CN115857434B - Self-compensating interference control method of flexible electronic gear box - Google Patents
Self-compensating interference control method of flexible electronic gear box Download PDFInfo
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Abstract
The invention relates to a self-compensating interference control method of a flexible electronic gear box, and belongs to the technical field of electronic gear boxes. The method is suitable for a numerical control gear hobbing machine, a gear grinding machine, a gear honing machine and the like. According to the compound control method of the flexible electronic gear box, the strict mathematical linkage relation between the guide shaft and the following shaft is determined; selecting an active disturbance rejection controller as an electronic gear box controller, and determining key control parameters in the active disturbance rejection controller; determining the motion rule of each motion axis through a process of a diagonal roll cutting method; the coupling relation between the following shaft and the guide shaft is utilized to establish a single-shaft compensation model of the following shaft, so that the compensation of the active disturbance rejection controller of the following shaft is realized; the control accuracy of the electronic gear box is quantitatively given by calculating the maximum value, the average value and the root mean square value of the machining errors. According to the self-compensating interference control method of the flexible electronic gear box, the control precision of the electronic gear box can be stably improved by about 50%, so that the production cost is reduced and the gear machining precision is improved.
Description
Technical Field
The invention belongs to the field of electronic gearboxes, and particularly relates to a self-compensating interference control method of a flexible electronic gearbox.
Background
When the motion axis is controlled using the electronic gear box, the motion axis is divided into a guide axis and a following axis; the guide shaft means a movement shaft controlled by a controller having a normal input, and the following shaft means a movement shaft controlled by a controller as an input according to a movement rule of the guide shaft; the guide shaft of the numerical control gear hobbing machine tool comprises a B shaft for turning a cutter, a Y shaft for tangential feeding of the cutter, a Z shaft for axial feeding of the cutter, and a C shaft for turning a workpiece along the following shaft; in the prior art, a master-slave control method is generally adopted in the control method of the electronic gear box, wherein the master-slave control method takes the output position signals of the controllers of the guide shaft B shaft, the Y shaft and the Z shaft as the input position signals of the electronic gear box, and the output position signals of the electronic gear box are taken as the input position signals of the controller of the following shaft C shaft, so that a strict mathematical linkage relation is kept between the following shaft and the guide shaft; however, the controller has the problems of tracking error, internal interference, external interference and the like, and secondary control error is brought to the following shaft C-axis controller, and finally, the secondary control error is directly reflected on the control precision of the electronic gear box, so that the control method of the electronic gear box in the prior art has the problem of low control precision.
Because of the problem of secondary control errors of the following-axis C-axis controller, a common method is to consider the use of various modern controllers or methods for improving the controllers to reduce the tracking errors of the controllers, thereby indirectly improving the control accuracy of the electronic gearbox. The scheme 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 always has the tracking error and the numerical control gear machine tool has internal interference and external interference. To solve this problem, the present invention provides a self-compensating disturbance control method for an electronic gear box, starting from the control method and controller selection aspects of the electronic gear box.
Disclosure of Invention
In order to improve the control precision of the flexible electronic gear box, the invention provides a self-compensating interference control method of the flexible electronic gear box.
1. A self-compensating interference control method of a flexible electronic gear box is characterized in that the flexible electronic gear box is a software module which utilizes mathematical operation to realize movement of a movement shaft according to a strict speed ratio relation according to a gear machine tool processing technological parameter set value in a gear numerical control system; the flexible electronic gear box executes the calculated movement by determining the movement axis controller, so that the numerical control gear hobbing machine tool is realized; the numerical control gear hobbing machine tool is provided with an X axis for radial feeding of the cutter, a Y axis for tangential feeding of the cutter, a Z axis for axial feeding of the cutter, an A axis for adjusting the mounting angle of the cutter, a B axis for rotating the cutter and a C axis for rotating the workpiece; the motion axis is divided into two types of guide axis and following axis; the guide shaft is a main motion and is respectively a B shaft for rotating the cutter, a Y shaft for tangential feeding of the cutter and a Z shaft for axial feeding of the cutter; the following shaft is a C shaft which rotates for the workpiece from the motion; the input signal of the B axis of the cutter rotation is a first position signal, the input signal of the X axis of the cutter radial feeding is a second position signal, the input signal of the Y axis of the cutter tangential feeding is a third position signal, and the input signal of the Z axis of the cutter axial feeding is a fourth position signal; the flexible electronic gear box realizes a control function based on a semi-physical simulation platform Dspace, and is characterized by comprising the following operation steps of:
(1) Control method for determining flexible electronic gear box
The flexible electronic gear box adopts a compound control method, wherein the compound control method is to directly use an output position signal obtained by a first position signal through a guide shaft B shaft, an initial input position signal before a third position signal passes through a guide shaft Y shaft and an initial input position signal before a fourth position signal passes through a guide shaft Z shaft as input position signals of the flexible electronic gear box; the output position signal of the flexible electronic gear box is directly used as the input position signal of the following shaft C shaft, so that the following shaft C shaft and the three guide shafts keep a strict mathematical linkage relation of the formula (1);
in the formula (1): z is Z b The number of cutter heads is the number of cutter heads, and the cutter heads are dimensionless; z is Z c The number of teeth of the workpiece is zero; n is n c The unit is r/s for following the rotation speed of the shaft C; n is n b The unit is r/s for guiding the rotation speed of the shaft B; v y The unit is mm/s for guiding the Y-axis moving speed of the shaft; v z The Z-axis moving speed of the guide shaft is measured in mm/s; beta is the helix angle of the gear, in degrees; lambda is the angle of attachment of the tool, unitDegree of degree; m is m n The normal modulus of the gear is dimensionless; k (K) b The guide shaft B axis coefficient is dimensionless; k (K) y The Y-axis coefficient of the guide shaft is dimensionless; k (K) z The Z-axis coefficient of the guide shaft is dimensionless; when the helix angle of the hob is right-handed, beta>0 and K b =1; beta when the helix angle is left-handed<0 and K b -1; when beta and v z When the symbols are the same, K z When the symbol is reversed, K is = -1 z =1; when v y >K at 0 time y When v is =1 y <K at 0 time y ＝-1；
(2) Selecting motion axis controller parameters
The motion axis controller of the flexible electronic gear box is controlled by an active disturbance rejection controller, and the active disturbance rejection controller comprises a tracking differentiator, a linear state error feedback module and an extended state observer; selecting parameter beta in a linear state error feedback module 1 、β 2 And parameter b in the extended state observer 0 As a basic parameter of the active disturbance rejection controller, the active disturbance rejection controller is used for controlling the motion of a motion axis; the four position signals are respectively obtained by adjusting an input position signal through an active disturbance rejection controller, and four disturbance rejection position signals for outputting and eliminating system disturbance are respectively obtained by compensating disturbance existing in a motion axis controller based on the active disturbance rejection controller;
(3) Determining motion rule of motion axis by diagonal roll cutting method
When a gear is machined by adopting a diagonal rolling cutting method, a B shaft for turning a cutter rotates around the axis of the B shaft, an X shaft for radially feeding the cutter is responsible for feeding and retracting the cutter before cutting, and a Y shaft for tangentially feeding the cutter and a Z shaft for axially feeding the cutter move simultaneously during cutting to form a movement rule along diagonal movement; the motion rule of the following shaft C is determined by the output position signal of the flexible electronic gearbox according to the step (1); the motion rule of the following axis C is synthesized by the motion rules of the three guide axes B, Y and Z according to the relation of the formula (1);
(3.1) the motion rule of the B axis of the cutter rotation is that the cutter rotates at a constant rotating speed, and the first position signal is a straight line rising at a constant speed;
(3.2) the X axis of the radial feeding of the cutter does not participate in the cutting process, and the motion rule is that the cutter firstly feeds forward to the radial direction of the workpiece before cutting; remains stationary during cutting; finishing the radial negative tool withdrawal of the cutting tool to the workpiece; the second position signal is a trapezoid movement rule, wherein the trapezoid movement rule of the second position signal is that a left bevel edge of a trapezoid is in feed movement, a right bevel edge of the trapezoid is in withdrawal movement, and an upper bottom of the trapezoid is in a static state;
(3.3) the Y axis of tangential feeding of the cutter participates in the cutting process, and the motion rule is that the cutter is kept motionless before cutting; when the cutter cuts a workpiece, the cutter firstly feeds forward in the tangential direction of the workpiece; finishing cutting and waiting for the X-axis cutter to retract to a safe position; the tool is returned to the tangential direction of the workpiece; the third position signal is a trapezoid movement rule, wherein the trapezoid movement rule of the third position signal is that a left bevel edge of a trapezoid is in feed movement, a right bevel edge of the trapezoid is in withdrawal movement, and an upper bottom of the trapezoid is in a static state;
(3.4) the Z axis of the axial feeding of the cutter participates in the cutting process, and the motion rule is that the cutter is kept motionless before cutting; when the cutter cuts a workpiece, the cutter firstly feeds forward in the axial direction of the workpiece; finishing cutting and waiting for the X-axis cutter to retract to a safe position; the tool withdraws from the axial direction of the workpiece; the fourth position signal is a trapezoid movement rule, wherein the trapezoid movement rule of the fourth position signal is that a left bevel edge of a trapezoid is in feed movement, a right bevel edge of the trapezoid is in withdrawal movement, and an upper bottom of the trapezoid is in a static state;
