CN115857434B - A self-compensation interference control method for a flexible electronic gearbox - Google Patents

Abstract

The present invention relates to a self-compensating interference control method for a flexible electronic gearbox, and belongs to the technical field of electronic gearboxes. The method is applicable to CNC gear hobbing machines, gear grinding machines, gear honing machines, etc. According to the composite control method of the flexible electronic gearbox, a strict mathematical linkage relationship between the leading axis and the following axis is determined; an anti-disturbance controller is selected as the electronic gearbox controller, and key control parameters in the anti-disturbance controller are determined; the motion law of each motion axis is determined by the process of "diagonal rolling method"; a single-axis compensation model of the following axis is established by utilizing the coupling relationship between the following axis and the leading axis to realize compensation of the anti-disturbance controller of the following axis; the control accuracy of the electronic gearbox is quantitatively given by calculating the maximum value, average value, and root mean square value of the processing error. The present invention can stably improve the control accuracy of the electronic gearbox by about 50% through the self-compensating interference control method of the flexible electronic gearbox, thereby reducing production costs and improving gear processing accuracy.

Description

A self-compensation interference control method for a flexible electronic gearbox

Technical Field

The invention belongs to the field of electronic gear boxes, and in particular relates to a self-compensation interference control method of a flexible electronic gear box.

Background Art

When an electronic gearbox is used to control a motion axis, the motion axis is divided into a leading axis and a following axis; a leading axis refers to a motion axis controlled by a controller having a conventional input, and a following axis refers to a motion axis controlled by a controller that uses the motion law of the leading axis as input; the leading axis of a CNC gear hobbing machine tool includes a B axis for tool rotation, a Y axis for tool tangential feed, and a Z axis for tool axial feed, and the following axis is a C axis for workpiece rotation; the control method of an electronic gearbox in the prior art usually adopts a master-slave control method, in which the output position signals of the controllers of the leading axis B axis, Y axis, and Z axis are used as input position signals of the electronic gearbox, and the output position signals of the electronic gearbox are used as input position signals of the controller of the following axis C axis, thereby maintaining a strict mathematical linkage relationship between the following axis and the leading axis; however, since the controller may have tracking errors, and the CNC gear hobbing machine tool may have internal interference and external interference, secondary control errors are brought to the controller of the following axis C axis, which are ultimately directly reflected in the control accuracy of the electronic gearbox, so the control method of the electronic gearbox in the prior art has the problem of low control accuracy.

Since the C-axis controller of the following axis has the problem of secondary control error, the common method is to consider using various modern controllers or improving the controller method to reduce the controller tracking error, thereby indirectly improving the control accuracy of the electronic gearbox. The solution of simply reducing the tracking error of the controller does not fundamentally solve the problem of secondary control error of the C-axis controller of the following axis, because the controller will always have tracking error and the CNC gear machine tool will have internal interference and external interference. In order to solve this problem, we should start from the control method and controller selection of the electronic gearbox. The present invention provides a self-compensation interference control method of the electronic gearbox.

Summary of the invention

In order to improve the control accuracy of a flexible electronic gearbox, the present invention provides a self-compensation interference control method for a flexible electronic gearbox.

1. A self-compensation interference control method for a flexible electronic gearbox, wherein the flexible electronic gearbox is a software module in a gear numerical control system that uses mathematical operations to realize the movement of a motion axis according to a strict speed ratio relationship based on the setting value of a gear machine tool processing process parameter; by determining the motion axis controller, the flexible electronic gearbox executes the motion obtained by the operation to realize the processing of a CNC gear hobbing machine tool; the CNC gear hobbing machine tool has an X-axis for radial feed of a tool, a Y-axis for tangential feed of a tool, a Z-axis for axial feed of a tool, an A-axis for adjusting the tool installation angle, a B-axis for tool rotation, and a C-axis for workpiece rotation; the motion axis is divided into a guide axis and a follower axis. There are two types of following axes; the leading axis is the main motion, which are the B axis for tool rotation, the Y axis for tool tangential feed and the Z axis for tool axial feed; the following axis is the slave motion, which is the C axis for workpiece rotation; the input signal of the B axis for tool rotation is the first position signal, the input signal of the X axis for tool radial feed is the second position signal, the input signal of the Y axis for tool tangential feed is the third position signal, and the input signal of the Z axis for tool axial feed is the fourth position signal; the flexible electronic gearbox realizes the control function based on the semi-physical simulation platform Dspace, which is characterized in that the self-compensation interference control operation steps are as follows:

(1) Determine the flexible electronic gearbox control method

The flexible electronic gearbox adopts a composite control method, wherein the composite control method is to use the output position signal obtained by the first position signal through the guide axis B axis, the initial input position signal before the third position signal passes through the guide axis Y axis, and the initial input position signal before the fourth position signal passes through the guide axis Z axis, and these three position signals are directly used as the input position signal of the flexible electronic gearbox; and the output position signal of the flexible electronic gearbox is directly used as the input position signal of the follower axis C axis, so that the strict mathematical linkage relationship of formula (1) is maintained between the follower axis C axis and the three guide axes;

In formula (1), _Zb is the number of tool heads, dimensionless; _Zc is the number of workpiece teeth, dimensionless; _nc is the C-axis speed of the following axis, in r/s; _nb is the B-axis speed of the leading axis, in r/s; _vy is the Y-axis moving speed of the leading axis, in mm/s; _vz is the Z-axis moving speed of the leading axis, in mm/s; β is the helix angle of the gear, in degrees; λ is the installation angle of the tool, in degrees; _mn is the normal module of the gear, dimensionless; _Kb is the B-axis coefficient of the leading axis, dimensionless; _Ky is the Y-axis coefficient of the leading axis, dimensionless; _Kz is the Z-axis coefficient of the leading axis, dimensionless; when the helix angle of the hob is right-handed, β>0 and _Kb =1; when the helix angle is left-handed, β<0 and _Kb =-1; when β and _vz have the same sign, _Kz =-1, and when they have opposite signs, _Kz =1; when _vy >0, _Ky =1, when v _y <0, _Ky =-1;

(2) Select the motion axis controller parameters

The motion axis controller of the flexible electronic gearbox is controlled by an auto-disturbance rejection controller, which includes a tracking differentiator, a linear state error feedback module and an extended state observer; parameters β ₁ and β ₂ in the linear state error feedback module and parameter b ₀ in the extended state observer are selected as basic parameters of the auto-disturbance rejection controller to control the motion of the motion axis; the four position signals are respectively obtained by adjusting the input position signal through the auto-disturbance rejection controller to obtain four interference-removed position signals for outputting system interference elimination, and the four interference-removed position signals are respectively four compensation signals for compensating the interference existing in the motion axis controller based on the auto-disturbance rejection controller;

(3) Determine the motion law of the motion axis using the “diagonal rolling method”

When the "diagonal rolling method" is used to process gears, the B axis of the tool rotates around its own axis, the X axis of the tool radial feed is responsible for the tool feed and retract before cutting, and the Y axis of the tool tangential feed and the Z axis of the tool axial feed move simultaneously during cutting to form a motion law of diagonal movement; from step (1), it can be seen that the motion law of the following axis C is determined by the output position signal of the flexible electronic gearbox; the motion law of the following axis C is obtained by synthesizing the motion laws of the three guide axes B axis, Y axis and Z axis according to the relationship of formula (1);

(3.1) The B-axis motion law of the tool rotation is to rotate at a constant speed, and the first position signal is a straight line that rises at a uniform speed;

(3.2) The X-axis of the radial feed of the tool does not participate in the cutting process. The motion law is that the tool first feeds in the positive radial direction of the workpiece before cutting; it remains stationary during cutting; and the tool retracts in the negative radial direction of the workpiece after cutting is completed. The second position signal is a trapezoidal motion law. The trapezoidal motion law of the second position signal is that the left hypotenuse of the trapezoid is the feed motion, the right hypotenuse is the retract motion, and the upper bottom is a static state.

(3.3) The Y axis of the tool tangential feed participates in the cutting process, and the motion rule is to remain motionless before cutting; when the tool cuts the workpiece, the tool first feeds in the positive direction of the tangent of the workpiece; after the cutting is completed, wait for the X axis to retract to a safe position; the tool retracts in the negative direction of the tangent of the workpiece; the third position signal is a trapezoidal motion rule, and the trapezoidal motion rule of the third position signal is that the left hypotenuse of the trapezoid is the feed motion, the right hypotenuse is the retract motion, and the upper bottom is a static state;

(3.4) The Z axis of the tool axial feed participates in the cutting process, and the motion rule is to remain motionless before cutting; when the tool cuts the workpiece, the tool first feeds in the positive axial direction of the workpiece; after the cutting is completed, wait for the X axis to retract to a safe position; the tool retracts in the negative axial direction of the workpiece; the fourth position signal is a trapezoidal motion rule, and the trapezoidal motion rule of the fourth position signal is that the left hypotenuse of the trapezoid is the feed motion, the right hypotenuse is the retract motion, and the upper bottom is a static state;

(4) Establishing a single-axis compensation model for the C-axis

By using the coupling relationship between the following axis C-axis, the X-axis of the tool radial feed and the Y-axis of the tool tangential feed, a single-axis compensation model of the following axis C-axis is established to realize the self-disturbance rejection controller compensation of the following axis C-axis; the steps for establishing the single-axis compensation model of the following axis C-axis are as follows:

(4.1) The output position signal of the flexible electronic gearbox is used to obtain the tracking error E _c through the anti-disturbance control of the following axis C, and the tracking error E _c is multiplied by the proportional coefficient K _cc to obtain the compensation amount ΔE _c of the following axis C;

ΔE _c ＝K _cc E _c (2)

In formula (2), ΔE _c is the compensation amount of the following axis C axis, in mm; E _c is the tracking error of the following axis C axis, in mm; K _cc is the proportional coefficient of the tracking error of the following axis C axis, dimensionless;

(4.2) The second position signal is passed through the X-axis anti-disturbance controller of the tool radial feed to obtain the tracking error _Ex , and the tracking error _Ex is multiplied by the proportional coefficient _Kcx to obtain the compensation amount _ΔEx of the X-axis of the tool radial feed;

