rate are dynamically updated; subsequently, a lumped parameter thermal network model is constructed to solve the preliminary predicted temperature of the shaft core, and temperature correction is completed by combining heat transfer path equivalent resistance and heat capacity to construct a thermal hysteresis inverse compensation factor. The application realizes high-precision real-time prediction of the high-speed motorized spindle shaft core temperature under full working conditions by coupling centrifugal expansion and thermal deformation to dynamically update key thermal parameters, combining lumped parameter thermal network solving and thermal hysteresis inverse compensation correction.

Description

Technical Field

[0001] This invention relates to the field of mechanical transmission component performance testing technology, specifically a method for predicting the temperature of a high-speed electric spindle core. Background Technology

[0002] High-speed electric spindles are core functional components of high-end CNC machine tools, widely used in precision milling, high-speed grinding, and other machining scenarios. Spindle core temperature is a key parameter characterizing the spindle's thermal state and determining its thermal deformation; accurate and real-time acquisition of this temperature is essential for achieving spindle thermal error compensation and ensuring workpiece machining accuracy. Since the spindle core is located within a high-speed rotating, enclosed assembly structure, it is impossible to directly deploy sensors to collect temperature without damaging the spindle structure or affecting its rotational dynamic balance. Therefore, indirect calculation and modeling simulation based on external measuring points have become the mainstream technical approach for obtaining spindle core temperature.

[0003] Currently, one type of existing technology involves placing temperature measuring points at external locations where sensors can be easily installed, such as the front and rear bearing seats, the outer wall of the housing, and the stator ends of the spindle. Based on a pre-defined heat transfer empirical mapping relationship, the temperature of the spindle core region is inferred from the temperature of the external measuring points. This method does not require modification of the internal structure of the spindle, has low implementation costs, and can obtain certain calculation results under steady-state low-speed conditions. Another type of existing technology uses the lumped parameter thermal network method, which divides the spindle core, bearings, stator, housing, and other components into lumped heat capacity nodes. It constructs a set of thermal balance equations by combining the thermal resistance between components, the convective thermal resistance, and the heat source inside the bearing. The spindle core temperature distribution is obtained through numerical solution. This method can reflect the distribution law of the overall temperature field of the spindle, does not rely on a large amount of measured data, and is a commonly used technique for spindle thermal characteristic analysis.

[0004] The aforementioned existing technologies have the following shortcomings in practical applications: First, relying on external measuring points to indirectly estimate the spindle core temperature results in multiple heat transfer paths from the measuring points to the core level, and the temperature signal suffers from severe thermal inertia lag. Under transient conditions of acceleration and deceleration, the external temperature measurement data lags behind the actual core temperature, leading to poor estimation accuracy and real-time performance, which cannot meet the requirements for real-time compensation of thermal errors in high-speed machining.

[0005] Second, traditional lumped parameter thermal network models take fixed empirical values ​​for thermophysical parameters such as air gap heat transfer coefficient, bearing contact thermal resistance, and bearing heat generation rate, without taking into account the dynamic changes in air gap, bearing clearance, and contact load caused by the coupling of centrifugal expansion and thermal deformation during high-speed operation. This results in a large error in the calculation of spindle core temperature under high-speed variable transient conditions, making it difficult to accurately characterize the transient temperature field distribution of the spindle.

[0006] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0007] The purpose of this invention is to provide a method for predicting the core temperature of a high-speed electric spindle, so as to solve the problems mentioned in the background art.

[0008] To achieve the above objectives, the present invention provides the following technical solution: A method for predicting the core temperature of a high-speed electric spindle, comprising the following steps: Step 1: Collect real-time operating parameters of the electric spindle and temperature at multiple external measuring points to obtain initial air gap thickness, initial bearing clearance, and component thermophysical parameters as initial boundary conditions for iteration; Step 2: Calculate the centrifugal expansion of the rotating component based on real-time operating parameters. Utilize the global temperature field obtained in the previous iteration step to calculate the thermal deformation of each component. Couple centrifugal deformation and thermal deformation to obtain the transient actual air gap thickness and the real-time working clearance of the bearing. Based on the contact state after the change in bearing clearance, solve the actual contact load of the bearing through the bearing mechanical model. Step 3: Using the transient actual air gap thickness, the actual bearing contact load, and the real-time working clearance as input parameters, update the equivalent heat transfer coefficient of the air gap through the convective heat transfer criterion, update the contact thermal resistance of the bearing mating surface through a semi-empirical formula, and calculate the bearing heat generation rate through the bearing heat generation model. Step 4: Construct a lumped parameter thermal network model of the main shaft, load all dynamic thermal parameters, set the temperature of the external measuring point as the temperature boundary of the model node, and obtain the preliminary predicted temperature of the shaft core through implicit numerical iteration. Step 5: Based on the transient temperature gradient of the external measuring point, and combined with the equivalent thermal resistance and heat capacity of the heat transfer path from the measuring point to the shaft core, construct the thermal hysteresis inverse compensation factor, and use the thermal hysteresis inverse compensation factor to correct the preliminary predicted temperature of the shaft core, so as to obtain the corrected predicted temperature of the shaft core. Step 6: Assign the global temperature field of the current iteration step to the initial conditions for the next time step, jump to step 2 to loop and complete the deformation solution, thermal parameter update and temperature solution, and realize the real-time prediction of the core temperature by relying on rolling time sequence iteration.

[0009] Furthermore, the initial air gap thickness, initial bearing clearance, and component thermophysical parameters were obtained using the following methods: Retrieve the stator and rotor structure design drawings of the high-speed electric spindle motor, and read the radial single-sided gap dimension between the inner circle of the stator and the outer circle of the rotor under the state of normal temperature, no centrifugal force, and no temperature rise. The radial single-sided gap dimension between the inner circle of the stator and the outer circle of the rotor is the initial air gap thickness. Based on the model of the angular contact ball bearing selected for the spindle, the bearing manufacturer's catalog is consulted to obtain the bearing's original radial clearance group. Combined with the spindle's axial preload assembly method and preload parameters, the remaining effective clearance after preload cancellation is calculated and used as the initial assembly clearance of the bearing, which is recorded as the initial bearing clearance. Based on the actual processing materials of each component of the high-speed electric spindle, the corresponding national standard material property parameter manual and industry-standard thermal database were consulted to uniformly select fixed thermal property parameters under normal temperature reference conditions. Specifically, these parameters include the thermal conductivity, specific heat capacity at constant pressure, density, and coefficient of linear expansion of each component material. All thermal property parameters adopt the standard values ​​corresponding to the physical materials of the components.

[0010] Furthermore, the centrifugal expansion of the rotating component is calculated based on real-time operating parameters. Using the global temperature field obtained in the previous iteration, the thermal deformation of each component is calculated. The method used is as follows: Using the shaft core and bearing inner ring as rotating components, and the calibrated initial geometric dimensions, material elastic modulus and density as basic parameters, and the collected spindle speed as input, the radial centrifugal expansion of the key mating surfaces of each rotating component is solved based on the elasticity theory of rotating thick-walled cylinders. The key mating surfaces include the outer circle mating surface of the shaft core and the raceway surface of the inner ring of the bearing. Based on the calibrated initial geometric dimensions and linear expansion coefficients of each component, and combined with the nodal temperature distribution of the global temperature field in the current iteration step, the internal temperature gradient of each component is obtained by radial layering. The initial value of radial thermal deformation of the key mating surface of the rotating and stationary components is obtained by integral calculation. The radial dimensions and temperature gradient of the components are corrected by closed-loop iteration until the difference in radial thermal deformation of the key mating surface between the two iterations is less than the preset convergence threshold, and the final thermal deformation of each component is obtained.

