Multi-axis cooperative motion control system for high-precision engraving and milling machine

Abstract

The invention relates to the technical field of industrial automation control, in particular to a multi-axis cooperative motion control system for a high-precision engraving and milling machine. According to the system, Z-axis motor information is collected in real time, and friction heat energy is calculated and accumulated; calculating a temperature rise estimated value and a lubrication failure factor of each lead screw segment according to friction heat distribution in each thermal state updating period, and calculating a stiffness coefficient array through nonlinear coupling; and further calculating a rigidity attenuation deformation compensation amount based on the real-time rigidity coefficient and the cutting counter-force, and superposing the rigidity attenuation deformation compensation amount to a Z-axis position control loop. The problems of rigidity softening and force-induced deformation caused by Z-axis local heat accumulation and lubrication failure in the microstructure machining process are solved, the track overlap ratio of multi-axis linkage machining is recovered through double-physical-field coupling observation and compensation, and the contour machining precision of a microstructure mold is improved.

Description

Technical Field

[0001] This invention relates to the field of industrial automation control technology, and more specifically to a multi-axis cooperative motion control system for a high-precision engraving machine. Background Technology

[0002] High-precision engraving machines are widely used in the manufacture of microstructure molds such as Fresnel lenses and holographic anti-counterfeiting textures. In this type of machining process, the Z-axis needs to perform long-term and high-frequency reciprocating cutting motions within an extremely narrow stroke range. This high-frequency micro-motion condition prevents the ball screw from achieving full-range ball rolling, causing frictional heat to concentrate and accumulate in localized micro-areas that are difficult to conduct and dissipate. Simultaneously, it prevents fresh grease from flowing back to the contact area, leading to localized lubrication deficiency and grease shear thinning. Under the combined effect of the loss of preload due to thermal expansion caused by localized temperature rise and the deterioration of contact stiffness due to lubrication failure, the axial contact stiffness of the screw in the machining area will be significantly lower than its nominal cold-state value.

[0003] While existing fully closed-loop control systems can eliminate positioning errors through precision detection using grating rulers, they cannot detect elastic deformation caused by cutting forces resulting from a decrease in local stiffness. In multi-axis collaborative machining, this unexpected elastic compression caused by the softening of local stiffness along the Z-axis disrupts the overlap of the tool tip's trajectory in three-dimensional space, leading to insufficient cutting depth of microstructures and out-of-tolerance profile accuracy. Summary of the Invention

[0004] To address the technical problem that existing fully closed-loop control systems cannot detect elastic deformation caused by cutting force resulting from a decrease in the local stiffness of the Z-axis leadscrew, leading to insufficient microstructure cutting depth and excessive deviations in contour surface accuracy, the present invention aims to provide a multi-axis cooperative motion control system for high-precision engraving machines. The specific technical solution adopted is as follows: This invention proposes a multi-axis cooperative motion control system for a high-precision engraving machine, the system comprising: The frictional heat accumulation module is used to collect the current data and real-time position of the Z-axis motor at each moment, determine the lead screw segment at each moment based on the real-time position, analyze the heat distribution generated by frictional work based on the current data at each moment, and obtain the frictional heat increment of the lead screw segment at each moment; the frictional heat increment is accumulated according to the lead screw segment to obtain the cumulative frictional heat of the lead screw segment. The stiffness observation module is used to calculate the temperature rise estimate of each lead screw segment based on the distribution of the cumulative frictional heat and frictional heat increment between the lead screw segment and adjacent lead screw segments, and to obtain the lubrication failure factor of each lead screw segment based on the Z-axis motion state of the current thermal state update cycle; the temperature rise estimate and the lubrication failure factor are fused to calculate the stiffness coefficient of each lead screw segment, and the stiffness coefficient array of the current thermal state update cycle is obtained. The deformation compensation module is used to obtain the cutting reaction force at each moment based on the current data, and to calculate the stiffness attenuation deformation compensation amount of the Z-axis motor at the real-time position based on the stiffness coefficient array updated in the current thermal state and the cutting reaction force. The stiffness attenuation deformation compensation amount is used to correct the Z-axis position.

[0005] Furthermore, determining the lead screw segment at each moment based on the real-time position at each moment includes: The initial segments of the Z-axis are obtained by uniformly dividing the Z-axis length. The initial segment where the real-time position of the Z-axis motor is located at each moment is taken as the lead screw segment corresponding to the real-time position at each moment. Furthermore, the step of analyzing the heat distribution generated by frictional work based on the current data at each moment to obtain the frictional heat increment of the lead screw segment at each moment includes: The micro-motion friction driving current is separated from the current data by high-pass filtering. The instantaneous friction power is calculated based on the micro-motion friction driving current and the real-time speed of the Z-axis. The frictional heat increment at each moment is calculated based on the adjacent time interval and the instantaneous friction power at each moment.

[0006] Further, the step of calculating the estimated temperature rise of each lead screw segment based on the distribution of the cumulative frictional heat and the increase in frictional heat between the lead screw segment and adjacent lead screw segments includes: Obtain the estimated temperature rise of each lead screw segment in the previous thermal state update cycle. For each lead screw segment and its left and right adjacent lead screw segments, integrate the increase in frictional heat with the estimated temperature rise of the previous thermal state update cycle to obtain the estimated temperature rise of the current thermal state update cycle.

[0007] Furthermore, the process of obtaining the temperature rise estimate for the current thermal state update cycle includes: Based on the sum of the temperature rise estimate and frictional heat increment of each lead screw segment in the previous thermal state update cycle, the intermediate temperature rise estimate of each lead screw segment is calculated; the weighted sum of the intermediate temperature rise estimates of each lead screw segment and its left and right adjacent lead screw segments, and the natural heat loss, is used to obtain the temperature rise estimate of each lead screw segment in the current thermal state update cycle.

