A method for acquiring thermal errors of a main shaft of a precision machine tool based on MC-RNM and I-TNM algorithms

Abstract

The application discloses a kind of based on MC-RNM and I-TNM algorithm's precision machine tool spindle thermal error acquisition method, comprising the following steps, step 1, using Matlab obtains the rotational speed of machine tool spindle, the current position of machine tool spindle and actual environment temperature;Step 2, according to the rotational speed of machine tool spindle obtained, the current position of machine tool spindle and actual environment temperature, based on MC-RNM algorithm real-time calculation spindle net radiation heat transfer;Step 3, according to the spindle net radiation heat transfer, based on I-TNM algorithm to establish the spindle thermal error analytical model considering radiation heat transfer;Step 4, according to the spindle thermal error analytical model of radiation heat transfer, real-time calculation spindle transient thermal error;It can be real-time read spindle rotational speed, spindle current position, current environment temperature, establish the overall coordinate system and local coordinate system of spindle system, spindle workspace, and based on MC-RNM calculation spindle net radiation heat transfer, based on I-TNM algorithm to establish the spindle thermal error analytical model, iterative solution simultaneous equations solution obtains spindle transient temperature field, node transient temperature value is obtained with the spindle transient thermal error;It improves the prediction accuracy and stability of thermal error model, with strong applicability, robustness good advantage.

Description

Technical Field

[0001] This invention belongs to the field of precision machine tool technology, specifically relating to a method for obtaining thermal error of precision machine tool spindle based on MC-RNM and I-TNM algorithms. Background Technology

[0002] Precision is a leading indicator for high-end CNC machine tools. During machine tool operation, changes in internal and external heat sources such as motor heating, frictional heat, cutting heat, and ambient temperature can cause thermal deformation of machine tool components. This leads to deviations in the relative position between the tool and the workpiece from the predetermined value, known as thermal error, which in turn reduces machine tool precision. As the performance of CNC machine tools gradually improves, thermal error has become a major factor affecting machine tool precision. Studies show that thermal error accounts for 40%-70% of the errors in precision machine tools. Among these, spindle thermal error directly affects the tool tip position, severely impacting machining quality.

[0003] The spindle is the core component and main heat source of CNC machine tools. Therefore, establishing an effective spindle thermal error modeling method is crucial in current research on CNC machine tool thermal error compensation. Although there is a large amount of research on methods for obtaining CNC machine tool spindle thermal errors, the practical application of various error modeling techniques is not high. They are difficult to apply as a common solution to various process conditions and applications of CNC machine tool machining, thus hindering the achievement of higher precision in CNC machine tool machining and the realization of robust thermal error modeling under complex working conditions. Summary of the Invention

[0004] The purpose of this invention is to solve the technical problem that existing spindle thermal error acquisition methods cannot achieve higher precision in CNC machine tool machining and robust modeling of thermal errors under complex working conditions, and to provide a precision machine tool spindle thermal error acquisition method based on MC-RNM and I-TNM algorithms.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] This invention provides a method for obtaining the thermal error of a precision machine tool spindle based on MC-RNM and I-TNM algorithms, comprising the following steps:

[0007] Step 1: Use Matlab to obtain the spindle speed, current position, and ambient temperature. Step 2: Based on the obtained spindle speed, current position, and ambient temperature, calculate the spindle net radiative heat transfer in real time using the MC-RNM algorithm. Step 3: Based on the spindle net radiative heat transfer, establish an analytical model of spindle thermal error based on the I-TNM algorithm. Step 4: Calculate the spindle transient thermal error in real time based on the analytical model of spindle thermal error.

[0008] Furthermore, before obtaining the machine tool spindle speed, the current position of the machine tool spindle and the actual ambient temperature in step 1, the following steps are also included: setting the CNC and the industrial control computer under the same local area network, and connecting the CNC and the industrial control computer by developing an application program.

