CN113009882A - Numerical control machine tool thermal error adaptive compensation method - Google Patents
Numerical control machine tool thermal error adaptive compensation method Download PDFInfo
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- G05B19/404—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
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Abstract
The invention belongs to the field of error compensation of numerical control machines, and discloses a thermal error self-adaptive compensation method of a numerical control machine, which comprises the following steps: obtaining the thermal error of a feed shaft and the corresponding key point temperature by adopting a laser interferometer and a temperature sensor according to a specific measurement mode; establishing a thermal error prediction model of the screw under the excitation of a multi-time varying-state heat source; automatically identifying thermal characteristic parameters in the temperature field prediction model by adopting an interior point method; establishing a self-adaptive adjusting model aiming at a frictional heat generation coefficient Q in a thermal error prediction model under the excitation of a multi-time-varying dynamic heat source; providing a thermal error adaptive compensation method which considers the short-term friction characteristic change of the screw-nut pair and can correct the friction heat generation coefficient Q in real time; and finally, realizing the compensation of the thermal error of the machine tool through a thermal error compensation system. The numerical control machine thermal error adaptive compensation method used by the invention has high prediction precision, solves the problem of fluctuation of thermal error compensation precision caused by short-term friction characteristic change, and improves the robustness of the thermal error compensation method.
Description
Technical Field
The invention belongs to the field of error compensation of numerical control machines, and particularly relates to a thermal error adaptive compensation method of a numerical control machine.
Background
The thermal error of the machine tool is one of important factors causing the stability and the precision reduction of a high-end numerical control machine tool. The literature data and the previous test results show that the error caused by thermal deformation in the precision machining process can reach 40-70% of the total error of the machine tool. The existence of machine tool thermal errors causes low part machining precision and high rejection rate; in order to reduce thermal errors, a heat engine is needed after the machine tool is started, so that the energy consumption is high and the time consumption is long; precision machining also requires a constant temperature plant, resulting in increased part machining costs.
Methods for suppressing thermal errors are classified into an error avoidance method and an error compensation method. The error avoidance method reduces the thermal error of the machine tool from the perspective of eliminating the heat source. The main methods are an in-axis cooling system, a machine tool thermal symmetric structure design, a constant temperature workshop for controlling the environmental temperature and the like. Error avoidance can significantly reduce machine tool thermal errors, but also has some limitations. First, as the accuracy requirements of the machine tool increase, the cost of hardware facilities for error avoidance increases exponentially. Secondly, in order to effectively eliminate the heat source, many methods require intervention from the design and manufacturing links of machine tool components, thus increasing manufacturing costs and making it difficult to retrofit factory-delivered machine tools. The error compensation method is to artificially create a reverse error to offset the original thermal error in real time. The error compensation method has the advantages of low cost, wide applicability and the like. In recent years, with the development of the fields of computers, measurement, sensing and the like, an error compensation method gradually becomes a main method for intelligently compensating the thermal error of the machine tool, and has wide research and application prospects.
For the numerical control machine tool thermal error compensation method, extensive research is carried out by both domestic and foreign scholars. In 2011, Xu et al, in the 51 st curling chart article of International Journal of Machine Tools and Manual, the Thermal error for and performance evaluation for an air-cooling ball scanning system, provided the heat generation and dissipation equations of the bearing and the screw-nut pair, and established the Thermal characteristic model of the screw based on finite element analysis and an improved lumped heat capacity method. In 2012, WuC et al, in the 59 th curling sheet of International Journal of Advanced Manufacturing Technology, the "Thermal error compensation method for machine center", established a mathematical model between temperature variables and Thermal errors based on multiple regression. In 2015, Feng et al, in the 93 th curling chart of International Journal of Machine Tools & Manual, in the "Thermally induced porous and compensated based on thermal characteristics analysis", analyzed the heat transfer mechanism of the nut, neglected the heat transfer process, deduced the temperature prediction model of the nut in the processes of temperature rise and temperature drop, but did not consider the influence of the heat generation of the lead screw bearing seat. In 2011, Miao Enming et al, applied to a numerical control machine tool thermal error compensation high-order multi-order autoregressive distribution lag modeling method: 201110379618.X, a high-order multi-order autoregressive distribution hysteresis modeling method is provided. In 2013, the term cross is applied to a numerical control machine error compensation system and method based on human-computer interface secondary development in the patent of' application number: 201310245088.9, a compensation method for Siemens 840d numerical control system and a linear feed shaft thermal error compensation model are provided based on human-computer interface secondary development. In 2014, the ceramic beneficiary and the like apply the following number in a patent 'numerical control machine tool thermal error compensation method': 201410161210.9, obtaining a key temperature point of thermal error compensation based on finite element simulation analysis and based on particle swarm optimization, and realizing the thermal error compensation of the numerical control machine tool by taking the temperature measurement value at the key temperature point as the basis. In 2016, Huangzhi et al filed for application number of "method and system for online compensation of thermal error of numerically controlled machine tool" in the patent: 201610159196.8, providing a method and a system for online compensation of thermal error of a numerical control machine, wherein the method calculates theoretical thermal error value of the numerical control machine according to a multiple linear regression thermal error model. In 2019, the application number of Tan Peak is as follows: 201910517281.0, a method for predicting thermal error of a numerically controlled machine tool based on the wrapping principle is provided.
