Intelligent control method for numerical control grinding machine based on multi-axis linkage precision compensation and real-time monitoring

Abstract

The application discloses a numerical control grinding machine intelligent control method based on multi-axis linkage precision compensation and real-time monitoring and relates to the technical field of numerical control grinding machines, and comprises the following steps: S1, receiving each axis instruction position sequence output by an interpolator, obtaining each axis instruction acceleration according to the each axis instruction position sequence, calculating the ratio of the absolute value of each axis instruction acceleration to the corresponding axis acceleration threshold to obtain an acceleration demand ratio, and taking the difference between the acceleration demand ratio of a rotary shaft and a linear shaft participating in current grinding profile formation as an inter-axis mismatch degree. The numerical control grinding machine intelligent control method provided by the application adopts a coordination strategy of linear shaft controlled deceleration and rotary shaft condition activated feedforward, deceleration reduces the target speed that a rotary shaft needs to chase, makes the feedforward compensation quantity change more gently in the mismatch section, and reduces the possibility of exciting rotary shaft speed loop oscillation; the feedforward compensates for the efficiency loss caused by deceleration, suppresses profile deviation, and reduces the influence on machining efficiency.

Description

Technical Field

[0001] This invention relates to the field of CNC grinding machine technology, specifically to an intelligent control method for CNC grinding machines based on multi-axis linkage precision compensation and real-time monitoring. Background Technology

[0002] When grinding workpieces with varying curvature contours, CNC grinding machines require the coordinated operation of linear and rotary axes. Due to the large inertia and low speed loop bandwidth of the rotary axis, and the small inertia and fast response of the linear axis, the dynamic response characteristics of the two axes inherently differ. The impact is limited in sections with gentle curvature, but in sections where curvature changes abruptly, the lag in the rotary axis response leads to a mismatch in motion rhythm with the linear axis, resulting in profile deviations. Taking non-circular grinding of camshafts as an example, when grinding to the tip lift transition zone, the C-axis needs to complete a significant acceleration and deceleration within a very short angular range, while the X-axis only needs a small reciprocating motion. The lag in the C-axis causes the grinding wheel contact point to shift along the profile normal, forming a periodic profile deviation where the tip bulges and then recedes. This is a unique accuracy bottleneck in this type of machining scenario.

[0003] Existing technologies primarily reduce contour errors through cross-coupling control or multi-dimensional error modeling compensation. Cross-coupling control calculates the contour error based on the tracking error of each axis and allocates compensation according to the coupling gain. However, its compensation method for each axis does not distinguish the response differences between linear and rotary axes. For rotary axes, it uses positive compensation to make them catch up with the command. However, in the curvature abrupt change section, the command angular acceleration has already reached its peak, and the positive compensation amount changes abruptly, posing a risk of inducing oscillations in the rotary axis speed loop. Multi-dimensional error modeling schemes process various errors independently and then compensate them in series, but they do not address the coupling characteristics of dynamic mismatch between axes during grinding. Moreover, the compensation is still mainly based on positive catching up, facing the same limitations. In addition, existing solutions generally adopt a strategy of applying compensation throughout the entire process, introducing unnecessary disturbances in the curvature level section, and do not adaptively adjust the compensation intensity according to real-time operating conditions. To address these issues, we propose an intelligent control method for CNC grinding machines based on multi-axis linkage accuracy compensation and real-time monitoring. Summary of the Invention

[0004] To address the problems raised in the background art, this invention provides an intelligent control method for CNC grinding machines based on multi-axis linkage accuracy compensation and real-time monitoring, specifically including the following steps: S1. Receive the command position sequence of each axis output by the interpolator, obtain the command acceleration of each axis according to the command position sequence of each axis, calculate the ratio of the absolute value of the command acceleration of each axis to the corresponding axis acceleration threshold to obtain the acceleration demand ratio, and take the difference between the acceleration demand ratio of the rotary axis and the linear axis participating in the current grinding profile as the axis mismatch degree. When the mismatch degree exceeds the preset threshold and meets the preset continuous condition, it is marked as a mismatch risk segment. S2. Only in the mismatch risk segment, the linear axis feed rate command is multiplied by a scaling factor. The scaling factor is determined jointly by the coordination factor and the degree of mismatch exceeding the threshold and is not lower than a preset lower limit. At the same time, the feedforward compensation amount is determined based on the current command angular velocity of the rotary axis and applied to the rotary axis servo speed loop. In the non-mismatch segment, no scaling factor is applied and no feedforward compensation is applied. S3. Real-time reading of the position feedback of each axis, calculation of tracking error, and projection onto the profile normal direction. The difference between the normal tracking error components of the rotation axis and the linear axis is taken as the inter-axis synchronization deviation. When the synchronization deviation exceeds the positive threshold, the coordination coefficient is increased according to the preset step size rule. When the synchronization deviation is lower than the negative threshold, the coordination coefficient is decreased according to the preset step size rule. When the synchronization deviation is between the positive and negative thresholds, the coordination coefficient remains unchanged. The updated coordination coefficient is fed back to the scaling coefficient calculation stage.

[0005] Preferably, S1 includes: Receive the command position sequences of the linear axis and the rotary axis output by the interpolator, and perform second-order difference on the command position sequences of the linear axis and the rotary axis according to the interpolation period to obtain the command acceleration of the linear axis and the command angular acceleration of the rotary axis. The obtained acceleration command is low-pass filtered; The ratio of the absolute value of the linear axis commanded acceleration to the linear axis acceleration threshold is used to obtain the linear axis acceleration demand ratio. The ratio of the absolute value of the rotary axis commanded angular acceleration to the rotary axis acceleration threshold is used to obtain the rotary axis acceleration demand ratio. The difference between the acceleration demand ratio of the rotating axis and the acceleration demand ratio of the linear axis is used as the mismatch degree between the axes. When the inter-axis mismatch exceeds a preset threshold and meets a preset duration condition, the corresponding trajectory segment is marked as a mismatch risk segment; the preset duration condition is that the number of interpolation cycles in which the inter-axis mismatch continuously exceeds the preset threshold is not less than a preset number of points.

[0006] Preferably, the acceleration threshold of each axis is calibrated by a ramp response experiment: an acceleration-increasing ramp displacement command is applied to the axis under test, the actual displacement response of the axis is monitored, and the maximum command acceleration with the maximum dynamic tracking error not exceeding the allowable value is used as the acceleration threshold of the axis.