(4) Establishing a single-axis compensation model following the C axis of the shaft
The method comprises the steps of establishing a single-axis compensation model of a following shaft C shaft by utilizing a coupling relation among the following shaft C shaft, an X shaft for radial feeding of a cutter and a Y shaft for tangential feeding of the cutter, and realizing the compensation of an active disturbance rejection controller of the following shaft C shaft; the operation steps for establishing the uniaxial compensation model following the axis C are as follows:
(4.1) the tracking error E is obtained by the active disturbance rejection controller following the C axis of the shaft by the output position signal of the flexible electronic gear box c And will track error E c Multiplying by a scaling factor K cc Obtaining the compensation delta E of the C axis of the following axis c ；
ΔE c ＝K cc E c (2)
In the formula (2): ΔE c The unit is mm for the compensation quantity following the axis C; e (E) c The tracking error of the C-axis is the unit of mm; k (K) cc The proportional coefficient of tracking error of the C-axis of the follow-up axis is dimensionless;
(4.2) obtaining the tracking error E by the active disturbance rejection controller of the X axis of the radial feeding of the cutter x And will track error E x Multiplying by a scaling factor K cx Obtaining the compensation delta E of the X axis of the radial feeding of the cutter x ；
ΔE x ＝K cx E x (3)
In the formula (3): ΔE x The compensation quantity of the X axis of the radial feeding of the cutter is in mm; e (E) x An X-axis tracking error for radial feeding of the cutter is shown in mm; k (K) cx The proportional coefficient of the X-axis tracking error for radial feeding of the cutter is dimensionless;
(4.3) the third position signal is passed through the active disturbance rejection controller of Y-axis of tangential feed of cutter to obtain tracking error E y And will track error E y Multiplying by a scaling factor K cy Obtaining the compensation delta E of the Y axis of tangential feeding of the cutter y ；
ΔE y ＝K cy E y (4)
In the formula (4): ΔE y The compensation quantity of the Y axis of tangential feeding of the cutter is in mm; e (E) y Y-axis tracking error for tangential feeding of the cutter is in mm; k (K) cy The proportional coefficient of the Y-axis tracking error for tangential feeding of the cutter is dimensionless;
(4.4) the compensation amount ΔE to be followed by the axis C c Compensation delta E of X-axis of radial feeding of cutter x And Y-axis compensation delta E for tangential feed of the tool y Adding to obtain the total compensation quantity E ccc ；
E ccc ＝(ΔE c +ΔE x +ΔE y ) (5)
In formula (5): e (E) ccc The total compensation amount is in mm; ΔE c The unit is mm for the compensation quantity following the axis C; ΔE x X-axis for radial feeding of toolsThe unit of the compensation quantity is mm; ΔE y The compensation quantity of the Y axis for tangential feeding of the cutter is in mm;
(4.5) the total compensation amount E ccc Multiplying by a scaling factor K eccc Obtaining the final compensation value delta E' c ；
ΔE′ c ＝K eccc E ccc +σ′ c (6)
In formula (6): ΔE' c The final compensation value is in mm; e (E) ccc The unit is mm for the total compensation quantity; k (K) eccc The proportional coefficient is the total compensation quantity, and the dimensionless is realized; sigma'. c The correction amount is taken as a value according to actual conditions, and the unit is mm;
(4.6) adding the final compensation value ΔE' c And tracking error E of the following axis C c Subtracting to obtain the input position signal delta E' of the following axis C-axis active disturbance rejection controller " c The tracking error compensation of the active disturbance rejection controller following the C axis of the shaft is realized, and the control precision of the flexible electronic gear box is improved;
ΔE″ c ＝ΔE′ c -E c (7)
in the formula (7): ΔE' c The unit is mm for the input position signal of the following axis C-axis auto-disturbance rejection controller; ΔE' c The unit is mm for the final compensation value following the axis C; e (E) c The tracking error of the C axis of the follow-up axis is in mm;
(5) Calculating a machining error value
Three evaluation indexes of machining errors are established by the relative position relation of a cutter and a workpiece in the gear hobbing process and are respectively tooth profile deviation F α See formula (8); tooth pitch deviation F p See formula (9); deviation of tooth direction F β See formula (10);
in formula (8): f (F) α Tooth profile deviation is given in mm; z is Z c The number of teeth of the workpiece is zero; m is m n The normal modulus of the workpiece is dimensionless; alpha is the workpiecePressure angle in degrees; beta is the helix angle of the workpiece, and the unit is degree; e (E) c The tracking error of the C axis for the rotation of the workpiece is in mm; e (E) x An X-axis tracking error for radial feeding of the cutter is shown in mm; e (E) y Y-axis tracking error for tangential feeding of the cutter is in mm; e (E) a The A-axis tracking error for adjusting the installation angle of the cutter is measured in degrees; k (K) αc The value of the proportionality coefficient of the C axis of the follow-up axis is 1 or-1, and the proportionality coefficient is dimensionless; k, K αx The proportional coefficient of the X axis for radial feeding of the cutter is 1 or-1, and is dimensionless; k (K) αy The proportional coefficient of the Y axis for tangential feeding of the cutter is 1 or-1, and the value is dimensionless; sigma (sigma) α The tooth profile deviation correction is determined by the processing technological parameters and the characteristic parameters of a machine tool, and the unit is mm;
in the formula (9): f (F) p The tooth pitch deviation is in mm; z is Z c The number of teeth of the workpiece is zero; m is m n The normal modulus of the workpiece is dimensionless; alpha is the workpiece pressure angle in degrees; beta is the helix angle of the workpiece, and the unit is degree; e (E) c The tracking error of the C axis for the rotation of the workpiece is in mm; e (E) x An X-axis tracking error for radial feeding of the cutter is shown in mm; e (E) y Y-axis tracking error for tangential feeding of the cutter is in mm; e (E) a The A-axis tracking error for adjusting the installation angle of the cutter is measured in degrees; k (K) pc The value of the proportionality coefficient of the C axis of the follow-up axis is 1 or-1, and the proportionality coefficient is dimensionless; k (K) px The proportional coefficient of the X axis for radial feeding of the cutter is 1 or-1, and is dimensionless; k (K) py The proportional coefficient of the Y axis for tangential feeding of the cutter is 1 or-1, and the value is dimensionless; sigma (sigma) p The tooth pitch deviation correction is determined by the processing technological parameters and the characteristic parameters of a machine tool, and the unit is mm;
in the formula (10): f (F) β The tooth direction deviation is in mm; z is Z c The number of teeth of the workpiece is zero; m is m n The normal modulus of the workpiece is dimensionless; alpha is the workpiece pressure angle in degrees; beta is the helix angle of the workpiece, and the unit is degree; e (E) c The tracking error of the C axis for the rotation of the workpiece is in mm; e (E) y Y-axis tracking error for tangential feeding of the cutter is in mm; e (E) z Z-axis tracking error for axial feeding of the cutter is in mm; k (K) βc The value of the proportionality coefficient of the C axis of the follow-up axis is 1 or-1, and the proportionality coefficient is dimensionless; k (K) βy The proportional coefficient of the Y axis for tangential feeding of the cutter is 1 or-1, and the value is dimensionless; k (K) βz The proportional coefficient of the Z axis for axial feeding of the cutter is 1 or-1, and the value is dimensionless; sigma (sigma) β The tooth direction deviation correction amount is determined by the processing technological parameters and the characteristic parameters of a machine tool, and the unit is mm;
the calculation method of maximum value, average value and root mean square value is introduced to realize the evaluation index tooth profile deviation F of the machining error α Deviation of tooth pitch F p Deviation of tooth direction F β Is calculated quantitatively;
under the condition of adopting a self-compensating interference control method of the flexible electronic gear box, the maximum values of the tooth profile deviation, the tooth pitch deviation and the tooth direction deviation are shown in a formula (11); average values of tooth profile deviation, tooth pitch deviation and tooth direction deviation are shown in formula (12); root mean square values of tooth profile deviation, pitch deviation and tooth direction deviation, see formula (13);
M α ＝max(|F α |)；M p ＝max(|F p |)；M β ＝max(|F β |) (11)
In the formula (11): m is M α The unit is mm and the maximum value of tooth profile deviation is shown; m is M p The unit is mm and the maximum value of the tooth pitch deviation is shown; m is M β The unit is mm and the maximum value of the tooth direction deviation is the unit;
in the formula (12): a is that α The mean value of tooth profile deviation is given in mm; a is that p The mean value of the tooth pitch deviation is given in mm; a is that β The average value of the tooth direction deviation is given in mm; n is the number of data points collected in the total period, k is 1-n and is a positive integer, and dimensionless;
in the formula (13): r is R α The tooth profile deviation is root mean square value, and the unit is mm; r is R p The unit is mm, which is the root mean square value of the tooth pitch deviation; r is R β The root mean square value of the tooth direction deviation is in mm; n is the number of data points collected in the total period, k is 1-n and is a positive integer, and dimensionless.
2. A self-compensating disturbance control method for a flexible electronic gearbox in accordance with claim 1, wherein: the specific implementation process of the motion law in the step (3) is as follows:
(3.1) the motion rule of the B axis of the cutter rotation is that the cutter rotates at a constant rotating speed, and the first position signal is a straight line with a slope of 0.8-1 rising at a constant speed;
(3.2) the X axis of the radial feeding of the cutter does not participate in the cutting process, the motion rule is that the motion is increased at a constant speed within 0-5s, and the slope is 1-1.2; the gradient is 0 after being kept unchanged within 5-10 s; the constant speed is reduced to 0 within 10-15s, and the slope is-1.2 to-1; the slope is 0 after being kept unchanged for 15-20 s;
(3.3) the Y axis of tangential feeding of the cutter participates in the cutting process, wherein the motion rule is kept unchanged within 0-5s, and the slope is 0; the gradient is 2 to 2.2 after the constant speed is increased within 5 to 10 seconds; the slope is 0 after being kept unchanged within 10-15 s; the constant speed is reduced to 0 within 15-20s, and the slope is-2.2 to-2;
(3.4) the Z axis of the axial feeding of the cutter participates in the cutting process, wherein the motion rule is kept unchanged within 0-5s, and the slope is 0; the gradient is 4 to 4.2 after the constant speed is increased within 5 to 10 seconds; the slope is 0 after being kept unchanged within 10-15 s; the constant speed is reduced to 0 within 15-20s, and the slope is-4.2 to-4.