[0008] Furthermore, the step of obtaining the lubrication failure factor of each lead screw segment based on the Z-axis motion state of the current thermal state update cycle includes: Obtain the lubrication failure factor of the previous thermal state update cycle, and statistically analyze the stroke range of the Z-axis motion within the current thermal state update cycle; If the stroke range is less than the preset lubrication backflow threshold, the lubrication failure factor of each screw segment in the current thermal state update cycle is determined based on the preset frictional heat coefficient and the cumulative result of the lubrication failure factor of the previous thermal state update cycle. If the stroke range is greater than or equal to the preset lubrication backflow threshold, the lubrication failure factor of each screw segment in the previous thermal state update cycle is attenuated to obtain the lubrication failure factor of each screw in the current thermal state update cycle.

[0009] Furthermore, the process of fusing the temperature rise estimate and the lubrication failure factor to calculate the stiffness coefficient of each screw segment, resulting in a stiffness coefficient array for the current thermal state update cycle, includes: The estimated temperature rise and the lubrication failure factor for each screw segment are nonlinearly coupled to obtain the stiffness coefficient, and the stiffness coefficients of all screw segments constitute a stiffness coefficient array.

[0010] Furthermore, the stiffness coefficient array of the current thermal state update cycle and the stiffness attenuation deformation compensation amount of the Z-axis motor at the real-time position calculated by the cutting reaction force include: The real-time stiffness coefficients at each moment are obtained by interpolation based on the stiffness coefficient array of the current thermal state update cycle. The first theoretical deformation is calculated based on the cutting reaction force and the nominal cold stiffness of the leadscrew. The second theoretical deformation is calculated based on the first theoretical deformation and the real-time stiffness coefficient. The difference between the first theoretical deformation and the second theoretical deformation is used as the stiffness attenuation deformation compensation amount.

[0011] Furthermore, the step of interpolating the stiffness coefficient array based on the current thermal state update cycle to obtain the real-time stiffness coefficient at each moment includes: Based on the real-time position, the corresponding lead screw segment position is determined. The stiffness coefficients of the lead screw segments to the left and right of the lead screw segment position are obtained from the stiffness coefficient array and linearly interpolated to obtain the real-time stiffness coefficient of the lead screw segment position.

[0012] Furthermore, the method for calculating the cutting reaction force includes: The net torque current is obtained from the current data, and the net torque current is multiplied by the thrust constant of the Z-axis motor to obtain the cutting reaction force.

[0013] The present invention has the following beneficial effects: This invention collects the current data and real-time position of the Z-axis motor at each moment through a frictional heat accumulation module. Based on the current data, it analyzes the heat distribution generated by frictional work to obtain the frictional heat increment. This frictional heat increment is then accumulated according to the lead screw segments to obtain the cumulative frictional heat of each segment, achieving a precise mapping from time-domain energy to spatial-domain distribution, providing accurate heat source input for local thermal state simulation. The stiffness observation module calculates the estimated temperature rise of each lead screw segment based on the distribution of cumulative frictional heat and frictional heat increments between the lead screw segments and adjacent segments. Based on the Z-axis motion state of the current thermal state update cycle, it obtains the lubrication failure factor of each lead screw segment. The estimated temperature rise and lubrication failure factor are then fused to calculate the stiffness coefficient of each lead screw segment, resulting in a stiffness coefficient array for the current thermal state update cycle. This ensures that the stiffness coefficient reflects the preload loss ratio under the combined effects of heat accumulation and lubrication failure, solving the problem of stiffness estimation distortion in the micro-motion region using a single thermal model. The deformation compensation module acquires the cutting reaction force at each moment based on the current data. It then calculates the stiffness attenuation deformation compensation amount of the Z-axis motor in its real-time position based on the stiffness coefficient array updated according to the current thermal state and the cutting reaction force. This compensation is used to correct the Z-axis position, achieving real-time correction of the cutting depth error and ensuring that the compensation action only targets the elastic yield caused by the cutting behavior. This invention constructs a closed-loop system of heat source extraction, dual-field state observation, and force-induced deformation compensation, achieving stiffness softening correction without relying on external sensors. This restores the rigid support of the tool tip in the Z-axis direction during multi-axis linkage machining, ensuring the geometric overlap of the three-dimensional spatial trajectory and improving the contour machining accuracy of microstructure molds. Attached Figure Description

[0014] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a structural block diagram of a multi-axis cooperative motion control system for a high-precision engraving machine, provided as an embodiment of the present invention. Detailed Implementation

[0016] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a multi-axis cooperative motion control system for a high-precision engraving machine proposed according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0017] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0018] The following description, in conjunction with the accompanying drawings, details a specific solution for a multi-axis collaborative motion control system for a high-precision engraving machine provided by the present invention.

[0019] Example 1: Please see Figure 1 The diagram shows a structural block diagram of a multi-axis cooperative motion control system for a high-precision engraving machine according to an embodiment of the present invention. The system includes a friction heat accumulation module 101, a stiffness observation module 102, and a deformation compensation module 103.

[0020] The friction heat accumulation module 101 is used to collect the current data and real-time position of the Z-axis motor at each moment, determine the lead screw segment at each moment based on the real-time position at each moment, analyze the heat distribution generated by friction work based on the current data at each moment, and obtain the friction heat increment of the lead screw segment at each moment; the friction heat increment is accumulated according to the lead screw segment to obtain the cumulative friction heat of the lead screw segment.

[0021] This module separates the micro-current component used to overcome high-frequency frictional resistance from the current data using a high-pass filter, calculates the instantaneous frictional power in combination with the feedback speed, and maps and accumulates the energy integral in the time domain to the corresponding discrete lead screw segment in real time according to the real-time position index, thereby constructing a heat source energy that accurately corresponds to the spatial distribution of the physical lead screw, providing a pure and accurately positioned energy input for the subsequent thermal field evolution.