[0007] Preferably, S2 includes: The scaling factor of the linear axis feed rate is calculated by combining the coordination coefficient and the difference between the mismatch degree exceeding the threshold, and the scaling factor is not lower than the preset lower limit value. The scaling factor is applied to the linear axis feed rate command to output the corrected linear axis feed rate; while applying the scaling factor to the linear axis feed rate command, the command angular velocity of the rotary axis is synchronously adjusted by the same scaling factor to keep the geometric relationship of the motion trajectory of the linear axis and the rotary axis unchanged. The feedforward compensation amount is determined based on the product of the current commanded angular velocity of the rotary axis and the speed feedforward gain, and this feedforward compensation amount is applied to the rotary axis servo speed loop. When the trajectory segment is in a non-mismatched segment, no scaling factor is applied and no rotation axis feedforward compensation is applied.

[0008] Preferably, the scaling factor is determined by a nonlinear mapping function based on the normalized difference between the coordination factor and the mismatch exceeding a threshold. The nonlinear mapping function satisfies the following: the scaling factor is 1 when the mismatch does not exceed the threshold; the more the mismatch exceeds the threshold, the smaller the scaling factor becomes, but it is not lower than a preset lower limit; and the rate of change of the scaling factor with the normalized difference decreases as the difference increases.

[0009] Preferably, the initial value of the coordination coefficient is:

[0010] In the formula, k c B is the initial value of the coordination coefficient. rot B is the bandwidth of the rotational shaft velocity loop; lin The bandwidth of the linear axis velocity loop; If the calculated initial value is less than the lower limit of the coordination coefficient, the lower limit value is taken as the initial value; if it is greater than the upper limit, the upper limit value is taken as the initial value. The feedforward compensation amount increases from zero to the target compensation amount at a preset ramp rate when entering the mismatch risk section, and decreases from the current compensation amount to zero at a preset ramp rate when exiting the mismatch risk section; during the process of the feedforward compensation amount increasing or decreasing at the ramp rate, the closed-loop correction of the coordination coefficient is suspended; only after the feedforward compensation amount reaches the target value and enters a stable compensation state is it allowed to perform closed-loop correction of the coordination coefficient based on the inter-axis synchronization deviation.

[0011] Preferably, S3 includes: The position feedback of each axis is read in real time, and the difference between the commanded position and the actual position of the linear axis is calculated to obtain the linear axis tracking error. The difference between the commanded angular position and the actual angular position of the rotary axis is calculated to obtain the rotary axis tracking error. Project the linear axis tracking error and the rotation axis tracking error onto the profile normal direction at the current contact point to obtain the linear axis normal component and the rotation axis normal component; The difference between the normal component of the rotation axis and the normal component of the linear axis is taken as the inter-axis synchronization deviation; When the synchronization deviation exceeds the positive threshold, the coordination coefficient is increased according to the preset step size rule; when the synchronization deviation is lower than the negative threshold, the coordination coefficient is decreased according to the preset step size rule; when the synchronization deviation is between the positive and negative thresholds, the coordination coefficient remains unchanged. The updated coordination coefficients are fed back to the scaling coefficient calculation step in step S2.

[0012] Preferably, projecting the tracking error onto the profile normal direction specifically involves multiplying the linear axis tracking error by the cosine of the angle between the current contact point profile normal and the linear axis movement direction to obtain the linear axis normal component, and multiplying the rotation axis angular position tracking error by the current grinding radius and the sine of the angle to obtain the rotation axis normal component.

[0013] Preferably, the coordination coefficient is subject to upper and lower limits. When the corrected coordination coefficient exceeds the limit range, the boundary value is taken, with the lower limit being greater than 0 and the upper limit not exceeding 1.

[0014] Preferably, the step of increasing or decreasing the coordination coefficient according to the preset step size rule specifically means: increasing or decreasing by a fixed step size value, adding the preset step size value to the coordination coefficient when increasing, and subtracting the preset step size value from the coordination coefficient when decreasing; or increasing or decreasing by a fixed proportional step size, multiplying the coordination coefficient by 1 and the sum of the step size ratio when increasing, and multiplying the coordination coefficient by 1 and the difference between the step size ratio when decreasing.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: The intelligent control method for CNC grinding machines proposed in this invention adopts a coordinated strategy of controlled deceleration of linear axes and condition-activated feedforward of rotary axes. Deceleration reduces the target speed that the rotary axis needs to catch up with, making the feedforward compensation change more smoothly in the mismatch section and reducing the possibility of triggering oscillations in the rotary axis speed loop. Feedforward compensates for the efficiency loss caused by deceleration, suppressing profile deviations while reducing the impact on machining efficiency. Based on the acceleration demand ratio, the mismatch between axes is identified, and the dynamic demand of the trajectory is associated with the actual response capability of each axis. When the feed rate is low, even if the curvature change is large, compensation will not be falsely triggered. Coordination is only initiated when the dynamic load difference between axes is significant, avoiding unnecessary intervention in the smooth machining section. Feedforward compensation is activated and deceleration is applied only in the mismatch risk section. In the non-mismatch section, the commands of each axis are not interfered with, reducing the noise disturbance introduced by continuous compensation. The feedforward entry and exit adopts a ramp transition to reduce the impact of sudden current changes during compensation start and stop. The coordination coefficient is corrected according to the measured feedback of the synchronization deviation between axes, so that the deceleration amplitude and feedforward intensity are adaptively adjusted with the working conditions, achieving the purpose of adapting to the drift of axis response characteristics in long-term continuous machining. Attached Figure Description

[0016] Figure 1 This is a flowchart of the intelligent control method for CNC grinding machines according to the present invention. Detailed Implementation

[0017] The following description is intended to disclose the invention and enable those skilled in the art to implement it. The preferred embodiments described below are merely examples, and other obvious variations will occur to those skilled in the art.

[0018] Reference Figure 1As shown, the intelligent control method for CNC grinding machines based on multi-axis linkage accuracy compensation and real-time monitoring includes the following steps: Step 1: Receive the command position sequence of each axis output by the interpolator, obtain the command acceleration of each axis according to the command position sequence, calculate the ratio of the absolute value of the command acceleration of each axis to the corresponding axis acceleration threshold to obtain the acceleration demand ratio, and take the difference between the acceleration demand ratio of the rotary axis and the linear axis participating in the current grinding profile as the axis mismatch degree. When the mismatch degree exceeds the preset threshold and meets the preset continuous condition, it is marked as a mismatch risk segment. Since the acceleration demand ratio is the normalized dimensionless value of the command acceleration of each axis relative to its own acceleration threshold, although the physical dimensions of the linear axis acceleration and the rotary axis angular acceleration are different, the normalized demand ratio can be directly subtracted to measure the relative imbalance of the dynamic load intensity of the two axes.