The beneficial technical effects of the invention are as follows:
(1) According to the self-compensating interference control method of the flexible electronic gear box, through the designed control method of the composite electronic gear box, secondary control errors caused by tracking errors of the guide shaft on the following shaft can be avoided; the active disturbance rejection controller is adopted, so that the influence of internal disturbance and external disturbance of the numerical control gear hobbing machine tool on the controller can be eliminated; the method comprises the steps of establishing a single-axis compensation model of a following shaft C by using a coupling relation among the following shaft C, an X axis for radial feeding of a cutter and a Y axis for tangential feeding of the cutter, and realizing the compensation of an active disturbance rejection controller of the following shaft C; these methods improve gear machining accuracy; the control precision of the electronic gear box is stably improved by about 50 percent, so that the machining precision of the numerical control gear hobbing machine tool is improved.
(2) The self-compensating interference control method of the flexible electronic gear box can be applied to numerical control machine tools such as gear grinding machines and gear honing machines. And different controllers are not required to be designed for different numerical control gear machine tools, so that the method has wide applicability.
Drawings
FIG. 1 is a schematic diagram of the distribution of each axis of motion of a gear hobbing machine;
FIG. 2 is a schematic diagram of a self-compensating disturbance control flow for a flexible electronic gearbox;
FIG. 3 is a schematic diagram of an active disturbance rejection controller;
FIG. 4 is a schematic diagram of the motion law of the motion axis controller;
fig. 5 is a schematic diagram of a follow-axis C-axis uniaxial compensation model.
Detailed Description
In order to more specifically describe the implementation technical means and innovative features of the present invention, the technical scheme of the present invention will be described in further detail by way of examples with reference to the accompanying drawings.
Example 1
A self-compensating interference control method of a flexible electronic gear box is characterized in that the flexible electronic gear box is a software module which utilizes mathematical operation to realize movement of a movement shaft according to a strict speed ratio relation according to a gear machine tool processing technological parameter set value in a gear numerical control system; and the flexible electronic gearbox executes the calculated motion by determining the motion axis controller, so that the numerical control gear hobbing machine tool is realized. Referring to fig. 1, the numerical control gear hobbing machine has an X axis for radial feeding of the tool, a Y axis for tangential feeding of the tool, a Z axis for axial feeding of the tool, an a axis for adjustment of the tool mounting angle, a B axis for turning of the tool, and a C axis for turning of the workpiece. The motion axis is divided into two types of guide axis and following axis; the guide shaft is a main motion and is respectively a B shaft for rotating the cutter, a Y shaft for tangential feeding of the cutter and a Z shaft for axial feeding of the cutter; the follower axis is the C axis that turns back from the motion to the workpiece. The input signal of the B axis of the cutter rotation is a first position signal, the input signal of the X axis of the cutter radial feeding is a second position signal, the input signal of the Y axis of the cutter tangential feeding is a third position signal, and the input signal of the Z axis of the cutter axial feeding is a fourth position signal. The flexible electronic gear box realizes a control function based on a semi-physical simulation platform Dspace, and the self-compensating interference control operation steps are as follows:
The parameters for the hobbing of this example 1 were chosen as follows:
the cutter parameters are as follows: right-hand hob, normal modulus m n Number of hob heads Z is 1 b 1, a hob pressure angle alpha of 20 degrees, a hob helix angle lambda of 1.97 degrees, a mounting angle gamma of 23.07 degrees and hob axial feed V z <0, tangential feed of hob V y >0; the parameters of the processed workpiece are as follows: gear normal modulus m n 1, gear tooth number Z c 65, the gear pressure angle alpha is 20 degrees, the gear is right-handed, and the helix angle beta is 15 degrees.
The self-compensating interference control method of the flexible electronic gear box comprises the following specific operation steps:
(1) Control method for determining flexible electronic gear box
The compound control flow of the flexible electronic gearbox is seen in fig. 2. The combined control method is that an output position signal obtained by a first position signal through a guide shaft B shaft, an initial input position signal before a third position signal passes through a guide shaft Y shaft and an initial input position signal before a fourth position signal passes through a guide shaft Z shaft are directly used as input position signals of a flexible electronic gear box; the output position signal of the flexible electronic gear box is directly used as the input position signal of the following shaft C shaft, so that the following shaft C shaft and the three guide shafts keep a strict mathematical linkage relation of the formula (1);
In the formula (1): z is Z b The number of cutter heads is the number of cutter heads, and the cutter heads are dimensionless; z is Z c The number of teeth of the workpiece is zero; n is n c The unit is r/s for following the rotation speed of the shaft C; n is n b The unit is r/s for guiding the rotation speed of the shaft B; v y The unit is mm/s for guiding the Y-axis moving speed of the shaft; v z The Z-axis moving speed of the guide shaft is measured in mm/s; beta is the helix angle of the gear, in degrees; lambda is the installation angle of the cutter and the unit is degree; m is m n The normal modulus of the gear is dimensionless; k (K) b The guide shaft B axis coefficient is dimensionless; k (K) y The Y-axis coefficient of the guide shaft is dimensionless; k (K) z The Z-axis coefficient of the guide shaft is dimensionless; when the helix angle of the hob is right-handed, beta>0 and K b =1; beta when the helix angle is left-handed<0 and K b -1; when beta and v z When the symbols are the same, K z When the symbol is reversed, K is = -1 z =1; when v y >K at 0 time y When v is =1 y <K at 0 time y ＝-1；
n c ＝0.0154n b +0.0013v z +0.0049v y (1)
Substituting specific data in the formula (1); k (K) b Take the value of 1, K z Take the value of 1, K y The value is 1;the value is 0.0154;the value is 0.0013; />The value is 0.0049;
(2) Selecting motion axis controller parameters
The motion axis controller of the flexible electronic gear box adopts the active disturbance rejectionA controller controls; the active disturbance rejection controller comprises a tracking differentiator, a linear state error feedback module and an extended state observer, see fig. 3. Selecting parameter beta in a linear state error feedback module 1 ＝200、β 2 Parameters b in =0.5 and extended state observer 0 =5, as a basic parameter of the active-disturbance-rejection controller, for controlling the motion of the motion axis. The four position signals are respectively obtained by adjusting an input position signal through an active disturbance rejection controller, and four disturbance rejection position signals for outputting and eliminating system disturbance are respectively obtained by compensating disturbance existing in a motion axis controller based on the active disturbance rejection controller;
(3) Determining motion rule of motion axis by diagonal roll cutting method
When a gear is machined by adopting a diagonal rolling cutting method, a B shaft for turning a cutter rotates around the axis of the B shaft, an X shaft for feeding the cutter radially is responsible for feeding and retracting the cutter before cutting, and a Y shaft for feeding the cutter tangentially and a Z shaft for feeding the cutter axially move simultaneously during cutting to form a movement rule along diagonal movement, and the method is shown in fig. 4. The motion rule of the following shaft C is determined by the output position signal of the flexible electronic gearbox according to the step (1); the motion rule of the following axis C is synthesized by the motion rules of the three guide axes B, Y and Z according to the relation of the formula (1);
(3.1) the B-axis motion rule of the tool rotation is that the tool rotates at a constant rotating speed, and the first position signal is a straight line with a slope of 0.8 rising at a constant speed.
(3.2) the X axis of the radial feeding of the cutter does not participate in the cutting process, the motion rule is that the cutter firstly feeds in the radial forward direction of the workpiece within 0-5s, and the slope is 1; the cutting is kept still within 5-10s, and the slope is 0; completing the radial negative tool withdrawal of the cutting tool to the workpiece within 10-15s, wherein the slope is-1; and the sample is kept still for 15-20s, and the slope is 0. The second position signal is a trapezoid movement rule, the trapezoid movement rule of the second position signal is that the left oblique side of the trapezoid is in feed movement, the right oblique side of the trapezoid is in withdrawal movement, and the upper bottom of the trapezoid is in a static state.
(3.3) the Y axis of tangential feeding of the cutter participates in the cutting process, the motion rule is that the cutter is kept motionless within 0-5s, and the slope is 0; when the cutter cuts a workpiece in 5-10s, the cutter firstly feeds forward in the tangential direction of the workpiece, and the slope is 2; finishing cutting within 10-15s, waiting for X-axis tool withdrawal to a safe position, wherein the slope is 0; and the tool is returned to the tangential negative direction of the workpiece within 15-20s, and the slope is-2. The third position signal is a trapezoid movement rule, the trapezoid movement rule of the third position signal is that the left oblique side of the trapezoid is in feed movement, the right oblique side of the trapezoid is in withdrawal movement, and the upper bottom of the trapezoid is in a static state.