ΔE _x =K _cx E _x (3)

In formula (3), _ΔEx is the compensation amount of the X-axis of the tool radial feed, in mm; _Ex is the X-axis tracking error of the tool radial feed, in mm; _Kcx is the proportional coefficient of the X-axis tracking error of the tool radial feed, dimensionless;

(4.3) The third position signal is passed through the Y-axis anti-disturbance controller of the tool tangential feed to obtain the tracking error E _y , and the tracking error E _y is multiplied by the proportional coefficient K _cy to obtain the compensation amount ΔE _y of the Y-axis of the tool tangential feed;

ΔE _y ＝K _cy E _y (4)

In formula (4), ΔE _y is the compensation amount of the Y axis of the tool tangential feed, in mm; E _y is the Y axis tracking error of the tool tangential feed, in mm; K _cy is the proportional coefficient of the Y axis tracking error of the tool tangential feed, dimensionless;

(4.4) Add the compensation amount ΔE _c of the following axis C, the compensation amount ΔE _x of the tool radial feed X axis, and the compensation amount ΔE _y of the tool tangential feed Y axis to obtain the total compensation amount E _ccc ;

E _ccc =(ΔE _c +ΔE _x +ΔE _y ) (5)

In formula (5), E _ccc is the total compensation amount, in mm; ΔE _c is the compensation amount of the following axis C, in mm; ΔE _x is the compensation amount of the X-axis of the tool radial feed, in mm; ΔE _y is the compensation amount of the Y-axis of the tool tangential feed, in mm;

(4.5) Multiply the total compensation amount E _ccc by the proportional coefficient Ke _ccc to obtain the final compensation value ΔE'_c;

ΔE′ _c =K _eccc E _ccc +σ′ _c (6)

In formula (6), _ΔE'c is the final compensation value, in mm; _Eccc is the total compensation, in mm; _Keccc is the proportional coefficient of the total compensation, dimensionless; _σ'c is the correction value, which is determined according to the actual situation, in mm;

(4.6) Subtract the final compensation value _ΔE'c from the tracking error _Ec of the following axis C to obtain the input position signal ΔE" _c of the following axis C's active disturbance rejection controller, thereby compensating for the tracking error of the active disturbance rejection controller of the following axis C and improving the control accuracy of the flexible electronic gearbox;

ΔE″ _c ＝ΔE′ _c -E _c (7)

In formula (7), ΔE” _c is the input position signal of the C-axis ADRC of the following axis, in mm; ΔE' _c is the final compensation value of the C-axis of the following axis, in mm; E _c is the tracking error of the C-axis of the following axis, in mm;

(5) Calculate the processing error value

The three evaluation indicators of machining error are established based on the relative position relationship between the tool and the workpiece during gear hobbing, namely, the tooth profile deviation F _α , see formula (8); the pitch deviation F _p , see formula (9); the tooth guide deviation F _β , see formula (10);

In formula (8): _Fα is the tooth profile deviation, in mm; _Zc is the number of teeth of the workpiece, dimensionless; _mn is the normal module of the workpiece, dimensionless; α is the pressure angle of the workpiece, in degrees; β is the helix angle of the workpiece, in degrees; _Ec is the C-axis tracking error of the workpiece rotation, in mm; _Ex is the X-axis tracking error of the tool radial feed, in mm; _Ey is the Y-axis tracking error of the tool tangential feed, in mm; _Ea is the A-axis tracking error of the tool installation angle adjustment, in degrees; _Kαc is the proportional coefficient of the following axis C axis, which takes a value of 1 or -1, dimensionless; _Kαx is the proportional coefficient of the X-axis of the tool radial feed, which takes a value of 1 or -1, dimensionless; _Kαy is the proportional coefficient of the Y-axis of the tool tangential feed, which takes a value of 1 or -1, dimensionless; _σα is the tooth profile deviation correction, which is determined by the processing parameters and the characteristic parameters of the machine tool, in mm;

In formula (9): _Fp is the pitch deviation, in mm; _Zc is the number of teeth of the workpiece, dimensionless; _mn is the normal module of the workpiece, dimensionless; α is the pressure angle of the workpiece, in degrees; β is the helix angle of the workpiece, in degrees; _Ec is the C-axis tracking error of the workpiece rotation, in mm; _Ex is the X-axis tracking error of the tool radial feed, in mm; _Ey is the Y-axis tracking error of the tool tangential feed, in mm; _Ea is the A-axis tracking error of the tool installation angle adjustment, in degrees; _Kpc is the proportional coefficient of the following axis C axis, which takes a value of 1 or -1, dimensionless; _Kpx is the proportional coefficient of the X-axis of the tool radial feed, which takes a value of 1 or -1, dimensionless; _Kpy is the proportional coefficient of the Y-axis of the tool tangential feed, which takes a value of 1 or -1, dimensionless; _σp is the pitch deviation correction, which is determined by the processing parameters and the characteristic parameters of the machine tool, in mm;

In formula (10), F _β is the tooth deviation, in mm; Z _c is the number of teeth of the workpiece, dimensionless; m _n is the normal module of the workpiece, dimensionless; α is the pressure angle of the workpiece, in degrees; β is the helix angle of the workpiece, in degrees; E _c is the C-axis tracking error of the workpiece rotation, in mm; E _y is the Y-axis tracking error of the tool tangential feed, in mm; E _z is the Z-axis tracking error of the tool axial feed, in mm; K _βc is the proportional coefficient of the following axis C axis, which is 1 or -1, dimensionless; K _βy is the proportional coefficient of the Y-axis of the tool tangential feed, which is 1 or -1, dimensionless; K _βz is the proportional coefficient of the Z-axis of the tool axial feed, which is 1 or -1, dimensionless; σ _β is the tooth deviation correction, which is determined by the machining process parameters and the characteristic parameters of the machine tool, in mm;

The calculation methods of maximum value, average value and root mean square value are introduced to realize the quantitative calculation of tooth profile deviation F _α , tooth pitch deviation F _p and tooth direction deviation F _β which are the evaluation indicators of machining error;

When the self-compensation interference control method of the flexible electronic gearbox is adopted, the maximum values of the tooth profile deviation, tooth pitch deviation and tooth direction deviation are shown in formula (11); the average values of the tooth profile deviation, tooth pitch deviation and tooth direction deviation are shown in formula (12); the root mean square value of the tooth profile deviation, tooth pitch deviation and tooth direction deviation is shown in formula (13);

M _α =max(|F _α |); M _p =max(|F _p |); M _β =max(|F _β |) (11)

In formula (11), M _α is the maximum value of tooth profile deviation, in mm; M _p is the maximum value of pitch deviation, in mm; M _β is the maximum value of tooth guide deviation, in mm;

In formula (12), A _α is the average value of tooth profile deviation, in mm; A _p is the average value of pitch deviation, in mm; A _β is the average value of tooth direction deviation, in mm; n is the number of data points collected in the total cycle, k is a positive integer ranging from 1 to n, dimensionless;

In formula (13), R _α is the root mean square value of the tooth profile deviation, in mm; R _p is the root mean square value of the pitch deviation, in mm; R _β is the root mean square value of the tooth direction deviation, in mm; n is the number of data points collected in the total period, k is a positive integer ranging from 1 to n and is dimensionless.

2. The self-compensation interference control method of a flexible electronic gearbox according to claim 1 is characterized in that: the specific implementation process of the motion law in step (3) is as follows:

(3.1) The B-axis motion law of the tool rotation is to rotate at a constant speed, and the first position signal is a straight line with a slope of 0.8 to 1 and a uniform rising speed;

(3.2) The X-axis of the radial feed of the tool does not participate in the cutting process. The movement law is that the speed increases uniformly within 0-5s, with a slope of 1 to 1.2; it remains unchanged within 5-10s, with a slope of 0; it decreases uniformly to 0 within 10-15s, with a slope of -1.2 to -1; it remains unchanged within 15-20s, with a slope of 0;

(3.3) The Y axis of the tool tangential feed participates in the cutting process. The movement law is that it remains unchanged within 0-5s, with a slope of 0; it increases uniformly within 5-10s, with a slope of 2 to 2.2; it remains unchanged within 10-15s, with a slope of 0; it decreases uniformly to 0 within 15-20s, with a slope of -2.2 to -2;

(3.4) The Z axis of the tool axial feed participates in the cutting process. The movement law is that it remains unchanged within 0-5s, with a slope of 0; it increases uniformly within 5-10s, with a slope of 4 to 4.2; it remains unchanged within 10-15s, with a slope of 0; and it decreases uniformly to 0 within 15-20s, with a slope of -4.2 to -4.

The beneficial technical effects of the present invention are embodied in the following aspects:

(1) The present invention provides a self-compensating interference control method for a flexible electronic gearbox. By designing a control method for a composite electronic gearbox, it is possible to avoid the tracking error of the guide axis from causing a secondary control error to the follower axis. By adopting an anti-disturbance controller, it is possible to eliminate the influence of internal and external interference on the controller of a CNC gear hobbing machine. By utilizing the coupling relationship between the follower axis C-axis, the X-axis for radial feed of the tool, and the Y-axis for tangential feed of the tool, a single-axis compensation model for the follower axis C-axis is established to realize self-disturbance control compensation for the follower axis C-axis. These methods improve the gear machining accuracy. The control accuracy of the electronic gearbox is stably improved by about 50%, thereby improving the machining accuracy of the CNC gear hobbing machine.

(2) The self-compensation interference control method of a flexible electronic gearbox of the present invention can be applied to CNC machine tools such as gear grinding machines and gear honing machines, and does not require different controllers to be designed for different CNC gear machine tools, and has wide applicability.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a schematic diagram of the distribution of the motion axes of a gear hobbing machine;

FIG2 is a schematic diagram of a self-compensation interference control process of a flexible electronic gearbox;

Figure 3 is a schematic diagram of an active disturbance rejection controller;

FIG4 is a schematic diagram of the motion law of the motion axis controller;

FIG5 is a schematic diagram of a single-axis compensation model of the follower axis C-axis.

DETAILED DESCRIPTION

In order to more specifically describe the technical means for implementing the present invention and the innovative features, the technical solution of the present invention is further described in detail below through embodiments in conjunction with the accompanying drawings.