[0019] Step one includes: Receive the command position sequences of the linear axis and the rotary axis output by the interpolator, and perform second-order difference on the command position sequences of the linear axis and the rotary axis according to the interpolation period to obtain the command acceleration of the linear axis and the command angular acceleration of the rotary axis. The specific calculation formula is as follows: For the linear axis, the command linear acceleration a in the kth interpolation cycle lin (k):

[0020] Among them, P lin (k) represents the linear axis command position (in mm) during the kth interpolation cycle, and T is the interpolation cycle (in seconds); a lin (k) is in mm / s 2 .

[0021] For the rotation axis, the command angular acceleration a in the kth interpolation cycle rot (k):

[0022] Where, θ rot (k) represents the command angular position of the rotation axis in the kth interpolation cycle, in rad; a rot (k) is in rad / s 2 .

[0023] The obtained command acceleration is low-pass filtered; the low-pass filter uses a first-order inertial filter, whose discrete mathematical model is as follows:

[0024] Where a(k) is the original command acceleration in the kth interpolation cycle, a f(k-1) represents the filtered acceleration in the (k-1)th interpolation cycle, and β is the filter coefficient. Its core characteristic is the trade-off between the filter's response speed to the current input and its preservation of historical trends, controlled by the filter coefficient β: a larger β results in faster input response but weaker noise suppression; a smaller β results in smoother output but increased response lag. The range of β values ​​is determined by the interpolation frequency and the frequency of the high-frequency acceleration noise to be suppressed. The cutoff frequency is higher than the upper limit of the actual acceleration / deceleration dynamic frequency and lower than the minimum value of the controlled shaft's mechanical resonance frequency, ensuring that high-frequency noise above resonance is filtered out while retaining low-frequency components reflecting the actual acceleration / deceleration dynamic. If β is less than zero, the filter will completely ignore the current input and fail to track signal changes; if β exceeds 1, the filter's weight on the current input will be too large, and the output will gradually diverge and lose stability. Therefore, the range of β values ​​is greater than zero and does not exceed 1.

[0025] In the initial stage of motion, a zero-order hold initialization method is used, with the initial value of the command acceleration in the first interpolation cycle set to 0. In the second interpolation cycle, a first-order differential approximation is used to calculate the acceleration. From the third interpolation cycle onwards, second-order differential acceleration calculation is enabled, and filtered using a first-order inertial filter to prevent acceleration calculation errors caused by transient filter responses. In the initial stage of motion, due to missing position data from previous interpolation cycles, directly using second-order differential calculation would lead to abnormal jumps in acceleration values, potentially causing misjudgments of mismatch and false triggering of compensation. This initialization method, through zero-order hold and first-order differential transitions, gradually establishes the historical data chain required for second-order differential calculation. Simultaneously, it uses a first-order inertial filter to suppress transient fluctuations, ensuring that the acceleration calculation remains stable from the initial stage of motion and avoiding malfunctions in the compensation system.

[0026] The linear axes participating in the current grinding profile shaping are determined dynamically: In each interpolation cycle, the absolute value of the commanded acceleration of all linear axes is calculated, and the linear axis with the largest absolute acceleration value is selected as the current linear axis participating in compensation. If the absolute values ​​of the commanded acceleration of multiple linear axes are equal, the linear axis with the smallest angle to the normal of the current grinding profile is selected first; if the angles are also the same, the X-axis is selected by default. When the participating axis is switched, the coordination coefficient remains unchanged, and a new closed-loop correction begins after a preset transition period. The transition period should cover the velocity loop and position loop after the participating axis switch. The dynamic adjustment process of the ring is not less than the rounded-up value of the ratio of the step response adjustment time of the switched axis speed ring to the interpolation period, to ensure that each ring regulator has entered a steady state during switching. For example, the transition period can be selected as an integer not less than 10. For grinding machines with fixed processes, the linear axes participating in compensation can also be determined in a pre-specified manner. In multi-linear axis linkage grinding scenarios, the main motion axes of different trajectory segments will change. If a certain linear axis is fixedly selected for compensation, the mismatch calculation will be distorted when the motion amplitude of that axis is small, and the dynamic mismatch between axes cannot be accurately identified. This dynamic judgment method selects the linear axis with the largest acceleration as the compensation axis in real time to ensure that the mismatch calculation always reflects the dynamic load difference between the most active motion axis and the rotary axis. The transition period design during axis switching avoids sudden changes in the coordination coefficient caused by axis switching, ensuring a smooth transition of the compensation system.