Through the analysis of the research, the paper and the patent lack the research on the thermal coupling behavior law of the screw and the thermal elongation response process of the feed shaft with a specific structure, and do not mention a thermal error adaptive compensation method capable of correcting the thermal parameters of the model in real time.
Disclosure of Invention
The invention aims to provide a thermal error adaptive compensation method considering friction characteristic changes of a lead screw and nut pair, overcomes the defects of the existing thermal error adaptive compensation method of a numerical control machine tool, and realizes prediction and compensation of a thermal error of a machine tool feed shaft.
The technical scheme of the invention is as follows:
a thermal error self-adaptive compensation method considering friction characteristic changes of a lead screw and nut pair is characterized in that in a thermal characteristic parameter identification test of a semi-closed loop feed shaft, temperature sensors are arranged at three positions of a lathe bed, a front bearing seat and a rear bearing seat near a lead screw, the feed shaft reciprocates at any speed and range to heat and then stops at any position to cool, and the positioning error and the key point temperature of the machine tool are tested once every a period of time to 10 min; establishing a thermal error prediction model of the screw under the excitation of a multi-time varying-state heat source; next, automatically identifying thermal characteristic parameters in the temperature field prediction model by adopting an interior point method; establishing a self-adaptive adjustment model aiming at a frictional heat generation coefficient in a thermal error prediction model under the excitation of a multi-time-varying dynamic heat source; providing a thermal error adaptive compensation method which considers the short-term friction characteristic change of the screw-nut pair and can correct the coefficient of heat generation of friction in real time; and finally, realizing the compensation of the thermal error of the machine tool through a thermal error compensation system.
The method comprises the following specific steps:
first, the thermal characteristic parameter identification test of the feed shaft
The first temperature sensor 4, the second temperature sensor 11 and the third temperature sensor 12 are respectively arranged at three positions of the front bearing block 3, the lathe bed 14 near the lead screw and the rear bearing block 13; a spectroscope 6 of the laser interferometer is fixed on a workbench 7 through a magnetic gauge stand, and a reflective mirror 9 is fixed on a main shaft 10 through the magnetic gauge stand; the semi-closed loop feeding shaft reciprocates at any speed and in any range to be heated, and the positioning error and the temperature values of the first temperature sensor 4, the second temperature sensor 11 and the third temperature sensor 12 are tested once every a period of time to 10min until the feeding shaft reaches thermal balance; and stopping cooling the semi-closed loop feeding shaft at any position, and testing the positioning error and the temperature values of the first temperature sensor 4, the second temperature sensor 11 and the third temperature sensor 12 at intervals of time-10 min.