(3.4) the Z axis of axial feeding of the cutter participates in the cutting process, the motion rule is that the cutter is kept motionless within 0-5s, and the slope is 0; when the cutter cuts a workpiece in 5-10s, the cutter firstly feeds forward in the axial direction of the workpiece, and the slope is 4; finishing cutting within 10-15s, waiting for X-axis tool withdrawal to a safe position, wherein the slope is 0; and the tool in 15-20s is retracted towards the axial direction of the workpiece, and the slope is-4. The fourth position signal is a trapezoid movement rule, the trapezoid movement rule of the fourth position signal is that the left oblique side of the trapezoid is in feed movement, the right oblique side of the trapezoid is in withdrawal movement, and the upper bottom of the trapezoid is in a static state.
(4) Establishing a single-axis compensation model following the C axis of the shaft
And establishing a single-axis compensation model of the following axis C shaft by using the coupling relation among the following axis C shaft, the X shaft for radial feeding of the cutter and the Y shaft for tangential feeding of the cutter, and realizing the compensation of the active disturbance rejection controller of the following axis C shaft, see figure 5. The operation steps for establishing the uniaxial compensation model following the axis C are as follows:
(4.1) the tracking error E is obtained by the active disturbance rejection controller following the C axis of the shaft by the output position signal of the flexible electronic gear box c And will track error E c Multiplying by a scaling factor K cc Obtaining the compensation delta E of the C axis of the following axis c ；
ΔE c ＝K cc E c (2)
In the formula (2): ΔE c The unit is mm for the compensation quantity following the axis C; e (E) c The tracking error of the C-axis is the unit of mm; k (K) cc The proportional coefficient of tracking error of the C-axis of the follow-up axis is dimensionless;
ΔE c ＝E c (2)
substituting a specific number into formula (2)According to the above; k (K) cc The value is 1;
(4.2) obtaining the tracking error E by the active disturbance rejection controller of the X axis of the radial feeding of the cutter x And will track error E x Multiplying by a scaling factor K cx Obtaining the compensation delta E of the X axis of the radial feeding of the cutter x ；
ΔE x ＝K cx E x (3)
In the formula (3): ΔE x The compensation quantity of the X axis of the radial feeding of the cutter is in mm; e (E) x An X-axis tracking error for radial feeding of the cutter is shown in mm; k (K) cx The proportional coefficient of the X-axis tracking error for radial feeding of the cutter is dimensionless;
ΔE x ＝0.6198E x (3)
substituting specific data in the formula (3); k (K) cx The value is 0.6198;
(4.3) the third position signal is passed through the active disturbance rejection controller of Y-axis of tangential feed of cutter to obtain tracking error E y And will track error E y Multiplying by a scaling factor K cy Obtaining the compensation delta E of the Y axis of tangential feeding of the cutter y ；
ΔE y ＝K cy E y (4)
In the formula (4): ΔE y The compensation quantity of the Y axis of tangential feeding of the cutter is in mm; e (E) y Y-axis tracking error for tangential feeding of the cutter is in mm; k (K) cy The proportional coefficient of the Y-axis tracking error for tangential feeding of the cutter is dimensionless;
ΔE y ＝1.7019E y (4)
substituting specific data in the formula (4); k (K) cy The value is 1.7019;
(4.4) the compensation amount ΔE to be followed by the axis C c Compensation delta E of X-axis of radial feeding of cutter x And Y-axis compensation delta E for tangential feed of the tool y Adding to obtain the total compensation quantity E ccc ；
E ccc ＝(ΔE c +ΔE x +ΔE y ) (5)
In formula (5): e (E) ccc The total compensation amount is in mm; ΔE c The unit is mm for the compensation quantity following the axis C; ΔE x The compensation quantity of the X axis for radial feeding of the cutter is in mm; ΔE y The compensation quantity of the Y axis for tangential feeding of the cutter is in mm;
E ccc ＝E c +0.6198E x +1.7019E y (5)
substituting specific data in the formula (5);
(4.5) the total compensation amount E ccc Multiplying by a scaling factor K eccc Obtaining the final compensation value delta E' c ；
ΔE′ c ＝K eccc E ccc +σ′ c (6)
In formula (6): ΔE' c The final compensation value is in mm; e (E) ccc The unit is mm for the total compensation quantity; k (K) eccc The proportional coefficient is the total compensation quantity, and the dimensionless is realized; sigma'. c The correction amount is taken as a value according to actual conditions, and the unit is mm;
ΔE′ c ＝E c +0.6198E x +1.7019E y (6)
substituting specific data in the formula (6); k (K) eccc The value is 1; sigma'. c The value is 0;
(4.6) adding the final compensation value ΔE' c And tracking error E of the following axis C c Subtracting to obtain the input position signal delta E' of the following axis C-axis active disturbance rejection controller " c The tracking error compensation of the active disturbance rejection controller following the C axis of the shaft is realized, and the control precision of the flexible electronic gear box is improved;
ΔE″ c ＝ΔE′ c -E c (7)
in the formula (7): ΔE' c The unit is mm for the input position signal of the following axis C-axis auto-disturbance rejection controller; ΔE' c The unit is mm for the final compensation value following the axis C; e (E) c The tracking error of the C axis of the follow-up axis is in mm;
ΔE″ c ＝0.6198E x +1.7019E y (7)
substituting specific data in the formula (7);
(5) Calculating a machining error value
Three evaluation indexes of machining errors are established by the relative position relation of a cutter and a workpiece in the gear hobbing process and are respectively tooth profile deviation F α See formula (8); tooth pitch deviation F p See formula (9); deviation of tooth direction F β See formula (10);
in formula (8): f (F) α Tooth profile deviation is given in mm; z is Z c The number of teeth of the workpiece is zero; m is m n The normal modulus of the workpiece is dimensionless; alpha is the workpiece pressure angle in degrees; beta is the helix angle of the workpiece, and the unit is degree; e (E) c The tracking error of the C axis for the rotation of the workpiece is in mm; e (E) x An X-axis tracking error for radial feeding of the cutter is shown in mm; e (E) y Y-axis tracking error for tangential feeding of the cutter is in mm; e (E) a The A-axis tracking error for adjusting the installation angle of the cutter is measured in degrees; k (K) αc The value of the proportionality coefficient of the C axis of the follow-up axis is 1 or-1, and the proportionality coefficient is dimensionless; k, K αx The proportional coefficient of the X axis for radial feeding of the cutter is 1 or-1, and is dimensionless; k (K) αy The proportional coefficient of the Y axis for tangential feeding of the cutter is 1 or-1, and the value is dimensionless; sigma (sigma) α The tooth profile deviation correction is determined by the processing technological parameters and the characteristic parameters of a machine tool, and the unit is mm;
F α ＝0.5518E c +0.3420E x +0.8645cosE a E y (8)
substituting specific data in the formula (8); k (K) αc Take the value of 1, K αx Take the value of 1, K αy The value is 1;the value is 0.5518; the sin alpha has a value of 0.3420; the cosγcosα takes a value of 0.8645; sigma (sigma) α The value is 0;
in the formula (9): f (F) p The tooth pitch deviation is in mm; z is Z c The number of teeth of the workpiece is zero; m is m n The normal modulus of the workpiece is dimensionless; alpha is the workpiece pressure angle in degrees; beta is the helix angle of the workpiece, and the unit is degree; e (E) c The tracking error of the C axis for the rotation of the workpiece is in mm; e (E) x An X-axis tracking error for radial feeding of the cutter is shown in mm; e (E) y Y-axis tracking error for tangential feeding of the cutter is in mm; e (E) a The A-axis tracking error for adjusting the installation angle of the cutter is measured in degrees; k (K) pc The value of the proportionality coefficient of the C axis of the follow-up axis is 1 or-1, and the proportionality coefficient is dimensionless; k (K) px The proportional coefficient of the X axis for radial feeding of the cutter is 1 or-1, and is dimensionless; k (K) py The proportional coefficient of the Y axis for tangential feeding of the cutter is 1 or-1, and the value is dimensionless; sigma (sigma) p The tooth pitch deviation correction is determined by the processing technological parameters and the characteristic parameters of a machine tool, and the unit is mm;
F p ＝0.5872E c +0.3640E x +0.9200cosE a E y (9)
substituting specific data in the formula (9); k (K) pc Take the value of 1, K px Take the value of 1, K py The value is 1;the value is 0.5872; tan alpha has a value of 0.3640; cos gamma 0.9200; sigma (sigma) p The value is 0;
in the formula (10): f (F) β The tooth direction deviation is in mm; z is Z c The number of teeth of the workpiece is zero; m is m n The normal modulus of the workpiece is dimensionless; alpha is the workpiece pressure angle in degrees; beta is the helix angle of the workpiece, and the unit is degree; e (E) c The tracking error of the C axis for the rotation of the workpiece is in mm; e (E) y Y-axis tracking error for tangential feeding of the cutter is in mm; e (E) z Z-axis tracking error for axial feeding of the cutter is in mm; k (K) βc The value of the proportionality coefficient of the C axis of the follow-up axis is 1 or-1, and the proportionality coefficient is dimensionless; k (K) βy The proportional coefficient of the Y axis for tangential feeding of the cutter is 1 or-1, and the value is dimensionless; k (K) βz The proportional coefficient of the Z axis for axial feeding of the cutter is 1 or-1, and the value is dimensionless; sigma (sigma) β The tooth direction deviation correction amount is determined by the processing technological parameters and the characteristic parameters of a machine tool, and the unit is mm;
F β ＝0.5872E c +0.9200E y +0.2679E z (10)
substituting specific data in the formula (10); k (K) βc Take the value of 1, K βy Take the value of 1, K βz The value is 1;the value is 0.5872; cos gamma 0.9200; tan beta has a value of 0.2679; sigma (sigma) β The value is 0;
the calculation method of maximum value, average value and root mean square value is introduced to realize the evaluation index tooth profile deviation F of the machining error α Deviation of tooth pitch F p Deviation of tooth direction F β Is calculated quantitatively;
under the condition of adopting a self-compensating interference control method of the flexible electronic gear box, the maximum values of the tooth profile deviation, the tooth pitch deviation and the tooth direction deviation are shown in a formula (11); average values of tooth profile deviation, tooth pitch deviation and tooth direction deviation are shown in formula (12); root mean square values of tooth profile deviation, pitch deviation and tooth direction deviation, see formula (13);
M α ＝max(|F α |)；M p ＝max(|F p |)；M β ＝max(|F β |) (11)
in the formula (11): m is M α The unit is mm and the maximum value of tooth profile deviation is shown; m is M p The unit is mm and the maximum value of the tooth pitch deviation is shown; m is M β The unit is mm and the maximum value of the tooth direction deviation is the unit;
M α ＝0.00632；M p ＝0.00616；M β ＝0.00872 (11)
substituting specific data in the formula (11); e (E) c 、E x 、E y 、E z And E is a The value is the tracking error of the flexible electronic gear box during the actual running of the self-compensating interference control method;
in the formula (12): a is that α The mean value of tooth profile deviation is given in mm; a is that p The mean value of the tooth pitch deviation is given in mm; a is that β The average value of the tooth direction deviation is given in mm; n is the number of data points collected in the total period, k is 1-n and is a positive integer, and dimensionless;
A α ＝0.00058；A p ＝0.00059；A β ＝0.00073 (12)
substituting specific data in the formula (12); e (E) c 、E x 、E y 、E z And E is a The value is the tracking error of the flexible electronic gear box during the actual running of the self-compensating interference control method;
in the formula (13): r is R α The tooth profile deviation is root mean square value, and the unit is mm; r is R p The unit is mm, which is the root mean square value of the tooth pitch deviation; r is R β The root mean square value of the tooth direction deviation is in mm; n is the number of data points collected in the total period, k is 1-n and is a positive integer, and dimensionless.