Example 1

A self-compensation interference control method for a flexible electronic gearbox, wherein the flexible electronic gearbox is a software module in a gear numerical control system that uses mathematical operations to realize the movement of a motion axis according to a strict speed ratio relationship based on the setting value of a gear machine tool processing process parameter; by determining the motion axis controller, the flexible electronic gearbox executes the motion obtained by the operation to realize the processing of a CNC gear hobbing machine tool. Referring to FIG1 , the CNC gear hobbing machine tool has an X-axis for radial feed of the tool, a Y-axis for tangential feed of the tool, a Z-axis for axial feed of the tool, an A-axis for adjusting the tool installation angle, a B-axis for tool rotation, and a C-axis for workpiece rotation. The motion axis is divided into two categories: a leading axis and a following axis; the leading axis is the main motion, which is the B-axis for tool rotation, the Y-axis for tool tangential feed, and the Z-axis for tool axial feed; the following axis is the slave motion, which is the C-axis for workpiece rotation. The input signal of the B axis of tool rotation is the first position signal, the input signal of the X axis of tool radial feed is the second position signal, the input signal of the Y axis of tool tangential feed is the third position signal, and the input signal of the Z axis of tool axial feed is the fourth position signal. The flexible electronic gearbox realizes the control function based on the semi-physical simulation platform Dspace. The operation steps of self-compensation interference control are as follows:

The parameters for gear hobbing in this embodiment 1 are selected as follows:

The tool parameters are: right-handed hob, normal module _mn is 1, hob head number _Zb is 1, hob pressure angle α is 20°, hob helix angle λ is 1.97°, installation angle γ is 23.07°, hob axial feed _Vz <0, hob tangential feed _Vy >0; the parameters of the workpiece are: gear normal module _mn is 1, gear tooth number _Zc is 65, gear pressure angle α is 20°, gear is right-handed, and helix angle β is 15°.

The specific operation steps of the self-compensation interference control method of the flexible electronic gearbox are as follows:

(1) Determine the flexible electronic gearbox control method

The composite control process of the flexible electronic gearbox is shown in Figure 2. The composite control method is to use the output position signal obtained by the first position signal through the guide axis B axis, the initial input position signal before the guide axis Y axis through the third position signal, and the initial input position signal before the guide axis Z axis through the fourth position signal. These three position signals are directly used as the input position signal of the flexible electronic gearbox; and the output position signal of the flexible electronic gearbox is directly used as the input position signal of the follower axis C axis, so that the strict mathematical linkage relationship of formula (1) is maintained between the follower axis C axis and the three guide axes;

In formula (1), _Zb is the number of tool heads, dimensionless; _Zc is the number of workpiece teeth, dimensionless; _nc is the C-axis speed of the following axis, in r/s; _nb is the B-axis speed of the leading axis, in r/s; _vy is the Y-axis moving speed of the leading axis, in mm/s; _vz is the Z-axis moving speed of the leading axis, in mm/s; β is the helix angle of the gear, in degrees; λ is the installation angle of the tool, in degrees; _mn is the normal module of the gear, dimensionless; _Kb is the B-axis coefficient of the leading axis, dimensionless; _Ky is the Y-axis coefficient of the leading axis, dimensionless; _Kz is the Z-axis coefficient of the leading axis, dimensionless; when the helix angle of the hob is right-handed, β>0 and _Kb =1; when the helix angle is left-handed, β<0 and _Kb =-1; when β and _vz have the same sign, _Kz =-1, and when they have opposite signs, _Kz =1; when _vy >0, _Ky =1, when v _y <0, _Ky =-1;

n _c =0.0154n _b +0.0013v _z +0.0049v _y (1)

Substitute specific data into formula (1); K _b takes the value of 1, K _z takes the value of 1, and _Ky takes the value of 1; The value is 0.0154; The value is 0.0013; The value is 0.0049;

(2) Select the motion axis controller parameters

The motion axis controller of the flexible electronic gearbox is controlled by an auto-disturbance rejection controller; the auto-disturbance rejection controller includes a tracking differentiator, a linear state error feedback module and an extended state observer, see Figure 3. The parameters β ₁ = 200, β ₂ = 0.5 in the linear state error feedback module and the parameter b ₀ = 5 in the extended state observer are selected as the basic parameters of the auto-disturbance rejection controller to control the motion of the motion axis. The four position signals are respectively obtained by adjusting the input position signal through the auto-disturbance rejection controller to obtain four interference-removed position signals that eliminate system interference. The four interference-removed position signals are respectively four compensation signals based on the auto-disturbance rejection controller to compensate for the interference existing in the motion axis controller;

(3) Determine the motion law of the motion axis using the “diagonal rolling method”

When the "diagonal rolling method" is used to process gears, the B axis of the tool rotates around its own axis, the X axis of the tool radial feed is responsible for the tool feed and retract before cutting, and the Y axis of the tool tangential feed and the Z axis of the tool axial feed move simultaneously during cutting to form a diagonal movement law, see Figure 4. From step (1), it can be seen that the movement law of the following axis C is determined by the output position signal of the flexible electronic gearbox; the movement law of the following axis C is obtained by synthesizing the movement laws of the three guide axes B axis, Y axis and Z axis according to the relationship of formula (1);

(3.1) The B-axis motion law of the tool rotation is to rotate at a constant speed, and the first position signal is a straight line with a slope of 0.8 and a uniform rising speed.

(3.2) The X-axis of the radial feed of the tool does not participate in the cutting process. The motion law is that within 0-5s, the tool first feeds into the workpiece in the positive radial direction with a slope of 1; within 5-10s, it remains stationary during cutting with a slope of 0; within 10-15s, the cutting tool is completed and the tool retracts in the negative radial direction of the workpiece with a slope of -1; within 15-20s, it remains stationary with a slope of 0. The second position signal is a trapezoidal motion law. The trapezoidal motion law of the second position signal is that the left hypotenuse of the trapezoid is the feed motion, the right hypotenuse is the retract motion, and the upper base is a static state.

(3.3) The Y axis of the tool tangential feed participates in the cutting process, and the motion law is to remain motionless within 0-5s, with a slope of 0; when the tool cuts the workpiece within 5-10s, the tool first feeds in the positive direction of the workpiece tangentially, with a slope of 2; within 10-15s, the cutting is completed and the X axis is waited for to retract to a safe position, with a slope of 0; within 15-20s, the tool retracts in the negative direction of the workpiece tangentially, with a slope of -2. The third position signal is a trapezoidal motion law. The trapezoidal motion law of the third position signal is that the left hypotenuse of the trapezoid is the feed motion, the right hypotenuse is the retract motion, and the upper bottom is static.

(3.4) The Z axis of the tool axial feed participates in the cutting process, and the motion law is to remain motionless within 0-5s, with a slope of 0; when the tool cuts the workpiece within 5-10s, the tool first feeds in the positive axial direction of the workpiece, with a slope of 4; within 10-15s, the cutting is completed and the X axis is waited for to retract to a safe position, with a slope of 0; within 15-20s, the tool retracts in the negative axial direction of the workpiece, with a slope of -4. The fourth position signal is a trapezoidal motion law. The trapezoidal motion law of the fourth position signal is that the left hypotenuse of the trapezoid is the feed motion, the right hypotenuse is the retract motion, and the upper bottom is a static state.

(4) Establishing a single-axis compensation model for the C-axis

By using the coupling relationship between the following axis C axis, the X axis of the tool radial feed and the Y axis of the tool tangential feed, a single-axis compensation model of the following axis C axis is established to realize the self-disturbance rejection controller compensation of the following axis C axis, as shown in Figure 5. The steps for establishing the single-axis compensation model of the following axis C axis are as follows:

(4.1) The output position signal of the flexible electronic gearbox is used to obtain the tracking error E _c through the anti-disturbance control of the following axis C, and the tracking error E _c is multiplied by the proportional coefficient K _cc to obtain the compensation amount ΔE _c of the following axis C;

ΔE _c ＝K _cc E _c (2)

In formula (2), ΔE _c is the compensation amount of the following axis C axis, in mm; E _c is the tracking error of the following axis C axis, in mm; K _cc is the proportional coefficient of the tracking error of the following axis C axis, dimensionless;

ΔE _c ＝E _c (2)

Substitute specific data into formula (2); K _cc takes the value of 1;

(4.2) The second position signal is passed through the X-axis anti-disturbance controller of the tool radial feed to obtain the tracking error _Ex , and the tracking error _Ex is multiplied by the proportional coefficient _Kcx to obtain the compensation amount _ΔEx of the X-axis of the tool radial feed;

ΔE _x =K _cx E _x (3)

In formula (3), _ΔEx is the compensation amount of the X-axis of the tool radial feed, in mm; _Ex is the X-axis tracking error of the tool radial feed, in mm; _Kcx is the proportional coefficient of the X-axis tracking error of the tool radial feed, dimensionless;

ΔE _x = 0.6198E _x (3)

Substitute the specific data into formula (3); K _cx takes the value of 0.6198;

(4.3) The third position signal is passed through the Y-axis anti-disturbance controller of the tool tangential feed to obtain the tracking error E _y , and the tracking error E _y is multiplied by the proportional coefficient K _cy to obtain the compensation amount ΔE _y of the Y-axis of the tool tangential feed;

ΔE _y ＝K _cy E _y (4)

In formula (4), ΔE _y is the compensation amount of the Y axis of the tool tangential feed, in mm; E _y is the Y axis tracking error of the tool tangential feed, in mm; K _cy is the proportional coefficient of the Y axis tracking error of the tool tangential feed, dimensionless;

ΔE _y =1.7019E _y (4)

Substitute specific data into formula (4); K _cy is taken as 1.7019;

(4.4) Add the compensation amount ΔE _c of the following axis C, the compensation amount ΔE _x of the tool radial feed X axis, and the compensation amount ΔE _y of the tool tangential feed Y axis to obtain the total compensation amount E _ccc ;

E _ccc =(ΔE _c +ΔE _x +ΔE _y ) (5)