[0009] Furthermore, the net radiative heat transfer of the spindle includes the following steps:

[0010] Step 1: Establish the overall coordinate system and local coordinate system of the spindle system and spindle workspace; Step 2: Generate several emission points and radiation beams on the heat exchange surface; Step 3: Calculate the radiation heat transfer angle coefficient between each heat exchange surface; Step 4: Calculate the net radiation heat transfer of the spindle system based on the radiation heat transfer angle coefficient.

[0011] Furthermore, the origin of the overall coordinate system is set at the intersection of the spindle rotation center and the workspace plane where the spindle is located, and the X / Y / Z axis directions of the overall coordinate system are the same as the X / Y / Z axis directions of the machine tool absolute coordinate system; the X / Y / Z axis directions of the overall coordinate system are the same as the X / Y / Z axis directions of the local coordinate system; the origin of the local coordinate system is the emission point of a randomly generated radiation energy beam on the heat exchange surface.

[0012] Furthermore, the calculation of the radiation heat transfer angle coefficient between each heat transfer surface is as follows:

[0013] Among them, X i,j Let be the angle coefficient of a heat transfer surface i with respect to any heat transfer surface j. Let i be the total energy of the radiation beam that directly reaches j from heat exchange surface i. E is the total energy of the radiation beam emitted from heat exchange surface i and reaching heat exchange surface j after several reflections. z Let i be the total radiant energy emitted by a certain heat exchange surface i.

[0014] Furthermore, the net radiative heat transfer of the spindle system specifically involves: establishing a spindle radiation network model after determining the radiative heat transfer angle coefficient; obtaining the effective radiation of each heat transfer surface according to Kirchhoff's laws; and then... Calculate the net radiative heat transfer on each heat exchange surface of the spindle;

[0015] Where, φ i Let σ be the net radiative heat transfer on each heat exchange surface of the main axis, σ be the blackbody radiation constant, and ε be the emissivity of surface i. i The temperature is T i The effective radiation of surface i is J i .

[0016] Furthermore, the analytical model for principal axis thermal error in radiation heat transfer includes the following steps:

[0017] Step 1: Introduce the net radiative heat transfer into the thermal network model; Step 2: Establish an improved thermal network model of the spindle system that considers radiative heat transfer; Step 3: Establish a thermal error model of the spindle system.

[0018] Furthermore, the establishment of the improved thermal network model of the main shaft system considering radiative heat transfer specifically involves: dividing the main shaft into thermal nodes, establishing a thermal resistance network diagram, establishing the transient thermal balance equation of the j-th node of the thermal network based on the law of conservation of energy and Kirchhoff's laws, and applying it to all thermal nodes of the entire main shaft system. Based on the transient thermal balance equations of each node, the improved thermal network model of the main shaft system is obtained.

[0019] Furthermore, the coordinates of the emission point are controlled by the program, generating several X, Y, and Z coordinates within the range of the corresponding coordinates of the heat exchange surface, which are combined to form the emission point coordinates; the radiation energy beam is generated from the emission point.

[0020] Furthermore, the emission direction of the radiation beam is determined by two angles, δ and η, where δ is the angle between the emission direction of the radiation beam and the normal to the heat exchange surface, and η is the angle between the projection of the radiation beam on the heat exchange surface and a certain coordinate in the local coordinate system.

[0021] Compared with the prior art, the present invention has the following beneficial technical effects:

[0022] This invention discloses a method for obtaining thermal errors of precision machine tool spindles based on MC-RNM and I-TNM algorithms. It can read spindle speed, current spindle position, and current ambient temperature in real time, establish the overall and local coordinate systems of the spindle system and workspace, and calculate the net radiative heat transfer of the spindle based on MC-RNM and establish an analytical model of spindle thermal errors based on the I-TNM algorithm. This method overcomes the shortcomings of poor robustness and insufficient generalization ability of data-driven models, and compensates for the deficiencies of existing analytical models in boundary handling and neglect of radiative heat transfer. This invention improves the prediction accuracy and stability of the thermal error model and has the advantages of strong applicability and good robustness. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating the method for obtaining thermal errors of precision machine tool spindles based on MC-RNM and I-TNM algorithms according to the present invention.