R α ＝0.00091；R p ＝0.00091；R β ＝0.00113 (13)
Substituting specific data in the formula (13); e (E) c 、E x 、E y 、E z And E is a The value is the tracking error of the flexible electronic gear box during the actual running of the self-compensating interference control method;
the control method of the electronic gear box in the prior art is different from the control method of the electronic gear box in the step (1) of the flexible electronic gear box; the control method of the electronic gear box in the prior art adopts a master-slave control method, wherein the master-slave control method takes the output position signals of the controllers of the B shaft, the Y shaft and the Z shaft of the three guide shafts as the input position signals of the electronic gear box, and the output position signals of the electronic gear box are taken as the input position signals of the controller of the C shaft of the following shaft, so that the C shaft of the following shaft and the three guide shafts keep a strict mathematical linkage relation; other steps in the control method of the electronic gear box in the prior art are the same as those of the flexible electronic gear box of the invention, and the maximum values of tooth profile deviation, tooth pitch deviation and tooth direction deviation are obtained by implementing the control method of the electronic gear box in the prior art, wherein the maximum values are shown in a formula (14); average values of tooth profile deviation, pitch deviation and tooth direction deviation are shown in formula (15); root mean square values of tooth profile deviation, pitch deviation, and tooth direction deviation are shown in equation (16).
M α ′＝0.01770；M p ′＝0.01720；M β ′＝0.02508 (14)
In formula (14): m is M α ' is the maximum value of the tooth profile deviation of the control method of the electronic gear box in the prior art, and the unit is mm; m is M p ' is the maximum value of the pitch deviation of the control method of the electronic gear box in the prior art, and the unit is mm; m is M β ' is the maximum value of the gear deflection in mm of the control method of the electronic gear box in the prior art.
A α ′＝0.00113；A p ′＝0.00112；A β ′＝0.00133 (15)
In formula (15): a is that α ' is the mean value of tooth profile deviation of the control method of the electronic gear box in the prior art, and the unit is mm; a is that p ' is the average value of the pitch deviation of the control method of the electronic gear box in the prior art, and the unit is mm; a is that β ' is the average value of the gear direction deviation of the control method of the electronic gear box in the prior art, and the unit is mm;
R α ′＝0.00191；R p ′＝0.00195；R β ′＝0.00231 (16)
in formula (16): r is R α ' is an electronic tooth in the prior artThe root mean square value of the tooth profile deviation of the control method of the wheel box is in mm; r is R p ' is the root mean square value of the tooth pitch deviation of the control method of the electronic gear box in the prior art, and the unit is mm; r is R β ' is the root mean square value of the tooth direction deviation of the control method of the electronic gear box in the prior art, and the unit is mm;
compared with the control method of the electronic gear box in the prior art, the self-compensating disturbance control method of the flexible electronic gear box is adopted, the maximum value of tooth profile deviation is reduced from 0.01770mm of the control method of the electronic gear box in the prior art to 0.00632mm of the self-compensating disturbance control method of the flexible electronic gear box, the average value of tooth profile deviation is reduced from 0.00113mm of the control method of the electronic gear box in the prior art to 0.00058mm of the self-compensating disturbance control method of the flexible electronic gear box, and the root mean square value of tooth profile deviation is reduced from 0.00191mm of the control method of the electronic gear box in the prior art to 0.00091mm of the self-compensating disturbance control method of the flexible electronic gear box; the maximum value of the pitch deviation is reduced from 0.01720mm of the control method of the electronic gear box in the prior art to 0.00616mm of the self-compensating disturbance control method of the flexible electronic gear box, the average value of the pitch deviation is reduced from 0.00112mm of the control method of the electronic gear box in the prior art to 0.00059mm of the self-compensating disturbance control method of the flexible electronic gear box, and the root mean square value of the pitch deviation is reduced from 0.00195mm of the control method of the electronic gear box in the prior art to 0.00091mm of the self-compensating disturbance control method of the flexible electronic gear box; the maximum value of the gear direction deviation is reduced from 0.02508mm of the control method of the electronic gear box in the prior art to 0.00872mm of the self-compensating disturbance control method of the flexible electronic gear box, the average value of the gear direction deviation is reduced from 0.00133mm of the control method of the electronic gear box in the prior art to 0.00073mm of the self-compensating disturbance control method of the flexible electronic gear box, and the root mean square value of the gear direction deviation is reduced from 0.00231mm of the control method of the electronic gear box in the prior art to 0.00113mm of the self-compensating disturbance control method of the flexible electronic gear box.
The self-compensating interference control method of the flexible electronic gear box can be seen to obtain much higher precision than the control method of the electronic gear box in the prior art when the tooth profile deviation, the tooth pitch deviation and the tooth direction deviation are evaluated from the angles of the maximum value, the average value and the root mean square value, and the precision can be stably improved by about 50%, so that the flexible electronic gear box can improve the gear machining precision.
Example 2
A self-compensating interference control method of a flexible electronic gear box is characterized in that the flexible electronic gear box is a software module which utilizes mathematical operation to realize movement of a movement shaft according to a strict speed ratio relation according to a gear machine tool processing technological parameter set value in a gear numerical control system; and the flexible electronic gearbox executes the calculated motion by determining the motion axis controller, so that the numerical control gear hobbing machine tool is realized. Referring to fig. 1, the numerical control gear hobbing machine has an X axis for radial feeding of the tool, a Y axis for tangential feeding of the tool, a Z axis for axial feeding of the tool, an a axis for adjustment of the tool mounting angle, a B axis for turning of the tool, and a C axis for turning of the workpiece. The motion axis is divided into two types of guide axis and following axis; the guide shaft is a main motion and is respectively a B shaft for rotating the cutter, a Y shaft for tangential feeding of the cutter and a Z shaft for axial feeding of the cutter; the follower axis is the C axis that turns back from the motion to the workpiece. The input signal of the B axis of the cutter rotation is a first position signal, the input signal of the X axis of the cutter radial feeding is a second position signal, the input signal of the Y axis of the cutter tangential feeding is a third position signal, and the input signal of the Z axis of the cutter axial feeding is a fourth position signal. The flexible electronic gear box realizes a control function based on a semi-physical simulation platform Dspace, and the self-compensating interference control operation steps are as follows:
The parameters for the hobbing of this example 2 were chosen as follows:
the cutter parameters are as follows: left-hand hob, normal modulus m n Number of hob heads Z is 2 b 1, a hob pressure angle alpha of 20 degrees, a hob helix angle lambda of 2.03 degrees, a mounting angle gamma of 21.38 degrees and hob axial feed V z >0, tangential feed of hob V y <0; the parameters of the processed workpiece are as follows: gear normal modulus m n 2, gear tooth number Z c 49, the gear pressure angle alpha is 20 degrees, the gear is left-handed, and the helix angle beta is-15 degrees.