[0027] The acceleration demand ratio measures the current dynamic load intensity of an axis by the normalization of the absolute value of the commanded acceleration relative to the acceleration threshold of that axis. A higher demand ratio indicates that the axis is closer to its dynamic response limit, which means that the axis is at a higher risk of a significant increase in tracking error at the current acceleration level. The mismatch between shafts reflects the relative imbalance between the rotary shaft and the linear shaft in terms of dynamic load intensity. When the dynamic load of the rotary shaft accounts for a higher proportion of its response capability than that of the linear shaft, the mismatch is positive, indicating that the rotary shaft is relatively more difficult to follow commands and is more likely to become a weak link in profile accuracy. When the mismatch between axes exceeds a preset threshold and meets a preset continuity condition, the corresponding trajectory segment is marked as a mismatch risk segment. The preset threshold is determined by collecting tracking error data of linear and rotary axes at different feed rates, and statistically analyzing the critical mismatch value corresponding to when the synchronization deviation between axes begins to significantly deviate from the reference value. This threshold must be greater than zero because a zero value means that any small difference in demand ratio will trigger compensation and misjudge normal operating conditions as risk segments. For example, this threshold can be selected to be no more than 1. The preset persistence condition is that the number of interpolation cycles in which the inter-axis mismatch exceeds the preset threshold is not less than the preset number of points. The lower limit of the preset number of points should be sufficient to exclude false triggering caused by occasional noise. A single point anomaly cannot distinguish between noise and trend, two points being consistent may still be accidental, and three or more consecutive points can be initially confirmed as persistent. Therefore, the preset number of points is an integer not less than 3, and the product of the preset number of points and the interpolation cycle is not less than the speed loop step response rise time to ensure that the judgment window covers at least one speed loop dynamic response cycle and excludes transient fluctuations in the speed loop's own adjustment process. For example, the product of the preset number of points and the interpolation cycle can be selected to be not less than one-tenth of the rotational axis speed loop response time to avoid false triggering caused by occasional noise or brief disturbances. The acceleration thresholds for each axis are calibrated through a ramp response experiment: A ramp displacement command with increasing acceleration is applied to the measured axis, and the actual displacement response of the axis is monitored. The maximum command acceleration, where the maximum dynamic tracking error does not exceed the allowable value, is used as the acceleration threshold for that axis. Specifically, starting with a lower command acceleration, the acceleration value of the ramp displacement command is gradually increased, with each increase not exceeding a preset proportion of the previous command acceleration, for example, 10% (relative proportion, i.e., Δa). i ≤0.1·a i-1 The selection of this ratio should ensure that the change in acceleration between two adjacent tests is sufficient to distinguish whether the maximum dynamic tracking error exceeds the allowable value without the step size being too large and skipping the critical value; calculate the maximum dynamic tracking error between the actual displacement and the commanded displacement under each acceleration value, and record the maximum commanded acceleration whose maximum dynamic tracking error does not exceed the allowable value as the acceleration threshold of that axis; The maximum dynamic tracking error criterion is determined based on the maximum allowable dynamic tracking error of the measured axis. This allowable value is usually much smaller than the final contour accuracy requirement of the workpiece. When the maximum difference between the actual displacement and the commanded displacement reaches a preset allowable value, it is determined to exceed the threshold. The lower limit of this preset allowable value should be higher than the measurement noise level, and the upper limit should not exceed the allowable dynamic tracking error of the measured axis. For example, this preset ratio can be selected as 0.5% of the commanded displacement. During calibration, each acceleration value should be tested at least a preset number of times to ensure the repeatability of the results. A single test cannot confirm the repeatability of the results, two tests can only compare consistency but cannot rule out randomness, and three or more tests are needed to confirm that the results are statistically significant. Therefore, this preset number of tests should not be less than 3. For example, each acceleration value should be tested at least 3 times, and the maximum commanded acceleration in which the maximum dynamic tracking error does not exceed the allowable value in all 3 tests should be taken as the acceleration threshold of that axis. Linear axes and rotary axes should be calibrated independently, and the servo parameters of each axis should be consistent with those during actual machining. Step 2: Only within the mismatch risk zone, multiply the linear axis feed rate command by a scaling factor. The scaling factor is determined jointly by the coordination factor and the degree of mismatch exceeding the threshold and is not lower than a preset lower limit. At the same time, determine the feedforward compensation amount based on the current commanded angular velocity of the rotary axis and apply it to the rotary axis servo speed loop. In the non-mismatch zone, do not apply a scaling factor or feedforward compensation. Step two includes: The scaling factor of the linear axis feed rate is calculated jointly based on the difference between the coordination coefficient and the degree of mismatch exceeding the threshold, and this scaling factor is not lower than a preset lower limit. The scaling factor is determined based on the coordination coefficient and the degree of mismatch exceeding the threshold, and is adjusted downward from 1. The larger the coordination coefficient and the greater the degree of mismatch exceeding the threshold, the greater the reduction in feed rate. When the reduction causes the scaling factor to fall below the preset lower limit, the preset lower limit is used to prevent excessive reduction in feed rate from causing deterioration of grinding surface quality or abnormal fluctuations in grinding force. The scaling factor must have a lower limit because an excessively low feed rate will result in insufficient cutting thickness of a single abrasive grain to form an effective cut, and the grinding force will degenerate from a normal cutting state to a scraping state, causing large fluctuations in force and deterioration of surface quality. The lower limit should ensure that the scaled feed rate is still higher than the minimum value required for normal cutting in the grinding process. For example, the preset lower limit of the scaling factor can be selected from 0.2 to 0.8. The grinding force analysis and demonstration are as follows: Maximum undeformed cutting thickness h of a single abrasive grain max With feed rate V f They are directly proportional, and the formula is:

[0028] When the feed rate is below the critical value, h max If the cutting edge radius of the abrasive grain is smaller than the blunt radius of the abrasive grain, the abrasive grain cannot cut into the workpiece material and only produces squeezing and scraping on the surface. At this time, the grinding force will increase significantly, leading to burns, cracks and rapid wear of the grinding wheel on the workpiece surface.

[0029] By setting the lower limit value of the scaling factor λ min This ensures the scaled feed rate:

[0030] Where V f0 V is the original feed rate. f_critical This is the minimum critical feed rate for the grinding process, thereby preventing the grinding condition from deteriorating.

[0031] Applying a scaling factor to the interpolator's feed rate input causes the interpolator to generate the linear axis command position increment according to the scaled feed rate. The output command position sequence naturally matches the actual feed rate, preventing abnormal accumulation of the integral term in the position loop due to inconsistencies between the command and actual rates. Simultaneously, the interpolator synchronously adjusts the rotary axis's command angular velocity according to the same scaling factor, ensuring the geometric relationship between the linear and rotary axes remains unchanged, avoiding profile distortion caused by single-axis deceleration. That is, the rotary axis command angular velocity... , among which ω rot (k) represents the original command angular velocity, and λ is the scaling factor.

[0032] The target value of the feedforward compensation is determined by the current commanded angular velocity of the rotating axis and the speed loop gain. In essence, it is the steady-state tracking deviation generated by the speed loop at the current angular velocity due to the limited gain. This deviation is injected into the speed loop input in advance in the form of feedforward, so that the speed loop generates drive output in advance in the high angular velocity range of the rotating axis, thereby reducing the tracking error of the rotating axis. When the trajectory segment is in a non-mismatch segment, no scaling factor is applied and no rotation axis feedforward compensation is applied; The scaling factor is calculated using an exponential nonlinear mapping function, which avoids the negative value problem of linear formulas, while maintaining the differentiated compensation characteristic that the greater the mismatch, the greater the deceleration.

[0033] First, define the normalized difference when the mismatch exceeds the threshold:

[0034] Where ΔM max The maximum normalized difference is preset (1.0 for example), ensuring that ΔM norm The range of values ​​for ΔM is [0, ΔM] max ] Normalization benchmark selection: preset threshold M th This is because the threshold itself reflects the critical degree of dynamic matching between axes. Normalization based on the threshold can eliminate the influence of differences in the absolute value of the threshold under different working conditions, making the degree of mismatch under different processing conditions comparable. When M th When the typical value is 0.3 to 0.8, (MM) th ) / M th The range is roughly between 0 and 2, in conjunction with ΔM max A 1.0 truncation ensures that the scaling factor changes smoothly within a reasonable range.