[0011] Furthermore, by coupling centrifugal deformation and thermal deformation, the transient actual air gap thickness and the real-time operating clearance of the bearing are obtained. Based on the contact state after the change in bearing clearance, the actual contact load of the bearing is solved through a bearing mechanical model. The method used is as follows: Based on the calibrated initial air gap thickness, the air gap increment caused by the radial thermal deformation of the inner circle of the stator core is superimposed, the air gap reduction caused by the radial centrifugal expansion and radial thermal deformation of the outer circle of the rotor is deducted, and the actual air gap thickness under transient conditions is obtained by combining the radial deviation of the coaxiality of the stator and rotor assembly. Using the calibrated initial bearing clearance as a reference, the reduction in clearance caused by radial centrifugal expansion and radial thermal deformation of the inner ring raceway surface is subtracted, and the increase in clearance caused by radial thermal deformation of the outer ring raceway surface is added to obtain the real-time operating clearance of the bearing under transient conditions. Using the real-time operating clearance of the bearing as input, and combining the number of rolling elements, contact angle and raceway curvature, the contact deformation between the rolling elements and the inner and outer raceways is calculated based on Hertzian contact theory. At the same time, the additional load effect caused by the centrifugal force of the rolling elements under high-speed conditions is also taken into account. The normal contact load of a single rolling element is obtained by solving the problem, and finally the normal contact load of all rolling elements is accumulated to obtain the actual contact load of the bearing.

[0012] Furthermore, in step 3, the methods used to update the equivalent heat transfer coefficient of the air gap, update the contact thermal resistance of the bearing mating surface, and calculate the bearing heat generation rate are as follows: Using the transient actual air gap thickness and real-time spindle speed as core inputs, and combining the physical properties of the air gap cooling medium, the corresponding rotating Reynolds number and Nusselt number are calculated through the annular rotating slot convection heat transfer criterion equation, and the transient air gap equivalent heat transfer coefficient is obtained. Using the actual contact load and working clearance of the transient bearing as input, the contact pressure distribution at the raceway interface is obtained based on Hertzian contact theory. The effective heat transfer contact area of ​​the bearing is then corrected. The contact thermal resistance of the transient bearing is solved by combining the semi-empirical formula for contact thermal resistance and taking into account the additional thermal resistance of the lubricating oil film and the contact logarithm correction. Using the actual contact load, working clearance, and real-time spindle speed of the transient bearing as inputs, the rolling friction heat generation, sliding friction heat generation, and lubricant stirring friction heat generation are calculated separately through the bearing friction torque heat generation model. The total bearing friction torque is obtained by superposition, and the bearing heat generation rate is obtained by angular velocity conversion.

[0013] Furthermore, in step 4, the preliminary predicted temperature of the shaft core is obtained based on the following method: Dynamic thermal parameters include the air gap equivalent heat transfer coefficient, bearing mating surface contact thermal resistance, and bearing heat generation rate. The high-speed electric spindle's spindle core, front bearing, rear bearing, stator core, and housing are divided into mutually independent lumped thermal capacity nodes. Based on the heat transfer paths between each component, a lumped parameter thermal network topology structure is constructed that simultaneously includes radial thermal resistance, axial thermal resistance, and convective thermal resistance. The equivalent heat transfer coefficient of the air gap obtained by dynamic update is converted into the convective thermal resistance of the stator and rotor air gap. The contact thermal resistance of the bearing mating surface is taken as the contact thermal resistance between the inner and outer rings of the bearing. The bearing heat generation rate is taken as the internal heat source term of the corresponding bearing thermal node. All of these are substituted into the lumped parameter thermal network model to establish a transient thermal balance equation set. Using the real-time collected temperatures of each external measuring point as the temperature boundary constraints of the corresponding thermal nodes, the transient thermal equilibrium equations are discretized using an implicit Euler discretization scheme. The equations are iteratively solved until the temperature deviation of each thermal node is less than the preset convergence threshold, and finally the preliminary predicted temperature of the shaft core is obtained.

[0014] Furthermore, based on the transient temperature gradient at external measuring points, and combined with the equivalent thermal resistance and heat capacity of the heat transfer path from the measuring points to the shaft core, a thermal hysteresis inverse compensation factor is constructed. The method used is as follows: Based on the constructed lumped parameter thermal network model, the complete heat transfer path from each external measuring point to the core node is extracted. Each heat transfer path is equivalent to a first-order thermal resistance-thermal capacity inertial element. The equivalent thermal resistance, equivalent thermal capacity and corresponding thermal hysteresis time constant of each heat transfer path are calibrated. The transient temperature gradient of each measuring point is obtained by performing time-domain difference calculation on the real-time temperature data of each external measuring point, and the rotational speed is obtained by performing time-domain difference calculation on the real-time spindle speed. Based on the thermal hysteresis time constant, a basic compensation term is constructed by combining the transient temperature gradient, and the speed change rate is introduced to correct the severity of the operating condition, thus obtaining the operating condition rate correction coefficient. Finally, a thermal hysteresis inverse compensation factor adapted to different operating conditions is generated.

[0015] Furthermore, the initial predicted temperature of the shaft core is corrected using a thermal hysteresis inverse compensation factor to obtain the corrected predicted temperature of the shaft core. The method used is as follows: Using the initial predicted temperature of the shaft core obtained from the thermal network solution as the correction benchmark, the path weight coefficients of the corresponding thermal hysteresis inverse compensation factor for each measuring point are assigned according to the heat transfer path length and thermal resistance ratio from each external measuring point to the shaft core, and the global comprehensive compensation factor is obtained by weighted fusion. Based on the initial predicted temperature of the shaft core at the current moment and the corrected temperature of the shaft core at the previous moment, the transient temperature change rate of the shaft core is calculated. The transient thermal hysteresis compensation amount is obtained by combining the global comprehensive compensation factor. The compensation direction is adaptively matched according to the temperature change trend: positive compensation amount is superimposed during the heating process, and negative compensation amount is superimposed during the cooling process. Setting a compensation amplitude threshold limits the transient thermal hysteresis compensation amount. The constrained compensation amount is then superimposed on the initial predicted temperature of the shaft core to obtain the corrected predicted temperature of the shaft core.

[0016] Compared with the prior art, the beneficial effects of the present invention are: To address the shortcomings of traditional lumped-parameter thermal networks, which use fixed thermal parameters and result in large errors under high-speed transient conditions, this invention solves for the actual transient air gap thickness, bearing working clearance, and actual contact load by coupling centrifugal expansion and thermal deformation. This dynamically updates the equivalent heat transfer coefficient of the air gap, the contact thermal resistance of the bearing mating surface, and the bearing heat generation rate, which are then substituted into the lumped-parameter thermal network model to solve for the shaft core temperature. This invention overcomes the limitation of using fixed empirical values ​​for key thermal parameters and can truly reflect the dynamic changes in air gap heat transfer characteristics, bearing contact state, and heat generation intensity under high-speed operation, significantly improving the accuracy of shaft core temperature prediction under high-speed, variable-speed, and transient conditions. To address the shortcomings of thermal inertia lag and insufficient real-time performance in indirect calculations from external measuring points, this invention constructs a thermal lag inverse compensation factor based on the transient temperature gradient of external measuring points and the thermal resistance and thermal capacity characteristics of the heat transfer path. This factor corrects the initial predicted temperature of the shaft core, eliminating the need to deploy sensors inside the rotating shaft core to offset the temperature delay along the long heat transfer path, thus ensuring real-time prediction to meet the requirements for real-time thermal error compensation. Simultaneously, by using a rolling time-series iteration mechanism to repeatedly calculate the current global temperature field as the initial condition for the next moment, continuous and stable prediction of the shaft core temperature can be achieved under all operating conditions. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating a method for predicting the core temperature of a high-speed electric spindle according to the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0019] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0020] Example: Please see Figure 1 A method for predicting the core temperature of a high-speed electric spindle, comprising the following steps: Step 1: Collect real-time operating parameters of the electric spindle and temperatures at multiple external measuring points to obtain initial air gap thickness, initial bearing clearance, and component thermophysical parameters as initial boundary conditions for iteration.