The self-compensating interference control method of the flexible electronic gear box comprises the following specific operation steps:
(1) Control method for determining flexible electronic gear box
The compound control flow of the flexible electronic gearbox is seen in fig. 2. The combined control method is that an output position signal obtained by a first position signal through a guide shaft B shaft, an initial input position signal before a third position signal passes through a guide shaft Y shaft and an initial input position signal before a fourth position signal passes through a guide shaft Z shaft are directly used as input position signals of a flexible electronic gear box; the output position signal of the flexible electronic gear box is directly used as the input position signal of the following shaft C shaft, so that the following shaft C shaft and the three guide shafts keep a strict mathematical linkage relation of the formula (1);
In the formula (1): z is Z b The number of cutter heads is the number of cutter heads, and the cutter heads are dimensionless; z is Z c The number of teeth of the workpiece is zero; n is n c The unit is r/s for following the rotation speed of the shaft C; n is n b The unit is r/s for guiding the rotation speed of the shaft B; v y The unit is mm/s for guiding the Y-axis moving speed of the shaft; v z The Z-axis moving speed of the guide shaft is measured in mm/s; beta is the helix angle of the gear, in degrees; lambda is the installation angle of the cutter and the unit is degree; m is m n The normal modulus of the gear is dimensionless; k (K) b The guide shaft B axis coefficient is dimensionless; k (K) y The Y-axis coefficient of the guide shaft is dimensionless; k (K) z The Z-axis coefficient of the guide shaft is dimensionless; when the helix angle of the hob is right-handed, beta>0 and K b =1; beta when the helix angle is left-handed<0 and K b -1; when beta and v z When the symbols are the same, K z When the symbol is reversed, K is = -1 z =1; when v y >K at 0 time y When v is =1 y <K at 0 time y ＝-1；
n c ＝-0.0204n b -0.0008v z -0.0032v y (1)
Substituting specific data in the formula (1); k (K) b Take the value of-1, K z Take the value of 1, K y The value is-1;the value is 0.0204;the value is-0.0008; />The value is 0.0032;
(2) Selecting motion axis controller parameters
The motion axis controller of the flexible electronic gear box is controlled by an active disturbance rejection controller; the active disturbance rejection controller comprises a tracking differentiator, a linear state error feedback module and an extended state observer, see fig. 3. Selecting parameter beta in a linear state error feedback module 1 ＝135、β 2 Parameters b in =1 and extended state observer 0 =6, as a basic parameter of the active-disturbance-rejection controller, for controlling the motion of the motion axis. The four position signals are respectively obtained by adjusting an input position signal through an active disturbance rejection controller, and four disturbance rejection position signals for outputting and eliminating system disturbance are respectively obtained by compensating disturbance existing in a motion axis controller based on the active disturbance rejection controller;
(3) Determining motion rule of motion axis by diagonal roll cutting method
When a gear is machined by adopting a diagonal rolling cutting method, a B shaft for turning a cutter rotates around the axis of the B shaft, an X shaft for feeding the cutter radially is responsible for feeding and retracting the cutter before cutting, and a Y shaft for feeding the cutter tangentially and a Z shaft for feeding the cutter axially move simultaneously during cutting to form a movement rule along diagonal movement, and the method is shown in fig. 4. The motion rule of the following shaft C is determined by the output position signal of the flexible electronic gearbox according to the step (1); the motion rule of the following axis C is synthesized by the motion rules of the three guide axes B, Y and Z according to the relation of the formula (1);
and (3.1) the motion rule of the axis B of the tool rotation is that the tool rotates at a constant rotating speed, and the first position signal is a straight line with a slope of 1 rising at a constant speed.
(3.2) the X axis of the radial feeding of the cutter does not participate in the cutting process, the motion rule is that the cutter firstly feeds in the radial forward direction of the workpiece within 0-5s, and the slope is 1.2; the cutting is kept still within 5-10s, and the slope is 0; completing the radial negative tool withdrawal of the cutting tool to the workpiece within 10-15s, wherein the slope is-1.2; and the sample is kept still for 15-20s, and the slope is 0. The second position signal is a trapezoid movement rule, the trapezoid movement rule of the second position signal is that the left oblique side of the trapezoid is in feed movement, the right oblique side of the trapezoid is in withdrawal movement, and the upper bottom of the trapezoid is in a static state.
(3.3) the Y axis of tangential feeding of the cutter participates in the cutting process, the motion rule is that the cutter is kept motionless within 0-5s, and the slope is 0; when the cutter cuts a workpiece in 5-10s, the cutter firstly feeds forward in the tangential direction of the workpiece, and the slope is 2.2; finishing cutting within 10-15s, waiting for X-axis tool withdrawal to a safe position, wherein the slope is 0; the tangential negative direction tool withdrawal of the tool to the workpiece is carried out within 15-20s, and the slope is-2.2. The third position signal is a trapezoid movement rule, the trapezoid movement rule of the third position signal is that the left oblique side of the trapezoid is in feed movement, the right oblique side of the trapezoid is in withdrawal movement, and the upper bottom of the trapezoid is in a static state.
(3.4) the Z axis of axial feeding of the cutter participates in the cutting process, the motion rule is that the cutter is kept motionless within 0-5s, and the slope is 0; when the cutter cuts a workpiece in 5-10 seconds, the cutter firstly feeds forward in the axial direction of the workpiece, and the slope is 4.2; finishing cutting within 10-15s, waiting for X-axis tool withdrawal to a safe position, wherein the slope is 0; the tool is retracted towards the axial direction of the workpiece within 15-20s, and the slope is-4.2. The fourth position signal is a trapezoid movement rule, the trapezoid movement rule of the fourth position signal is that the left oblique side of the trapezoid is in feed movement, the right oblique side of the trapezoid is in withdrawal movement, and the upper bottom of the trapezoid is in a static state.
(4) Establishing a single-axis compensation model following the C axis of the shaft
And establishing a single-axis compensation model of the following axis C shaft by using the coupling relation among the following axis C shaft, the X shaft for radial feeding of the cutter and the Y shaft for tangential feeding of the cutter, and realizing the compensation of the active disturbance rejection controller of the following axis C shaft, see figure 5. The operation steps for establishing the uniaxial compensation model following the axis C are as follows:
(4.1) Flexible electronic gearbox output position SignalThe number obtains tracking error E through an active disturbance rejection controller following the C axis of the shaft c And will track error E c Multiplying by a scaling factor K cc Obtaining the compensation delta E of the C axis of the following axis c ；
ΔE c ＝K cc E c (2)
In the formula (2): ΔE c The unit is mm for the compensation quantity following the axis C; e (E) c The tracking error of the C-axis is the unit of mm; k (K) cc The proportional coefficient of tracking error of the C-axis of the follow-up axis is dimensionless;
ΔE c ＝E c (2)
substituting specific data in the formula (2); k (K) cc The value is 1;
(4.2) obtaining the tracking error E by the active disturbance rejection controller of the X axis of the radial feeding of the cutter x And will track error E x Multiplying by a scaling factor K cx Obtaining the compensation delta E of the X axis of the radial feeding of the cutter x ；
ΔE x ＝K cx E x (3)
In the formula (3): ΔE x The compensation quantity of the X axis of the radial feeding of the cutter is in mm; e (E) x An X-axis tracking error for radial feeding of the cutter is shown in mm; k (K) cx The proportional coefficient of the X-axis tracking error for radial feeding of the cutter is dimensionless;
ΔE x ＝0.4111E x (3)
substituting specific data in the formula (3); k (K) cx The value is 0.4111;
(4.3) the third position signal is passed through the active disturbance rejection controller of Y-axis of tangential feed of cutter to obtain tracking error E y And will track error E y Multiplying by a scaling factor K cy Obtaining the compensation delta E of the Y axis of tangential feeding of the cutter y ；
ΔE y ＝K cy E y (4)
In the formula (4): ΔE y The compensation quantity of the Y axis of tangential feeding of the cutter is in mm; e (E) y Y-axis tracking error for tangential feeding of the cutter is in mm; k (K) cy Is a cutterThe proportional coefficient of the Y-axis tracking error of tangential feeding is dimensionless;
ΔE y ＝1.0518E y (4)
substituting specific data in the formula (4); k (K) cy The value is 1.0518;
(4.4) the compensation amount ΔE to be followed by the axis C c Compensation delta E of X-axis of radial feeding of cutter x And Y-axis compensation delta E for tangential feed of the tool y Adding to obtain the total compensation quantity E ccc ；
E ccc ＝(ΔE c +ΔE x +ΔE y ) (5)
In formula (5): e (E) ccc The total compensation amount is in mm; ΔE c The unit is mm for the compensation quantity following the axis C; ΔE x The compensation quantity of the X axis for radial feeding of the cutter is in mm; ΔE y The compensation quantity of the Y axis for tangential feeding of the cutter is in mm;
E ccc ＝E c +0.4111E x +1.0518E y (5)
substituting specific data in the formula (5);
(4.5) the total compensation amount E ccc Multiplying by a scaling factor K eccc Obtaining the final compensation value delta E' c ；
ΔE′ c ＝K eccc E ccc +σ′ c (6)
In formula (6): ΔE' c The final compensation value is in mm; e (E) ccc The unit is mm for the total compensation quantity; k (K) eccc The proportional coefficient is the total compensation quantity, and the dimensionless is realized; sigma'. c The correction amount is taken as a value according to actual conditions, and the unit is mm;
ΔE′ c ＝E c +0.4111E x +1.0518E y (6)
substituting specific data in the formula (6); k (K) eccc The value is 1; sigma'. c The value is 0;
(4.6) adding the final compensation value ΔE' c And tracking error E of the following axis C c Subtracting to obtain the input position signal delta E' of the following axis C-axis active disturbance rejection controller " c The tracking error compensation of the active disturbance rejection controller following the C axis of the shaft is realized, and the control precision of the flexible electronic gear box is improved;
ΔE″ c ＝ΔE′ c -E c (7)
in the formula (7): ΔE' c The unit is mm for the input position signal of the following axis C-axis auto-disturbance rejection controller; ΔE' c The unit is mm for the final compensation value following the axis C; e (E) c The tracking error of the C axis of the follow-up axis is in mm;
ΔE″ c ＝0.4111E x +1.0518E y (7)
substituting specific data in the formula (7);
(5) Calculating a machining error value
Three evaluation indexes of machining errors are established by the relative position relation of a cutter and a workpiece in the gear hobbing process and are respectively tooth profile deviation F α See formula (8); tooth pitch deviation F p See formula (9); deviation of tooth direction F β See formula (10);
