Machine tool feed shaft thermal error mechanism modeling method capable of automatically identifying parameters on line

Abstract

The invention belongs to the field of numerical control machine tool thermal error compensation, and provides a machine tool feed shaft thermal error mechanism modeling method capable of automatically identifying parameters on line. The thermal error model is established on the basis of friction heat generation and structural heat transfer analysis; the model can calculate a thermal error compensation value by using motion information and environment temperature in a numerical control system, and also can calculate the temperatures of a bearing, a nut and a lead screw; the model can autonomously complete unknown parameter identification by only needing a machine tool heat engine heating up and cooling stopping process with the duration of less than one hour, and unequal test links from several hours to several days do not need to be manually carried out any more; model parameters can be autonomously used for thermal error compensation after being identified, and manual operation is not needed. According to the method, the thermal error compensation precision and the implementation efficiency are both considered, and a new path can be opened up for application of the thermal error compensation technology of the numerical control machine tool.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of thermal error compensation of numerical control machine tools, and relates to a machine tool feed shaft thermal error mechanism modeling method capable of online autonomous identification of parameters. BACKGROUND

[0002] Thermal error compensation is an effective measure to reduce the thermal error of a machine tool. A thermal error model is used to calculate a compensation value to offset or reduce the original thermal error of the machine tool. This method has been widely studied by researchers due to its advantage of significantly improving the accuracy level of the machine tool at low cost. Establishing an accurate thermal error model is the key to effectively implementing thermal error compensation. Researchers have invested a lot of effort in how to improve the accuracy of the thermal error model.

[0003] At present, machine tool thermal error models mainly include data-driven models and models based on thermal behavior mechanisms. The optimal temperature measurement points required by data-driven models cannot be determined in advance, and a large number of temperature sensors are needed for temperature measurement point optimization. Invention patent CN202311356384.6 uses a long short-term memory network to build a thermal error model of a machine tool feed shaft, uses artificially collected temperature and thermal error data to train the thermal error model offline, and can migrate the thermal error model to other feed shafts; Invention patent CN202310730754.1 establishes a machine tool feed shaft thermal error prediction model according to the HPO-SVR regression optimization algorithm principle, divides multiple temperature and lead screw thermal error measurement data into training set and test set two parts, and uses training set data to train the thermal error model offline; Invention patent CN202310684985.3 predicts the thermal error of the machine tool feed system based on a CNN-GRU combined neural network, artificially divides the collected machine tool temperature field and thermal error data into training set and test set, and uses the training set to train the model offline; Invention patent CN202410689797.4 establishes a thermal drift error prediction model based on a Gaussian process regression model GPR and a multi-input, multi-output thermal expansion error prediction model based on temperature rise speed-thermal expansion error data. The modeling process also needs to carry out artificial test experiments of thermal positioning errors, and the model needs to be trained offline. Due to the complex motion state of the machine tool during operation, in order to ensure the accuracy of the data-driven model, a large amount of temperature and thermal error data need to be tested manually, and the model needs to be trained offline.

[0004] To ensure the accuracy and robustness of thermal error compensation, researchers have begun to pay attention to the establishment of thermal error model based on the thermal behavior mechanism of machine tools. The invention patent CN201910099610.4 establishes a thermal error prediction model based on the thermal error mechanism of the feed shaft. First, the thermal error of the feed shaft is tested based on the laser interferometer and temperature sensor, and the thermal characteristic parameters in the model are artificially identified offline according to the thermal error test data. The invention patent CN202310065660.7 establishes a thermal error model of the feed shaft of the machine tool based on the mechanisms of friction heat generation, heat conduction and convection heat dissipation. When the model calculation accuracy is reduced, the online update of the model parameters can be realized. However, when the model is initially put into use, the unknown parameters still need to be artificially identified offline. The invention patent CN201710310577.6 discloses a thermal expansion error modeling and compensation method of a semi-closed loop feed shaft under the excitation of multiple time-varying dynamic heat sources. The thermal characteristic parameter identification test of the semi-closed loop feed shaft needs to be carried out, which requires artificial offline operation before the thermal error compensation application. The invention patent CN202311342333.8 discloses a machine tool whole machine thermal error in-machine modeling compensation method. The in-machine measurement reference block is set up, and the whole machine thermal error model is established by measuring the displacement of the reference block during the machining process of the machine tool. The model parameters are the in-machine measured reference block coordinate values, so frequent periodic in-machine measurement operation is required.