[0024] Figure 2 This is a schematic diagram of the overall coordinate system and the local coordinate system in an embodiment of the present invention;

[0025] Figure 3 This is a schematic diagram of the thermal node arrangement in an embodiment of the present invention;

[0026] Figure 4 This is a schematic diagram of the improved heat network structure in an embodiment of the present invention;

[0027] Figure 5 This is a schematic diagram of the temperature sensor arrangement in an embodiment of the present invention;

[0028] Figure 6 This is a comparison chart of the transient temperatures measured experimentally and calculated by analytical models based on the MC-RNM and I-TNM algorithms in this embodiment of the invention.

[0029] Figure 7 This is a comparison chart of the transient thermal errors measured experimentally and calculated by analytical models based on the MC-RNM and I-TNM algorithms in this embodiment of the invention. Detailed Implementation

[0030] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0031] This invention discloses a method for obtaining thermal errors of precision machine tool spindles based on MC-RNM and I-TNM algorithms, such as... Figure 1 As shown, it includes the following steps:

[0032] Step 1: Use Matlab to obtain the machine tool spindle speed, the current position of the machine tool spindle, and the actual ambient temperature. Specifically:

[0033] Step 1.1: Connect the CNC and the industrial computer using a network cable with an RJ45 interface. In the CNC's HMI interface, set the embedded Ethernet IP address, subnet mask, and port parameters. In the industrial computer, enable TCP / IPv4 and set an appropriate IP address and subnet mask to ensure that the CNC and the industrial computer are on the same local area network.

[0034] Step 1.2: Use C++ to develop an application program on the industrial control computer to call the FOCAS function, which enables TCP / IP-based communication. Pass the IP and port parameters to the function to connect the CNC to the industrial control computer.

[0035] Step 1.3: In the industrial computer application, the FOCAS function extracts CNC information at a frequency of 1 second, reads the current spindle speed and the current position coordinates of the spindle in real time, and stores them in the SQL database in real time;

[0036] Step 1.4: Use a PT100 platinum resistance sensor to monitor the ambient temperature of the machine tool spindle system in real time, and convert and collect the real-time ambient temperature data monitored by the sensor through an NI data acquisition card with an integrated temperature transmitter;

[0037] Step 1.5: Use LabVIEW to write a data acquisition and storage application on the industrial computer to store the ambient temperature data transmitted from the NI acquisition card into the SQL database in real time;

[0038] Step 1.6: Write an application program on the industrial control computer using Matlab, and call the SQL statement function in Matlab to read the spindle speed, current spindle position and ambient temperature data stored in real time by SQL.

[0039] Step 2: Based on the obtained spindle speed, current spindle position, and actual ambient temperature, calculate the spindle net radiative heat transfer in real time using the MC-RNM algorithm. Specifically:

[0040] Step 2.1: Establish the spindle system, the global coordinate system, and the local coordinate system of the spindle workspace;

[0041] like Figure 2 As shown, the origin of the global coordinate system is set at the intersection of the spindle rotation center line and the workspace plane where the spindle is located. The X / Y / Z axis directions of the global coordinate system are set in the same way as the X / Y / Z axis directions of the machine tool absolute coordinate system.

[0042] A radiation beam emission point is randomly generated on the heat exchange surface and serves as the origin of the local coordinate system for that beam. The X / Y / Z axes of the local coordinate system are all set to be the same as the X / Y / Z axes of the global coordinate system. The radiation beams emitted from each heat exchange surface in the workspace point inwards, while the radiation beams emitted from each outer surface of the spindle point outwards.