in formula (8): f (F) α Tooth profile deviation is given in mm; z is Z c The number of teeth of the workpiece is zero; m is m n The normal modulus of the workpiece is dimensionless; alpha is the workpiece pressure angle in degrees; beta is the helix angle of the workpiece, and the unit is degree; e (E) c The tracking error of the C axis for the rotation of the workpiece is in mm; e (E) x An X-axis tracking error for radial feeding of the cutter is shown in mm; e (E) y Y-axis tracking error for tangential feeding of the cutter is in mm; e (E) a The A-axis tracking error for adjusting the installation angle of the cutter is measured in degrees; k (K) αc The value of the proportionality coefficient of the C axis of the follow-up axis is 1 or-1, and the proportionality coefficient is dimensionless; k, K αx The proportional coefficient of the X axis for radial feeding of the cutter is 1 or-1, and is dimensionless; k (K) αy The proportional coefficient of the Y axis for tangential feeding of the cutter is 1 or-1, and the value is dimensionless; sigma (sigma) α For correcting tooth profile deviation, the method is characterized by processing parametersDetermining characteristic parameters of a machine tool, wherein the unit is mm;
F α ＝0.8320E c +0.3420E x +0.8750cosE a E y (8)
substituting specific data in the formula (8); k (K) αc Take the value of 1, K αx Take the value of 1, K αy The value is 1;the value is 0.8320; the sin alpha has a value of 0.3420; the cosγcosα takes a value of 0.8750; sigma (sigma) α The value is 0;
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in the formula (9): f (F) p The tooth pitch deviation is in mm; z is Z c The number of teeth of the workpiece is zero; m is m n The normal modulus of the workpiece is dimensionless; alpha is the workpiece pressure angle in degrees; beta is the helix angle of the workpiece, and the unit is degree; e (E) c The tracking error of the C axis for the rotation of the workpiece is in mm; e (E) x An X-axis tracking error for radial feeding of the cutter is shown in mm; e (E) y Y-axis tracking error for tangential feeding of the cutter is in mm; e (E) a The A-axis tracking error for adjusting the installation angle of the cutter is measured in degrees; k (K) pc The value of the proportionality coefficient of the C axis of the follow-up axis is 1 or-1, and the proportionality coefficient is dimensionless; k (K) px The proportional coefficient of the X axis for radial feeding of the cutter is 1 or-1, and is dimensionless; k (K) py The proportional coefficient of the Y axis for tangential feeding of the cutter is 1 or-1, and the value is dimensionless; sigma (sigma) p The tooth pitch deviation correction is determined by the processing technological parameters and the characteristic parameters of a machine tool, and the unit is mm;
F p ＝0.8854E c +0.3640E x +0.9312cosE a E y (9)
substituting specific data in the formula (9); k (K) pc Take the value of 1, K px Take the value of 1, K py The value is 1;the value is 0.8854; tan alpha has a value of 0.3640; cos gamma 0.9312; sigma (sigma) p The value is 0;
in the formula (10): f (F) β The tooth direction deviation is in mm; z is Z c The number of teeth of the workpiece is zero; m is m n The normal modulus of the workpiece is dimensionless; alpha is the workpiece pressure angle in degrees; beta is the helix angle of the workpiece, and the unit is degree; e (E) c The tracking error of the C axis for the rotation of the workpiece is in mm; e (E) y Y-axis tracking error for tangential feeding of the cutter is in mm; e (E) z Z-axis tracking error for axial feeding of the cutter is in mm; k (K) βc The value of the proportionality coefficient of the C axis of the follow-up axis is 1 or-1, and the proportionality coefficient is dimensionless; k (K) βy The proportional coefficient of the Y axis for tangential feeding of the cutter is 1 or-1, and the value is dimensionless; k (K) βz The proportional coefficient of the Z axis for axial feeding of the cutter is 1 or-1, and the value is dimensionless; sigma (sigma) β The tooth direction deviation correction amount is determined by the processing technological parameters and the characteristic parameters of a machine tool, and the unit is mm;
F β ＝0.8854E c +0.9312E y -0.2679E z (10)
substituting specific data in the formula (10); k (K) βc Take the value of 1, K βy Take the value of 1, K βz The value is 1;the value is 0.8854; cos gamma 0.9312; tan beta takes on a value of-0.2679; sigma (sigma) β The value is 0;
the calculation method of maximum value, average value and root mean square value is introduced to realize the evaluation index tooth profile deviation F of the machining error α Deviation of tooth pitch F p Deviation of tooth direction F β Is calculated quantitatively;
under the condition of adopting a self-compensating interference control method of the flexible electronic gear box, the maximum values of the tooth profile deviation, the tooth pitch deviation and the tooth direction deviation are shown in a formula (11); average values of tooth profile deviation, tooth pitch deviation and tooth direction deviation are shown in formula (12); root mean square values of tooth profile deviation, pitch deviation and tooth direction deviation, see formula (13);
M α ＝max(|F α |)；M p ＝max(|F p |)；M β ＝max(|F β |) (11)
in the formula (11): m is M α The unit is mm and the maximum value of tooth profile deviation is shown; m is M p The unit is mm and the maximum value of the tooth pitch deviation is shown; m is M β The unit is mm and the maximum value of the tooth direction deviation is the unit;
M α ＝0.00641；M p ＝0.00635；M β ＝0.00429 (11)
substituting specific data in the formula (11); e (E) c 、E x 、E y 、E z And E is a The value is the tracking error of the flexible electronic gear box during the actual running of the self-compensating interference control method;
in the formula (12): a is that α The mean value of tooth profile deviation is given in mm; a is that p The mean value of the tooth pitch deviation is given in mm; a is that β The average value of the tooth direction deviation is given in mm; n is the number of data points collected in the total period, k is 1-n and is a positive integer, and dimensionless;
A α ＝0.00029；A p ＝0.00030；A β ＝0.00022 (12)
substituting specific data in the formula (12); e (E) c 、E x 、E y 、E z And E is a The value is the tracking error of the flexible electronic gear box during the actual running of the self-compensating interference control method;
in the formula (13): r is R α The tooth profile deviation is root mean square value, and the unit is mm; r is R p The unit is mm, which is the root mean square value of the tooth pitch deviation; r is R β The root mean square value of the tooth direction deviation is in mm; n is the number of data points collected in the total period, k is 1-n and is a positive integer, and dimensionless.
R α ＝0.00059；R p ＝0.00059；R β ＝0.00044 (13)
Substituting specific data in the formula (13); e (E) c 、E x 、E y 、E z And E is a The value is the tracking error of the flexible electronic gear box during the actual running of the self-compensating interference control method;
the control method of the electronic gear box in the prior art is different from the control method of the electronic gear box in the step (1) of the flexible electronic gear box; the control method of the electronic gear box in the prior art adopts a master-slave control method, wherein the master-slave control method takes the output position signals of the controllers of the B shaft, the Y shaft and the Z shaft of the three guide shafts as the input position signals of the electronic gear box, and the output position signals of the electronic gear box are taken as the input position signals of the controller of the C shaft of the following shaft, so that the C shaft of the following shaft and the three guide shafts keep a strict mathematical linkage relation; other steps in the control method of the electronic gear box in the prior art are the same as those of the flexible electronic gear box of the invention, and the maximum values of tooth profile deviation, tooth pitch deviation and tooth direction deviation are obtained by implementing the control method of the electronic gear box in the prior art, wherein the maximum values are shown in a formula (14); average values of tooth profile deviation, pitch deviation and tooth direction deviation are shown in formula (15); root mean square values of tooth profile deviation, pitch deviation, and tooth direction deviation are shown in equation (16).
M α ′＝0.01831；M p ′＝0.01816；M β ′＝0.01104 (14)
In formula (14): m is M α ' is the maximum value of the tooth profile deviation of the control method of the electronic gear box in the prior art, and the unit is mm; m is M p ' is the maximum value of the pitch deviation of the control method of the electronic gear box in the prior art, and the unit is mm; m is M β ' is the maximum value of the gear deflection in mm of the control method of the electronic gear box in the prior art.
A α ′＝0.00062；A p ′＝0.00063；A β ′＝0.00047 (15)
In formula (15): a is that α ' is the mean value of tooth profile deviation of the control method of the electronic gear box in the prior art, and the unit is mm; a is that p ' is the average value of the pitch deviation of the control method of the electronic gear box in the prior art, and the unit is mm; a is that β ' is the average value of the gear direction deviation of the control method of the electronic gear box in the prior art, and the unit is mm;
R α ′＝0.00132；R p ′＝0.00134；R β ′＝0.00095 (16)
in formula (16): r is R α ' is the root mean square value of the tooth profile deviation of the control method of the electronic gear box in the prior art, and the unit is mm; r is R p ' is the root mean square value of the tooth pitch deviation of the control method of the electronic gear box in the prior art, and the unit is mm; r is R β ' is the root mean square value of the tooth direction deviation of the control method of the electronic gear box in the prior art, and the unit is mm;
compared with the control method of the electronic gear box in the prior art, the self-compensating disturbance control method of the flexible electronic gear box is adopted, the maximum value of tooth profile deviation is reduced from 0.018311mm of the control method of the electronic gear box in the prior art to 0.00641mm of the self-compensating disturbance control method of the flexible electronic gear box, the average value of tooth profile deviation is reduced from 0.00062mm of the control method of the electronic gear box in the prior art to 0.00029mm of the self-compensating disturbance control method of the flexible electronic gear box, and the root mean square value of tooth profile deviation is reduced from 0.00132mm of the control method of the electronic gear box in the prior art to 0.00059mm of the self-compensating disturbance control method of the flexible electronic gear box; the maximum value of the pitch deviation is reduced from 0.01816mm of the control method of the electronic gear box in the prior art to 0.00635mm of the self-compensating disturbance control method of the flexible electronic gear box, the average value of the pitch deviation is reduced from 0.00063mm of the control method of the electronic gear box in the prior art to 0.00030mm of the self-compensating disturbance control method of the flexible electronic gear box, and the root mean square value of the pitch deviation is reduced from 0.00134mm of the control method of the electronic gear box in the prior art to 0.00059mm of the self-compensating disturbance control method of the flexible electronic gear box; the maximum value of the gear direction deviation is reduced from 0.01104mm of the control method of the electronic gear box in the prior art to 0.00429mm of the self-compensating disturbance control method of the flexible electronic gear box, the average value of the gear direction deviation is reduced from 0.00047mm of the control method of the electronic gear box in the prior art to 0.00022mm of the self-compensating disturbance control method of the flexible electronic gear box, and the mean square root value of the gear direction deviation is reduced from 0.00095mm to 0.00044mm of the self-compensating disturbance control method of the flexible electronic gear box in the control method of the electronic gear box in the prior art.