[0035] The scaling factor is calculated using the following formula:

[0036] In the formula, λ is the scaling factor, λ mink is the preset lower limit value (dimensionless). c ΔM is the coordination coefficient. norm This is the normalized difference when the mismatch exceeds the threshold.

[0037] When ΔM norm When λ = 0, λ = 1 (no deceleration); as ΔM... norm As λ increases, λ gradually decreases and approaches λ. min This ensures the maximum deceleration range in the event of severe mismatch while avoiding sudden changes in the compensation intensity.

[0038] Coordination coefficient k c The dimensionless coefficient used to adjust the matching relationship between the linear axis deceleration amplitude and the rotary axis feedforward strength, its physical meaning is: the reduction ratio of the linear axis feed rate corresponding to a unit mismatch increment. c The larger the value, the greater the deceleration amplitude of the linear axis under the same mismatch degree, and the stronger the compensation for insufficient dynamic response of the rotary axis.

[0039] The initial value of the coordination coefficient reflects the inherent difference in the dynamic response capabilities of the rotary axis and the linear axis: the closer the speed loop bandwidths of the two axes are, the closer the initial value is to zero, indicating that the dynamic response capabilities of the two axes are matched and no compensation is needed; the lower the speed loop bandwidth of the rotary axis is than that of the linear axis, the larger the initial value is, indicating that the inherent deficiency of the dynamic response capability of the rotary axis is higher and stronger compensation is required. The speed loop bandwidth is tested using a sinusoidal scanning method. During testing, the servo system of the axis under test is first set to closed-loop speed loop control mode, maintaining servo parameters consistent with actual machining. Then, a sinusoidal speed command with a constant amplitude is applied to the speed loop input. The amplitude can be 10% of the rated speed, and the frequency gradually increases from 0.1 Hz. During the test, the speed command signal and the actual speed feedback signal are simultaneously acquired, and the amplitude ratio at each frequency point is calculated, i.e., the ratio of the actual speed amplitude to the commanded speed amplitude. When the amplitude ratio decays to... When the value is approximately 0.707, the corresponding input signal frequency is the speed loop bandwidth of that axis, measured in Hertz. The test is repeated three times, and the average of the three test results is taken as the final speed loop bandwidth value. The initial value of the coordination coefficient is:

[0040] In the formula, k c B is the initial value of the coordination coefficient. rot B is the bandwidth of the rotational shaft velocity loop; lin The bandwidth of the linear axis velocity loop; If the calculated initial value is less than the lower limit of the coordination coefficient, the lower limit value is taken as the initial value; if it is greater than the upper limit, the upper limit value is taken as the initial value.

[0041] The theoretical basis for the initial value formula is: the bandwidth of the velocity loop determines the system's response speed to changes in commands, and the bandwidth ratio B between the rotational axis and the linear axis... rot / B lin This reflects the relative ratio of the dynamic response capabilities of the two axes. When B rot =B lin At this time, the response capabilities of the two axes are perfectly matched, and no deceleration is required (k c0 =0); B rot =0.5B lin At this time, the response speed of the rotating axis is only half that of the linear axis, and the initial value k is... c =0.5 indicates that a unit mismatch increment corresponds to a 50% reduction in feed rate.

[0042] It should be noted that the initial value formula is an approximation derived based on the ideal case where the two axes are only limited by the bandwidth of the speed loop. In actual machining, the hysteresis of the rotary axis is also affected by factors such as position loop gain, friction, and inertia ratio. Therefore, the initial value is only used as a reference value when the system starts up, and will be adaptively adjusted according to the actual synchronization deviation between axes through closed-loop correction.

[0043] The velocity feedforward compensation method is adopted. The target value of the feedforward compensation is determined based on the product of the current commanded angular velocity of the rotating axis and the velocity feedforward gain. The calculation formula is as follows:

[0044] In the formula, u ff (k) represents the target value of the feedforward compensation in the kth interpolation cycle, with units consistent with the speed loop input signal, typically V or A; vff This is the velocity feedforward gain, with units consistent with the velocity loop input unit ·s / rad; ω rot (k) represents the commanded angular velocity of the rotation axis in the kth interpolation cycle, in rad / s.

[0045] Velocity feedforward gain k vff Through experimental calibration: Under closed-loop velocity loop conditions, a step velocity command with constant amplitude is applied, and the steady-state velocity error, k, is measured. vff The gain value that makes the feedforward compensation exactly eliminate the steady-state error is selected. This feedforward compensation is added to the input of the rotary axis servo speed loop in additive form, and together with the output of the speed loop error controller, drives the servo motor.

[0046] When entering the mismatch risk zone, the feedforward compensation amount increases from zero to the target compensation amount at a preset ramp rate, and when exiting the mismatch risk zone, it decreases from the current compensation amount to zero at a preset ramp rate. The feedforward compensation uses a linear ramp function for the cut-in and cut-out transition, with a ramp rate R. ffThe feedforward compensation is determined by the settling time and the maximum rate response capability of the rotating shaft. The specific steps are as follows: The setup time T for the feedforward compensation is set according to process requirements. ramp Calculate the initial ramp rate R ff_init :

[0047] In the formula, u ff_target The target value for the feedforward compensation is set; the ability of this rate to not exceed the maximum rate response of the rotating axis is verified.

[0048] In the formula, R ff_max The maximum ramp rate that the rotating shaft velocity loop can respond to; a rot_th Rotational axis acceleration threshold (unit: rad / s) 2 ).

[0049] The final ramp rate is the smaller of the two:

[0050] In the formula, R ff The feedforward compensation amount is the ramp rate that the system ultimately adopts; The physical meaning of this method is clear: the feedforward compensation amount smoothly reaches the target value within the set establishment time, while ensuring that its rate of change does not exceed the response limit of the rotational shaft velocity loop, thus avoiding velocity loop oscillation.

[0051] When entering the mismatch risk phase, the feedforward compensation amount increases periodically according to the following formula:

[0052] When exiting the mismatch risk segment, the feedforward compensation amount decreases periodically according to the following formula:

[0053] In the formula, u ff (k) represents the feedforward compensation amount for the kth interpolation cycle; u ff (k-1) represents the feedforward compensation amount for the (k-1)th interpolation period; T is the interpolation period, u ff_target (k) represents the target value of the feedforward compensation in the kth interpolation cycle. When entering the mismatch risk section, if the current feedforward compensation is less than the target compensation, it is increased cycle by cycle at the ramp rate until the target compensation is reached; when exiting the mismatch risk section, it is decreased cycle by cycle at the ramp rate until it drops to zero; during the process of the feedforward compensation increasing or decreasing at the ramp rate, the closed-loop correction of the coordination coefficient is suspended; only after the feedforward compensation reaches the target value and enters a stable compensation state is the closed-loop correction of the coordination coefficient based on the inter-axis synchronization deviation allowed.