In formula (5), E _ccc is the total compensation amount, in mm; ΔE _c is the compensation amount of the following axis C, in mm; ΔE _x is the compensation amount of the X-axis of the tool radial feed, in mm; ΔE _y is the compensation amount of the Y-axis of the tool tangential feed, in mm;

E _ccc ＝E _c +0.6198E _x +1.7019E _y (5)

Substitute specific data into formula (5);

(4.5) Multiply the total compensation amount E _ccc by the proportional coefficient Ke _ccc to obtain the final compensation value ΔE'_c;

ΔE′ _c =K _eccc E _ccc +σ′ _c (6)

In formula (6), _ΔE'c is the final compensation value, in mm; _Eccc is the total compensation, in mm; _Keccc is the proportional coefficient of the total compensation, dimensionless; _σ'c is the correction value, which is determined according to the actual situation, in mm;

ΔE′ _c =E _c +0.6198E _x +1.7019E _y (6)

Substitute specific data into formula (6); K _eccc takes the value of 1; σ′ _c takes the value of 0;

(4.6) Subtract the final compensation value _ΔE'c from the tracking error _Ec of the following axis C to obtain the input position signal ΔE" _c of the following axis C's active disturbance rejection controller, thereby compensating for the tracking error of the active disturbance rejection controller of the following axis C and improving the control accuracy of the flexible electronic gearbox;

ΔE″ _c ＝ΔE′ _c -E _c (7)

In formula (7), ΔE” _c is the input position signal of the C-axis ADRC of the following axis, in mm; ΔE' _c is the final compensation value of the C-axis of the following axis, in mm; E _c is the tracking error of the C-axis of the following axis, in mm;

ΔE″ _c =0.6198E _x +1.7019E _y (7)

Substitute specific data into formula (7);

(5) Calculate the processing error value

The three evaluation indicators of machining error are established based on the relative position relationship between the tool and the workpiece during gear hobbing, namely, the tooth profile deviation F _α , see formula (8); the pitch deviation F _p , see formula (9); the tooth guide deviation F _β , see formula (10);

In formula (8): _Fα is the tooth profile deviation, in mm; _Zc is the number of teeth of the workpiece, dimensionless; _mn is the normal module of the workpiece, dimensionless; α is the pressure angle of the workpiece, in degrees; β is the helix angle of the workpiece, in degrees; _Ec is the C-axis tracking error of the workpiece rotation, in mm; _Ex is the X-axis tracking error of the tool radial feed, in mm; _Ey is the Y-axis tracking error of the tool tangential feed, in mm; _Ea is the A-axis tracking error of the tool installation angle adjustment, in degrees; _Kαc is the proportional coefficient of the following axis C axis, which takes a value of 1 or -1, dimensionless; _Kαx is the proportional coefficient of the X-axis of the tool radial feed, which takes a value of 1 or -1, dimensionless; _Kαy is the proportional coefficient of the Y-axis of the tool tangential feed, which takes a value of 1 or -1, dimensionless; _σα is the tooth profile deviation correction, which is determined by the processing parameters and the characteristic parameters of the machine tool, in mm;

F _α =0.5518E _c +0.3420E _x +0.8645cosE _a E _y (8)

Substitute specific data into formula (8); K _αc is 1, K _αx is 1, and K _αy is 1; The value is 0.5518; the value of sinα is 0.3420; the value of cosγcosα is 0.8645; the value of σ _α is 0;

In formula (9): _Fp is the pitch deviation, in mm; _Zc is the number of teeth of the workpiece, dimensionless; _mn is the normal module of the workpiece, dimensionless; α is the pressure angle of the workpiece, in degrees; β is the helix angle of the workpiece, in degrees; _Ec is the C-axis tracking error of the workpiece rotation, in mm; _Ex is the X-axis tracking error of the tool radial feed, in mm; _Ey is the Y-axis tracking error of the tool tangential feed, in mm; _Ea is the A-axis tracking error of the tool installation angle adjustment, in degrees; _Kpc is the proportional coefficient of the following axis C axis, which takes a value of 1 or -1, dimensionless; _Kpx is the proportional coefficient of the X-axis of the tool radial feed, which takes a value of 1 or -1, dimensionless; _Kpy is the proportional coefficient of the Y-axis of the tool tangential feed, which takes a value of 1 or -1, dimensionless; _σp is the pitch deviation correction, which is determined by the processing parameters and the characteristic parameters of the machine tool, in mm;

F _p ＝0.5872E _c +0.3640E _x +0.9200cosE _a E _y (9)

Substitute specific data into formula (9); K _pc is 1, K _px is 1, and K _py is 1; The value is 0.5872; tanα is 0.3640; cosγ is 0.9200; σ _p is 0;

In formula (10), F _β is the tooth deviation, in mm; Z _c is the number of teeth of the workpiece, dimensionless; m _n is the normal module of the workpiece, dimensionless; α is the pressure angle of the workpiece, in degrees; β is the helix angle of the workpiece, in degrees; E _c is the C-axis tracking error of the workpiece rotation, in mm; E _y is the Y-axis tracking error of the tool tangential feed, in mm; E _z is the Z-axis tracking error of the tool axial feed, in mm; K _βc is the proportional coefficient of the following axis C axis, which is 1 or -1, dimensionless; K _βy is the proportional coefficient of the Y-axis of the tool tangential feed, which is 1 or -1, dimensionless; K _βz is the proportional coefficient of the Z-axis of the tool axial feed, which is 1 or -1, dimensionless; σ _β is the tooth deviation correction, which is determined by the machining process parameters and the characteristic parameters of the machine tool, in mm;

_Fβ ＝0.5872E _c +0.9200E _y +0.2679E _z (10)

Substitute specific data into formula (10); K _βc is 1, K _βy is 1, and K _βz is 1; The value is 0.5872; the value of cosγ is 0.9200; the value of tanβ is 0.2679; the value of _σβ is 0;

The calculation methods of maximum value, average value and root mean square value are introduced to realize the quantitative calculation of tooth profile deviation F _α , tooth pitch deviation F _p and tooth direction deviation F _β which are the evaluation indicators of machining error;

When the self-compensation interference control method of the flexible electronic gearbox is adopted, the maximum values of the tooth profile deviation, tooth pitch deviation and tooth direction deviation are shown in formula (11); the average values of the tooth profile deviation, tooth pitch deviation and tooth direction deviation are shown in formula (12); the root mean square value of the tooth profile deviation, tooth pitch deviation and tooth direction deviation is shown in formula (13);

M _α =max(|F _α |); M _p =max(|F _p |); M _β =max(|F _β |) (11)

In formula (11), M _α is the maximum value of tooth profile deviation, in mm; M _p is the maximum value of pitch deviation, in mm; M _β is the maximum value of tooth guide deviation, in mm;

M _α =0.00632; M _p =0.00616; M _β =0.00872 (11)

Substitute specific data into formula (11); E _c , _Ex , E _y , E _z and E _a are the tracking errors of the self-compensation disturbance control method of the flexible electronic gearbox during actual operation;

In formula (12), A _α is the average value of tooth profile deviation, in mm; A _p is the average value of pitch deviation, in mm; A _β is the average value of tooth direction deviation, in mm; n is the number of data points collected in the total cycle, k is a positive integer ranging from 1 to n, dimensionless;

A _α =0.00058; A _p =0.00059; A _β =0.00073 (12)

Substitute specific data into formula (12); E _c , _Ex , E _y , E _z and E _a are the tracking errors of the self-compensation disturbance control method of the flexible electronic gearbox during actual operation;

In formula (13), R _α is the root mean square value of the tooth profile deviation, in mm; R _p is the root mean square value of the pitch deviation, in mm; R _β is the root mean square value of the tooth direction deviation, in mm; n is the number of data points collected in the total period, k is a positive integer ranging from 1 to n and is dimensionless.

R _α =0.00091; R _p =0.00091; R _β =0.00113 (13)

Substitute specific data into formula (13); E _c , _Ex , E _y , E _z and E _a are the tracking errors of the self-compensation disturbance control method of the flexible electronic gearbox during actual operation;

The control method of the electronic gearbox in the prior art is different from the control method of the electronic gearbox in the flexible electronic gearbox of the present invention in step (1); the control method of the electronic gearbox in the prior art adopts a master-slave control method, and the master-slave control method is to use the output position signals of the controllers of the three guide axes B axis, Y axis and Z axis as the input position signals of the electronic gearbox, and the output position signals of the electronic gearbox as the input position signals of the controller of the following axis C axis, so that a strict mathematical linkage relationship is maintained between the following axis C axis and the three guide axes; the other steps in the control method of the electronic gearbox in the prior art are the same as the other steps of the flexible electronic gearbox of the present invention, and the maximum values of the tooth profile deviation, tooth pitch deviation and tooth direction deviation are obtained by implementing the control method of the electronic gearbox in the prior art, see formula (14); the average values of the tooth profile deviation, tooth pitch deviation and tooth direction deviation are see formula (15); the root mean square values of the tooth profile deviation, tooth pitch deviation and tooth direction deviation are see formula (16).

M _α ′ = 0.01770; M _p ′ = 0.01720; M _β ′ = 0.02508 (14)

In formula (14), M _α ′ is the maximum value of the tooth profile deviation of the control method of the electronic gearbox in the prior art, and the unit is mm; M _p ′ is the maximum value of the tooth pitch deviation of the control method of the electronic gearbox in the prior art, and the unit is mm; M _β ′ is the maximum value of the tooth guide deviation of the control method of the electronic gearbox in the prior art, and the unit is mm.