Secondly, establishing a lead screw thermal error prediction model under multi-time varying-state heat source excitation
Considering the screw 5 as being composed of an infinite number of infinitesimal Δ x, if the radiation effect of other external heat sources is not considered, the screw 5 infinitesimal Δ x mainly conducts heat transfer by three ways: the heat conduction process between the lead screw micro element and the adjacent lead screw micro element, the heat convection heat exchange process between the lead screw micro element and the ambient air and the heat radiation heat dissipation process to the ambient environment. Discretizing the position and the test time of the screw 5, neglecting the heat radiation effect of the screw 5 on the surrounding environment, and obtaining a temperature field model of the ball screw 5:
wherein c is the specific heat capacity, ρ is the material density of the ball screw 5, and dsIs the diameter of the screw 5, k is the thermal conductivity, hcvThe surface heat convection coefficient of the screw 5 is shown, and Q is shown as the sliding of the nut 8 through LiThe friction heat generation amount (friction heat generation coefficient for short) at one time, L is the length of the screw 5 unit, tau is the temperature acquisition time interval, and N is the friction L of the nut 8 within tauiNumber of times, TLi-τjIs LiAt taujTemperature value at time, Ta-τjIs taujThe temperature of the air surrounding the screw 5 at the moment.
The ball screw 5 at an arbitrary timing τ is calculated as followsjThermal error model E off：
In the formula, the coefficient of thermal expansion is alphaeThe value is 11.7 μm/(m.DEG C.).
Third, thermal characteristic parameter identification
Identifying thermal characteristic parameters in the thermal error prediction model by a parameter automatic optimization method, and performing parameter optimization according to the formula (3):
wherein E isf(u, v) represents the prediction error value at the v test point in the u test, Eft(u, v) represents the test error value of the v measuring point in the u measuring time. U is the total number of tests and V is the number of points per test.
Fourthly, establishing a self-adaptive adjustment model of the single-time friction heat generation coefficient Q of the lead screw infinitesimal
Based on the law of energy conversion, the coefficient of heat generation by friction Q of the system can be calculated as follows:
in the formula, SrThe relative distance between the objects in the system, M is the friction torque generated by the relative movement between the objects in the system, and D is the friction force arm.
The lead screw friction pair moment can be calculated according to the following formula:
Mw＝k0ηFpsinαcos2λ(dbcosα+ds) (5)
in the formula, k0Is a proportionality coefficient, eta is a comprehensive friction factor of the screw-nut pair, FpIs nut pretightening force, alpha is a contact angle of the pretightening force and the normal surface of the axis of the screw rod 5, lambda is a helix angle of the difference between the screw rod helix line and the axis of the screw rod, dbIs the diameter of the ball, dsIs the diameter of the lead screw.
If the change of the bearing condition of the ball is not considered, F is setpWithout change, the change in the total friction torque at this time is mainly determined by the lubrication state of the balls in the screw 5 and the nut 8. Total friction established based on change rule of lubrication state of screw nut pairThe friction torque model is as follows:
in the formula, FcIs coulomb friction force, FsAt maximum static friction, σ2Is a viscous friction coefficient, nsbIs a critical rotation speed, n is a steady-state slip rotation speed, PhIs a lead screw lead.
The adaptive adjustment model Q (n) for Q can be calculated as follows:
in the formula etasIs the maximum static friction factor, ηcIs the Coulomb friction factor, SaIs the relative displacement between the nut 8 and the lead screw 5.
Due to FpIs not changed, and the parameter k0、Fp、α、λ、Sa、ηc、ηs、nsb、σ2None of the values of (c) is affected by n. At the same time, Q is non-directional. Therefore, let:
a1＝k0Fpsinαcos2λSa (8)
a2＝ηssgn(n) (9)
a3＝ηcsgn(n) (10)
a4＝σ2PhSa (11)
equation (7) can be simplified as:
in the formula, a1、a2、a3、a4、nsbAre unknown parameters.
Fifthly, identifying the parameters of the self-adaptive adjustment model of the single-time friction heat generation coefficient Q of the lead screw infinitesimal
The identification process of each parameter is as follows:
1) when n is equal to 0, the inside of the screw nut pair is in a static friction state. In this case, the following equation (12) can be used:
Q(0)＝a1a2 (13)
2) when n is>>nsbAt this time, the lead screw 5 is in a high-speed rotation state. In this case, the following equation (12) can be used:
Q(n)＝a1a3+a4n (14)
3) when n is equal to nsbWhen the screw rod nut pair is used, the mixed lubrication and the hydrodynamic lubrication are arranged at the junction. Then it can be approximated by equation (12):
Q(nsb)＝a1a3+a1(a2-a3)e-1+a4nsb
≈0.3679a1a2+0.6321a1a3+a4nsb (15)
sixth, thermal error compensation write
The temperature sensor transmits the temperature signal to the collector, the temperature signal is transmitted to the compensator after being processed by the collector, the compensator writes the compensation quantity into the numerical control system after calculating the compensation quantity, and the compensation of the thermal error of the machine tool is realized in a mode of integral deviation of a mechanical coordinate system of the machine tool.