[0022] First, the current data of the Z-axis motor is obtained through the servo bus interface of the CNC (Computer Numerical Control) controller, and the real-time position and speed of the Z-axis are obtained through the Z-axis motor encoder.

[0023] Furthermore, the lead screw segment at each moment is determined based on the real-time position at each moment, including: The initial segments of the Z-axis are obtained by uniformly dividing the Z-axis length. The initial segment where the real-time position of the Z-axis motor is located at each moment is taken as the lead screw segment corresponding to the real-time position at each moment.

[0024] In a specific example, to accurately characterize continuous physical-thermal processes in a discrete digital control system, a unified spatial mapping reference must first be established. Since the heat conduction and wear characteristics of the Z-axis leadscrew are distributed axially, the effective physical stroke L of the Z-axis is linearly divided into N fixed-length physical segments as initial segments, with the length of each initial segment denoted as . Define the lead screw segment index n as a unique spatial identifier, with a value range of... This index has a unique bijective relationship with the physical location. The formula for calculating the index value can be expressed as: Where n represents the index of the lead screw segment where the instantaneous frictional power occurs at time t. Indicates taking the value downwards. This represents the length of the real-time position on the leadscrew at time t. This represents the length of a single initial segment. Adding 1 ensures that the frictional heat generated at any given time can be collected into the discrete grid corresponding to its physical location, thus establishing a unique index relationship between time-domain energy and spatial-domain grid.

[0025] Furthermore, based on the current data at each moment, the heat distribution generated by frictional work is analyzed to obtain the increase in frictional heat in the screw segment at each moment, including: The micro-motion friction driving current is separated from the current data by high-pass filtering. The instantaneous friction power is calculated based on the micro-motion friction driving current and the real-time speed of the Z-axis. The frictional heat increment at each moment is calculated based on the adjacent time interval and the instantaneous friction power at each moment.

[0026] In a specific example, during the machining of Fresnel lenses and microstructure molds, the Z-axis motor performs high-frequency, short-stroke reciprocating motion. In this case, the total current output by the servo drive includes a significant DC component used to balance the gravity of the Z-axis slide plate, and a low-frequency component used to follow the macroscopic curved surface contour. These two current components are mainly converted into mechanical potential energy or macroscopic kinetic energy, and do not directly cause severe local frictional heating on the lead screw raceway. Directly using the total current to calculate the heating power would lead to a severely inflated and distorted heat source estimation. Therefore, it is necessary to separate the high-frequency current component, which is used only to overcome microscopic cutting resistance and viscous friction, from a frequency domain perspective.

[0027] Preferably, the total current is filtered using a second-order Butterworth high-pass filter. The filter's cutoff frequency is set to 15Hz. This parameter is chosen based on the ratio of the typical microstructure texture processing feed rate to the texture space period, aiming to retain the high-frequency disturbance signal induced by fretting friction while effectively attenuating the DC component of gravity and the low-frequency component of the contour. After filtering, the fretting friction drive current at each moment is output, which represents the effective torque current output by the motor to overcome high-frequency frictional resistance at the current moment.

[0028] Since frictional resistance always does negative work and is converted into heat energy, the instantaneous frictional power can be calculated based on the fretting friction driving current and the Z-axis velocity at time t. The formula for the instantaneous frictional power at time t can be expressed as: ;in, This represents the instantaneous frictional power at time t. This represents the fretting friction driving current at time t. This represents the velocity along the Z-axis at time t. This represents the thrust constant of the Z-axis motor.

[0029] Multiplying the instantaneous frictional power at time t by the time interval between time t and the previous time interval yields the increase in frictional heat at time t. This increase in frictional heat reflects the accumulated heat production from friction over a historical time interval at time t.

[0030] Since heat generation is a process of continuous energy accumulation over time, and the rapid movement of the Z-axis during machining causes the position of the heat source on the leadscrew to constantly change, in order to construct a heat source model that accurately corresponds to the leadscrew, the instantaneously generated heat power must be mapped in real time to the physical segment where the current Z-axis is located.

[0031] To match the macroscopic time characteristics of the heat conduction process, the increase in frictional heat at each moment cannot be directly used for thermal analysis; instead, its heat integral over a certain period of time must be calculated. This time period is defined as the thermal state update cycle, and during the duration of each thermal state update cycle, a heat accumulation operation is performed at the end of each moment.

[0032] Preferably, the length of the thermal state update cycle is 100 sampling times, with a 1 ms interval between adjacent sampling times. At the end of each thermal state update cycle, the change in stiffness coefficient is analyzed based on the accumulated frictional heat within that cycle. It should be understood that time t in the above steps is any time within a thermal state update cycle.

[0033] In a specific example, the system allocates a long N-dimensional array of accumulated frictional heat from the leadscrew segments in memory and initializes all elements of this array to zero, serving as the energy container for the first cycle. During the duration of one thermal state update cycle, the increase in frictional heat generated at time t is calculated. The index of the leadscrew segment at time t along the Z-axis is obtained using the method described above; this index corresponds to the leadcrew segment where the instantaneous frictional power at time t is applied. The value of the element at the index in the accumulated frictional heat array is then added to the increase in frictional heat at time t, completing one accumulation. The value of each element in the array represents the accumulated frictional heat of the leadscrew segment corresponding to each index within one thermal state update cycle.

[0034] It should be noted that when a thermal state update cycle ends, the current copy of the accumulated frictional heat array of the lead screw segment is passed to the stiffness observation module 102 for thermal state update, and then all elements in the array are cleared to zero for energy accumulation in the next cycle. This ensures the continuity and non-overlap of energy data and provides a conserved energy input boundary for subsequent thermal and rheological coupling calculations.