A _α ′ = 0.00113; A _p ′ = 0.00112; A _β ′ = 0.00133 (15)

In formula (15), A _α ′ is the average value of the tooth profile deviation of the control method of the electronic gearbox in the prior art, in mm; A _p ′ is the average value of the tooth pitch deviation of the control method of the electronic gearbox in the prior art, in mm; A _β ′ is the average value of the tooth guide deviation of the control method of the electronic gearbox in the prior art, in mm;

R _α ′ = 0.00191; R _p ′ = 0.00195; R _β ′ = 0.00231 (16)

In formula (16), R _α ′ is the root mean square value of the tooth profile deviation of the control method of the electronic gearbox in the prior art, in mm; R _p ′ is the root mean square value of the pitch deviation of the control method of the electronic gearbox in the prior art, in mm; R _β ′ is the root mean square value of the tooth guide deviation of the control method of the electronic gearbox in the prior art, in mm;

Compared with the control method of the electronic gearbox in the prior art, the self-compensating interference control method of the flexible electronic gearbox adopts a maximum value of the tooth profile deviation reduced from 0.01770mm in the control method of the electronic gearbox in the prior art to 0.00632mm in the self-compensating interference control method of the flexible electronic gearbox, an average value of the tooth profile deviation reduced from 0.00113mm in the control method of the electronic gearbox in the prior art to 0.00058mm in the self-compensating interference control method of the flexible electronic gearbox, and a root mean square value of the tooth profile deviation reduced from 0.00191mm in the control method of the electronic gearbox in the prior art to 0.00091mm in the self-compensating interference control method of the flexible electronic gearbox; the maximum value of the pitch deviation reduced from 0.01720mm in the control method of the electronic gearbox in the prior art to 0.00616mm in the self-compensating interference control method of the flexible electronic gearbox, and an average value of the pitch deviation reduced from 0.00113mm in the control method of the electronic gearbox in the prior art to 0.00058mm in the self-compensating interference control method of the flexible electronic gearbox. The control method of the electronic gearbox is reduced from 0.00112mm to 0.00059mm in the self-compensating interference control method of the flexible electronic gearbox, and the root mean square value of the pitch deviation is reduced from 0.00195mm in the control method of the electronic gearbox in the prior art to 0.00091mm in the self-compensating interference control method of the flexible electronic gearbox; the maximum value of the tooth deviation is reduced from 0.02508mm in the control method of the electronic gearbox in the prior art to 0.00872mm in the self-compensating interference control method of the flexible electronic gearbox, the average value of the tooth deviation is reduced from 0.00133mm in the control method of the electronic gearbox in the prior art to 0.00073mm in the self-compensating interference control method of the flexible electronic gearbox, and the root mean square value of the tooth deviation is reduced from 0.00231mm in the control method of the electronic gearbox in the prior art to 0.00113mm in the self-compensating interference control method of the flexible electronic gearbox.

It can be seen that the self-compensating interference control method of the flexible electronic gearbox of the present invention, when evaluating the tooth profile deviation, pitch deviation and tooth direction deviation from the perspective of maximum value, average value and root mean square value, the obtained accuracy is much higher than the control method of the electronic gearbox in the prior art, and the accuracy can be stably improved by about 50%. Therefore, the flexible electronic gearbox of the present invention can improve the gear processing accuracy.

Example 2

A self-compensation interference control method for a flexible electronic gearbox, wherein the flexible electronic gearbox is a software module in a gear numerical control system that uses mathematical operations to realize the movement of a motion axis according to a strict speed ratio relationship based on the setting value of a gear machine tool processing process parameter; by determining the motion axis controller, the flexible electronic gearbox executes the motion obtained by the operation to realize the processing of a CNC gear hobbing machine tool. Referring to FIG1 , the CNC gear hobbing machine tool has an X-axis for radial feed of the tool, a Y-axis for tangential feed of the tool, a Z-axis for axial feed of the tool, an A-axis for adjusting the tool installation angle, a B-axis for tool rotation, and a C-axis for workpiece rotation. The motion axis is divided into two categories: a leading axis and a following axis; the leading axis is the main motion, which is the B-axis for tool rotation, the Y-axis for tool tangential feed, and the Z-axis for tool axial feed; the following axis is the slave motion, which is the C-axis for workpiece rotation. The input signal of the B axis of tool rotation is the first position signal, the input signal of the X axis of tool radial feed is the second position signal, the input signal of the Y axis of tool tangential feed is the third position signal, and the input signal of the Z axis of tool axial feed is the fourth position signal. The flexible electronic gearbox realizes the control function based on the semi-physical simulation platform Dspace. The operation steps of self-compensation interference control are as follows:

The parameters for gear hobbing in this embodiment 2 are selected as follows:

The tool parameters are: left-handed hob, normal module _mn is 2, hob head number _Zb is 1, hob pressure angle α is 20°, hob helix angle λ is 2.03°, installation angle γ is 21.38°, hob axial feed _Vz >0, hob tangential feed _Vy <0; the parameters of the workpiece being processed are: gear normal module _mn is 2, gear tooth number _Zc is 49, gear pressure angle α is 20°, the gear is left-handed, and the helix angle β is -15°.

The specific operation steps of the self-compensation interference control method of the flexible electronic gearbox are as follows:

(1) Determine the flexible electronic gearbox control method

The composite control process of the flexible electronic gearbox is shown in Figure 2. The composite control method is to use the output position signal obtained by the first position signal through the guide axis B axis, the initial input position signal before the third position signal through the guide axis Y axis, and the initial input position signal before the fourth position signal through the guide axis Z axis as the input position signal of the flexible electronic gearbox; and the output position signal of the flexible electronic gearbox is directly used as the input position signal of the follower axis C axis, so that the strict mathematical linkage relationship of formula (1) is maintained between the follower axis C axis and the three guide axes;

In formula (1), _Zb is the number of tool heads, dimensionless; _Zc is the number of workpiece teeth, dimensionless; _nc is the C-axis speed of the following axis, in r/s; _nb is the B-axis speed of the leading axis, in r/s; _vy is the Y-axis moving speed of the leading axis, in mm/s; _vz is the Z-axis moving speed of the leading axis, in mm/s; β is the helix angle of the gear, in degrees; λ is the installation angle of the tool, in degrees; _mn is the normal module of the gear, dimensionless; _Kb is the B-axis coefficient of the leading axis, dimensionless; _Ky is the Y-axis coefficient of the leading axis, dimensionless; _Kz is the Z-axis coefficient of the leading axis, dimensionless; when the helix angle of the hob is right-handed, β>0 and _Kb =1; when the helix angle is left-handed, β<0 and _Kb =-1; when β and _vz have the same sign, _Kz =-1, and when they have opposite signs, _Kz =1; when _vy >0, _Ky =1, when v _y <0, _Ky =-1;

n _c =-0.0204n _b -0.0008v _z -0.0032v _y (1)

Substitute specific data into formula (1); K _b takes the value of -1, K _z takes the value of 1, and _Ky takes the value of -1; The value is 0.0204; The value is -0.0008; The value is 0.0032;

(2) Select the motion axis controller parameters

The motion axis controller of the flexible electronic gearbox is controlled by an auto-disturbance rejection controller; the auto-disturbance rejection controller includes a tracking differentiator, a linear state error feedback module and an extended state observer, see Figure 3. The parameters β ₁ = 135, β ₂ = 1 in the linear state error feedback module and the parameter b ₀ = 6 in the extended state observer are selected as the basic parameters of the auto-disturbance rejection controller to control the motion of the motion axis. The four position signals are respectively obtained by adjusting the input position signal through the auto-disturbance rejection controller to obtain four interference-removed position signals that eliminate system interference. The four interference-removed position signals are respectively four compensation signals based on the auto-disturbance rejection controller to compensate for the interference existing in the motion axis controller;

(3) Determine the motion law of the motion axis using the “diagonal rolling method”

When the "diagonal rolling method" is used to process gears, the B axis of the tool rotates around its own axis, the X axis of the tool radial feed is responsible for the tool feed and retract before cutting, and the Y axis of the tool tangential feed and the Z axis of the tool axial feed move simultaneously during cutting to form a diagonal movement law, see Figure 4. From step (1), it can be seen that the movement law of the following axis C is determined by the output position signal of the flexible electronic gearbox; the movement law of the following axis C is obtained by synthesizing the movement laws of the three guide axes B axis, Y axis and Z axis according to the relationship of formula (1);

(3.1) The B-axis motion law of the tool rotation is to rotate at a constant speed, and the first position signal is a straight line with a slope of 1 and a uniform rising speed.

(3.2) The X-axis of the radial feed of the tool does not participate in the cutting process. The motion law is that within 0-5s, the tool first feeds into the workpiece in the positive radial direction with a slope of 1.2; it remains stationary during cutting within 5-10s with a slope of 0; within 10-15s, the cutting tool is completed and the tool retracts in the negative radial direction of the workpiece with a slope of -1.2; it remains stationary within 15-20s with a slope of 0. The second position signal is a trapezoidal motion law. The trapezoidal motion law of the second position signal is that the left hypotenuse of the trapezoid is the feed motion, the right hypotenuse is the retract motion, and the upper base is a static state.

(3.3) The Y axis of the tool tangential feed participates in the cutting process. The motion law is to remain motionless within 0-5s, with a slope of 0; when the tool cuts the workpiece within 5-10s, the tool first feeds in the positive direction of the workpiece tangentially, with a slope of 2.2; within 10-15s, the cutting is completed and the X axis is waited for to retract to a safe position, with a slope of 0; within 15-20s, the tool retracts in the negative direction of the workpiece tangentially, with a slope of -2.2. The third position signal is a trapezoidal motion law. The trapezoidal motion law of the third position signal is that the left hypotenuse of the trapezoid is the feed motion, the right hypotenuse is the retract motion, and the upper bottom is static.

(3.4) The Z axis of the tool axial feed participates in the cutting process, and the motion law is to remain motionless within 0-5s, with a slope of 0; when the tool cuts the workpiece within 5-10s, the tool first feeds in the positive axial direction of the workpiece, with a slope of 4.2; within 10-15s, the cutting is completed and the X axis is waited for to retract to a safe position, with a slope of 0; within 15-20s, the tool retracts in the negative axial direction of the workpiece, with a slope of -4.2. The fourth position signal is a trapezoidal motion law. The trapezoidal motion law of the fourth position signal is that the left hypotenuse of the trapezoid is the feed motion, the right hypotenuse is the retract motion, and the upper bottom is a static state.