[0043] The outer surface of the main shaft is a cylindrical curved surface. Similarly, the emission point when a radiation energy beam is emitted is taken as the origin of the local coordinate system of the radiation energy beam. The Z-axis direction of the global coordinate system is selected as the Z-direction of the local coordinate system. The Y-direction of the local coordinate system is selected as the direction of the surface normal at the emission point of the radiation energy beam, with the direction pointing to the outside of the curved surface as the positive direction. At this time, hold the Z-axis with your left hand, with your thumb pointing in the positive direction of the Z-axis. The other four fingers start from the positive direction of the Y-axis and rotate 90 degrees clockwise around the origin to obtain the positive direction of the X-axis of the local coordinate system.

[0044] Under the established global coordinate system, the global coordinates of the eight vertices of the main axis workspace are: A(X1, Y1, Z1), B(X1, Y1, Z2), C(X2, Y1, Z2), D(X2, Y1, Z1), A'(X1, Y2, Z1), B'(X1, Y2, Z2), C'(X2, Y2, Z2), D'(X2, Y2, Z1).

[0045] Step 2.2: Generate several emission points and radiation beams on the heat exchange surface;

[0046] The program controls the random generation of several X, Y, and Z coordinates within the range of the corresponding coordinates of the heat exchange surface. These coordinates are randomly combined to form several random emission point coordinates within the range of the heat exchange surface. After generating the required number of emission points on the heat exchange surface, several radiation beams can be generated from each emission point. The emission direction of the radiation beams is determined by two angles: the angle δ between the emission direction of the radiation beams and the normal of the heat exchange surface, and the angle η between the projection of the radiation beams on the heat exchange surface and a certain coordinate axis of the local coordinate system.

[0047] Direction vector with modulus of 1 along the direction of radiation beam emission Point K is located on the radiation beam and is considered as the direction point of the radiation beam. Let the global coordinates of the emission point O be (X0, Y0, Z0), the global coordinates of the direction point K be (X0', Y0', Z0'), and the local coordinates of the direction point K be (X', Y', Z'). The local coordinate system has the emission point as its origin, so the local coordinates of the emission point are (0, 0, 0). At this point, the program randomly generates the values ​​of δ and η within the allowable range of actual angles, satisfying:

[0048]

[0049] Several randomly generated emission points and several randomly generated angle values ​​δ and η together describe the randomly generated radiation beam. For a given emission point (X0, Y0, Z0) and a given angle δ and angle η, the local coordinates (X', Y', Z') of the direction point K satisfy the following equation:

[0050]

[0051] The overall coordinates (X0', Y0', Z0') of the direction point are obtained through coordinate transformation, and (X0', Y0', Z0') = (X0+X', Y0+Y', Z0+Z').

[0052] The equation for the radiation beam in the global coordinate system is:

[0053] Step 2.3: Calculate the radiation heat transfer angle coefficient between each heat transfer surface;

[0054] Transform the radiation beam equation into parametric form, let:

[0055] The parametric equation for the radiation beam is:

[0056]

[0057] Solving the equations for the radiation beam and the heat exchange surface simultaneously yields the coordinates of the intersection point between the radiation beam and the heat exchange surface. The intersection point is then checked for positive t-values ​​to exclude points where the backward extension of the radiation beam intersects the heat exchange surface. The intersection point with the smallest t-value is then selected as the first heat exchange surface the radiation beam reaches; this is the actual heat exchange surface the beam arrives at. Upon reaching the heat exchange surface, a portion of the beam is absorbed, and the remainder is reflected. If the emissivity of the heat exchange surface is ε, the total energy Q carried by the radiation beam multiplied by the emissivity ε represents the energy absorbed by the heat exchange surface, and Q(1-ε) represents the energy of the reflected beam. The reflected beam is then re-emitted from this arrival point, randomly reaching a heat exchange surface again following the same steps. Part of the reflected beam's energy is absorbed, and the remaining energy is reflected again. This process is repeated until the radiation energy of the beam falls below a certain threshold (1×10⁻⁶ in this embodiment). -5 J indicates that the radiation beam has been completely absorbed.