[0035] The stiffness observation module 102 is used to calculate the temperature rise estimate of each lead screw segment based on the distribution of the cumulative frictional heat and frictional heat increment between the lead screw segment and adjacent lead screw segments, and to obtain the lubrication failure factor of each lead screw segment based on the Z-axis motion state of the current thermal state update cycle; and to calculate the stiffness coefficient of each lead screw segment by fusing the temperature rise estimate and the lubrication failure factor to obtain the stiffness coefficient array of the current thermal state update cycle.

[0036] The high-frequency, short-stroke fretting conditions unique to microstructure machining can lead to simultaneous heat accumulation and lubrication failure in localized areas of the lead screw raceway, rendering traditional single-entity temperature rise models inadequate for characterizing localized preload loss. This invention utilizes a high-frequency fretting heat source and motion statistics to drive a dual-physics field observer incorporating both thermal diffusion and rheological damage mechanisms. By quantifying the nonlinear amplification effect of lubrication failure on thermally induced stiffness decay, the invention calculates the segmented stiffness coefficients of the lead screw that reflect the actual physical conditions, thereby solving the problem of unobservable localized stiffness softening.

[0037] Furthermore, based on the distribution of cumulative frictional heat and frictional heat increment between the lead screw segment and adjacent lead screw segments, the estimated temperature rise of each lead screw segment is calculated, including: Obtain the estimated temperature rise of each lead screw segment in the previous thermal state update cycle. For each lead screw segment and its left and right adjacent lead screw segments, integrate the increase in frictional heat with the estimated temperature rise of the previous thermal state update cycle to obtain the estimated temperature rise of the current thermal state update cycle.

[0038] In a specific example, the thermal characteristics of the leadscrew exhibit a localized frictional heat that causes the temperature of that region to rise, while the heat is conducted and diffused to adjacent, lower-temperature metal entities. The surface airflow generated by the leadscrew's rotation produces a convective cooling effect. To reconstruct the heat accumulation distribution including the temperature gradient, for each leadscrew segment and its left and right adjacent segments, the estimated temperature rise from the previous thermal state update cycle and the frictional heat increment for the current cycle are obtained. The thermal diffusion process is then simulated through a spatial convolution operation.

[0039] To ensure that the iterative observation algorithm has a definite convergence boundary at system startup and to avoid cold-start calculation divergence due to undefined initial states, the state space must be initialized before the servo system is enabled. The initial moment is defined as the starting point of the macroscopic thermal state update cycle. At this time, the leadscrew is in thermal equilibrium with the ambient temperature, and the raceway grease has not yet been damaged by fretting shear and is in a full state.

[0040] Preferably, the estimated temperature rise of the lead screw segment is initialized to zero, representing no temperature rise relative to the ambient temperature; the lubrication failure factor of the lead screw segment is initialized to zero, representing that the lubricating oil film is in an ideal hydrodynamic pressure state; and the stiffness coefficient is initialized to 1, representing that the lead screw is in the nominal cold stiffness state.

[0041] It should be noted that the nominal cold stiffness represents the ideal axial stiffness value of the Z-axis ball screw drive system when there is no heat generation and good lubrication, that is, the ability of the Z-axis drive chain to resist axial deformation. The above initialization process is only executed once after the system is powered on, and subsequent state updates are based on the evolution results of the previous cycle.

[0042] Furthermore, the process of obtaining the temperature rise estimate for the current thermal state update cycle includes: Based on the sum of the temperature rise estimate and frictional heat increment of each lead screw segment in the previous thermal state update cycle, the intermediate temperature rise estimate of each lead screw segment is calculated; the weighted sum of the intermediate temperature rise estimates of each lead screw segment and its left and right adjacent lead screw segments, and the natural heat loss, is used to obtain the temperature rise estimate of each lead screw segment in the current thermal state update cycle.

[0043] In a specific example, the temperature rise estimate for the current thermal state update cycle is obtained through spatial convolution operations, and a thermal diffusivity convolution kernel is defined. This is used to characterize the heat conduction capacity between adjacent segments, and its element values ​​satisfy the normalization condition (i.e., the sum of the elements is 1 to ensure energy conservation). Characterizes the heat retention capability of the current lead screw segment. To characterize the heat conduction capacity to adjacent lead screw segments, for each segment on the lead screw, obtain the lead screw segment sequence composed of its left and right adjacent lead screw segments, and calculate the estimated temperature rise of the current lead screw segment through a convolution operation. The calculation formula can be expressed as: in, This represents the estimated temperature rise of the nth lead screw segment in the mth thermal state update cycle, where the mth thermal state update cycle is the current thermal state update cycle. j represents the index value of the sequence consisting of the current lead screw segment and its left and right adjacent lead screw segments, and m-1 represents the previous thermal state update cycle of the mth thermal state update cycle. This represents the estimated temperature rise of each lead screw segment in the previous thermal state update cycle within the lead screw segment sequence. This represents the cumulative frictional heat during the current thermal state update cycle of each lead screw segment in the lead screw segment sequence. This represents the preset thermal sensitivity coefficient, used to map Joule thermal energy into an equivalent temperature rise increment and perform unit conversion. This represents the dynamic cooling coefficient, which reflects the impact of the convective cooling effect caused by the surface airflow generated by the screw rotation on the estimated temperature rise.

[0044] Based on the sum of the temperature rise estimate and frictional heat increment of each lead screw segment in the previous thermal state update cycle, the intermediate temperature rise estimate of each lead screw segment is obtained by summing the results. Then, the intermediate temperature rise estimates of adjacent lead screw segments are weighted and summed, with the weights being defined thermal diffusion convolution kernels, to obtain the temperature rise estimate of each lead screw segment in the current thermal state update cycle.