The invention has the beneficial effects that:
1. the processing precision of the part is improved, namely the processing range and the processing capacity of the machine tool are improved.
2. Solves the problem of poor repeated precision in the production process of batch parts, reduces the rejection rate, and improves the process capability index of the machine tool
3. The heat engine process after the machine tool is started is eliminated, the processing energy consumption is reduced, the processing time is reduced, and the processing efficiency is improved.
4. The self-adaptive compensation method for the thermal error of the machine tool is provided, the problem that the thermal error compensation precision fluctuates due to the short-term friction characteristic change of the lead screw and nut pair is solved, and the robustness of the thermal error compensation technology is further improved.
Drawings
FIG. 1 is a schematic diagram of thermal error testing and temperature measurement point arrangement of a feed shaft.
FIG. 2 is a flow chart of the vertical machining center feed shaft thermal error efficient test.
Fig. 3 is a schematic diagram of a total friction torque model in consideration of a change in a lubrication state.
FIG. 4 is a block diagram of a thermal error compensation hardware system.
FIG. 5 is a diagram of the results of Y-axis thermal error testing of the vertical machining center before compensation.
FIG. 6 is a graph of the compensated Y-axis thermal error test results of the vertical machining center.
Fig. 7a) is a comparison graph of thermal error prediction accuracy change before the adaptive function is started.
Fig. 7b) is a comparison graph of the thermal error prediction accuracy change after the adaptive function is started.
In the figure: 1 laser head of laser interferometer; 2, a servo motor; 3, a front bearing seat; 4 a first temperature sensor; 5, a lead screw; 6 spectroscope of laser interferometer; 7, a workbench; 8, a nut; 9 a mirror of a laser interferometer; 10, a main shaft; 11 a second temperature sensor; 12 a third temperature sensor; 13 a rear bearing seat; 14 lathe bed.
Detailed Description
In order to make the technical scheme and the beneficial effects of the invention clearer, the invention is described in detail below with reference to the attached drawings in combination with the specific implementation mode of the thermal error adaptive compensation of the numerical control machine tool. The present embodiment is based on the technical solution of the present invention, and a detailed implementation and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
The embodiment of the present invention will be described in detail by taking adaptive compensation of thermal errors in the Y axis of a vertical machining center as an example. The maximum moving speed of the Y axis is 24000mm/min, and the stroke range is 0-550 mm.
First, the thermal characteristic parameter identification test of the feed shaft
The first temperature sensor 4, the second temperature sensor 11 and the third temperature sensor 12 are respectively arranged at three positions of the front bearing block 3, the lathe bed 14 near the lead screw and the rear bearing block 13; a spectroscope 6 of the laser interferometer is fixed on a workbench 7 through a magnetic gauge stand, and a reflective mirror 9 is fixed on a main shaft 10 through the magnetic gauge stand. A schematic diagram of the temperature measurement point arrangement and laser interferometer mounting is shown in FIG. 1.
The specific flow of the high-efficiency thermal error test is as follows: a. and in a cold state, testing the reciprocating positioning error of the Y-axis lead screw within the mechanical coordinate range of between 3 and 500 and 0mm by using a laser interferometer, wherein the feeding speed is 5000mm/min, and recording the temperature value of the temperature sensor. b.Y shaft carries out no-load reciprocating heat engine motion within the mechanical coordinate range of-420 to-80 mm at the feed speed of 5000mm/min, and the duration is 10 min. c.Y, stopping the movement of the shaft, testing the reciprocating positioning error of the screw rod within the mechanical coordinate range of 1-500-0 mm by using a laser interferometer, wherein the feeding speed is 5000mm/min, and recording the temperature value of the temperature sensor. d. Repeating steps b and c until the Y axis reaches thermal equilibrium. e.Y the shaft stops moving and naturally cools for 10 min. f.Y, testing the reciprocating positioning error of the screw rod within the mechanical coordinate range of 1-500-0 mm by using a laser interferometer at the feeding speed of 5000mm/min, and recording the temperature value of the temperature sensor. g. And e and f are repeated until the temperature decrease trend of the Y axis becomes slow and the temperature approaches the room temperature. Flow test flow is shown in figure 2.