[0054] The coordination coefficient closed-loop correction and feedforward ramp transition are managed by a state machine for timing coordination. The system switches states through software flags, defined as: uncompensated state, feedforward ramp rising state, stable compensation state, and feedforward ramp falling state. The transition conditions and actions for each state are as follows: The trigger condition for transitioning from the uncompensated state to the feedforward ramp-up state is that the inter-axis mismatch exceeds a preset threshold M for N consecutive interpolation cycles. th Where N is the same as the preset number of points in step one, and is an integer not less than 3, at which point the mismatch risk segment is determined to begin. After entering this state, the system initializes the feedforward compensation to zero and simultaneously disables the coordination coefficient closed-loop correction function.

[0055] When the feedforward slope rises, the system transitions to a stable compensation state if the absolute value of the difference between the current feedforward compensation and the target compensation does not exceed five percent of the target compensation, and this state lasts for at least three interpolation cycles. After entering the stable compensation state, the system activates the coordination coefficient closed-loop correction function.

[0056] The trigger condition for exiting the stable compensation state and entering the feedforward ramp descent state is that the inter-axis mismatch decreases to a preset threshold M for N consecutive interpolation cycles. th In the following steps, where N is the same as the previously mentioned value, the mismatch risk segment is considered to have ended. Upon entering this state, the system disables the coordination coefficient closed-loop correction function and records the current feedforward compensation amount as the starting value for slope descent.

[0057] The trigger condition for returning from the feedforward ramp descent state to the uncompensated state is that the absolute value of the current feedforward compensation amount does not exceed a preset minimum compensation threshold, such as one percent of the target compensation amount. After returning to the uncompensated state, the system resets the feedforward compensation amount to zero and restores the original command output of each axis.

[0058] Upon entering the mismatch risk phase, the system first enters a feedforward ramp-up state, during which the coordination coefficient closed-loop correction remains closed to prevent misjudgment based on an incomplete compensation state before the feedforward quantity is established. Once the feedforward compensation quantity reaches the target value and meets the stability condition, the system enters a stable compensation state and the coordination coefficient closed-loop correction is activated. At this point, the feedforward has fully played its role and the system is in a steady-state compensation condition, allowing the closed-loop correction to accurately adjust the coordination coefficient based on the actual tracking error feedback. Upon exiting the mismatch risk phase, the system first enters a feedforward ramp-down state and the coordination coefficient closed-loop correction is closed. Once the feedforward compensation quantity drops below the minimum threshold, the system returns to the non-compensation state. Step 3: Real-time reading of the position feedback of each axis, calculation of tracking error, and projection onto the profile normal direction. The difference between the normal tracking error components of the rotation axis and the linear axis is taken as the inter-axis synchronization deviation. When the synchronization deviation exceeds the positive threshold, the coordination coefficient is increased according to the preset step size rule. When the synchronization deviation is lower than the negative threshold, the coordination coefficient is decreased according to the preset step size rule. When the synchronization deviation is between the positive and negative thresholds, the coordination coefficient remains unchanged. The updated coordination coefficient is fed back to the scaling coefficient calculation stage. Step three includes: The position feedback of each axis is read in real time, and the deviation between the commanded position and the actual position of each axis is used as the tracking error. The tracking error of the linear axis and the tracking error of the rotary axis are obtained respectively. Projecting the linear axis tracking error and the rotation axis tracking error onto the profile normal direction at the current contact point, respectively, yields the linear axis normal component and the rotation axis normal component. The specific calculation formula is consistent with the claims.

[0059] In the formula, e lin_n e represents the tracking error component along the linear axis normal. lin The linear axis tracking error is expressed in mm; θ is the acute angle between the current contact point profile normal and the direction of linear axis movement; e rot_n e represents the tracking error component along the rotation axis normal. rot Rotary axis angular position tracking error, unit: rad; r is the current grinding radius, unit: mm.

[0060] The derivation process of the geometric relationship is as follows: Let the parameterized generatrix equation of the workpiece profile be r = r(θ). rot ), where θ rot Let be the rotation axis angular position, and r be the grinding radius at the corresponding angular position. The slope of the tangent to the generatrix at the current contact point is ▏dr / dθ. rot (Taking the absolute value eliminates the influence of direction), therefore, the acute angle α between the tangent and the direction of motion of the linear axis (let's say the positive direction of the X-axis) satisfies tanα = ▏dr / dθ rot ▏.

[0061] Since the normal is perpendicular to the tangent, the acute angle between the normal and the direction of motion of the linear axis is θ = 90° - α, i.e., cosθ = sinα, sinθ = cosα. This angle is always within the range of 0° to 90°, ensuring that the projected components are all positive, and the physical meaning is clear.

[0062] When the workpiece profile is a discrete point sequence {(θ) i r i When the input to the system is in the form of i=1,2,...,n}, in each interpolation cycle, the current command angular position θ of the rotation axis is determined. rot(k); where θ i Let r be the rotation axis angle position corresponding to the i-th discrete point; i Let be the grinding radius corresponding to the i-th discrete point; n is the total number of discrete points of the workpiece profile. The current grinding radius r(k) and the generatrix slope dr / dθ are calculated by linear interpolation. rot (k): Find the condition that satisfies θ i ≤θ rot (k)≤θ i+1 Two adjacent discrete points; calculate the current grinding radius:

[0063] Where r(k) is the current grinding radius calculated in the kth interpolation cycle; r i r i+1 Grinding radius of two adjacent discrete points; θ i θ i+1 θ represents the rotation axis angle position corresponding to two adjacent discrete points; rot (k) represents the current commanded angular position of the rotation axis; k is the index of the interpolation cycle; θ rot (k) represents the command angular position of the rotation axis in the kth interpolation cycle; calculate the slope of the busbar:

[0064] Or equivalently represented as:

[0065] Wherein, θ(k) is the acute angle between the profile normal of the kth interpolation cycle and the direction of linear axis movement; the above calculations are all simple arithmetic operations and table lookup interpolation, which can be easily completed within the 1ms interpolation cycle of a conventional CNC system, meeting the real-time requirements.