[0021] This embodiment uses a Type 170 high-speed milling electric spindle with a rated power of 24kW and a maximum speed of 24000r / min as the implementation object. The specific implementation process of step 1 is as follows: Furthermore, the specific methods for implementing multi-source operating parameter and external measuring point temperature acquisition are as follows: A multi-channel synchronous data acquisition chassis is used as the acquisition core, configured with analog input modules and digital input modules, and a fixed sampling frequency of 10Hz is set. The hardware clock built into the acquisition chassis is used as a unified time reference to sample all channel data in parallel at equal intervals. Each set of sampled data is attached with a unified system timestamp, and the timing is aligned according to the timestamp in the data buffer to ensure that the time deviation of data from different sources such as speed, power, and temperature is less than 10ms, thus eliminating subsequent calculation errors caused by timing mismatch of multi-source data. The real-time spindle speed is acquired through a 2500-line incremental encoder built into the electric spindle. The speed pulse signal output by the driver is then input to the digital channel of the acquisition system, where it is converted into the real-time speed value. The spindle output power is read from the operating parameter interface of the spindle servo drive unit and transmitted to the acquisition system via an analog signal. The inlet flow rate and temperature of the lubricating medium are acquired by a turbine flow sensor and a platinum resistance sensor installed on the spindle lubrication inlet pipe. The 4-20mA analog signals output by these two sensors are input to the corresponding channels of the acquisition system. In this embodiment, the lubricating medium is an oil-air mixture, and the inlet temperature range is 20-30℃.

[0022] It should be noted that a total of 5 external temperature measuring points are set up, all of which use Class A precision PT100 contact platinum resistance sensors, which are fixed to the outer wall of the spindle by threaded installation or thermally conductive adhesive bonding. The specific locations are as follows: Measuring point 1 is set at the axial end face of the outer ring of the front bearing housing, corresponding to the installation position of the outer ring of the front bearing; measuring point 2 is set at the axial end face of the outer ring of the rear bearing housing, corresponding to the installation position of the outer ring of the rear bearing; measuring point 3 is set on the outer wall surface at the axial midpoint of the housing; measuring point 4 is set on the inner wall of the housing corresponding to the front end core of the stator; measuring point 5 is set on the inner wall of the housing corresponding to the rear end core of the stator; all temperature sensors are installed after being calibrated with a 0℃ ice-water mixture and a constant temperature oil bath, and the temperature measurement error is ≤±0.1℃.

[0023] Furthermore, initial boundary condition calibration was performed. All calibration work was completed under the reference conditions of cold, unloaded state, spindle stationary, and ambient temperature stable at 25°C. The specific method is as follows: For the initial air gap thickness calibration, the structural design drawings of the electric spindle stator and rotor were retrieved, and the nominal geometric dimensions under normal temperature static conditions were read: for example, the nominal inner diameter of the stator core is 120mm, and the nominal outer diameter of the rotor is 119.4mm, thus the nominal radial single-sided air gap thickness is 0.3mm; after assembly, 8 measuring points were evenly selected in the circumferential direction of the stator and rotor air gap and 3 cross sections were selected in the axial direction for cold-state measurement, and the arithmetic mean of all measuring points was taken as the corrected initial air gap thickness; For the initial bearing clearance calibration, in this embodiment, the spindle uses two sets of P4-grade 7014C angular contact ball bearings installed back-to-back. According to the bearing manufacturer's catalog, the original radial clearance of the C2 group of this bearing model is 12-20μm, and the median value of 16μm is taken as the original clearance reference. Combined with the assembly process parameters, the interference fit between the bearing inner ring and the spindle journal is 0.005mm, and the interference fit between the outer ring and the bearing housing bore is 0.002mm. The bearing inner ring is considered equivalent to a thick-walled cylinder under internal pressure. Based on the geometric dimensions of the inner ring's inner and outer diameters, the elastic modulus and Poisson's ratio of the bearing material, and the interference fit between the inner ring and the journal, the radial displacement formula for the elastic deformation of a thick-walled cylinder is substituted into the equation to calculate the radial expansion of the inner ring raceway surface. This expansion, converted into a diameter increment, represents the reduction in clearance caused by the inner ring interference. Similarly, the bearing outer ring is considered equivalent to a thick-walled cylinder under external pressure. Based on the inner and outer diameters of the outer ring, material parameters, and the interference fit between the outer ring and the bearing housing bore, the radial contraction of the outer ring raceway surface is calculated. This contraction, converted into a diameter reduction, represents the reduction in clearance caused by the outer ring interference. The sum of these two values ​​represents the total reduction in clearance caused by the interference fit. Based on the original radial clearance of the bearing at the factory, the total clearance reduction caused by the interference fit is first deducted, and then the positioning preload radial clearance offset amount calculated by combining the axial preload with the bearing contact angle is deducted to finally obtain the initial bearing clearance after cold assembly.

[0024] Based on the actual machining materials of each component of the spindle, and referring to the national standard handbook of thermophysical parameters of metallic materials and the engineering thermal database, parameter values ​​under a standard temperature of 25℃ were uniformly selected: the spindle core material is 40CrNiMoA alloy structural steel, with a thermal conductivity of 42W / (m²). K), specific heat capacity at constant pressure 470 J / (kg) K), density 7850 kg / m³, coefficient of linear expansion 11.5 × 10⁻⁶ -6 / ℃; the bearing material is GCr15 bearing steel, with a thermal conductivity of 46W / (m). K), specific heat capacity at constant pressure 460 J / (kg) K), density 7810 kg / m³, coefficient of linear expansion 12.5 × 10⁻⁶ -6 / ℃; the stator core is a 50W470 silicon steel sheet laminate structure, and the equivalent thermal conductivity obtained by steady-state heat flow method is 5W / (m). K), equivalent isobaric specific heat capacity 480 J / (kg) K), equivalent density 7650kg / m³; casing material is HT250 gray cast iron, thermal conductivity 50W / (m³). K), specific heat capacity at constant pressure 460 J / (kg) K), density 7200 kg / m³, linear expansion coefficient 10 × 10⁻⁶ -6 / ℃; All parameters are entered into the model parameter library and used as the basic physical property input for subsequent thermal deformation calculations and thermal network solutions. The real-time operating data, external measuring point temperatures, and the calibrated initial air gap thickness, initial bearing clearance, and thermophysical parameters of each component, together constitute the initial boundary conditions for temperature prediction, which are then input into subsequent steps for iterative calculation.

[0025] In this embodiment, step 1 acquires time-consistent operating parameters and temperature data from multiple measurement points through a multi-channel synchronous time-aligned acquisition mechanism. Combined with the accurate calibration and classification of the initial air gap and initial bearing clearance under the cold-state benchmark, and the obtained component thermal property parameters, a complete and reliable iterative initial boundary condition is constructed. This provides an accurate cold-state geometric and property benchmark for subsequent centrifugal expansion and thermal deformation coupling calculations and dynamic thermal parameter updates. It also provides an effective temperature boundary constraint and thermal hysteresis compensation characteristic data source for solving the lumped parameter thermal network. This avoids the cumulative calculation errors caused by multi-source data time mismatch and initial parameter deviation from the source, which is the basic premise for ensuring the accuracy of shaft core temperature prediction and rolling iteration stability under all operating conditions.

[0026] Step 2: Calculate the centrifugal expansion of the rotating component based on the real-time operating parameters. Utilize the global temperature field obtained in the previous iteration step to calculate the thermal deformation of each component. Couple centrifugal deformation and thermal deformation to obtain the transient actual air gap thickness and the real-time working clearance of the bearing. Based on the contact state after the change in bearing clearance, solve the actual contact load of the bearing through the bearing mechanical model.

[0027] This embodiment uses the aforementioned calibrated initial geometric parameters, thermal property parameters, and real-time acquired spindle speed as inputs to complete the centrifugal expansion, thermal deformation solution, and force-thermal coupling calculation according to the following process: The specific method for determining the radial centrifugal expansion of the rotating component is as follows: This step is based on the elasticity theory of rotating thick-walled cylinders. The calculation objects are two types of components: the shaft core and the inner ring of the bearing, which rotate synchronously with the main shaft.