Secondly, establishing a lead screw thermal error prediction model under multi-time varying-state heat source excitation
Considering the screw 5 as being composed of an infinite number of infinitesimal Δ x, if the radiation effect of other external heat sources is not considered, the screw 5 infinitesimal Δ x mainly conducts heat transfer by three ways: the heat conduction process between the lead screw micro element and the adjacent lead screw micro element, the heat convection heat exchange process between the lead screw micro element and the ambient air and the heat radiation heat dissipation process to the ambient environment. Discretizing the position and the test time of the screw 5, neglecting the heat radiation effect of the screw 5 on the surrounding environment, and obtaining a temperature field model of the ball screw 5:
wherein c is the specific heat capacity, ρIs the material density of the ball screw 5, dsIs the diameter of the screw 5, k is the thermal conductivity, hcvThe surface heat convection coefficient of the screw 5 is shown, and Q is shown as the sliding of the nut 8 through LiThe friction heat generation amount (friction heat generation coefficient for short) at one time, L is the length of the screw 5 unit, tau is the temperature acquisition time interval, and N is the friction L of the nut 8 within tauiNumber of times, TLi-τjIs LiAt taujTemperature value at time, Ta-τjIs taujThe temperature of the air surrounding the screw 5 at the moment.
The ball screw 5 at an arbitrary timing τ is calculated as followsjThermal error model E off：
In the formula, the coefficient of thermal expansion is alphaeThe value is 11.7 μm/(m.DEG C.).
Third, thermal characteristic parameter identification
Identifying thermal characteristic parameters in the thermal error prediction model by a parameter automatic optimization method, and performing parameter optimization according to the formula (3):
wherein E isf(u, v) represents the prediction error value at the v test point in the u test, Eft(u, v) represents the test error value of the v measuring point in the u measuring time. U is the total number of tests and V is the number of points per test. The result of the identification is that Q is 4.494J, hcv＝62.521W/m2·℃，k＝72.478W/m·℃
Fourthly, establishing an energy conversion law-based self-adaptive adjustment model of the single-time friction heat generation coefficient Q of the screw rod infinitesimal, wherein the friction heat generation coefficient Q of the system can be calculated according to the following formula:
in the formula, SrThe relative distance between the objects in the system, M is the friction torque generated by the relative movement between the objects in the system, and D is the friction force arm.
The lead screw friction pair moment can be calculated according to the following formula:
Mw＝k0ηFpsinαcos2λ(dbcosα+ds)
in the formula, k0Is a proportionality coefficient, eta is a comprehensive friction factor of the screw-nut pair, FpIs nut pretightening force, alpha is a contact angle of the pretightening force and the normal surface of the axis of the screw rod 5, lambda is a helix angle of the difference between the screw rod helix line and the axis of the screw rod, dbIs the diameter of the ball, dsIs the diameter of the lead screw.
If the change of the bearing condition of the ball is not considered, F is setpWithout change, the change in the total friction torque at this time is mainly determined by the lubrication state of the balls in the screw 5 and the nut 8. The total friction moment model established based on the change rule of the lubricating state of the screw-nut pair is as follows:
in the formula, FcIs coulomb friction force, FsAt maximum static friction, σ2Is a viscous friction coefficient, nsbIs a critical rotation speed, n is a steady-state slip rotation speed, PhIs a lead screw lead. A model of the total frictional torque taking into account changes in the lubrication state is shown in FIG. 3
The adaptive adjustment model Q (n) for Q can be calculated as follows:
in the formula etasIs the maximum static friction factor, ηcIs the Coulomb friction factor, SaIs the relative displacement between the nut 8 and the lead screw 5.