[0066] The inter-axis synchronization deviation reflects the degree of inconsistency between the tracking errors of the two axes in the direction most sensitive to profile accuracy. A positive value indicates that the normal deviation of the rotating axis is greater than that of the linear axis and the lag of the rotating axis is more severe, while a negative value indicates that the normal deviation of the linear axis is greater. When the synchronization deviation exceeds the positive threshold, the coordination coefficient is increased according to a preset step size rule; when the synchronization deviation is below the negative threshold, the coordination coefficient is decreased according to a preset step size rule; when the synchronization deviation is between the positive and negative thresholds, the coordination coefficient remains unchanged. The positive and negative thresholds are opposites of each other, and their setting method considers both statistical noise and workpiece contour accuracy requirements. Specifically: Statistical noise threshold e noise Under normal machining conditions, data on the synchronous deviation between shafts are collected and their standard deviation σ is calculated. noise =2σ, which can control the probability of false triggering under normal working conditions to below 5%; Contour accuracy threshold e tol Let the required contour error tolerance of the workpiece be δ (unit: mm), then e tol =0.5~0.8·δ, ensuring that the coordination coefficient correction directly serves the final machining accuracy target; Final positive threshold e th+ =max(e noise e tol ), negative threshold e th- =-e th+ .

[0067] The updated coordination coefficients are fed back to the scaling coefficient calculation stage in step two. Control delay and stability verification: This system adopts a closed-loop control structure with a single-cycle delay, meaning the synchronization deviation calculated in the k-th interpolation cycle is used to adjust the coordination coefficient in the (k+1)-th interpolation cycle. For a conventional CNC system with a 1ms interpolation cycle, this delay is much smaller than the response time of the speed loop and position loop (typically 10~20ms), therefore it will not significantly affect the closed-loop stability. By setting reasonable step sizes and dead zones, the system can remain stable even in high-speed machining scenarios.

[0068] The adjustment of the coordination coefficient according to the preset step size rule is implemented in two ways: the first is a fixed step size method, where the adjustment amount is independent of the current value of the coordination coefficient and is suitable for situations where the working range of the coordination coefficient is narrow; the second is a fixed proportional step size method, where the adjustment amount is proportional to the current value of the coordination coefficient and the adjustment range adapts to the size of the coordination coefficient and is suitable for situations where the working range of the coordination coefficient is wide. In both methods, the single adjustment amount should meet the closed-loop stability constraint, that is, the change in the scaling coefficient caused by a single adjustment should not cause a perceptible step jump in the linear axis feed rate. The upper limit of the adjustment amount is determined by reverse derivation of this constraint. For example, the single adjustment amount can be selected to be no more than 10% to 20% of the current value of the coordination coefficient. To analyze the stability of the step size, let the single adjustment amount of the coordination coefficient be Δk. c Then the change in the scaling factor Δλ≈-k c ·ΔM norm ·Δk c (Approximate value under nonlinear mapping). To ensure the stability of the closed-loop system, the change in synchronization deviation caused by a single adjustment must not exceed 1 / 3 of the threshold, i.e., Δe. sync ≤e th+ / 3.

[0069] By experimentally determining the DC gain ▏G(0)▏ between the change in coordination coefficient and the change in synchronization deviation, the maximum allowable step size can be derived. , where G(0) is the DC gain of the transfer function.

[0070] To prevent over-adjustment of the coordination coefficient, the following protection mechanisms are added: When the coordination coefficient is adjusted in the same direction three times in a row, the step size is halved. Three consecutive adjustments in the same direction indicate that the system has a continuous synchronization deviation trend. Reducing the step size can avoid over-adjustment and oscillation caused by excessive adjustment.

[0071] When the sign of the synchronization deviation is opposite to that of the previous cycle, pause the adjustment; strictly enforce the upper and lower limits of the coordination coefficient to ensure k c ∈[k c_min k c_max 】

[0072] The coordination coefficient has upper and lower limits. When the corrected coordination coefficient exceeds the constraint range, the boundary value in the corresponding direction is taken. The lower limit must be greater than zero to ensure that the scaling factor always deviates from 1 when the coordination coefficient is not zero, thus producing a perceptible feed rate reduction effect. At the same time, the deviation of the scaling factor corresponding to the lower limit from 1 should not be less than the system feed rate resolution; otherwise, the scaling effect will be swallowed up by the quantization precision. For example, the lower limit of the coordination coefficient can be selected to be no less than 0.1, and the upper limit can not exceed 1 to prevent the scaling factor from being reduced excessively. The coordination coefficient after the limit is fed back to the scaling factor calculation stage in step two for the calculation of the scaling factor in the next interpolation cycle.

[0073] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention. The scope of protection claimed by the appended claims and their equivalents is defined.

Claims

1. A CNC grinding machine intelligent control method based on multi-axis linkage accuracy compensation and real-time monitoring, characterized in that, Includes the following steps: S1. Receive the command position sequence of each axis output by the interpolator, obtain the command acceleration of each axis according to the command position sequence of each axis, calculate the ratio of the absolute value of the command acceleration of each axis to the corresponding axis acceleration threshold to obtain the acceleration demand ratio, and take the difference between the acceleration demand ratio of the rotary axis and the linear axis participating in the current grinding profile as the axis mismatch degree. When the mismatch degree exceeds the preset threshold and meets the preset continuous condition, it is marked as a mismatch risk segment. S2. Only in the mismatch risk segment, the linear axis feed rate command is multiplied by a scaling factor. The scaling factor is determined jointly by the coordination factor and the degree of mismatch exceeding the threshold and is not lower than a preset lower limit. At the same time, the feedforward compensation amount is determined based on the current command angular velocity of the rotary axis and applied to the rotary axis servo speed loop. In the non-mismatch segment, no scaling factor is applied and no feedforward compensation is applied. S3. Real-time reading of the position feedback of each axis, calculation of tracking error, and projection onto the profile normal direction. The difference between the normal tracking error components of the rotation axis and the linear axis is taken as the inter-axis synchronization deviation. When the synchronization deviation exceeds the positive threshold, the coordination coefficient is increased according to the preset step size rule. When the synchronization deviation is lower than the negative threshold, the coordination coefficient is decreased according to the preset step size rule. When the synchronization deviation is between the positive and negative thresholds, the coordination coefficient remains unchanged. The updated coordination coefficient is fed back to the scaling coefficient calculation stage.