[0028] Using the initial geometric dimensions, material elastic modulus, and density of each rotating component as the basic parameters, and the real-time collected spindle speed as the dynamic input, each rotating component is equivalent to a rotating thick-walled cylindrical structure. Substituting into the radial displacement calculation formula of the rotating thick-walled cylinder, the radial centrifugal expansion at the two key mating surfaces, namely the outer circle mating surface of the shaft core and the inner ring raceway surface of the bearing, is calculated respectively. The initial geometric dimensions calibrated in the cold state were used directly as the calculation benchmark in the first iteration. In subsequent iterations, the actual dimensions of the component after thermal deformation correction in the previous iteration were used as the calculation benchmark to ensure that the centrifugal expansion calculation results matched the actual geometric state of the component under transient conditions.

[0029] The specific method for iteratively solving the radial thermal deformation of each component is as follows: This step uses a combination of radial layered integration and closed-loop iteration to solve the problem, covering all rotating and stationary components including the shaft core, bearing inner ring, bearing outer ring, stator core, and housing.

[0030] First, each component is divided into multiple computational units radially. Then, the average temperature of each unit is extracted by combining the global temperature field node temperature data of the current iteration step to obtain the radial temperature gradient distribution inside the component. Using the linear expansion coefficients of each component calibrated in step 1 as a reference, the initial values ​​of radial thermal deformation at each key mating surface are calculated by radial integration. The obtained initial value of radial thermal deformation is used to correct the radial dimension and internal temperature gradient distribution of the corresponding component, and the above integral calculation process is repeated. A thermal deformation convergence threshold is preset. When the difference in radial thermal deformation of the key mating surface obtained in the previous two iterations is less than the convergence threshold, the iteration is terminated, and the final radial thermal deformation of the key mating surface of each component is output. It should be noted that the thermal deformation convergence threshold is usually set based on absolute error: for precision components such as high-speed electric spindles, the threshold is generally set to 0.01-0.1μm. When the difference in radial thermal deformation of the key mating surfaces between two consecutive iterations is less than this value, convergence is determined. This magnitude is much smaller than the actual amplitude of the spindle's thermal deformation, so it will not affect the accuracy of subsequent calculations, and can also control the number of iterations and ensure computational efficiency.

[0031] Furthermore, based on the radial centrifugal expansion and radial thermal deformation obtained above, and following the logic of geometric deformation superposition and mechanical property mapping, three types of transient intermediate parameters are obtained through coupled solution. These parameters are directly used for the dynamic updating of subsequent key thermal parameters. The specific method is as follows: Calculate the transient actual air gap thickness: Using the initial air gap thickness calibrated in step 1 as the calculation benchmark, the stator is a stationary component that only has thermal deformation, and the air gap increment caused by the radial thermal deformation of the inner circle of the stator core is superimposed; the rotor is a rotating component that is subjected to both centrifugal expansion and thermal deformation, and the air gap reduction caused by the combined radial centrifugal expansion and radial thermal deformation of the outer circle of the rotor is deducted; at the same time, the radial deviation of the coaxiality of the stator and rotor assembly is corrected, and finally the actual air gap thickness under transient conditions is obtained. Calculate the real-time operating clearance of the transient bearing: Using the initial bearing clearance calibrated in step 1 as the calculation benchmark, the inner ring of the bearing rotates synchronously with the shaft, and is subjected to radial centrifugal expansion and radial thermal deformation, which causes the clearance to decrease. Subtract the clearance decrease caused by the combined effects of the above two deformations. The outer ring of the bearing is fixed to the bearing housing and is only subjected to radial thermal deformation, which causes the clearance to increase. Add the clearance increase caused by this deformation. Finally, the real-time operating clearance of the bearing under transient conditions is obtained. Calculate the actual contact load of the bearing: Using the real-time operating clearance of the transient bearing as input, and combining the structural parameters such as the number of rolling elements, contact angle, and raceway curvature of the corresponding bearing, calculate the contact deformation between the rolling elements and the inner and outer raceways based on Hertzian contact theory, and establish the mapping relationship between clearance and contact load; at the same time, take into account the additional influence of the centrifugal force of the rolling elements on the load of the outer raceway under high-speed conditions, solve for the normal contact load of a single rolling element, and sum the normal contact loads of all rolling elements to obtain the total actual contact load of the bearing; The transient actual air gap thickness, real-time bearing operating clearance, and actual bearing contact load obtained from the above solutions are used as core intermediate parameters input into subsequent step 3 for dynamic updating of the three types of key thermal parameters.

[0032] In this embodiment, step 2 solves the centrifugal expansion problem based on the elasticity of a rotating thick-walled cylinder, calculates the thermal deformation through radial layering iteration, and combines geometric deformation superposition with Hertzian contact mechanics mapping to achieve force-thermal coupling, outputting the transient actual air gap thickness, the real-time working clearance of the bearing, and the actual contact load. Step 2 accurately quantifies the dynamic influence of the coupling effect of centrifugal expansion and thermal deformation on the air gap morphology and bearing contact state inside the spindle during high-speed operation. It fundamentally compensates for the inherent defects of traditional thermal network models that ignore deformation coupling effects and use fixed geometric and mechanical parameters, providing accurate physical input and calculation basis for the subsequent dynamic updating of three key thermal parameters: air gap heat transfer coefficient, bearing contact thermal resistance, and heat generation rate.

[0033] Step 3: Using the transient actual air gap thickness, the actual bearing contact load, and the real-time working clearance as input parameters, update the equivalent heat transfer coefficient of the air gap through the convective heat transfer criterion, update the contact thermal resistance of the bearing mating surface through a semi-empirical formula, and calculate the bearing heat generation rate through the bearing heat generation model.

[0034] This embodiment takes the aforementioned high-speed electric spindle as the object, and uses the transient actual air gap thickness, real-time bearing working clearance, and actual bearing contact load obtained from the coupled solution in step 2 as the core inputs. Combined with the material thermal property parameters, lubricant property parameters calibrated in step 1, and the real-time acquired spindle speed, the dynamic update of three types of key thermal parameters is completed. The specific implementation process is as follows: The method for updating the equivalent heat transfer coefficient of the air gap is as follows: This step is based on the convective heat transfer criterion equation of the annular rotating gap. The transient actual air gap thickness is used as the characteristic length, and the circumferential linear velocity at the outer circle of the rotor is used as the characteristic velocity. The rotating Reynolds number under the corresponding operating condition is calculated by combining the kinematic viscosity of the cooling medium in the air gap. The rotating Reynolds number and Prandtl number of the cooling medium are substituted into the convective heat transfer Nusselt number criterion relationship corresponding to the annular rotating gap to obtain the Nusselt number under the current operating condition. According to the physical definition of the Nusselt number, combined with the thermal conductivity of the cooling medium and the characteristic length of the air gap, the equivalent heat transfer coefficient of the air gap under the transient operating condition is calculated. This heat transfer coefficient is updated in real time with the changes in air gap thickness and spindle speed, and is used to characterize the convective heat transfer intensity between the stator and rotor air gap, replacing the fixed empirical value used in the traditional thermal network model.

[0035] The specific method for updating the contact thermal resistance of the bearing mating surface is as follows: This step is based on Hertzian contact theory and combined with a semi-empirical formula for contact thermal resistance. First, based on the normal contact load of a single rolling element, and combined with the radius of curvature of the rolling element and the inner and outer raceways, the elastic modulus and Poisson's ratio of the corresponding materials, the geometric dimensions and effective heat transfer contact area of ​​the contact ellipse between the rolling element and the raceway are calculated. The effective contact area, contact load, and material thermal conductivity are substituted into the semi-empirical formula for contact thermal resistance to obtain the basic thermal resistance of the solid contact interface. On this basis, the additional thermal resistance generated by the lubricating oil film between the rolling element and the raceway is taken into account, and the overall correction is made by combining the total logarithm of the contact between the rolling element and the inner and outer rings. Finally, the contact thermal resistance of the bearing mating surface under transient conditions is obtained. This contact thermal resistance is adjusted in real time with the changes in bearing contact load and clearance state, and is used to characterize the contact thermal conductivity between the inner and outer rings of the bearing.