Due to FpIs not changed, and the parameter k0、Fp、α、λ、Sa、ηc、ηs、nsb、σ2None of the values of (c) is affected by n. At the same time, Q is non-directional. Therefore, let:
a1＝k0Fpsinαcos2λSa
a2＝ηssgn(n)
a3＝ηcsgn(n)
a4＝σ2PhSa
equation (7) can be simplified as:
in the formula, a1、a2、a3、a4、nsbAre unknown parameters.
Fifthly, identifying the parameters of the self-adaptive adjustment model of the single-time friction heat generation coefficient Q of the lead screw infinitesimal
The identification process of each parameter is as follows:
1) when n is equal to 0, the inside of the screw nut pair is in a static friction state. In this case, the following equation (12) can be used:
Q(0)＝a1a2
2) when n is>>nsbAt this time, the lead screw 5 is in a high-speed rotation state. In this case, the following equation (12) can be used:
Q(n)＝a1a3+a4n
3) when n is equal to nsbWhen the screw rod nut pair is used, the mixed lubrication and the hydrodynamic lubrication are arranged at the junction. Then it can be approximated by equation (12):
Q(nsb)＝a1a3+a1(a2-a3)e-1+a4nsb
≈0.3679a1a2+0.6321a1a3+a4nsb
adopting different feeding speeds to carry out Q parameter identification, wherein the identification result is Q3000＝1.403J，Q5000＝1.673J，Q7000＝1.731J。
Sixth, writing the thermal error compensation amount
The temperature sensor transmits the temperature signal to the collector, the temperature signal is transmitted to the compensator after being processed by the collector, the compensator writes the compensation quantity into the numerical control system after calculating the compensation quantity, and the compensation of the thermal error of the machine tool is realized in a mode of integral deviation of a mechanical coordinate system of the machine tool. The thermal error compensation hardware system architecture is shown in fig. 4.
By adopting the thermal error adaptive compensation method provided by the invention, the graphs of the test results of the thermal error of the Y axis before and after the thermal error compensation of the vertical machining center are shown in fig. 5 and 6, and the prediction precision change conditions of the thermal error before and after the adaptive function is started are shown in fig. 7.
It should be noted that the above-mentioned embodiments of the present invention are only used for illustrating the principle and flow of the present invention, and do not limit the present invention. Therefore, any modifications and equivalents made without departing from the spirit and scope of the present invention should be considered as included in the protection scope of the present invention.
Claims (1)
1. A self-adaptive compensation method for thermal errors of a numerical control machine tool is characterized by comprising the following steps:
first, the thermal characteristic parameter identification test of the semi-closed loop feed shaft
The first temperature sensor (4), the second temperature sensor (11) and the third temperature sensor (12) are respectively arranged at three positions of the front bearing seat (3), the lathe bed (14) near the screw rod and the rear bearing seat (13); a spectroscope (6) of the laser interferometer is fixed on a workbench (7) through a magnetic gauge stand, and a reflector (9) is fixed on a main shaft (10) through the magnetic gauge stand; the semi-closed loop feeding shaft reciprocates at any speed and in any range to be heated, and the positioning error and the temperature values of the first temperature sensor (4), the second temperature sensor (11) and the third temperature sensor (12) are tested once every a period of time to 10min until the feeding shaft reaches thermal balance; stopping the semi-closed loop feeding shaft at any position for cooling, and testing the positioning error and the temperature values of the first temperature sensor (4), the second temperature sensor (11) and the third temperature sensor (12) once every a period of time to 10 min;
secondly, establishing a lead screw thermal error prediction model under multi-time varying-state heat source excitation
Considering the screw (5) as being composed of an infinite number of infinitesimal deltax, if the radiation effect of other external heat sources is not considered, the screw (5) infinitesimal deltax conducts heat by three ways: the heat conduction process between the lead screw micro element and the adjacent lead screw micro element, the heat convection heat exchange process between the lead screw micro element and the ambient air and the heat radiation heat dissipation process to the ambient environment; discretizing the position and the test time of the screw (5), neglecting the heat radiation effect of the screw (5) on the surrounding environment, and obtaining a temperature field model of the ball screw (5):