[0045] It should be noted that for the boundary screw segments, an adiabatic boundary condition is used, that is, only the transmission effect of the adjacent inner screw segments is calculated.

[0046] Preferably, the thermal diffusive convolution kernel value is In other embodiments of the invention, the thermal diffusivity of the lead screw material can be determined experimentally. Segment length And the initial diffusion number is calculated based on the thermal state update period T. Then the initial kernel Then, a step heat source is applied to one end of the lead screw, and a thermal imager is used to record the measured curve of temperature conduction along the axial direction. The r value is then fine-tuned until it matches the measured conduction rate.

[0047] Preferably, the thermal induction coefficient can be calculated using the specific heat capacity c of the lead screw and the mass m of each segment of the lead screw. Its typical range of values ​​is In this embodiment, it is set to 0.02. In another embodiment, this coefficient can be obtained by experimental calibration, applying a heat source of known power (such as constant current heating) to the lead screw, measuring the rate of temperature rise per unit time, and fitting the coefficient.

[0048] Preferably, the heat loss due to convective cooling is deducted based on the dynamic cooling coefficient, that is, the heat loss is calculated in the above formula by... The product coupling operation is performed with the accumulated result to achieve the purpose of deducting the natural heat loss, where the dynamic cooling coefficient is... , This represents the natural cooling rate, which is the baseline proportion of heat loss through natural convection and radiation when the leadscrew is stationary. This indicates the forced air cooling term, which refers to the additional air cooling effect caused by the increased surface airflow velocity when the leadscrew rotates or moves at high speed. Represents the velocity gain coefficient. This indicates the average rotational speed or linear velocity. In this embodiment, , In another embodiment, these two parameters can be calibrated experimentally, first by measuring the natural temperature drop curve of the lead screw when it is at rest. Then, the temperature drop rate of the lead screw at different speeds was measured, and its linear slope as a function of speed was obtained by fitting. .

[0049] Because the physical essence of heat conduction is the diffusion of energy from high to low in a medium, it mathematically follows a second-order partial differential equation. The discretized numerical solution of this equation (finite difference method) is formally expressed as the temperature at the current position at the next moment depending on the weighted sum of its current temperature and the temperatures at adjacent positions. Therefore, by performing convolution operations with the spatial temperature distribution array of the previous cycle using a convolution kernel, and by superimposing the newly input frictional heat energy source term of the current cycle and deducting the convective cooling loss during the calculation process, the accumulation, diffusion and dissipation of heat along the screw axis can be accurately simulated in a discrete digital system, thereby iteratively calculating the temperature rise state value of the current cycle that includes the real temperature gradient distribution.

[0050] Furthermore, based on the Z-axis motion state of the current thermal update cycle, the lubrication failure factors of each lead screw segment are obtained, including: Obtain the lubrication failure factor of the previous thermal state update cycle, and statistically analyze the stroke range of the Z-axis motion within the current thermal state update cycle; If the stroke range is less than the preset lubrication backflow threshold, the lubrication failure factor of each screw segment in the current thermal state update cycle is determined based on the preset frictional heat coefficient and the cumulative result of the lubrication failure factor of the previous thermal state update cycle. If the stroke range is greater than or equal to the preset lubrication backflow threshold, the lubrication failure factor of each screw segment in the previous thermal state update cycle is attenuated to obtain the lubrication failure factor of each screw in the current thermal state update cycle.

[0051] In a specific example, because the lubrication state of the Z-axis is closely related to the motion stroke in microstructure machining, when the reciprocating motion stroke is less than a critical threshold, the balls cannot complete a full rolling cycle. This results in fresh grease from the non-contact area not being carried into the load area, and the grease in the contact area becoming thinner due to repeated shearing. To identify this localized lubrication failure, the system performs statistical analysis on the real-time position of the Z-axis within the current thermal state update cycle.

[0052] First, the travel range of the Z-axis motion trajectory within the current thermal state update cycle is calculated, which is the physical span covered by the Z-axis motion trajectory within the current thermal state update cycle. The difference between the maximum and minimum real-time positions of the Z-axis within the current thermal state update cycle is taken as the travel range of the current thermal state update cycle. Then, it is compared with a preset lubrication return threshold, which represents the minimum motion stroke required for the ball screw to form effective hydrodynamic lubrication return.

[0053] Preferably, the lubrication backflow threshold is set to 3 times the diameter of the ball (e.g., 10 mm).

[0054] Based on the comparison results, the lubrication failure factors of the center lead screw segment index at the current machining position and its neighborhood are updated. The center lead screw segment index at the current machining position is the lead screw segment index corresponding to the current Z-axis position, and its neighborhood is the grid range centered on it covering the physical length of the ball nut. The specific update process is as follows: When the stroke range is less than the lubrication return threshold, it indicates fretting wear. This indicates lubrication deficiency in the current region, and the lubrication failure factor for that region is increased. Specifically, the lubrication failure factor for the current thermal state renewal cycle is the sum of the lubrication failure factor for the previous thermal state renewal cycle and the wear accumulation step size for a single cycle. It should be noted that the maximum value of the lubrication failure factor must be limited to 1.0, representing completely dry friction.

[0055] When the stroke range is greater than or equal to the lubrication backflow threshold, the lubrication state is traversed, and it is determined that lubrication backflow and repair have occurred. It is necessary to attenuate and restore the lubrication failure factor of the entire stroke. That is, the lubrication failure factor of the current thermal state update cycle is the product of the lubrication failure factor of the previous thermal state update cycle and the lubrication recovery coefficient.

[0056] Preferably, the wear accumulation step size per cycle is used to characterize the rate at which the lubricating oil film performance degrades over time under fretting conditions. This parameter is determined based on the wear resistance characteristics of the grease and processing experience. In this embodiment, it is set to 0.0005, meaning that if the fretting condition continues for approximately 2000 cycles, the lubrication failure factor will accumulate to saturation.