[0005] As can be seen from the above discussion, the current thermal error model has an indispensable link before the application of thermal error compensation, which is the identification of unknown parameters of the model. Currently, the parameter identification of the thermal error model is offline. In order to improve the accuracy of parameter identification, several hours to several days of test are required to collect the thermal error and temperature data of the machine tool, and even the temperature measurement points need to be optimized. This offline parameter identification link is time-consuming and labor-intensive, which directly reduces the implementation efficiency of thermal error compensation and becomes an important reason affecting the popularization and application of the thermal error compensation technology. SUMMARY

[0006] To meet the needs of ensuring the compensation accuracy and improving the implementation efficiency in the field of thermal error compensation, the present application provides a machine tool feed shaft thermal error mechanism modeling method which can identify parameters online. The thermal error model is established based on the analysis of friction heat generation and structural heat transfer. The model can calculate the thermal error compensation value using the motion information and environmental temperature in the numerical control system, and can also calculate the temperature of the bearing, nut and screw. The model can autonomously complete the identification of unknown parameters in less than one hour of machine warm-up and stop cooling process, and no longer needs artificial test for several hours to several days. After the identification of model parameters, the model can be used for thermal error compensation without manual operation. The present application takes into account the thermal error compensation accuracy and implementation efficiency, and opens up a new path for the application of numerical control machine tool thermal error compensation technology.

[0007] In order to achieve the above object, the technical scheme adopted by the present application is:

[0008] Firstly, the thermal error mechanism model of the feed shaft is derived, and the known parameters and unknown parameters of the model are determined.

[0009] According to the kinematics and mechanics analysis of the ball and the raceway, the calculation equations of the friction heat and temperature of the bearing, the nut and the screw are derived, the temperature field and thermal deformation calculation equations of the screw are derived based on the heat transfer mechanism, and the thermal error model of the feed shaft is further obtained. In the model derivation, a series of parameters are involved, the design parameters of the bearing, the nut, the screw and the base structure can be obtained by searching or measuring, and are determined as known parameters. There are also unsearchable or measurable parameters in the rolling bearing pair and the ball screw pair, such as friction coefficient, load coefficient, convective heat transfer coefficient, etc., which are determined as unknown parameters.

[0010] Secondly, the thermal error mechanism model of the feed shaft is packaged, and the initialization configuration and installation are completed.

[0011] The thermal error model of the feed shaft is packaged as a software module, the known parameters are input into the model, and an initial value is set for the unknown parameters of the model. A connection channel between the thermal error model and the numerical control system is established through the network port and the network cable, so that the model can read the feed speed, the mechanical coordinate and the feed load information. Four temperature sensors are installed on the screw next to the feed shaft, the bearing seats at both ends of the screw and the nut, which are used to measure the ambient temperature of the feed shaft, the motor side bearing temperature, the remote bearing temperature and the nut temperature, and the thermal error model can read the four temperature data.

[0012] Thirdly, the online self-identification of the unknown parameters of the thermal error mechanism model is carried out.

[0013] The machine tool feed shaft is reciprocated in the full stroke range to heat for a time t1, and then kept in a stop motion state to cool for a time t2 (the heating time t1 + the cooling time t2 < 1 hour). During this process, the mechanism model automatically collects and stores the numerical control motion data (feed speed V, mechanical coordinate P, feed load F) and temperature data (ambient temperature Te, motor side bearing temperature Tb1, remote bearing temperature Tb2 and nut temperature Tn).