wherein c is the specific heat capacity, ρ is the material density of the screw (5), and dsIs the diameter of the screw (5), k is the coefficient of thermal conductivity, hcvThe surface of the screw rod (5) has a convective heat transfer coefficient, and Q is the sliding of the nut (8) through LiThe friction heat generation amount at one time, L is the length of a screw rod (5) unit, tau is a temperature acquisition time interval, and N is the friction L of the nut (8) within tauiNumber of times, TLi-τjIs LiAt taujTemperature value at time, Ta-τjIs taujThe ambient air temperature of the screw (5) at the moment;
the screw rod (5) is calculated at any time tau according to the following formulajThermal error model E off：
In the formula, the coefficient of thermal expansion is alphaeThe value is 11.7 mu m/(m DEG C);
third, thermal characteristic parameter identification
Identifying thermal characteristic parameters in the thermal error prediction model by a parameter automatic optimization method, and performing parameter optimization according to the formula (3):
wherein E isf(u, v) represents the prediction error value at the v test point in the u test, Eft(u, v) represents the test error value of the v measuring point in the u test; u is the total number of tests, and V is the number of points of each test;
fourthly, establishing a self-adaptive adjustment model of the single-time friction heat generation coefficient Q of the lead screw infinitesimal
Based on the law of energy conversion, the coefficient of heat generation by friction Q of the system is calculated according to the following formula:
in the formula, SrThe relative distance between objects which are mutually contacted in the system, M is the friction torque generated by the relative movement between the objects in the system, and D is the friction force arm;
the torque of the screw friction pair is calculated according to the following formula:
Mw＝k0ηFpsinαcos2λ(dbcosα+ds) (5)
in the formula, k0Is a proportionality coefficient, eta is a comprehensive friction factor of the screw-nut pair, FpIs nut pretightening force, alpha is a contact angle of the pretightening force and a normal surface of the axis of the screw rod (5), lambda is a helix angle of the difference between a screw rod helix line and the axis of the screw rod, and dbIs the diameter of the ball, dsThe diameter of the lead screw;
if the change of the bearing condition of the ball is not considered, F is setpIf the friction force is not changed, the change situation of the total friction moment is mainly determined by the lubrication state of the balls in the screw rod (5) and the nut (8); the total friction moment model established based on the change rule of the lubricating state of the screw-nut pair is as follows:
in the formula, FcIs coulomb friction force, FsAt maximum static friction, σ2Is a viscous friction coefficient, nsbIs a critical rotation speed, n is a steady-state slip rotation speed, PhIs a lead screw lead;
the adaptive adjustment model Q (n) for Q is calculated as follows:
in the formula etasIs the maximum static friction factor, ηcIs the Coulomb friction factor, SaIs the relative displacement between the nut (8) and the screw rod (5);
due to FpIs not changed, and the parameter k0、Fp、α、λ、Sa、ηc、ηs、nsb、σ2The value of (a) is not affected by n; meanwhile, Q is non-directional; therefore, let:
a1＝k0Fpsinαcos2λSa (8)
a2＝ηssgn(n) (9)
a3＝ηcsgn(n) (10)
a4＝σ2PhSa (11)
equation (7) is simplified to:
in the formula, a1、a2、a3、a4、nsbIs an unknown parameter;
fifthly, identifying the parameters of the self-adaptive adjustment model of the single-time friction heat generation coefficient Q of the lead screw infinitesimal
The identification process of each parameter is as follows:
1) when n is equal to 0, the inner part of the screw nut pair is in a static friction state; in this case, the following equation (12):
Q(0)＝a1a2 (13)
2) when n is>>nsbWhen the screw rod (5) is in a high-speed rotation state; in this case, the following equation (12) is used:
Q(n)＝a1a3+a4n (14)
3) when n is equal to nsbWhen the screw rod nut pair is used, the screw rod nut pair is positioned at the junction of mixed lubrication and hydrodynamic lubrication; then the equation (12) is:
Q(nsb)＝a1a3+a1(a2-a3)e-1+a4nsb＝0.3679a1a2+0.6321a1a3+a4nsb (15)
sixth, thermal error compensation write
The temperature sensor transmits the temperature signal to the collector, the temperature signal is transmitted to the compensator after being processed by the collector, the compensator writes the compensation quantity into the numerical control system after calculating the compensation quantity, and the compensation of the thermal error of the machine tool is realized in a mode of integral deviation of a mechanical coordinate system of the machine tool.
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