[0057] Preferably, the lubrication recovery coefficient is a preset proportionality coefficient used to characterize the repair rate of the lubricating oil film when an effective stroke occurs. In this embodiment, it is set to 0.9, which means that in each update cycle that meets the lubrication reflux conditions, the lubrication failure factor of the relevant area will decrease to 90% of the value of the previous cycle, reflecting the physical process of the lubrication state gradually improving with the circulation of the balls.

[0058] Furthermore, the stiffness coefficients of each screw segment are calculated by fusing the estimated temperature rise and lubrication failure factor to obtain a stiffness coefficient array for the current thermal state update cycle, including: The estimated temperature rise and the lubrication failure factor for each screw segment are nonlinearly coupled to obtain the stiffness coefficient, and the stiffness coefficients of all screw segments constitute a stiffness coefficient array.

[0059] In a specific example, since the attenuation of the lead screw contact stiffness is not solely determined by thermal expansion, the rupture of the lubricating oil film significantly reduces the load-bearing capacity of the contact surface, thereby amplifying the effect of thermally induced preload loss. To quantify this physical mechanism, a thermo-stiffness coupling model with the lubrication failure factor as the modulating term was constructed.

[0060] For each segment of the leadscrew across the entire stroke in a thermal update cycle, the current stiffness coefficient is calculated using the estimated temperature rise and lubrication failure factor after the update for this cycle. The calculation formula is as follows: in, represents the stiffness coefficient of the nth screw segment in the m-th hot state update cycle, and b represents the nominal stiffness reference in the cold state, with a value of 1. This represents the maximum stiffness attenuation rate, determined by the preload level of the leadscrew, and is used to prevent the calculated result from falling below the physical limits of the mechanical structure. This represents the basic thermal sensitivity coefficient, characterizing the rate of stiffness decay caused by a unit temperature rise under ideal lubrication conditions. This represents the rheological coupling gain coefficient, characterizing the amplification factor of stiffness decay due to lubrication failure. When the lubrication failure factor approaches 1, the rate of exponential decay increases significantly, simulating the sharp decrease in contact stiffness under dry friction conditions. This represents the lubrication failure factor of the nth lead screw segment in the m-th thermal state update cycle. This represents the estimated temperature rise of the nth lead screw segment during the mth thermal state update cycle.

[0061] Preferably, the maximum stiffness attenuation rate is set to 0.35, the basic thermal sensitivity coefficient is set to 0.05, and the rheological coupling gain coefficient is set to 2.0.

[0062] The stiffness coefficient is a core state quantity connecting macroscopic observation and microscopic control. Its physical meaning lies in quantifying the degree of attenuation of the actual load-bearing capacity of the lead screw drive chain under the current heat accumulation and lubrication state relative to the ideal cold state reference (for example, a value of 0.8 represents a stiffness drop to 80% of the factory value). This allows the control system to use Hooke's Law to inversely calculate the additional elastic deformation caused by the softening of stiffness based on the current cutting load, thereby achieving precise position feedforward compensation.

[0063] During a thermal state update cycle, the stiffness coefficients of all lead screw segments form a stiffness coefficient array, which is passed to the deformation compensation module 103 for Z-axis position correction.

[0064] The deformation compensation module 103 is used to obtain the cutting reaction force at each moment based on the current data, and to calculate the stiffness attenuation deformation compensation amount of the Z-axis motor at the real-time position based on the stiffness coefficient array of the current thermal state update cycle and the cutting reaction force. The stiffness attenuation deformation compensation amount is used to correct the Z-axis position.

[0065] This module, acting as the execution terminal of the control closed loop, aims to transform the macroscopic stiffness state calculated in the preceding steps into microscopic position control commands. In microstructure machining, the essence of multi-axis collaboration requires the tool tip to strictly follow the theoretical trajectory generated by X / Y / Z three-axis interpolation in three-dimensional space. However, local stiffness softening of the Z-axis leadscrew can cause axial elastic yielding exceeding the system's expectations under cutting forces, resulting in an actual cutting depth less than the theoretical commanded depth, thus compromising the geometric conformity of multi-axis collaboration. This module addresses this issue with dynamic inverse calculation based on Hooke's Law: given a fixed cutting reaction force, it calculates the additional deformation relative to the nominal stiffness under this condition based on the real-time derived stiffness retention rate, and injects this as a feedforward compensation value into the control loop, thereby compensating for the cutting depth loss caused by the decrease in stiffness.

[0066] Furthermore, the stiffness coefficient array of the current thermal state update cycle and the stiffness attenuation deformation compensation amount of the Z-axis motor at the real-time position calculated by the cutting reaction force include: The real-time stiffness coefficients at each moment are obtained by interpolation based on the stiffness coefficient array of the current thermal state update cycle. The first theoretical deformation is calculated based on the cutting reaction force and the nominal cold stiffness of the leadscrew. The second theoretical deformation is calculated based on the first theoretical deformation and the real-time stiffness coefficient. The difference between the first theoretical deformation and the second theoretical deformation is used as the stiffness attenuation deformation compensation amount.

[0067] Furthermore, the step of interpolating the stiffness coefficient array based on the current thermal state update cycle to obtain the real-time stiffness coefficient at each moment includes: Based on the real-time position, the corresponding lead screw segment position is determined. The stiffness coefficients of the lead screw segments to the left and right of the lead screw segment position are obtained from the stiffness coefficient array and linearly interpolated to obtain the real-time stiffness coefficient of the lead screw segment position.