(4) Establishing a single-axis compensation model for the C-axis

By using the coupling relationship between the following axis C axis, the X axis of the tool radial feed and the Y axis of the tool tangential feed, a single-axis compensation model of the following axis C axis is established to realize the self-disturbance rejection controller compensation of the following axis C axis, as shown in Figure 5. The steps for establishing the single-axis compensation model of the following axis C axis are as follows:

(4.1) The output position signal of the flexible electronic gearbox is obtained through the anti-disturbance control of the following axis C to obtain the tracking error E _c , and the tracking error E _c is multiplied by the proportional coefficient K _cc to obtain the compensation amount ΔE _c of the following axis C;

ΔE _c ＝K _cc E _c (2)

In formula (2), ΔE _c is the compensation amount of the following axis C axis, in mm; E _c is the tracking error of the following axis C axis, in mm; K _cc is the proportional coefficient of the tracking error of the following axis C axis, dimensionless;

ΔE _c ＝E _c (2)

Substitute specific data into formula (2); K _cc takes the value of 1;

(4.2) The second position signal is passed through the X-axis anti-disturbance controller of the tool radial feed to obtain the tracking error _Ex , and the tracking error _Ex is multiplied by the proportional coefficient _Kcx to obtain the compensation amount _ΔEx of the X-axis of the tool radial feed;

ΔE _x =K _cx E _x (3)

In formula (3), _ΔEx is the compensation amount of the X-axis of the tool radial feed, in mm; _Ex is the X-axis tracking error of the tool radial feed, in mm; _Kcx is the proportional coefficient of the X-axis tracking error of the tool radial feed, dimensionless;

ΔE _x =0.4111E _x (3)

Substitute the specific data into formula (3); K _cx takes the value of 0.4111;

(4.3) The third position signal is passed through the Y-axis anti-disturbance controller of the tool tangential feed to obtain the tracking error E _y , and the tracking error E _y is multiplied by the proportional coefficient K _cy to obtain the compensation amount ΔE _y of the Y-axis of the tool tangential feed;

ΔE _y ＝K _cy E _y (4)

In formula (4), ΔE _y is the compensation amount of the Y axis of the tool tangential feed, in mm; E _y is the Y axis tracking error of the tool tangential feed, in mm; K _cy is the proportional coefficient of the Y axis tracking error of the tool tangential feed, dimensionless;

ΔE _y =1.0518E _y (4)

Substitute specific data into formula (4); K _cy is taken as 1.0518;

(4.4) Add the compensation amount ΔE _c of the following axis C, the compensation amount ΔE _x of the tool radial feed X axis, and the compensation amount ΔE _y of the tool tangential feed Y axis to obtain the total compensation amount E _ccc ;

E _ccc =(ΔE _c +ΔE _x +ΔE _y ) (5)

In formula (5), E _ccc is the total compensation amount, in mm; ΔE _c is the compensation amount of the following axis C, in mm; ΔE _x is the compensation amount of the X-axis of the tool radial feed, in mm; ΔE _y is the compensation amount of the Y-axis of the tool tangential feed, in mm;

E _ccc ＝E _c +0.4111E _x +1.0518E _y (5)

Substitute specific data into formula (5);

(4.5) Multiply the total compensation amount E _ccc by the proportional coefficient Ke _ccc to obtain the final compensation value ΔE'_c;

ΔE′ _c =K _eccc E _ccc +σ′ _c (6)

In formula (6), _ΔE'c is the final compensation value, in mm; _Eccc is the total compensation, in mm; _Keccc is the proportional coefficient of the total compensation, dimensionless; _σ'c is the correction value, which is determined according to the actual situation, in mm;

ΔE′ _c =E _c +0.4111E _x +1.0518E _y (6)

Substitute specific data into formula (6); K _eccc takes the value of 1; σ′ _c takes the value of 0;

(4.6) Subtract the final compensation value _ΔE'c from the tracking error _Ec of the following axis C to obtain the input position signal ΔE" _c of the following axis C's active disturbance rejection controller, thereby compensating for the tracking error of the active disturbance rejection controller of the following axis C and improving the control accuracy of the flexible electronic gearbox;

ΔE″ _c ＝ΔE′ _c -E _c (7)

In formula (7), ΔE” _c is the input position signal of the C-axis ADRC of the following axis, in mm; ΔE' _c is the final compensation value of the C-axis of the following axis, in mm; E _c is the tracking error of the C-axis of the following axis, in mm;

ΔE″ _c =0.4111E _x +1.0518E _y (7)

Substitute specific data into formula (7);

(5) Calculate the processing error value

The three evaluation indicators of machining error are established based on the relative position relationship between the tool and the workpiece during gear hobbing, namely, the tooth profile deviation F _α , see formula (8); the pitch deviation F _p , see formula (9); the tooth guide deviation F _β , see formula (10);

In formula (8): _Fα is the tooth profile deviation, in mm; _Zc is the number of teeth of the workpiece, dimensionless; _mn is the normal module of the workpiece, dimensionless; α is the pressure angle of the workpiece, in degrees; β is the helix angle of the workpiece, in degrees; _Ec is the C-axis tracking error of the workpiece rotation, in mm; _Ex is the X-axis tracking error of the tool radial feed, in mm; _Ey is the Y-axis tracking error of the tool tangential feed, in mm; _Ea is the A-axis tracking error of the tool installation angle adjustment, in degrees; _Kαc is the proportional coefficient of the following axis C axis, which takes a value of 1 or -1, dimensionless; _Kαx is the proportional coefficient of the X-axis of the tool radial feed, which takes a value of 1 or -1, dimensionless; _Kαy is the proportional coefficient of the Y-axis of the tool tangential feed, which takes a value of 1 or -1, dimensionless; _σα is the tooth profile deviation correction, which is determined by the processing parameters and the characteristic parameters of the machine tool, in mm;

F _α ＝0.8320E _c +0.3420E _x +0.8750cosE _a E _y (8)

Substitute specific data into formula (8); K _αc is 1, K _αx is 1, and K _αy is 1; The value is 0.8320; the value of sinα is 0.3420; the value of cosγcosα is 0.8750; the value of σ _α is 0;

In formula (9): _Fp is the pitch deviation, in mm; _Zc is the number of teeth of the workpiece, dimensionless; _mn is the normal module of the workpiece, dimensionless; α is the pressure angle of the workpiece, in degrees; β is the helix angle of the workpiece, in degrees; _Ec is the C-axis tracking error of the workpiece rotation, in mm; _Ex is the X-axis tracking error of the tool radial feed, in mm; _Ey is the Y-axis tracking error of the tool tangential feed, in mm; _Ea is the A-axis tracking error of the tool installation angle adjustment, in degrees; _Kpc is the proportional coefficient of the following axis C axis, which takes a value of 1 or -1, dimensionless; _Kpx is the proportional coefficient of the X-axis of the tool radial feed, which takes a value of 1 or -1, dimensionless; _Kpy is the proportional coefficient of the Y-axis of the tool tangential feed, which takes a value of 1 or -1, dimensionless; _σp is the pitch deviation correction, which is determined by the processing parameters and the characteristic parameters of the machine tool, in mm;

F _p ＝0.8854E _c +0.3640E _x +0.9312cosE _a E _y (9)

Substitute specific data into formula (9); K _pc is 1, K _px is 1, and K _py is 1; The value is 0.8854; the value of tanα is 0.3640; the value of cosγ is 0.9312; the value of σ _p is 0;

In formula (10), F _β is the tooth deviation, in mm; Z _c is the number of teeth of the workpiece, dimensionless; m _n is the normal module of the workpiece, dimensionless; α is the pressure angle of the workpiece, in degrees; β is the helix angle of the workpiece, in degrees; E _c is the C-axis tracking error of the workpiece rotation, in mm; E _y is the Y-axis tracking error of the tool tangential feed, in mm; E _z is the Z-axis tracking error of the tool axial feed, in mm; K _βc is the proportional coefficient of the following axis C axis, which is 1 or -1, dimensionless; K _βy is the proportional coefficient of the Y-axis of the tool tangential feed, which is 1 or -1, dimensionless; K _βz is the proportional coefficient of the Z-axis of the tool axial feed, which is 1 or -1, dimensionless; σ _β is the tooth deviation correction, which is determined by the machining process parameters and the characteristic parameters of the machine tool, in mm;

F _β ＝0.8854E _c +0.9312E _y -0.2679E _z (10)

Substitute specific data into formula (10); K _βc is 1, K _βy is 1, and K _βz is 1; The value is 0.8854; the value of cosγ is 0.9312; the value of tanβ is -0.2679; the value of _σβ is 0;

The calculation methods of maximum value, average value and root mean square value are introduced to realize the quantitative calculation of tooth profile deviation F _α , tooth pitch deviation F _p and tooth direction deviation F _β which are the evaluation indicators of machining error;

When the self-compensation interference control method of the flexible electronic gearbox is adopted, the maximum values of the tooth profile deviation, tooth pitch deviation and tooth direction deviation are shown in formula (11); the average values of the tooth profile deviation, tooth pitch deviation and tooth direction deviation are shown in formula (12); the root mean square value of the tooth profile deviation, tooth pitch deviation and tooth direction deviation is shown in formula (13);

M _α =max(|F _α |); M _p =max(|F _p |); M _β =max(|F _β |) (11)

In formula (11), M _α is the maximum value of tooth profile deviation, in mm; M _p is the maximum value of pitch deviation, in mm; M _β is the maximum value of tooth guide deviation, in mm;

M _α =0.00641; M _p =0.00635; M _β =0.00429 (11)

Substitute specific data into formula (11); E _c , _Ex , E _y , E _z and E _a are the tracking errors of the self-compensation disturbance control method of the flexible electronic gearbox during actual operation;

In formula (12), A _α is the average value of tooth profile deviation, in mm; A _p is the average value of pitch deviation, in mm; A _β is the average value of tooth direction deviation, in mm; n is the number of data points collected in the total cycle, k is a positive integer ranging from 1 to n, dimensionless;

A _α =0.00029; A _p =0.00030; A _β =0.00022 (12)

Substitute specific data into formula (12); E _c , _Ex , E _y , E _z and E _a are the tracking errors of the self-compensation disturbance control method of the flexible electronic gearbox during actual operation;

In formula (13), R _α is the root mean square value of the tooth profile deviation, in mm; R _p is the root mean square value of the pitch deviation, in mm; R _β is the root mean square value of the tooth direction deviation, in mm; n is the number of data points collected in the total period, k is a positive integer ranging from 1 to n and is dimensionless.