[0036] The specific method for calculating the bearing heat generation rate is as follows: This step is based on the bearing friction torque heat generation model. The friction torque corresponding to the three types of friction heat generation is solved separately and then superimposed to obtain the total friction torque: the first is the rolling friction heat generation torque, which is based on the normal contact load of a single rolling element as input. Combined with the geometric dimensions of the contact area between the rolling element and the raceway, the rolling friction coefficient under the corresponding material and lubrication conditions is taken. The contact load is multiplied by the rolling friction coefficient to obtain the rolling friction force at a single contact surface. This rolling friction force is multiplied by the bearing pitch circle radius corresponding to the center of the rolling element to obtain the rolling friction torque of a single rolling element on one side of the raceway. After taking into account the torque contributions of the inner and outer rings, the total rolling friction torque of a single rolling element is obtained. Finally, multiply by the total number of rolling elements in the bearing to obtain the rolling friction heat generation torque of the entire bearing.

[0037] Secondly, the sliding friction heat torque is calculated. First, based on the real-time spindle speed and bearing geometric parameters, the revolution speed and rotation speed of the rolling elements are calculated. Combining the raceway curvature radius and contact angle, the equivalent relative sliding speeds on the contact surfaces between the rolling elements and the inner and outer raceways are solved respectively. Based on the normal contact load of a single rolling element, and combined with the sliding friction coefficient under the corresponding working condition, the contact load and the sliding friction coefficient are multiplied to obtain the sliding friction force. The sliding friction force is multiplied by the bearing pitch circle radius to obtain the sliding friction torque of a single rolling element on one side of the raceway. The contributions of the inner and outer rings are summed to obtain the total sliding friction torque of a single rolling element. Finally, multiplying by the total number of rolling elements, the sliding friction heat torque of the entire bearing is obtained.

[0038] Thirdly, the frictional thermal torque generated by lubricant stirring is determined. First, the geometric characteristics of the cavity inside the bearing are determined, including the bearing pitch circle diameter, rolling element diameter, and effective bearing width, to obtain the characteristic dimensions and effective flow area of ​​the annular space where the lubricant is located. The dynamic viscosity parameters of the lubricant at the operating temperature are taken, and combined with the angular velocity of the rolling element corresponding to the spindle speed, the fluid shear force generated by the stirring of the lubricant is calculated. The fluid shear force is multiplied by the corresponding radius of action and converted into viscous resistance torque. Then, the coefficient is corrected according to the effective oil filling amount corresponding to the actual lubrication method (oil-air lubrication, grease lubrication, etc.) to finally obtain the frictional thermal torque generated by lubricant stirring of the entire bearing.

[0039] After summing the three types of friction torques to obtain the total friction torque of the bearing, multiply it by the spindle angular velocity to perform power conversion, and obtain the total heat generated by the bearing per unit time, that is, the bearing heat generation rate under transient conditions. This heat generation rate is updated in real time with the changes in bearing contact load, working clearance and spindle speed, and serves as the internal heat source input of the bearing node in the thermal network model.

[0040] The air gap equivalent heat transfer coefficient, bearing mating surface contact thermal resistance, and bearing heat generation rate obtained by the above dynamic update together constitute the dynamic thermal parameter input of the thermal network model, which is passed into step 4 for iterative solution of the shaft core temperature field.

[0041] In this embodiment, step 3 is the core conversion link connecting the force-thermal coupling deformation calculation and the temperature field solution. It takes the transient actual air gap thickness, real-time bearing working clearance, and actual contact load output from step 2, and realizes real-time dynamic updates of three key thermal parameters: air gap equivalent heat transfer coefficient, bearing mating surface contact thermal resistance, and bearing heat generation rate, respectively, through the annular rotating gap convection heat transfer criterion, the semi-empirical formula for contact thermal resistance, and the bearing friction torque heat generation model. This completely replaces the traditional thermal network model's use of fixed empirical values. This step can truly reflect the dynamic modulation of the convective heat transfer intensity between the stator and rotor caused by air gap thickness fluctuations during high-speed operation, the real-time impact of bearing contact state changes on interface thermal conductivity, and the dynamic changes in bearing heat source intensity caused by load and speed fluctuations. This allows the input parameters of the thermal network model to accurately match the real heat transfer characteristics inside the spindle under transient conditions, fundamentally reducing the systematic deviation of the model caused by fixed thermal parameters, and providing an accurate thermal parameter basis for the subsequent high-precision iterative solution of the temperature field.

[0042] Step 4: Construct a lumped parameter thermal network model of the main shaft, load all dynamic thermal parameters, set the external measuring point temperature as the temperature boundary of the model node, and obtain the preliminary predicted temperature of the shaft core through implicit numerical iteration.

[0043] This embodiment takes the aforementioned high-speed electric spindle as the object, and uses three types of dynamic thermal parameters obtained in step 3—air gap equivalent heat transfer coefficient, bearing mating surface contact thermal resistance, and bearing heat generation rate—as the core inputs. Combined with the component geometric dimensions and thermal property parameters calibrated in step 1, a lumped parameter thermal network model is constructed, and the transient temperature field is solved. The specific implementation process is as follows: The specific method for constructing the lumped-parameter thermal network topology is as follows: The high-speed electric spindle is divided into nodes using the lumped heat capacity method. Based on the spindle's structural composition and heat transfer characteristics, the spindle core, front bearing inner ring, front bearing outer ring, rear bearing inner ring, rear bearing outer ring, stator core, and housing are each divided into independent lumped heat capacity thermal nodes. Each node corresponds to a lumped heat capacity parameter, characterizing the overall heat storage capacity of the component. According to the actual heat transfer paths between the components, corresponding thermal resistance units are set: radial thermal resistance is set between the spindle core and the bearing inner ring, between the bearing outer ring and the bearing housing, and between the stator core and the housing; axial thermal resistance is set between the front and rear bearings and between the front and rear ends of the stator core; convective thermal resistance is set between the air gap between the stator and rotor and between the outer wall of the housing and the environment. Through the connection of the above nodes and thermal resistance units, a lumped parameter thermal network topology covering radial heat transfer, axial heat transfer, and convective heat transfer is constructed.

[0044] The specific method for loading dynamic thermal parameters and establishing a transient thermal equilibrium equation set is as follows: The dynamic thermal parameters obtained in step 3 are mapped one by one to the corresponding units of the thermal network model: the equivalent heat transfer coefficient of the air gap is combined with the effective heat transfer area of ​​the stator and rotor air gap to convert it into the air gap convective thermal resistance between the stator and rotor, and connected to the heat transfer path between the stator node and the rotor node; the contact thermal resistance of the bearing mating surface is directly used as the contact thermal resistance between the inner ring node and the outer ring node of the corresponding bearing, replacing the original fixed contact thermal resistance parameter; the bearing heat generation rate is used as the internal heat source term of the corresponding bearing node and loaded into the thermal balance equation of the corresponding thermal node. Combining the heat capacity parameters of each node with all thermal resistance and heat source parameters, a transient thermal balance differential equation is established for each thermal node according to the law of conservation of energy. The differential equations of all nodes are combined to form a complete transient thermal balance equation system.

[0045] The specific method for applying temperature boundary constraints and performing numerical discretization is as follows: The temperatures of each external measuring point collected in real time in step 1 are assigned to the corresponding hot nodes in the thermal network as the first type of temperature boundary constraints of the model. The transient thermal equilibrium equations are discretized in the time domain using the implicit Euler discretization scheme: the node temperature at the previous moment is taken as a known quantity, and the differential term of temperature with respect to time is replaced by the ratio of the temperature difference between adjacent time steps to the time step length, so as to transform the transient differential equations into the linear algebraic equations of the current time step. An iterative method is used to solve the discretized algebraic equations. A preset node temperature convergence threshold is set. When the maximum temperature deviation of each node obtained from two consecutive iterations is less than the convergence threshold, the calculation is considered converged, and the temperature value of each hot node at the current moment is obtained. It should be noted that an absolute temperature error threshold is used, and the value is matched with the accuracy level of the external temperature sensor. Generally, it is taken as 1 / 10 to 1 / 5 of the sensor's temperature measurement error. In this embodiment, a PT100 temperature sensor (temperature measurement error ±0.1℃) is used, and the threshold is usually set to 0.01-0.02℃ to ensure that the calculation error is much smaller than the measurement error and will not drag down the overall prediction accuracy. When making the determination, the maximum value of the temperature difference between two consecutive iterations of all nodes is taken. If it is less than the threshold, the calculation is considered converged.