[0058] Let E be the total radiant energy emitted by a certain heat exchange surface i. z If the number of emitted radiation beams is n, then the radiation energy carried by each radiation beam is: The above tracking calculations are performed on all the radiant energy beams of the heat exchange surface, and the cumulative radiant energy of each heat exchange surface is finally calculated. Then, the angular coefficient X of heat exchange surface i with respect to any heat exchange surface j is obtained. i,j for:

[0059] in, Let i be the total energy of the radiation beam that directly reaches j from heat exchange surface i. Let be the total energy of the radiation beam emitted from heat exchange surface i and reaching heat exchange surface j after several reflections.

[0060] Step 2.4: Calculate the net radiative heat transfer of the spindle system based on the radiative heat transfer angle coefficient.

[0061] After determining the angular coefficients between the main shaft and each heat transfer surface in the workspace, a radiation network model of the main shaft is established. Based on Kirchhoff's laws, a set of equilibrium equations is established for the network nodes:

[0062]

[0063] Among them, J h J yJ7, J8, J9, J 10 The effective radiation of surfaces h, y, and 7-10 are respectively; E bh E by E b7 E b8 E b9 E b10 The radiative forces when surfaces h, y, and 7-10 are considered as blackbodies are determined by the Stefan-Boltzmann law:

[0064] E bi =σT i 4 i = h, y, 7, 8, 9, 10

[0065] σ is the blackbody radiation constant, σ = 5.67 × 10⁻⁶ -8 W / (m 2 .K 4 Substituting this into the above formula, we can obtain J. h J y J7, J8, J9, J 10 The value of φ7-φ can then be used to calculate the net radiative heat transfer φ7-φ on each heat transfer surface 7-10 of the main shaft. 10 .

[0066]

[0067] The heat dissipated by the spindle system through radiation heat transfer is φ7-φ 10 The sum of .

[0068] Let the emissivity of surface i be ε i The temperature is T i The emissivity of surface y is ε y The temperature is T y The area of ​​principal surface 7 is S7, its emissivity is ε7, and its temperature is T7; the area of ​​principal surface 8 is S8, its emissivity is ε8, and its temperature is T8; the area of ​​principal surface 9 is S9, its emissivity is ε9, and its temperature is T9; the area of ​​principal surface 10 is S... 10 Emission rate ε 10 The temperature is T 10 Based on the radiation heat transfer network method for multi-surface closed systems, an equivalent radiation heat transfer network diagram between each heat transfer surface can be established.

[0069] Step 3: Based on the net radiative heat transfer of the spindle, establish an analytical model of the spindle thermal error based on the I-TNM algorithm, including the following steps:

[0070] Step 3.1: Introduce the net radiative heat transfer into the thermal network model;

[0071] The radiative heat transfer process is expressed as the radiative heat transfer coefficient h, which is equivalent to the heat transfer coefficient in the convective heat transfer process. f :

[0072]

[0073] Where ε is the surface emissivity, σ is the blackbody radiation constant, T is the outer surface temperature of the simplified model when solving for radiative heat transfer, J is the effective surface radiation, and ΔT is the temperature difference between the outer surface and the air.

[0074] Thermal resistance R of thermal network nodes considering radiative heat transfer hf ,

[0075]

[0076] Where A is the actual outer surface area, h f denoted as , where h is the radiative heat transfer coefficient.

[0077] Step 3.2: Establish an improved thermal network model of the main shaft system that considers radiative heat transfer;

[0078] Dividing the spindle hot nodes as follows Figure 3 As shown, the improved heat network diagram of the spindle is established as follows. Figure 4 As shown, the transient thermal equilibrium equation of the j-th node in the thermal network is established based on the law of conservation of energy and Kirchhoff's laws.

[0079]

[0080] Where, ΔT j-r and R j-r Let Q be the temperature difference between the j-th node and its i-th neighboring node, and Q be the node thermal resistance. tj and Q rj c represents the heat generated by the node at the j-th node and the heat required for the temperature rise, respectively. j p j v j denoted as the specific heat capacity, density, and volume of the j-th node, respectively.