R _α =0.00059; R _p =0.00059; R _β =0.00044 (13)

Substitute specific data into formula (13); E _c , _Ex , E _y , E _z and E _a are the tracking errors of the self-compensation disturbance control method of the flexible electronic gearbox during actual operation;

The control method of the electronic gearbox in the prior art is different from the control method of the electronic gearbox in the flexible electronic gearbox of the present invention in step (1); the control method of the electronic gearbox in the prior art adopts a master-slave control method, and the master-slave control method is to use the output position signals of the controllers of the three guide axes B axis, Y axis and Z axis as the input position signals of the electronic gearbox, and the output position signals of the electronic gearbox as the input position signals of the controller of the following axis C axis, so that a strict mathematical linkage relationship is maintained between the following axis C axis and the three guide axes; the other steps in the control method of the electronic gearbox in the prior art are the same as the other steps of the flexible electronic gearbox of the present invention, and the maximum values of the tooth profile deviation, tooth pitch deviation and tooth direction deviation are obtained by implementing the control method of the electronic gearbox in the prior art, see formula (14); the average values of the tooth profile deviation, tooth pitch deviation and tooth direction deviation are see formula (15); the root mean square values of the tooth profile deviation, tooth pitch deviation and tooth direction deviation are see formula (16).

M _α ′ = 0.01831; M _p ′ = 0.01816; M _β ′ = 0.01104 (14)

In formula (14), M _α ′ is the maximum value of the tooth profile deviation of the control method of the electronic gearbox in the prior art, and the unit is mm; M _p ′ is the maximum value of the tooth pitch deviation of the control method of the electronic gearbox in the prior art, and the unit is mm; M _β ′ is the maximum value of the tooth guide deviation of the control method of the electronic gearbox in the prior art, and the unit is mm.

A _α ′ = 0.00062; A _p ′ = 0.00063; A _β ′ = 0.00047 (15)

In formula (15), A _α ′ is the average value of the tooth profile deviation of the control method of the electronic gearbox in the prior art, in mm; A _p ′ is the average value of the tooth pitch deviation of the control method of the electronic gearbox in the prior art, in mm; A _β ′ is the average value of the tooth guide deviation of the control method of the electronic gearbox in the prior art, in mm;

R _α ′ = 0.00132; R _p ′ = 0.00134; R _β ′ = 0.00095 (16)

In formula (16), R _α ′ is the root mean square value of the tooth profile deviation of the control method of the electronic gearbox in the prior art, in mm; R _p ′ is the root mean square value of the pitch deviation of the control method of the electronic gearbox in the prior art, in mm; R _β ′ is the root mean square value of the tooth guide deviation of the control method of the electronic gearbox in the prior art, in mm;

Compared with the control method of the electronic gearbox in the prior art, the self-compensating interference control method of the flexible electronic gearbox adopts a maximum value of the tooth profile deviation reduced from 0.018311mm in the control method of the electronic gearbox in the prior art to 0.00641mm in the self-compensating interference control method of the flexible electronic gearbox, and the average value of the tooth profile deviation reduced from 0.00062mm in the control method of the electronic gearbox in the prior art to 0.00029mm in the self-compensating interference control method of the flexible electronic gearbox, and the root mean square value of the tooth profile deviation reduced from 0.00132mm in the control method of the electronic gearbox in the prior art to 0.00059mm in the self-compensating interference control method of the flexible electronic gearbox; the maximum value of the pitch deviation reduced from 0.01816mm in the control method of the electronic gearbox in the prior art to 0.00635mm in the self-compensating interference control method of the flexible electronic gearbox, and the average value of the pitch deviation reduced from 0.00062mm in the control method of the electronic gearbox in the prior art to 0.00029mm in the self-compensating interference control method of the flexible electronic gearbox. The maximum value of the tooth deviation is reduced from 0.01104mm in the control method of the electronic gearbox in the prior art to 0.00429mm in the self-compensating interference control method of the flexible electronic gearbox, the average value of the tooth deviation is reduced from 0.00047mm in the control method of the electronic gearbox in the prior art to 0.00022mm in the self-compensating interference control method of the flexible electronic gearbox, and the root mean square value of the tooth deviation is reduced from 0.00095mm in the control method of the electronic gearbox in the prior art to 0.00044mm in the self-compensating interference control method of the flexible electronic gearbox.

It can be seen that the self-compensating interference control method of the flexible electronic gearbox of the present invention, when evaluating the tooth profile deviation, pitch deviation and tooth direction deviation from the perspective of maximum value, average value and root mean square value, the obtained accuracy is much higher than the control method of the electronic gearbox in the prior art, and the accuracy can be stably improved by about 50%. Therefore, the flexible electronic gearbox of the present invention can improve the gear processing accuracy.

Claims (2)