[0046] The specific method for outputting the solution results is as follows: Extract the convergence temperature value of the corresponding node of the core in the thermal network model as the initial predicted temperature of the core; at the same time, output the temperature data of all thermal nodes to form the global temperature field at the current moment. On the one hand, it is sent back to step 2 for thermal deformation calculation in the next iteration step, and on the other hand, it is sent to subsequent steps for thermal hysteresis inverse compensation correction.

[0047] In this embodiment, step 4 is the core computational hub for the quantitative solution of the spindle core temperature field in this invention. By constructing a lumped parameter thermal network topology covering all components of the spindle, it accurately maps the three types of thermal parameters dynamically updated in step 3 to the air gap convection thermal resistance, bearing contact thermal resistance, and internal heat source terms within the model. This completely replaces the fixed empirical parameters used in traditional thermal network models, enabling the heat transfer model to truly match the dynamic heat transfer characteristics inside the spindle under high-speed transient conditions. This reduces the systematic computational deviation caused by fixed parameters at the model input level. At the same time, the model is calibrated by using external measured temperatures as node temperature boundary constraints. Iterative solutions are then performed using the implicit Euler discretization scheme, which has stronger numerical stability. This ensures the convergence reliability of the transient temperature field solution, adapts to the computational needs of long-term rolling iterations, and improves the objective accuracy of the preliminary prediction results. This step not only builds upon the parameter update results of the preceding force-thermal coupling to complete the quantitative output of the temperature field, but also simultaneously generates the preliminary predicted temperature of the shaft core and the global temperature field. This provides benchmark data for subsequent thermal hysteresis inverse compensation correction and provides temperature field input for the thermal deformation calculation of the next iteration. It is a key link in the entire process of series force-thermal coupling, temperature solution and rolling iteration.

[0048] Step 5: Based on the transient temperature gradient of the external measuring point, and combined with the equivalent thermal resistance and thermal capacity of the heat transfer path from the measuring point to the shaft core, construct the thermal hysteresis inverse compensation factor, and use the thermal hysteresis inverse compensation factor to correct the preliminary predicted temperature of the shaft core, so as to obtain the corrected predicted temperature of the shaft core.

[0049] This embodiment takes the aforementioned high-speed electric spindle as the object, and uses the lumped parameter thermal network model constructed in step 4, the external measuring point temperature and spindle speed collected in real time in step 1, and the preliminary predicted spindle core temperature obtained in step 4 as inputs.

[0050] Furthermore, a thermal hysteresis inverse compensation factor is constructed, specifically through the following method: First, the equivalent heat transfer path and thermal hysteresis time constant calibration were completed. Based on the lumped parameter thermal network topology constructed in step 4, the complete series heat transfer path from each external measuring point's corresponding thermal node to the core thermal node was extracted one by one, clarifying the thermal resistance, contact resistance, and lumped heat capacity of each node distributed sequentially along each path. Combining the equivalent modeling method of heat transfer and control theory, a single complete heat transfer path was equivalent to a first-order thermal resistance-heat capacity inertial element. The step response method was used to complete the parameter calibration: under cold steady-state conditions, a constant speed step excitation was applied to the spindle, and the temperature response curves of the external measuring points and the core node were recorded simultaneously. The dynamic characteristics of the temperature response were extracted by the tangent method, and the equivalent thermal resistance and equivalent heat capacity corresponding to each heat transfer path were calculated. Then, based on the basic relationship that the thermal hysteresis time constant is equal to the product of the equivalent thermal resistance and the equivalent heat capacity, the thermal hysteresis time constant corresponding to each heat transfer path was solved. This constant is used to characterize the degree of thermal inertial delay in the transmission of the temperature signal along the path. Next, transient operating condition characteristic quantities are calculated. Time-domain difference operation is performed on the real-time temperature data of each external measuring point. The difference between the measuring point temperature at the current sampling time and the measuring point temperature at the previous sampling time is taken and then divided by the sampling time step to obtain the transient temperature gradient of each measuring point, which is used to characterize the degree of temperature change at the measuring point location. Simultaneous domain difference operation is used to process the real-time acquired spindle speed data to obtain the spindle speed change rate, which is used to characterize the degree of transient fluctuation of the spindle heat source intensity. Finally, a dynamic thermal hysteresis inverse compensation factor is generated. Using the thermal hysteresis time constant corresponding to each heat transfer path as the compensation benchmark, a basic compensation term is constructed by combining the transient temperature gradient at the corresponding measuring point. The amplitude of the basic compensation term is positively correlated with the absolute value of the temperature gradient, used to offset the thermal inertia hysteresis during steady-state heating and cooling. Based on this, a spindle speed change rate is introduced to construct a working condition rate correction coefficient. The working condition rate correction coefficient uses the spindle's rated acceleration and deceleration rate as a reference benchmark. First, the absolute value of the real-time speed change rate is normalized to obtain the working condition rate ratio. Then, a linear gain mapping relationship is established with a coefficient of 1 under constant speed conditions, ensuring that the correction coefficient synchronizes with the degree of speed change. The gain slope and limit parameters are increased, and upper and lower limits are set to suppress compensation distortion under abnormal operating conditions. Finally, the gain slope and limit parameters are optimized through bench calibration experiments to generate a correction coefficient that can be dynamically adjusted according to the operating conditions. This coefficient is used to amplify the compensation amplitude under variable speed conditions and adapt to the additional thermal hysteresis caused by sudden changes in heat source. The larger the speed change rate, the larger the correction coefficient value is, which is used to amplify the compensation amplitude under variable speed conditions and adapt to the additional thermal hysteresis caused by sudden changes in heat source. The basic compensation term and the operating speed correction coefficient are coupled and calculated to generate a thermal hysteresis inverse compensation factor that corresponds one-to-one with the measurement point position and operating conditions. This factor can be dynamically adjusted in real time according to the spindle operating status.