2. The intelligent control method for CNC grinding machines based on multi-axis linkage accuracy compensation and real-time monitoring according to claim 1, characterized in that, S1 includes: Receive the command position sequences of the linear axis and the rotary axis output by the interpolator, and perform second-order difference on the command position sequences of the linear axis and the rotary axis according to the interpolation period to obtain the command acceleration of the linear axis and the command angular acceleration of the rotary axis. The obtained acceleration command is low-pass filtered; The ratio of the absolute value of the linear axis commanded acceleration to the linear axis acceleration threshold is used to obtain the linear axis acceleration demand ratio. The ratio of the absolute value of the rotary axis commanded angular acceleration to the rotary axis acceleration threshold is used to obtain the rotary axis acceleration demand ratio. The difference between the acceleration demand ratio of the rotating axis and the acceleration demand ratio of the linear axis is used as the mismatch degree between the axes. When the inter-axis mismatch exceeds a preset threshold and meets a preset duration condition, the corresponding trajectory segment is marked as a mismatch risk segment; the preset duration condition is that the number of interpolation cycles in which the inter-axis mismatch continuously exceeds the preset threshold is not less than a preset number of points.

3. The intelligent control method for CNC grinding machines based on multi-axis linkage accuracy compensation and real-time monitoring according to claim 2, characterized in that, The acceleration thresholds for each axis are calibrated through a ramp response experiment: an increasing ramp displacement command is applied to the axis under test, the actual displacement response of the axis is monitored, and the maximum command acceleration, whose maximum dynamic tracking error does not exceed the allowable value, is used as the acceleration threshold for that axis.

4. The intelligent control method for CNC grinding machines based on multi-axis linkage accuracy compensation and real-time monitoring according to claim 1, characterized in that, S2 includes: The scaling factor of the linear axis feed rate is calculated by combining the coordination coefficient and the difference between the mismatch degree exceeding the threshold, and the scaling factor is not lower than the preset lower limit value. The scaling factor is applied to the linear axis feed rate command to output the corrected linear axis feed rate; while applying the scaling factor to the linear axis feed rate command, the command angular velocity of the rotary axis is synchronously adjusted by the same scaling factor to keep the geometric relationship of the motion trajectory of the linear axis and the rotary axis unchanged. The feedforward compensation amount is determined based on the product of the current commanded angular velocity of the rotary axis and the speed feedforward gain, and this feedforward compensation amount is applied to the rotary axis servo speed loop. When the trajectory segment is in a non-mismatched segment, no scaling factor is applied and no rotation axis feedforward compensation is applied.

5. The intelligent control method for CNC grinding machines based on multi-axis linkage accuracy compensation and real-time monitoring according to claim 4, characterized in that, The scaling factor is determined by a nonlinear mapping function based on the normalized difference between the coordination factor and the mismatch exceeding a threshold. This nonlinear mapping function satisfies the following conditions: the scaling factor is 1 when the mismatch does not exceed the threshold; the greater the mismatch exceeds the threshold, the smaller the scaling factor becomes, but it is not lower than a preset lower limit; and the rate of change of the scaling factor with the normalized difference decreases as the difference increases.

6. The intelligent control method for CNC grinding machines based on multi-axis linkage accuracy compensation and real-time monitoring according to claim 4, characterized in that, The initial value of the coordination coefficient is: In the formula, k c B is the initial value of the coordination coefficient. rot B is the bandwidth of the rotational shaft velocity loop; lin The bandwidth of the linear axis velocity loop; If the calculated initial value is less than the lower limit of the coordination coefficient, the lower limit value is taken as the initial value; if it is greater than the upper limit, the upper limit value is taken as the initial value. The feedforward compensation amount increases from zero to the target compensation amount at a preset ramp rate when entering the mismatch risk section, and decreases from the current compensation amount to zero at a preset ramp rate when exiting the mismatch risk section; during the process of the feedforward compensation amount increasing or decreasing at the ramp rate, the closed-loop correction of the coordination coefficient is suspended; only after the feedforward compensation amount reaches the target value and enters a stable compensation state is it allowed to perform closed-loop correction of the coordination coefficient based on the inter-axis synchronization deviation.

7. The intelligent control method for CNC grinding machines based on multi-axis linkage accuracy compensation and real-time monitoring according to claim 1, characterized in that, S3 includes: The position feedback of each axis is read in real time, and the difference between the commanded position and the actual position of the linear axis is calculated to obtain the linear axis tracking error. The difference between the commanded angular position and the actual angular position of the rotary axis is calculated to obtain the rotary axis tracking error. Project the linear axis tracking error and the rotation axis tracking error onto the profile normal direction at the current contact point to obtain the linear axis normal component and the rotation axis normal component; The difference between the normal component of the rotation axis and the normal component of the linear axis is taken as the inter-axis synchronization deviation; When the synchronization deviation exceeds the positive threshold, the coordination coefficient is increased according to the preset step size rule; when the synchronization deviation is lower than the negative threshold, the coordination coefficient is decreased according to the preset step size rule; when the synchronization deviation is between the positive and negative thresholds, the coordination coefficient remains unchanged. The updated coordination coefficients are fed back to the scaling coefficient calculation step in step S2.

8. The intelligent control method for CNC grinding machines based on multi-axis linkage accuracy compensation and real-time monitoring according to claim 7, characterized in that, The specific method of projecting the tracking error onto the profile normal direction is as follows: the linear axis tracking error is multiplied by the cosine of the angle between the current contact point profile normal and the linear axis movement direction to obtain the linear axis normal component, and the rotary axis angular position tracking error is multiplied by the current grinding radius and the sine of the angle to obtain the rotary axis normal component.

9. The intelligent control method for CNC grinding machines based on multi-axis linkage accuracy compensation and real-time monitoring according to claim 7, characterized in that, The coordination coefficient is subject to upper and lower limits. When the corrected coordination coefficient exceeds the limit range, the boundary value is taken. The lower limit is greater than 0 and the upper limit is no more than 1.

10. The intelligent control method for CNC grinding machines based on multi-axis linkage accuracy compensation and real-time monitoring according to claim 7, characterized in that, The specific method of increasing or decreasing the coordination coefficient according to the preset step size rule is as follows: increasing or decreasing by a fixed step size value, adding the preset step size value to the coordination coefficient when increasing, and subtracting the preset step size value from the coordination coefficient when decreasing; or increasing or decreasing by a fixed proportional step size, multiplying the coordination coefficient by 1 and the sum of the step size ratio when increasing, and multiplying the coordination coefficient by 1 and the difference between the step size ratio when decreasing.

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