1. A self-compensation interference control method for a flexible electronic gearbox, wherein the flexible electronic gearbox is a software module in a gear numerical control system that uses mathematical operations to realize the movement of a motion axis according to a strict speed ratio relationship based on the setting value of a gear machine tool processing process parameter; by determining the motion axis controller, the flexible electronic gearbox executes the motion obtained by the operation to realize the processing of a CNC gear hobbing machine tool; the CNC gear hobbing machine tool has an X-axis for radial feed of a tool, a Y-axis for tangential feed of a tool, a Z-axis for axial feed of a tool, an A-axis for adjusting the tool installation angle, a B-axis for tool rotation, and a C-axis for workpiece rotation; the motion axis is divided into a guide axis and a follower axis. There are two types of following axes; the leading axis is the main motion, which are the B axis for tool rotation, the Y axis for tool tangential feed and the Z axis for tool axial feed; the following axis is the slave motion, which is the C axis for workpiece rotation; the input signal of the B axis for tool rotation is the first position signal, the input signal of the X axis for tool radial feed is the second position signal, the input signal of the Y axis for tool tangential feed is the third position signal, and the input signal of the Z axis for tool axial feed is the fourth position signal; the flexible electronic gearbox realizes the control function based on the semi-physical simulation platform Dspace, which is characterized in that the self-compensation interference control operation steps are as follows: (1) Determine the flexible electronic gearbox control method The flexible electronic gearbox adopts a composite control method, wherein the composite control method is to use the output position signal obtained by the first position signal through the guide axis B axis, the initial input position signal before the guide axis Y axis through the third position signal, and the initial input position signal before the guide axis Z axis through the fourth position signal, and these three position signals are directly used as the input position signal of the flexible electronic gearbox; and the output position signal of the flexible electronic gearbox is directly used as the input position signal of the follower axis C axis, so that the strict mathematical linkage relationship of formula (1) is maintained between the follower axis C axis and the three guide axes; In formula (1), _Zb is the number of tool heads, dimensionless; _Zc is the number of workpiece teeth, dimensionless; _nc is the speed of the following axis C, in r/s; _nb is the speed of the leading axis B, in r/s; _vy is the moving speed of the leading axis Y, in mm/s; _vz is the moving speed of the leading axis Z, in mm/s; β is the helix angle of the gear, in degrees; λ is the installation angle of the tool, in degrees; _mn is the normal module of the gear, dimensionless; _Kb is the coefficient of the leading axis B, dimensionless; _Ky is the coefficient of the leading axis Y, dimensionless; _Kz is the coefficient of the leading axis Z, dimensionless; when the helix angle of the hob is right-handed, β>0 and _Kb = 1; when the helix angle is left-handed, β<0 and _Kb = -1; when β and _vz have the same sign, _Kz = -1, and when they have opposite signs, _Kz = 1; when _vy >0, _Ky = 1, and when _vy <0, _Ky = -1; (2) Select the motion axis controller parameters The motion axis controller of the flexible electronic gearbox is controlled by an auto-disturbance rejection controller, which includes a tracking differentiator, a linear state error feedback module and an extended state observer; parameters β ₁ and β ₂ in the linear state error feedback module and parameter b ₀ in the extended state observer are selected as basic parameters of the auto-disturbance rejection controller to control the motion of the motion axis; the four position signals are respectively obtained by adjusting the input position signal through the auto-disturbance rejection controller to obtain four interference-removed position signals for outputting system interference elimination, and the four interference-removed position signals are respectively four compensation signals for compensating the interference existing in the motion axis controller based on the auto-disturbance rejection controller; (3) Determine the motion law of the motion axis using the “diagonal rolling method” When the "diagonal rolling method" is used to process gears, the B axis of the tool rotates around its own axis, the X axis of the tool radial feed is responsible for the tool feed and retract before cutting, and the Y axis of the tool tangential feed and the Z axis of the tool axial feed move simultaneously during cutting to form a motion law of diagonal movement; from step (1), it can be seen that the motion law of the following axis C axis is determined by the output position signal of the flexible electronic gearbox; the motion law of the following axis C axis is obtained by synthesizing the motion laws of the three guide axes B axis, Y axis and Z axis according to the relationship of formula (1); (3.1) The B-axis motion law of the tool rotation is to rotate at a constant speed, and the first position signal is a straight line that rises at a uniform speed; (3.2) The X-axis of the radial feed of the tool does not participate in the cutting process. The motion law is that the tool first feeds in the positive radial direction of the workpiece before cutting; it remains stationary during cutting; and the tool retracts in the negative radial direction of the workpiece after cutting is completed. The second position signal is a trapezoidal motion law. The trapezoidal motion law of the second position signal is that the left hypotenuse of the trapezoid is the feed motion, the right hypotenuse is the retract motion, and the upper bottom is a static state. (3.3) The Y-axis of the tool tangential feed participates in the cutting process, and the motion rule is to remain motionless before cutting; when the tool cuts the workpiece, the tool first feeds in the positive direction of the tangent to the workpiece; after the cutting is completed, wait for the X-axis to retract to a safe position; the tool retracts in the negative direction of the tangent to the workpiece; the third position signal is a trapezoidal motion rule, and the trapezoidal motion rule of the third position signal is that the left hypotenuse of the trapezoid is the feed motion, the right hypotenuse is the retract motion, and the upper bottom is a static state; (3.4) The Z axis of the tool axial feed participates in the cutting process, and the motion rule is to remain motionless before cutting; when the tool cuts the workpiece, the tool first feeds in the positive axial direction of the workpiece; after the cutting is completed, wait for the X axis to retract to a safe position; the tool retracts in the negative axial direction of the workpiece; the fourth position signal is a trapezoidal motion rule, and the trapezoidal motion rule of the fourth position signal is that the left hypotenuse of the trapezoid is the feed motion, the right hypotenuse is the retract motion, and the upper bottom is a static state; (4) Establishing a single-axis compensation model for the C-axis By using the coupling relationship between the following axis C-axis, the X-axis of the tool radial feed and the Y-axis of the tool tangential feed, a single-axis compensation model of the following axis C-axis is established to realize the self-disturbance rejection controller compensation of the following axis C-axis; the steps for establishing the single-axis compensation model of the following axis C-axis are as follows: (4.1) The output position signal of the flexible electronic gearbox is used to obtain the tracking error E _c through the anti-disturbance control of the following axis C, and the tracking error E _c is multiplied by the proportional coefficient K _cc to obtain the compensation amount ΔE _c of the following axis C; ΔE _c ＝K _cc E _c (2) In formula (2), ΔE _c is the compensation amount of the following axis C axis, in mm; E _c is the tracking error of the following axis C axis, in mm; K _cc is the proportional coefficient of the tracking error of the following axis C axis, dimensionless; (4.2) The second position signal is passed through the X-axis anti-disturbance controller of the tool radial feed to obtain the tracking error _Ex , and the tracking error _Ex is multiplied by the proportional coefficient _Kcx to obtain the compensation amount _ΔEx of the X-axis of the tool radial feed; ΔE _x =K _cx E _x (3) In formula (3), _ΔEx is the compensation amount of the X-axis of the tool radial feed, in mm; _Ex is the X-axis tracking error of the tool radial feed, in mm; _Kcx is the proportional coefficient of the X-axis tracking error of the tool radial feed, dimensionless; (4.3) The third position signal is passed through the Y-axis anti-disturbance controller of the tool tangential feed to obtain the tracking error E _y , and the tracking error E _y is multiplied by the proportional coefficient K _cy to obtain the compensation amount ΔE _y of the Y-axis of the tool tangential feed; ΔE _y ＝K _cy E _y (4) In formula (4), ΔE _y is the compensation amount of the Y axis of the tool tangential feed, in mm; E _y is the Y axis tracking error of the tool tangential feed, in mm; K _cy is the proportional coefficient of the Y axis tracking error of the tool tangential feed, dimensionless; (4.4) Add the compensation amount ΔE _c of the following axis C, the compensation amount ΔE _x of the tool radial feed X axis, and the compensation amount ΔE _y of the tool tangential feed Y axis to obtain the total compensation amount E _ccc ; E _ccc =(ΔE _c +ΔE _x +ΔE _y ) (5) In formula (5), E _ccc is the total compensation amount, in mm; ΔE _c is the compensation amount of the following axis C, in mm; ΔE _x is the compensation amount of the X-axis of the tool radial feed, in mm; ΔE _y is the compensation amount of the Y-axis of the tool tangential feed, in mm; (4.5) Multiply the total compensation amount E _ccc by the proportional coefficient Ke _ccc to obtain the final compensation value ΔE'_c; ΔE′ _c ＝K _eccc E _ccc +σ′ _c (6) In formula (6), _ΔE'c is the final compensation value, in mm; _Eccc is the total compensation, in mm; _Keccc is the proportional coefficient of the total compensation, dimensionless; _σ'c is the correction value, which is determined according to the actual situation, in mm; (4.6) Subtract the final compensation value _ΔE'c from the tracking error _Ec of the following axis C to obtain the input position signal ΔE" _c of the following axis C's active disturbance rejection controller, thereby compensating for the tracking error of the active disturbance rejection controller of the following axis C and improving the control accuracy of the flexible electronic gearbox; ΔE″ _c ＝ΔE′ _c -E _c (7) In formula (7), ΔE” _c is the input position signal of the C-axis ADRC of the following axis, in mm; ΔE' _c is the final compensation value of the C-axis of the following axis, in mm; E _c is the tracking error of the C-axis of the following axis, in mm; (5) Calculate the processing error value The three evaluation indicators of machining error are established based on the relative position relationship between the tool and the workpiece during gear hobbing, namely, the tooth profile deviation F _α , see formula (8); the pitch deviation F _p , see formula (9); the tooth guide deviation F _β , see formula (10); In formula (8): _Fα is the tooth profile deviation, in mm; _Zc is the number of teeth of the workpiece, dimensionless; _mn is the normal module of the workpiece, dimensionless; α is the pressure angle of the workpiece, in degrees; β is the helix angle of the workpiece, in degrees; _Ec is the C-axis tracking error of the workpiece rotation, in mm; _Ex is the X-axis tracking error of the tool radial feed, in mm; _Ey is the Y-axis tracking error of the tool tangential feed, in mm; _Ea is the A-axis tracking error of the tool installation angle adjustment, in degrees; _Kαc is the proportional coefficient of the following axis C axis, which takes a value of 1 or -1, dimensionless; _Kαx is the proportional coefficient of the X-axis of the tool radial feed, which takes a value of 1 or -1, dimensionless; _Kαy is the proportional coefficient of the Y-axis of the tool tangential feed, which takes a value of 1 or -1, dimensionless; _σα is the tooth profile deviation correction, which is determined by the processing parameters and the characteristic parameters of the machine tool, in mm; In formula (9): _Fp is the pitch deviation, in mm; _Zc is the number of teeth of the workpiece, dimensionless; _mn is the normal module of the workpiece, dimensionless; α is the pressure angle of the workpiece, in degrees; β is the helix angle of the workpiece, in degrees; _Ec is the C-axis tracking error of the workpiece rotation, in mm; _Ex is the X-axis tracking error of the tool radial feed, in mm; _Ey is the Y-axis tracking error of the tool tangential feed, in mm; _Ea is the A-axis tracking error of the tool installation angle adjustment, in degrees; _Kpc is the proportional coefficient of the following axis C axis, which takes a value of 1 or -1, dimensionless; _Kpx is the proportional coefficient of the X-axis of the tool radial feed, which takes a value of 1 or -1, dimensionless; _Kpy is the proportional coefficient of the Y-axis of the tool tangential feed, which takes a value of 1 or -1, dimensionless; _σp is the pitch deviation correction, which is determined by the processing parameters and the characteristic parameters of the machine tool, in mm; In formula (10), F _β is the tooth deviation, in mm; Z _c is the number of teeth of the workpiece, dimensionless; m _n is the normal module of the workpiece, dimensionless; α is the pressure angle of the workpiece, in degrees; β is the helix angle of the workpiece, in degrees; E _c is the C-axis tracking error of the workpiece rotation, in mm; E _y is the Y-axis tracking error of the tool tangential feed, in mm; E _z is the Z-axis tracking error of the tool axial feed, in mm; K _βc is the proportional coefficient of the following axis C axis, which is 1 or -1, dimensionless; K _βy is the proportional coefficient of the Y-axis of the tool tangential feed, which is 1 or -1, dimensionless; K _βz is the proportional coefficient of the Z-axis of the tool axial feed, which is 1 or -1, dimensionless; σ _β is the tooth deviation correction, which is determined by the machining process parameters and the characteristic parameters of the machine tool, in mm; The calculation methods of maximum value, average value and root mean square value are introduced to realize the quantitative calculation of tooth profile deviation F _α , tooth pitch deviation F _p and tooth direction deviation F _β which are the evaluation indicators of machining error; When the self-compensation interference control method of the flexible electronic gearbox is adopted, the maximum values of the tooth profile deviation, tooth pitch deviation and tooth direction deviation are shown in formula (11); the average values of the tooth profile deviation, tooth pitch deviation and tooth direction deviation are shown in formula (12); the root mean square value of the tooth profile deviation, tooth pitch deviation and tooth direction deviation is shown in formula (13); M _α = max(|F _α |); M _p = max(|F _p |); M _β = max(|F _β |) (11) In formula (11), M _α is the maximum value of tooth profile deviation, in mm; M _p is the maximum value of pitch deviation, in mm; M _β is the maximum value of tooth guide deviation, in mm; In formula (12), A _α is the average value of tooth profile deviation, in mm; A _p is the average value of pitch deviation, in mm; A _β is the average value of tooth direction deviation, in mm; n is the number of data points collected in the total cycle, k is a positive integer ranging from 1 to n, dimensionless; In formula (13), R _α is the root mean square value of the tooth profile deviation, in mm; R _p is the root mean square value of the pitch deviation, in mm; R _{β is} the root mean square value of the tooth direction deviation, in mm; n is the number of data points collected in the total period, k is a positive integer ranging from 1 to n and is dimensionless. 2. The self-compensation interference control method of a flexible electronic gearbox according to claim 1 is characterized in that: the specific implementation process of the motion law in step (3) is as follows: (3.1) The B-axis motion law of the tool rotation is to rotate at a constant speed, and the first position signal is a straight line with a slope of 0.8 to 1 and a uniform rising speed; (3.2) The X-axis of the radial feed of the tool does not participate in the cutting process. The movement law is that the speed increases uniformly within 0-5s, with a slope of 1 to 1.2; it remains unchanged within 5-10s, with a slope of 0; it decreases uniformly to 0 within 10-15s, with a slope of -1.2 to -1; it remains unchanged within 15-20s, with a slope of 0; (3.3) The Y axis of the tool tangential feed participates in the cutting process. The movement law is that it remains unchanged within 0-5s, with a slope of 0; it increases uniformly within 5-10s, with a slope of 2 to 2.2; it remains unchanged within 10-15s, with a slope of 0; it decreases uniformly to 0 within 15-20s, with a slope of -2.2 to -2; (3.4) The Z axis of the tool axial feed participates in the cutting process. The movement law is that it remains unchanged within 0-5s, with a slope of 0; it increases uniformly within 5-10s, with a slope of 4 to 4.2; it remains unchanged within 10-15s, with a slope of 0; and it decreases uniformly to 0 within 15-20s, with a slope of -4.2 to -4.