[0051] Furthermore, the initial predicted temperature of the shaft core is corrected in real time using a thermal hysteresis inverse compensation factor. The specific method is as follows: First, the weighted fusion of compensation factors at multiple measuring points is completed, and the preliminary predicted temperature of the shaft core obtained in step 4 is used as the correction benchmark value. Based on the proportion of the total thermal resistance of the heat transfer path from each external measuring point to the shaft core to the total thermal resistance of all paths, the path weight coefficient of the corresponding thermal hysteresis inverse compensation factor for each measuring point is assigned. The higher the proportion of the thermal resistance of the heat transfer path, the greater the weight, indicating that the thermal hysteresis characteristics of the path have a more significant impact on the shaft core temperature. The thermal hysteresis inverse compensation factor of each measuring point is multiplied by the corresponding path weight coefficient and then summed to obtain the global comprehensive compensation factor applicable to the shaft core node. Next, the transient compensation amount is solved and the compensation direction is adaptively matched. Based on the preliminary predicted temperature of the shaft core at the current moment and the corrected temperature value of the shaft core at the previous moment, the transient temperature change rate of the shaft core is obtained through time-domain difference calculation. The global comprehensive compensation factor is combined with the transient temperature change rate of the shaft core to solve for the transient thermal hysteresis compensation amount at the current moment. It should be noted that this calculation is based on the temperature hysteresis characteristics of a first-order thermal resistance-thermal capacity inertial system. Its core physical law is: when the temperature changes at a constant rate, the steady-state temperature hysteresis of the system output relative to the input is equal to the product of the system thermal hysteresis time constant and the temperature change rate. The specific calculation process is as follows: First, clarify the physical meaning of the global comprehensive compensation factor: The global comprehensive compensation factor obtained by the path weighting and fusion mentioned above is essentially an equivalent thermal lag time characteristic parameter that integrates the thermal inertia characteristics of each heat transfer path and the degree of speed change under the operating conditions, and characterizes the overall lag time scale of the core temperature relative to the temperature of the external measuring point. The calculation first extracts the absolute value of the transient temperature change rate of the shaft core, retaining only the information on the severity of the temperature change and eliminating the influence of the direction sign on the calculation of the compensation amplitude. Then, the global comprehensive compensation factor is directly multiplied by the absolute value of the transient temperature change rate of the shaft core. The product of the two is the amplitude of the transient thermal hysteresis compensation at the current moment. This amplitude increases synchronously with the increase of the temperature change rate, matching the physical law that "the faster the temperature changes, the greater the thermal hysteresis difference". After completing the amplitude calculation, the compensation direction is matched with the temperature trend: During the heating process, the temperature of the external measuring point lags behind the temperature inside the shaft core. The initial predicted temperature of the shaft core based on the boundary of the measuring point will be lower than the actual value. Therefore, the compensation amount is positive, and the predicted temperature is raised after superposition. During the cooling process, the temperature drop of the external measuring point lags behind the temperature inside the shaft core. The initial predicted temperature will be higher than the actual value. Therefore, the compensation amount is negative, and the predicted temperature is lowered after superposition. This achieves adaptive matching between the compensation direction and the temperature change trend, avoiding overcompensation error when the working condition reverses. Finally, the compensation amount is limited and the corrected temperature output is completed. The compensation amplitude threshold is preset, and the calculated transient thermal hysteresis compensation amount is subject to upper and lower limit constraints to suppress compensation distortion under abnormal operating conditions such as temperature jumps and speed changes at the measuring point, and to ensure the stability of numerical calculation. The transient thermal hysteresis compensation amount after the limit constraint is superimposed on the initial predicted temperature of the shaft core to obtain the corrected predicted temperature of the shaft core. At the same time, the temperature data of the shaft core nodes in the global temperature field are updated synchronously, which serves as the final prediction result output at the current moment and is also passed into subsequent steps for rolling iterative calculation at the next moment.

[0052] In this embodiment, step 5 is the core correction step for solving the thermal inertia lag problem of external indirect temperature measurement, and it is also a key support for improving the real-time performance and accuracy of temperature prediction under transient conditions. Based on the actual heat transfer path of the lumped-parameter thermal network, it equates the heat transfer process from the measuring point to the shaft core to a first-order thermal resistance-thermal capacity inertial link to construct a compensation mechanism. This differs from pure signal advance processing without physical basis, ensuring the thermal rationality and versatility of the compensation logic. By coupling the transient temperature gradient and the spindle speed change rate as dual features to generate a compensation factor, it can simultaneously adapt to the thermal lag characteristics of both steady-state temperature rise and fall and high-speed speed change scenarios, compensating for the insufficient compensation accuracy of single temperature feature compensation under sudden heat source changes. Combined with path weight weighted fusion, adaptive matching of compensation direction, and compensation amplitude limiting constraint, it achieves global comprehensive correction of the thermal lag effect of multiple measuring points, taking into account the differences in the impact of different heat transfer paths on the shaft core temperature, and maintains numerical stability under abnormal scenarios such as operating condition reversal and measuring point jumps, effectively offsetting the temperature signal transmission delay deviation caused by long heat transfer paths. This step significantly improves the real-time performance and accuracy of spindle core temperature prediction under transient conditions without altering the internal structure of the spindle or disrupting the rotational dynamic balance. At the same time, the corrected spindle core temperature is updated to the global temperature field, providing a more accurate temperature reference for the thermal deformation calculation and thermal parameter solution of the next iteration, forming a positive cycle of prediction accuracy.

[0053] Step 6: Assign the global temperature field of the current iteration step to the initial conditions for the next time step, jump to step 2 and loop to complete the deformation solution, thermal parameter update and temperature solution, and realize the real-time prediction of the shaft core temperature by relying on rolling time sequence iteration; This step is a closed-loop execution phase of the rolling time-series iteration. The specific implementation process is as follows: After completing the core temperature correction and global temperature field update in step 5 at the current moment, the global temperature field of the current iteration step is assigned as the initial temperature condition for the next moment's calculation. Then, the process jumps back to step 2 and repeats the complete calculation process of centrifugal expansion and thermal deformation coupling solution, key thermal parameter dynamic update, lumped parameter thermal network solution, and thermal hysteresis inverse compensation correction. After each time step of iteration calculation is completed, the corrected core temperature value at the current moment is output synchronously. The rolling time-series iteration continues throughout the entire spindle operation cycle to achieve continuous real-time prediction of the core temperature.

[0054] In this embodiment, step 6 constructs a time-domain rolling closed-loop iteration mechanism, using the corrected global temperature field as the initial condition for calculation at the next moment. This achieves continuous transmission and coupling of the temperature field, deformation field, and thermal parameters in the time dimension, avoiding the problem of the initial conditions being disconnected from the actual working conditions when solving independently at a single moment. This allows the accuracy gain of the preceding dynamic thermal parameter update and thermal hysteresis compensation to form a positive cycle.

[0055] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0056] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0057] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0058] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for predicting the core temperature of a high-speed electric spindle, characterized in that, The specific steps include: Step 1: Collect real-time operating parameters of the electric spindle and temperature at multiple external measuring points to obtain initial air gap thickness, initial bearing clearance, and component thermophysical parameters as initial boundary conditions for iteration; Step 2: Calculate the centrifugal expansion of the rotating component based on real-time operating parameters. Utilize the global temperature field obtained in the previous iteration step to calculate the thermal deformation of each component. Couple centrifugal deformation and thermal deformation to obtain the transient actual air gap thickness and the real-time working clearance of the bearing. Based on the contact state after the change in bearing clearance, solve the actual contact load of the bearing through the bearing mechanical model. Step 3: Using the transient actual air gap thickness, the actual bearing contact load, and the real-time working clearance as input parameters, update the equivalent heat transfer coefficient of the air gap through the convective heat transfer criterion, update the contact thermal resistance of the bearing mating surface through a semi-empirical formula, and calculate the bearing heat generation rate through the bearing heat generation model. Step 4: Construct a lumped parameter thermal network model of the main shaft, load all dynamic thermal parameters, set the temperature of the external measuring point as the temperature boundary of the model node, and obtain the preliminary predicted temperature of the shaft core through implicit numerical iteration. Step 5: Based on the transient temperature gradient of the external measuring point, and combined with the equivalent thermal resistance and heat capacity of the heat transfer path from the measuring point to the shaft core, construct the thermal hysteresis inverse compensation factor, and use the thermal hysteresis inverse compensation factor to correct the preliminary predicted temperature of the shaft core, so as to obtain the corrected predicted temperature of the shaft core. Step 6: Assign the global temperature field of the current iteration step to the initial conditions for the next time step, jump to step 2 and loop to complete the deformation solution, thermal parameter update and temperature solution, and realize the real-time prediction of the shaft core temperature by relying on rolling time sequence iteration; The method used to obtain the preliminary predicted temperature of the shaft core is as follows: Dynamic thermal parameters include the air gap equivalent heat transfer coefficient, bearing mating surface contact thermal resistance, and bearing heat generation rate. The high-speed electric spindle's spindle core, front bearing, rear bearing, stator core, and housing are divided into mutually independent lumped thermal capacity nodes. Based on the heat transfer paths between each component, a lumped parameter thermal network topology structure is constructed that simultaneously includes radial thermal resistance, axial thermal resistance, and convective thermal resistance. The equivalent heat transfer coefficient of the air gap obtained by dynamic update is converted into the convective thermal resistance of the stator and rotor air gap. The contact thermal resistance of the bearing mating surface is taken as the contact thermal resistance between the inner and outer rings of the bearing. The bearing heat generation rate is taken as the internal heat source term of the corresponding bearing thermal node. All of these are substituted into the lumped parameter thermal network model to establish a transient thermal balance equation set. Using the real-time collected temperatures of each external measuring point as the temperature boundary constraints of the corresponding thermal nodes, the transient thermal equilibrium equations are discretized using an implicit Euler discretization scheme. The equations are iteratively solved until the temperature deviation of each thermal node is less than the preset convergence threshold, and finally the preliminary predicted temperature of the shaft core is obtained.