[0014] After reaching the time threshold t0 (t0 = t1 + t2), the model automatically starts the parameter identification function, which includes the following contents:

[0015] (1) The unknown parameters of the motor side ball bearing pair are self-optimized by using the stored numerical control motion data, the ambient temperature Te and the motor side bearing temperature Tb1, and the optimization algorithm is as follows:

[0016]

[0017] In the formula, Tb1test (t) is the measured value of the motor side bearing temperature at time t, Tb1 cal (t) is the calculated value of the motor side bearing temperature at time t, Par_b1 is the unknown parameter of the motor side ball bearing pair, Lb1 is the lower limit of the optimization range of the unknown parameter of the motor side ball bearing pair, Ub1 is the upper limit of the optimization range of the unknown parameter of the motor side ball bearing pair; the unknown parameters of the ball screw pair are autonomously optimized using the stored numerical control motion data, the environment temperature Te and the nut temperature Tn;

[0018] (2) The unknown parameters of the distal ball bearing pair are autonomously optimized using the stored numerical control motion data, the environment temperature Te and the distal bearing temperature Tb2, and the optimization algorithm is as follows:

[0019]

[0020] In the formula, Tb2 test (t) is the measured value of the distal bearing temperature at time t, Tb2 cal (t) is the calculated value of the distal bearing temperature at time t, Par_b2 is the unknown parameter of the distal ball bearing pair, Lb2 is the lower limit of the optimization range of the unknown parameter of the distal ball bearing pair, Ub2 is the upper limit of the optimization range of the unknown parameter of the distal ball bearing pair;

[0021] (3) The unknown parameters of the ball screw pair are autonomously optimized using the stored numerical control motion data, the environment temperature Te and the distal bearing temperature Tn, and the optimization algorithm is as follows:

[0022]

[0023] In the formula, Tn test (t) is the measured value of the nut temperature at time t, Tn cal (t) is the calculated value of the nut temperature at time t, Par_n is the unknown parameter of the ball screw pair, Ln is the lower limit of the optimization range of the unknown parameter of the ball screw pair, Un is the upper limit of the optimization range of the unknown parameter of the ball screw pair;

[0024] The above optimization is autonomously completed by the packaged mechanism model during operation, without the need for human intervention, so the parameter identification is online autonomous;

[0025] Fourthly, the thermal error compensation effect is verified, and the thermal error mechanism model is applied.

[0026] After completing the unknown parameter identification, the new parameters can be assigned to the thermal error model, and the process is autonomously completed online by the model, without the need for manual adjustment or configuration; the thermal error compensation effect is verified, and if the requirement is met, the thermal error model can be used for thermal error compensation work, and if the requirement is not met, the third step is returned for secondary autonomous identification.

[0027] Advantages of the present application:

[0028] (1) The present application provides a feed shaft thermal error mechanism modeling method which does not require manual testing of machine tool thermal error and temperature for several hours to several days, and can identify parameters online and independently, thereby ensuring the accuracy of thermal error compensation and improving the efficiency of thermal error compensation implementation;

[0029] (2) The thermal error mechanism model of the present application can not only calculate the thermal error compensation value, but also calculate the bearing, nut and screw temperature using the motion information and environmental temperature in the numerical control system;

[0030] (3) The present application only needs the machine tool to heat up and stop cooling for less than one hour, and the model can independently complete unknown parameter identification, and after parameter identification, the thermal error compensation is started independently without manual operation. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 is a schematic diagram of the online and independent parameter identification method for the thermal error mechanism model of the machine tool feed shaft.

[0032] Figure 2 is a flow chart of the thermal error mechanism modeling of the machine tool feed shaft which can identify parameters online and independently.

[0033] Figure 3 is a comparison result graph of the nut and bearing temperature calculation value and measured value before and after online and independent parameter identification; wherein (a) is the motor side bearing temperature, (b) is the far end bearing temperature, and (c) is the nut temperature.

[0034] Figure 4 is a feed shaft thermal error compensation result graph after online and independent parameter identification; wherein (a) is before compensation, and (b) is after compensation. DETAILED DESCRIPTION

[0035] The specific embodiments of the present application will be further described in combination with the drawings and technical solutions.

[0036] Taking the screw of the Y-axis of the three-axis vertical machining center VMC850Q as an example, the embodiments of the present application are described in detail. The machine tool is equipped with a FANUC numerical control system, the feed shaft adopts semi-closed loop control, ball screw transmission, and the screw is installed on the slide shoe through the bearing seat. Temperature sensors are arranged on the nut of the feed shaft, the bearing seat near the motor side, the bearing seat far from the motor side and the base beside the screw, respectively, to test the nut temperature, bearing seat temperature and environmental temperature around the screw, as shown in Figure 1 , and the specific process is shown in Figure 2 .