[0081] Applying this formula to all hot nodes of the entire spindle system and combining the resulting transient thermal balance equations for each node, we obtain an improved thermal network model of the spindle system.

[0082] Step 3.3: Establish the thermal error model of the spindle system.

[0083] The transient thermal error of the spindle is the sum of the thermal expansion deformation of each shaft segment:

[0084] Z=∑[α s L j (T j -T0)]

[0085] Where, α s L is the coefficient of thermal expansion. j and T j Let be the length of the shaft segment corresponding to the j-th node and the transient temperature of the node, respectively. The expression of the thermal error formula will be slightly different for different thermal node arrangement methods. j = 37, 38, 39, 40, 41, 42, 45, 46.

[0086] Step 4: Calculate the transient thermal error of the spindle in real time based on the analytical model of spindle thermal error in radiation heat transfer.

[0087] The improved thermal network model of the spindle system sets the initial values ​​for the temperatures of all nodes in the simultaneous equations. The remaining parameters in the equations are calculated, including the thermal resistance between nodes, the heat transfer coefficient, and the heat generation rate of each heat source. The Newton-Raphson method is then used to iteratively solve the entire simultaneous equations. The iterative calculation stops when the accuracy requirements are met. The temperature rise of each shaft segment is then substituted to obtain the thermal expansion deformation of each segment, which is accumulated to obtain the spindle transient thermal error. The current machine tool status is then checked. If the machine tool is still running, the program re-reads the current spindle position, spindle speed, and current ambient temperature, and updates the initial node temperatures based on the temperature field calculation results from the previous moment. The latest temperature field and thermal expansion error of the spindle are then re-iterated. This process is repeated until the program detects that the machine tool has stopped working.

[0088] To verify the effectiveness of the present invention, a thermal error experiment of a CNC machine tool was conducted. The experiment was performed using a PT-400H high-end precision boring machine in a laboratory with a controllable ambient temperature.

[0089] During the experiment, an NI SCXI-1600 series data acquisition card was used in conjunction with a high-precision NCDT300 eddy current sensor and a PT100 precision magnetic sensor to acquire real-time temperature and thermal expansion error data of the spindle system. The sensor arrangement method is as follows: Figure 5 As shown, temperature sensors T1 and T2 are installed on the left and lower sides of the flange on the left end face of the spindle, respectively. T3 and T4 are installed at the front and rear positions on one side of the outer cylindrical surface of the spindle, respectively. T5 and T6 are installed at the front and rear positions on the upper side of the outer cylindrical surface of the spindle, respectively. The average temperature of the left end face of the spindle is taken as the average of T1 and T2, and the average temperature of the outer cylindrical surface is taken as the average of T3 to T6. An eddy current displacement sensor is positioned directly opposite the end of the spindle detection rod to measure the axial thermal error of the spindle.

[0090] The spindle speed was 700 rpm, the initial structural temperature of each component was 25 ± 0.3℃, and the ambient temperature was maintained at 25 ± 0.3℃ throughout. The experimentally measured spindle temperature values ​​were compared with the thermal error and the predicted values ​​calculated by the analytical model based on MC-RNM and I-TNM algorithms, as shown below. Figure 6 and Figure 7As shown, the model's predicted values ​​for both the spindle temperature field and thermal error are very close to the experimental measurements, with a temperature prediction error of less than 0.09 degrees Celsius and a thermal error prediction error of less than 2.86 μm. Therefore, the analytical model for the thermal error of a precision machine tool spindle based on the MC-RNM and I-TNM algorithms proposed in this invention has high prediction accuracy, thus proving the feasibility of the method for obtaining the thermal error of a precision machine tool spindle based on the MC-RNM and I-TNM algorithms as an error modeling method.