2. The method for predicting the core temperature of a high-speed electric spindle according to claim 1, characterized in that, The method used to obtain the initial air gap thickness, initial bearing clearance, and component thermophysical parameters is as follows: Retrieve the stator and rotor structure design drawings of the high-speed electric spindle motor, and read the radial single-sided gap dimension between the inner circle of the stator and the outer circle of the rotor under the state of normal temperature, no centrifugal force, and no temperature rise. The radial single-sided gap dimension between the inner circle of the stator and the outer circle of the rotor is the initial air gap thickness. Based on the model of the angular contact ball bearing selected for the spindle, the bearing manufacturer's catalog is consulted to obtain the bearing's original radial clearance group. Combined with the spindle's axial preload assembly method and preload parameters, the remaining effective clearance after preload cancellation is calculated and used as the initial assembly clearance of the bearing, which is recorded as the initial bearing clearance. Based on the actual processing materials of each component of the high-speed electric spindle, the corresponding national standard material property parameter manual and industry-standard thermal database were consulted to uniformly select fixed thermal property parameters under normal temperature reference conditions. Specifically, these parameters include the thermal conductivity, specific heat capacity at constant pressure, density, and coefficient of linear expansion of each component material. All thermal property parameters adopt the standard values ​​corresponding to the physical materials of the components.

3. The method for predicting the core temperature of a high-speed electric spindle according to claim 1, characterized in that, The centrifugal expansion of the rotating component is calculated based on real-time operating parameters. The thermal deformation of each component is calculated using the global temperature field obtained from the previous iteration. The method used is as follows: Using the shaft core and bearing inner ring as rotating components, and the calibrated initial geometric dimensions, material elastic modulus and density as basic parameters, and the collected spindle speed as input, the radial centrifugal expansion of the key mating surfaces of each rotating component is solved based on the elasticity theory of rotating thick-walled cylinders. The key mating surfaces include the outer circle mating surface of the shaft core and the raceway surface of the inner ring of the bearing. Based on the calibrated initial geometric dimensions and linear expansion coefficients of each component, and combined with the nodal temperature distribution of the global temperature field in the current iteration step, the internal temperature gradient of each component is obtained by radial layering. The initial value of radial thermal deformation of the key mating surface of the rotating and stationary components is obtained by integral calculation. The radial dimensions and temperature gradient of the components are corrected by closed-loop iteration until the difference in radial thermal deformation of the key mating surface between two iterations is less than the preset convergence threshold, and the final thermal deformation of each component is obtained.

4. The method for predicting the core temperature of a high-speed electric spindle according to claim 3, characterized in that, The transient actual air gap thickness and real-time bearing operating clearance are obtained by coupling centrifugal deformation and thermal deformation. Based on the contact state after the bearing clearance changes, the actual contact load of the bearing is solved through a bearing mechanical model. The method used is as follows: Based on the calibrated initial air gap thickness, the air gap increment caused by the radial thermal deformation of the inner circle of the stator core is superimposed, the air gap reduction caused by the radial centrifugal expansion and radial thermal deformation of the outer circle of the rotor is deducted, and the actual air gap thickness under transient conditions is obtained by combining the radial deviation of the coaxiality of the stator and rotor assembly. Using the calibrated initial bearing clearance as a reference, the reduction in clearance caused by radial centrifugal expansion and radial thermal deformation of the inner ring raceway surface is subtracted, and the increase in clearance caused by radial thermal deformation of the outer ring raceway surface is added to obtain the real-time operating clearance of the bearing under transient conditions. Using the real-time operating clearance of the bearing as input, and combining the number of rolling elements, contact angle and raceway curvature, the contact deformation between the rolling elements and the inner and outer raceways is calculated based on Hertzian contact theory. At the same time, the additional load effect caused by the centrifugal force of the rolling elements under high-speed conditions is also taken into account. The normal contact load of a single rolling element is obtained by solving the problem, and finally the normal contact load of all rolling elements is accumulated to obtain the actual contact load of the bearing.

5. The method for predicting the core temperature of a high-speed electric spindle according to claim 1, characterized in that, In step 3, the methods used to update the equivalent heat transfer coefficient of the air gap, update the contact thermal resistance of the bearing mating surface, and calculate the bearing heat generation rate are as follows: Using the transient actual air gap thickness and real-time spindle speed as core inputs, and combining the physical properties of the air gap cooling medium, the corresponding rotating Reynolds number and Nusselt number are calculated through the annular rotating slot convection heat transfer criterion equation, and the transient air gap equivalent heat transfer coefficient is obtained. Using the actual contact load and working clearance of the transient bearing as input, the contact pressure distribution at the raceway interface is obtained based on Hertzian contact theory. The effective heat transfer contact area of ​​the bearing is then corrected. The contact thermal resistance of the transient bearing is solved by combining the semi-empirical formula for contact thermal resistance and taking into account the additional thermal resistance of the lubricating oil film and the contact logarithm correction. Using the actual contact load, working clearance, and real-time spindle speed of the transient bearing as inputs, the rolling friction heat generation, sliding friction heat generation, and lubricant stirring friction heat generation are calculated separately through the bearing friction torque heat generation model. The total bearing friction torque is obtained by superposition, and the bearing heat generation rate is obtained by angular velocity conversion.

6. The method for predicting the core temperature of a high-speed electric spindle according to claim 1, characterized in that, Based on the transient temperature gradient at external measuring points, and combined with the equivalent thermal resistance and heat capacity of the heat transfer path from the measuring points to the shaft core, a thermal hysteresis inverse compensation factor is constructed. The method used is as follows: Based on the constructed lumped parameter thermal network model, the complete heat transfer path from each external measuring point to the core node is extracted. Each heat transfer path is equivalent to a first-order thermal resistance-thermal capacity inertial element. The equivalent thermal resistance, equivalent thermal capacity and corresponding thermal hysteresis time constant of each heat transfer path are calibrated. The transient temperature gradient of each measuring point is obtained by performing time-domain difference calculation on the real-time temperature data of each external measuring point, and the rotational speed is obtained by performing time-domain difference calculation on the real-time spindle speed. Based on the thermal hysteresis time constant, a basic compensation term is constructed by combining the transient temperature gradient, and the speed change rate is introduced to correct the severity of the operating condition, thus obtaining the operating condition rate correction coefficient. Finally, a thermal hysteresis inverse compensation factor adapted to different operating conditions is generated.

7. The method for predicting the core temperature of a high-speed electric spindle according to claim 1, characterized in that, The initial predicted temperature of the shaft core is corrected using a thermal hysteresis inverse compensation factor to obtain the corrected predicted temperature of the shaft core. The method used is as follows: Using the initial predicted temperature of the shaft core obtained from the thermal network solution as the correction benchmark, the path weight coefficients of the corresponding thermal hysteresis inverse compensation factor for each measuring point are assigned according to the heat transfer path length and thermal resistance ratio from each external measuring point to the shaft core, and the global comprehensive compensation factor is obtained by weighted fusion. Based on the initial predicted temperature of the shaft core at the current moment and the corrected temperature of the shaft core at the previous moment, the transient temperature change rate of the shaft core is calculated. The transient thermal hysteresis compensation amount is obtained by combining the global comprehensive compensation factor. The compensation direction is adaptively matched according to the temperature change trend: positive compensation amount is superimposed during the heating process, and negative compensation amount is superimposed during the cooling process. Setting a compensation amplitude threshold limits the transient thermal hysteresis compensation amount. The constrained compensation amount is then superimposed on the initial predicted temperature of the shaft core to obtain the corrected predicted temperature of the shaft core.

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