[0037] (1) Derive the thermal error mechanism model of the feed shaft, determine the known parameters and unknown parameters of the model

[0038] A rotation of the same magnitude as the angular velocity of the center of the ball around the inner ring of the bearing and in the opposite direction is applied to the entire ball bearing to analyze the motion relationship of the inner and outer rings and the balls of the rolling bearing; the friction heat of the rotational motion of the contact area in the ball bearing includes the sliding friction heat and the rolling friction heat of the balls and the raceways of the inner and outer rings, wherein the calculation method of the sliding friction heat of the balls and the raceways is represented as

[0039]

[0040] Wherein, μ b is the sliding friction coefficient of the balls and the raceways in the ball bearing, F ai is the normal force at the contact point of the balls and the inner ring caused by the axial load, F ri is the normal force at the contact point of the balls and the inner ring caused by the radial load, N ai is the normal force at the contact point of the balls and the outer ring caused by the axial load, N ri is the normal force at the contact point of the balls and the outer ring caused by the radial load, S bI is the sliding stroke occurring in the process of driving the balls by the inner ring, S bO is the sliding stroke occurring in the process of the balls moving in the raceway of the outer ring;

[0041] The calculation method of the friction heat generated by the rolling of the balls in the raceways of the inner and outer rings is represented as

[0042]

[0043] In the formula, X bI is the rolling distance of the balls in the inner ring, X bO is the rolling distance of the balls in the outer ring, nb is the number of balls in the bearing, k is the rolling friction factor between the bearing steel and the bearing steel, r b is the diameter of the balls;

[0044] The heat generated by the bearing due to the applied load and viscous friction is calculated by the following formula

[0045]

[0046] In the formula, n S is the rotation speed of the screw, M υ is the torque caused by viscous friction, M q is the torque caused by the applied load;

[0047] Therefore, the heat generated by the friction of the balls and the inner and outer rings of the rolling bearing is represented as:

[0048] Q B = Q fμ + Qff +Q υq (7)

[0049] The calculation method of the differential sliding friction heat of the balls and the raceway in the screw nut pair is expressed as

[0050]

[0051] In the formula, μ n is the sliding friction coefficient of the balls and the raceway, P As_i is the contact pressure of the i-th loaded ball in the nut A and the screw raceway, P An_i is the contact pressure of the i-th loaded ball in the nut A and the nut raceway, P Bs_j is the pressure of the j-th loaded ball in the nut B and the screw raceway;

[0052] The ball screw is often in the form of an elongated rod. Since the axial temperature change rate is much greater than the radial temperature change rate, the heat conduction of the screw is regarded as a one-dimensional heat conduction problem, and the above differential equation is solved by using the difference method. The screw is divided into M segments, and the length of each segment is L, so that

[0053] When 1 < i < M,

[0054]

[0055] In the formula, T(i, t) is the temperature of the i-th segment of the screw at t, L is the length of each micro-segment of the ball screw, △Q SN (i) is the friction heat of the ball screw pair generated by the i-th segment of the screw in △t, h is the heat dissipation coefficient, T f (t) is the ambient temperature of the screw at t.

[0056] When i = 1,

[0057]

[0058] In the formula, T(1, t) is the temperature of the first segment of the screw at t, △Q fB is the friction heat generated by the motor side ball bearing pair in △t, r fB is the radius of the inner ring of the motor side ball bearing.

[0059] When i = M,

[0060]

[0061] In the formula, T(M, t) is the temperature of the M-th segment of the screw at t, △Q bB is the friction heat generated by the support end ball bearing pair in △t, r bB is the radius of the inner ring of the support end ball bearing.

[0062] After the temperature field of the screw is obtained, the thermal expansion amount of the screw can be further deduced:

[0063]

[0064] In the formula, Δl(t) is the thermal expansion amount of the screw at time t, coef is the thermal expansion coefficient of the screw, and T(i, t0) is the temperature of the i-th screw at time t0.

[0065] A series of parameters are involved in the model derivation. The design parameters of the bearing, nut, screw, and base structure can be found or measured, and are determined as known parameters, as shown in Table 1. There are also parameters that cannot be found or measured in the rolling bearing pair and the ball screw pair, such as the friction coefficient, the load coefficient, and the convective heat transfer coefficient, which are determined as unknown parameters, as shown in Table 2.