[0068] In a specific example, since the stiffness coefficient array is a stepped data defined based on a discrete grid of fixed length, while the Z-axis position changes continuously during machining, directly using the values ​​of the current grid would cause abrupt changes in the stiffness parameters when the Z-axis crosses the grid boundary, leading to abrupt changes in the compensation command and leaving visible tool marks on the smooth lens surface. Therefore, it is necessary to smoothly map the discrete macroscopic state to continuous microscopic coefficients.

[0069] At each moment, the lead screw segment index is calculated based on the real-time position using the method described above, but without rounding down. The decimal part is used as the weight r for linear interpolation. That is, the real-time stiffness coefficient at the current moment is the weighted sum of the stiffness coefficient of the lead screw segment where the real-time position on the Z-axis is located and the stiffness coefficient of the next adjacent lead screw segment. Here, the weight of the current lead screw segment is 1-r, and the weight of the next adjacent lead screw segment is r.

[0070] The weights of the linear interpolation determine whether the current stiffness coefficient resembles the left-hand lead screw segment (weight 1-r) or the right-hand lead screw segment (weight r). This ensures that the stiffness coefficient changes smoothly when the Z-axis moves, without abrupt jumps, and eliminates quantization noise caused by data discretization.

[0071] It should be noted that, in order to prevent array out-of-bounds errors at the end of the process, the index is clamped. Specifically, if the index is greater than or equal to N, the index is forced to be N-1 and r=1.

[0072] Furthermore, the method for calculating the cutting reaction force includes: The net torque current is obtained from the current data, and the net torque current is multiplied by the thrust constant of the Z-axis motor to obtain the cutting reaction force.

[0073] In a specific example, since a decrease in stiffness itself does not directly cause positional error, substantial elastic deformation only occurs when the leadscrew is subjected to axial cutting loads. Because the total torque output by the servo motor simultaneously includes components that overcome gravity, friction, and cutting forces, the static component must be eliminated to accurately calculate the deformation.

[0074] The net torque current is obtained by subtracting the gravity-maintaining current and inertial force from the real-time current data of the Z-axis motor. This net torque current is then multiplied by the motor's thrust constant to obtain an estimated value of the cutting reaction force. This calculation only extracts the dynamic load caused by the machining process, ensuring that the compensation action only applies to the cutting behavior and avoiding Z-axis zero-position drift caused by gravity balance errors.

[0075] Preferably, the gravity sustaining current is the average torque current required by the Z-axis motor to overcome the gravity of the skateboard and maintain a stationary hovering state. Its calibration method is as follows: control the Z-axis to move to the middle position of the stroke and keep it stationary and locked, continuously collect the q-axis current output by the motor within a preset time window (such as 1 second), and calculate its arithmetic mean as the gravity sustaining current.

[0076] Preferably, in high-frequency reciprocating machining, most of the torque output by the Z-axis motor is actually used to overcome the huge inertia of the moving parts for acceleration and deceleration, rather than for cutting. To avoid misinterpreting the accelerating torque as cutting reaction force, the inertial force component needs to be subtracted. The inertial force component is equal to the Z-axis acceleration multiplied by the inertial current coefficient. The acceleration is obtained from the velocity difference between time t and time t-1. The inertial current coefficient is calibrated by the following method: Under no-load (no cutting) conditions, the Z-axis is controlled to perform reciprocating motion with a known acceleration. The average current change after removing gravity is recorded. The result of dividing the average current change by the known acceleration is taken as the inertial current coefficient.

[0077] The first theoretical deformation is calculated based on the cutting reaction force and the nominal cold stiffness of the leadscrew. The second theoretical deformation is calculated based on the first theoretical deformation and the real-time stiffness coefficient. The difference between the first theoretical deformation and the second theoretical deformation is used as the stiffness attenuation deformation compensation.

[0078] Preferably, the nominal cold stiffness is calibrated by static loading test, specifically: under the condition that the Z-axis is in a cold state and well lubricated, the motor outputs a preset test torque to apply an axial static load, and the resulting axial elastic displacement is measured using a laser interferometer or a high-precision grating ruler. The ratio of load to displacement is then calculated as the nominal cold stiffness.

[0079] Based on the fundamental principles of materials mechanics, the axial deformation of a leadscrew is directly proportional to the applied force and inversely proportional to its stiffness. Conventional CNC systems perform position control based on nominal cold-state stiffness and cannot detect stiffness decay. This invention calculates the difference between the theoretical deformation under the current actual stiffness and the theoretical deformation under the nominal stiffness; this difference is the amount of tool deflection that needs to be compensated.

[0080] In a specific example, the formula for stiffness attenuation deformation compensation is: in, This represents the amount of stiffness attenuation deformation compensation at time t. This represents the cutting reaction force at time t. This represents the real-time stiffness coefficient at time t. This represents the nominal cold stiffness. This is the first theoretical deformation amount. This is the second theoretical deformation amount.

[0081] When the real-time stiffness coefficient is 1, it means that the stiffness has not decayed, and the value in parentheses is 0, so the compensation amount is 0. As the real-time stiffness coefficient decreases due to heat accumulation or lubrication failure, the compensation amount will increase sharply in an inverse nonlinear manner, which is consistent with the physical phenomenon that the deformation amount surges when the stiffness is severely deteriorated.

[0082] Finally, the calculated compensation amount is superimposed on the position command feedforward port of the Z-axis servo controller in real time. In the interpolation motion of the X, Y, and Z axes, this compensation action independently corrects the physical scaling error of the Z-axis, ensuring that the tool tip always fits on the theoretical three-dimensional curved surface trajectory.