[0091] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

Claims

1. A method for obtaining thermal error of a precision machine tool spindle based on MC-RNM and I-TNM algorithms, characterized in that, Includes the following steps: Step 1: Use Matlab to obtain the machine tool spindle speed, the current position of the machine tool spindle, and the actual ambient temperature; Step 2: Based on the obtained spindle speed, current position of the spindle and actual ambient temperature, calculate the net radiative heat transfer of the spindle in real time using the MC-RNM algorithm; Step 3: Based on the net radiative heat transfer of the spindle, establish an analytical model of spindle thermal error considering radiative heat transfer using the I-TNM algorithm; Step 4: Calculate the transient thermal error of the spindle in real time based on the analytical model of spindle thermal error considering radiation heat transfer; The spindle net radiative heat transfer includes the following steps: Step 1: Establish the overall coordinate system and local coordinate system of the spindle system and spindle workspace; the origin of the overall coordinate system is set at the intersection of the spindle rotation center and the plane of the spindle workspace, and the X / Y / Z axis directions of the overall coordinate system are the same as the X / Y / Z axis directions of the machine tool absolute coordinate system; the X / Y / Z axis directions of the overall coordinate system are the same as the X / Y / Z axis directions of the local coordinate system; the origin of the local coordinate system is the emission point of a randomly generated radiation beam from the heat exchange surface; Step 2: Generate several emission points and radiation beams on the heat exchange surface; Step 3: Calculate the radiation heat transfer angle coefficient between each heat transfer surface; the calculation of the radiation heat transfer angle coefficient between each heat transfer surface is as follows: ; in, For a certain heat exchange surface For any heat exchange surface angular coefficient, To from the heat exchange surface i Issue direct reach surface j The total energy of the radiation beam, Let i be the total energy of the radiation beam emitted from heat exchange surface i and reaching heat exchange surface j after several reflections. For a certain heat exchange surface i All the radiant energy emitted; Step 4: Calculate the net radiative heat transfer of the spindle system based on the radiative heat transfer angle coefficient; The net radiative heat transfer of the spindle system is specifically as follows: After determining the radiative heat transfer angle coefficient, a spindle radiation network model is established. The effective radiation of each heat transfer surface is obtained according to Kirchhoff's laws. Calculate the net radiative heat transfer on each heat exchange surface of the spindle; in, The net radiative heat transfer of each heat exchange surface of the main shaft. Let be the blackbody radiation constant, and be the surface radiation constant. emission rate The temperature is ,noodle The effective radiation is ; The analytical model for principal axis thermal error in radiation heat transfer includes the following steps: Step 1: Introduce the net radiative heat transfer into the thermal network model; Step 2: Establish an improved thermal network model of the principal shaft system considering radiative heat transfer; specifically: divide the principal shaft into thermal nodes, establish a thermal resistance network diagram, and establish the thermal network according to the law of conservation of energy and Kirchhoff's laws. j The transient thermal balance equations of each node are obtained and applied to all thermal nodes of the entire spindle system. Based on the transient thermal balance equations of each node, an improved thermal network model of the spindle system is obtained. Step 3: Establish a thermal error model for the spindle system.

2. The method for obtaining thermal error of precision machine tool spindle based on MC-RNM and I-TNM algorithms according to claim 1, characterized in that: Before obtaining the spindle speed, current position, and actual ambient temperature in step 1, the following steps are also included: setting the CNC and the industrial computer on the same local area network and connecting the CNC and the industrial computer by developing an application program.

3. The method for obtaining thermal error of precision machine tool spindle based on MC-RNM and I-TNM algorithms according to claim 1, characterized in that: The coordinates of the launch point are controlled by the program, which generates several X, Y, and Z coordinates within the range of the corresponding coordinates of the heat exchange surface, and these coordinates are combined to form the coordinates of the launch point. The radiation beam is generated from the emission point.

4. The method for obtaining thermal error of precision machine tool spindle based on MC-RNM and I-TNM algorithms according to claim 3, characterized in that: The emission direction of the radiation beam is determined by two angles, δ and ŋ. δ is the angle between the emission direction of the radiation beam and the normal of the heat exchange surface, and ŋ is the angle between the projection of the radiation beam on the heat exchange surface and a certain coordinate in the local coordinate system.

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