[0066] Table 1 Known parameters of the Y-axis thermal error mechanism model

[0067]

[0068] (2) Package the feed shaft thermal error mechanism model, complete the initialization configuration and installation;

[0069] The feed shaft thermal error model is packaged as a software module, the known parameters are input into the model, and an initial value is set for the unknown parameters of the model, as shown in Table 2. A connection channel is established between the thermal error model and the numerical control system through a network port and a network cable. The IP address of the numerical control system is 192.168.1.5, the port number is 62973, and the secondary development protocol provided by the FANUC system is FOCAS2, so that the model can read the feed speed, mechanical coordinates, and feed load information. Four temperature sensors are installed on the screw next to the feed shaft, the bearing seats at both ends of the screw, and the nut, for measuring the ambient temperature of the feed shaft, the motor-side bearing temperature, the remote bearing temperature, and the nut temperature, and enabling the thermal error model to read the four temperature data.

[0070] (3) Online self-identification of unknown parameters of the thermal error mechanism model;

[0071] The machine tool Y-axis is reciprocated at a feed speed of 6000 mm / min for 15 min to heat, and then the Y-axis is stopped for 15 min to cool. During this process, the mechanism model autonomously collects and stores numerical control motion data (feed speed V, mechanical coordinates P, and feed load F) and temperature data (ambient temperature Te, motor-side bearing temperature Tb1, remote bearing temperature Tb2, and nut temperature Tn).

[0072] After reaching the time threshold 30 min, the model autonomously starts the parameter identification function, and uses the stored CNC motion data, the environment temperature Te and the motor-side bearing temperature Tb1 to autonomously optimize the unknown parameters of the motor-side ball bearing pair; uses the stored CNC motion data, the environment temperature Te and the remote bearing temperature Tb2 to autonomously optimize the unknown parameters of the remote ball bearing pair; and uses the stored CNC motion data, the environment temperature Te and the remote bearing temperature Tn to autonomously optimize the unknown parameters of the ball screw pair. The initial values and the identified values of the unknown parameters are shown in Table 2, and the comparison results of the calculated and measured values of the nut and bearing temperatures before and after the online autonomous identification of the parameters are shown in Table 3. Figure 3

[0073] Table 2 Unknown parameters of the Y-axis thermal error mechanism model

[0074]

[0075]

[0076] (4) Verify the thermal error compensation effect, and apply the thermal error mechanism model.

[0077] After completing the identification of the unknown parameters, the new parameters can be assigned to the thermal error model, and the process is autonomously completed online by the model without manual adjustment or configuration. The thermal error compensation effect is verified, and if the thermal error model meets the requirements, it can be used for thermal error compensation work, and if it does not meet the requirements, it returns to the third step for secondary autonomous identification. The specific verification work process is as follows

[0078] 1) Before the test, the machine tool is not powered on and has been stopped for more than 5 hours, and the machine tool is in a thermal equilibrium state. The Y-axis thermal error in the open compensation and closed compensation states is measured by a laser interferometer.

[0079] 2) Make the machine tool Y-axis reciprocate in the full stroke range at a feed speed of 6000 mm / min for 10 min to heat the machine tool, and measure the Y-axis thermal error in the open compensation and closed compensation states by a laser interferometer.

[0080] 3) Repeat step 2) 5 times.

[0081] 4) Make the machine tool Y-axis stop moving for 10 min to cool the machine tool, and measure the X-axis thermal error in the open compensation and closed compensation states by a laser interferometer.

[0082] 5) Repeat step 4) 3 times, and arrange the test results.

[0083] The feed axis thermal error compensation results after the online autonomous identification of the parameters are shown in Table 4. Figure 4

[0084] ​​The above embodiments only express the implementation ways of the present application, and cannot be understood as the limitation to the scope of the present application patent. It should be pointed out that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application.