[0083] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0084] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

Claims

1. A multi-axis cooperative motion control system for a high-precision engraving machine, characterized in that, The system includes: The frictional heat accumulation module is used to collect the current data and real-time position of the Z-axis motor at each moment, determine the lead screw segment at each moment based on the real-time position, analyze the heat distribution generated by frictional work based on the current data at each moment, and obtain the frictional heat increment of the lead screw segment at each moment; the frictional heat increment is accumulated according to the lead screw segment to obtain the cumulative frictional heat of the lead screw segment. The stiffness observation module is used to calculate the temperature rise estimate of each lead screw segment based on the distribution of the cumulative frictional heat and frictional heat increment between the lead screw segment and adjacent lead screw segments, and to obtain the lubrication failure factor of each lead screw segment based on the Z-axis motion state of the current thermal state update cycle; the temperature rise estimate and the lubrication failure factor are fused to calculate the stiffness coefficient of each lead screw segment, and the stiffness coefficient array of the current thermal state update cycle is obtained. The deformation compensation module is used to obtain the cutting reaction force at each moment based on the current data, and to calculate the stiffness attenuation deformation compensation amount of the Z-axis motor at the real-time position based on the stiffness coefficient array updated in the current thermal state and the cutting reaction force. The stiffness attenuation deformation compensation amount is used to correct the Z-axis position.

2. The multi-axis cooperative motion control system for a high-precision engraving machine according to claim 1, characterized in that, The process of determining the lead screw segment at each moment based on the real-time position at each moment includes: The initial segments of the Z-axis are obtained by uniformly dividing the Z-axis length. The initial segment where the real-time position of the Z-axis motor is located at each moment is taken as the lead screw segment corresponding to the real-time position at each moment.

3. A multi-axis cooperative motion control system for a high-precision engraving machine according to claim 1, characterized in that, The step of analyzing the heat distribution generated by frictional work based on the current data at each moment to obtain the frictional heat increment of the lead screw segment at each moment includes: The micro-motion friction driving current is separated from the current data by high-pass filtering. The instantaneous friction power is calculated based on the micro-motion friction driving current and the real-time speed of the Z-axis. The frictional heat increment at each moment is calculated based on the adjacent time interval and the instantaneous friction power at each moment.

4. A multi-axis cooperative motion control system for a high-precision engraving machine according to claim 1, characterized in that, The calculation of the estimated temperature rise of each lead screw segment based on the distribution of cumulative frictional heat and frictional heat increment between the lead screw segment and adjacent lead screw segments includes: Obtain the estimated temperature rise of each lead screw segment in the previous thermal state update cycle. For each lead screw segment and its left and right adjacent lead screw segments, integrate the increase in frictional heat with the estimated temperature rise of the previous thermal state update cycle to obtain the estimated temperature rise of the current thermal state update cycle.

5. A multi-axis cooperative motion control system for a high-precision engraving machine according to claim 4, characterized in that, The process of obtaining the temperature rise estimate for the current thermal state update cycle includes: Based on the sum of the temperature rise estimate and frictional heat increment of each lead screw segment in the previous thermal state update cycle, the intermediate temperature rise estimate of each lead screw segment is calculated; the weighted sum of the intermediate temperature rise estimates of each lead screw segment and its left and right adjacent lead screw segments is then calculated, and natural heat loss is deducted to obtain the temperature rise estimate of each lead screw segment in the current thermal state update cycle.

6. A multi-axis cooperative motion control system for a high-precision engraving machine according to claim 1, characterized in that, The process of obtaining the lubrication failure factor for each lead screw segment based on the Z-axis motion state of the current thermal state update cycle includes: Obtain the lubrication failure factor of the previous thermal state update cycle, and statistically analyze the stroke range of the Z-axis motion within the current thermal state update cycle; If the stroke range is less than the preset lubrication backflow threshold, the lubrication failure factor of each screw segment in the current thermal state update cycle is determined based on the preset frictional heat coefficient and the cumulative result of the lubrication failure factor of the previous thermal state update cycle. If the stroke range is greater than or equal to the preset lubrication backflow threshold, the lubrication failure factor of each screw segment in the previous thermal state update cycle is attenuated to obtain the lubrication failure factor of each screw in the current thermal state update cycle.

7. A multi-axis cooperative motion control system for a high-precision engraving machine according to claim 1, characterized in that, The process of fusing the temperature rise estimate and lubrication failure factor to calculate the stiffness coefficients of each screw segment yields a stiffness coefficient array for the current thermal state update cycle, including: The estimated temperature rise and the lubrication failure factor for each screw segment are nonlinearly coupled to obtain the stiffness coefficient, and the stiffness coefficients of all screw segments constitute a stiffness coefficient array.

8. A multi-axis cooperative motion control system for a high-precision engraving machine according to claim 1, characterized in that, The stiffness coefficient array of the current thermal state update cycle and the stiffness attenuation deformation compensation amount of the Z-axis motor at the real-time position calculated by the cutting reaction force include: The real-time stiffness coefficients at each moment are obtained by interpolation based on the stiffness coefficient array of the current thermal state update cycle. The first theoretical deformation is calculated based on the cutting reaction force and the nominal cold stiffness of the leadscrew. The second theoretical deformation is calculated based on the first theoretical deformation and the real-time stiffness coefficient. The difference between the first theoretical deformation and the second theoretical deformation is used as the stiffness attenuation deformation compensation.

9. A multi-axis cooperative motion control system for a high-precision engraving machine according to claim 8, characterized in that, The process of interpolating the stiffness coefficient array based on the current thermal state update cycle to obtain the real-time stiffness coefficient at each moment includes: Based on the real-time position, the corresponding lead screw segment position is determined. The stiffness coefficients of the lead screw segments to the left and right of the lead screw segment position are obtained from the stiffness coefficient array and linearly interpolated to obtain the real-time stiffness coefficient of the lead screw segment position.

10. A multi-axis cooperative motion control system for a high-precision engraving machine according to claim 8, characterized in that, The method for calculating the cutting reaction force includes: The net torque current is obtained from the current data, and the net torque current is multiplied by the thrust constant of the Z-axis motor to obtain the cutting reaction force.

Images