Claims

1. A machine tool feed axis thermal error mechanism modeling method capable of online autonomous identification of parameters, characterized in that, The steps are as follows: First step, deduce the feed shaft thermal error mechanism model, determine the known parameters and unknown parameters of the model; According to the kinematics and mechanics analysis of the ball and the raceway, the friction heat generation and temperature calculation equation of the bearing, nut and screw are derived; Based on the heat transfer mechanism, the temperature field and thermal deformation calculation equation of the screw are derived, and the feed shaft thermal error mechanism model is further obtained; A series of parameters are involved in the derivation of the feed shaft thermal error mechanism model, the design parameters of bearing, nut, screw and foundation structure can be found or measured, and are determined as known parameters; There are also unsearchable or measurable parameters in the rolling bearing pair and the ball screw pair, such as friction coefficient, load coefficient and convective heat transfer coefficient, which are determined as unknown parameters; Second step, package the feed shaft thermal error mechanism model, complete the initialization configuration and installation; The feed shaft thermal error mechanism model is packaged as a software module, the known parameters are input into the feed shaft thermal error mechanism model, and a set of initial values is set for the unknown parameters; Through the network port and network cable, the connection channel between the feed shaft thermal error mechanism model and the numerical control system is established, so that the feed shaft thermal error mechanism model can read the feed speed, mechanical coordinate and feed load information; Four temperature sensors are installed on the screw beside the feed shaft of the machine tool, the bearing seat and the nut at both ends of the screw, which are used to measure the ambient temperature, motor side bearing temperature, remote bearing temperature and nut temperature of the feed shaft, and the feed shaft thermal error mechanism model reads the four temperature data; Third step, online self-identification of unknown parameters of feed shaft thermal error mechanism model; Make the machine tool feed shaft reciprocate in the full stroke range to heat for a time t1, and then keep the stop motion state to cool for a time t2, the heat time t1+ the cooling time t2 < 1 hour; In this process, the feed shaft thermal error mechanism model automatically collects and stores numerical control motion data and temperature data; Among them, the numerical control motion data includes feed speed V, mechanical coordinate P and feed load F; The temperature data includes ambient temperature Te, motor side bearing temperature Tb1, remote bearing temperature Tb2 and nut temperature Tn; After reaching the time threshold t0, that is, t0=t1+t2, the feed shaft thermal error mechanism model automatically starts the parameter identification function, including: (1) Use the stored numerical control motion data, ambient temperature Te and motor side bearing temperature Tb1 to optimize the unknown parameters of the motor side ball bearing pair, and the optimization algorithm is as follows: In the formula, Tb1 test (t) is the measured value of the motor side bearing temperature at time t, Tb1 cal (t) is the calculated value of the motor side bearing temperature at time t, Par_b1 is the unknown parameter of the motor side ball bearing pair, Lb1 is the lower limit of the optimization range of the unknown parameter of the motor side ball bearing pair, and Ub1 is the upper limit of the optimization range of the unknown parameter of the motor side ball bearing pair; the unknown parameters of the ball screw pair are autonomously optimized by using the stored numerical control motion data, the environmental temperature Te, and the nut temperature Tn. (2) Use the stored numerical control motion data, ambient temperature Te and remote bearing temperature Tb2 to optimize the unknown parameters of the remote ball bearing pair, and the optimization algorithm is as follows: wherein Tb2 test (t) is the measured value of the temperature of the distal bearing at time t, Tb2 cal (t) is the calculated value of the temperature of the distal bearing at time t, Par_b2 is the lower limit of the optimization range of the unknown parameter of the distal ball bearing pair, Ub2 is the upper limit of the optimization range of the unknown parameter of the distal ball bearing pair; (3) Use the stored numerical control motion data, ambient temperature Te and remote bearing temperature Tn to optimize the unknown parameters of the ball screw pair, and the optimization algorithm is as follows: wherein Tn test (t) is the measured value of the nut temperature at time t, Tn cal (t) is the calculated value of the nut temperature at time t, Par_n is the unknown parameter of the ball screw pair, Ln is the lower limit of the optimization range of the unknown parameter of the ball screw pair, and Un is the upper limit of the optimization range of the unknown parameter of the ball screw pair. Fourth step, verify the thermal error compensation effect, and apply the feed shaft thermal error mechanism model; After the unknown parameter identification is completed, the new parameters can be assigned to the feed axis thermal error mechanism model, which is completed autonomously online by the feed axis thermal error mechanism model, without the need for manual adjustment or configuration; the thermal error compensation effect is verified, and if the requirement is met, the feed axis thermal error mechanism model is used for thermal error compensation work, and if the requirement is not met, the second autonomous identification is returned to the third step.

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