The self-compensating interference control method of the flexible electronic gear box can be seen to obtain much higher precision than the control method of the electronic gear box in the prior art when the tooth profile deviation, the tooth pitch deviation and the tooth direction deviation are evaluated from the angles of the maximum value, the average value and the root mean square value, and the precision can be stably improved by about 50%, so that the flexible electronic gear box can improve the gear machining precision.
Claims (2)
1. A self-compensating interference control method of a flexible electronic gear box is characterized in that the flexible electronic gear box is a software module which utilizes mathematical operation to realize movement of a movement shaft according to a strict speed ratio relation according to a gear machine tool processing technological parameter set value in a gear numerical control system; the flexible electronic gear box executes the calculated movement by determining the movement axis controller, so that the numerical control gear hobbing machine tool is realized; the numerical control gear hobbing machine tool is provided with an X axis for radial feeding of the cutter, a Y axis for tangential feeding of the cutter, a Z axis for axial feeding of the cutter, an A axis for adjusting the mounting angle of the cutter, a B axis for rotating the cutter and a C axis for rotating the workpiece; the motion axis is divided into two types of guide axis and following axis; the guide shaft is a main motion and is respectively a B shaft for rotating the cutter, a Y shaft for tangential feeding of the cutter and a Z shaft for axial feeding of the cutter; the following shaft is a C shaft which rotates for the workpiece from the motion; the input signal of the B axis of the cutter rotation is a first position signal, the input signal of the X axis of the cutter radial feeding is a second position signal, the input signal of the Y axis of the cutter tangential feeding is a third position signal, and the input signal of the Z axis of the cutter axial feeding is a fourth position signal; the flexible electronic gear box realizes a control function based on a semi-physical simulation platform Dspace, and is characterized by comprising the following operation steps of:
(1) Control method for determining flexible electronic gear box
The flexible electronic gear box adopts a compound control method, wherein the compound control method is to directly use an output position signal obtained by a first position signal through a guide shaft B shaft, an initial input position signal before a third position signal passes through a guide shaft Y shaft and an initial input position signal before a fourth position signal passes through a guide shaft Z shaft as input position signals of the flexible electronic gear box; the output position signal of the flexible electronic gear box is directly used as the input position signal of the following shaft C shaft, so that the following shaft C shaft and the three guide shafts keep a strict mathematical linkage relation of the formula (1);
in the formula (1): z is Z b The number of cutter heads is the number of cutter heads, and the cutter heads are dimensionless; z is Z c The number of teeth of the workpiece is zero; n is n c The unit is r/s for following the rotation speed of the shaft C; n is n b The unit is r/s for guiding the rotation speed of the shaft B; v y The unit is mm/s for guiding the Y-axis moving speed of the shaft; v z The Z-axis moving speed of the guide shaft is measured in mm/s; beta is the helix angle of the gear, in degrees; lambda is the installation angle of the cutter and the unit is degree; m is m n The normal modulus of the gear is dimensionless; k (K) b The guide shaft B axis coefficient is dimensionless; k (K) y The Y-axis coefficient of the guide shaft is dimensionless; k (K) z The Z-axis coefficient of the guide shaft is dimensionless; when the helix angle of the hob is right-handed, beta>0 and K b =1; beta when the helix angle is left-handed<0 and K b -1; when beta and v z When the symbols are the same, K z When the symbol is reversed, K is = -1 z =1; when v y >K at 0 time y When v is =1 y <K at 0 time y ＝-1；
(2) Selecting motion axis controller parameters
The motion axis controller of the flexible electronic gear box is controlled by an active disturbance rejection controller, and the active disturbance rejection controller comprises a tracking differentiatorA linear state error feedback module and an extended state observer; selecting parameter beta in a linear state error feedback module 1 、β 2 And parameter b in the extended state observer 0 As a basic parameter of the active disturbance rejection controller, the active disturbance rejection controller is used for controlling the motion of a motion axis; the four position signals are respectively obtained by adjusting an input position signal through an active disturbance rejection controller, and four disturbance rejection position signals for outputting and eliminating system disturbance are respectively obtained by compensating disturbance existing in a motion axis controller based on the active disturbance rejection controller;
(3) Determining motion rule of motion axis by diagonal roll cutting method
When a gear is machined by adopting a diagonal rolling cutting method, a B shaft for turning a cutter rotates around the axis of the B shaft, an X shaft for radially feeding the cutter is responsible for feeding and retracting the cutter before cutting, and a Y shaft for tangentially feeding the cutter and a Z shaft for axially feeding the cutter move simultaneously during cutting to form a movement rule along diagonal movement; the motion rule of the following shaft C is determined by the output position signal of the flexible electronic gearbox according to the step (1); the motion rule of the following axis C is synthesized by the motion rules of the three guide axes B, Y and Z according to the relation of the formula (1);
(3.1) the motion rule of the B axis of the cutter rotation is that the cutter rotates at a constant rotating speed, and the first position signal is a straight line rising at a constant speed;
(3.2) the X axis of the radial feeding of the cutter does not participate in the cutting process, and the motion rule is that the cutter firstly feeds forward to the radial direction of the workpiece before cutting; remains stationary during cutting; finishing the radial negative tool withdrawal of the cutting tool to the workpiece; the second position signal is a trapezoid movement rule, wherein the trapezoid movement rule of the second position signal is that a left bevel edge of a trapezoid is in feed movement, a right bevel edge of the trapezoid is in withdrawal movement, and an upper bottom of the trapezoid is in a static state;
(3.3) the Y axis of tangential feeding of the cutter participates in the cutting process, and the motion rule is that the cutter is kept motionless before cutting; when the cutter cuts a workpiece, the cutter firstly feeds forward in the tangential direction of the workpiece; finishing cutting and waiting for the X-axis cutter to retract to a safe position; the tool is returned to the tangential direction of the workpiece; the third position signal is a trapezoid movement rule, wherein the trapezoid movement rule of the third position signal is that a left bevel edge of a trapezoid is in feed movement, a right bevel edge of the trapezoid is in withdrawal movement, and an upper bottom of the trapezoid is in a static state;
(3.4) the Z axis of the axial feeding of the cutter participates in the cutting process, and the motion rule is that the cutter is kept motionless before cutting; when the cutter cuts a workpiece, the cutter firstly feeds forward in the axial direction of the workpiece; finishing cutting and waiting for the X-axis cutter to retract to a safe position; the tool withdraws from the axial direction of the workpiece; the fourth position signal is a trapezoid movement rule, wherein the trapezoid movement rule of the fourth position signal is that a left bevel edge of a trapezoid is in feed movement, a right bevel edge of the trapezoid is in withdrawal movement, and an upper bottom of the trapezoid is in a static state;
(4) Establishing a single-axis compensation model following the C axis of the shaft
The method comprises the steps of establishing a single-axis compensation model of a following shaft C shaft by utilizing a coupling relation among the following shaft C shaft, an X shaft for radial feeding of a cutter and a Y shaft for tangential feeding of the cutter, and realizing the compensation of an active disturbance rejection controller of the following shaft C shaft; the operation steps for establishing the uniaxial compensation model following the axis C are as follows:
(4.1) the tracking error E is obtained by the active disturbance rejection controller following the C axis of the shaft by the output position signal of the flexible electronic gear box c And will track error E c Multiplying by a scaling factor K cc Obtaining the compensation delta E of the C axis of the following axis c ；
ΔE c ＝K cc E c (2)
In the formula (2): ΔE c The unit is mm for the compensation quantity following the axis C; e (E) c The tracking error of the C-axis is the unit of mm; k (K) cc The proportional coefficient of tracking error of the C-axis of the follow-up axis is dimensionless;
(4.2) obtaining the tracking error E by the active disturbance rejection controller of the X axis of the radial feeding of the cutter x And will track error E x Multiplying by a scaling factor K cx Obtaining the compensation delta E of the X axis of the radial feeding of the cutter x ；
ΔE x ＝K cx E x (3)
In the formula (3): ΔE x The compensation quantity of the X axis of the radial feeding of the cutter is in mm; e (E) x X-axis tracking error for radial feed of toolsDifference in mm; k (K) cx The proportional coefficient of the X-axis tracking error for radial feeding of the cutter is dimensionless;
(4.3) the third position signal is passed through the active disturbance rejection controller of Y-axis of tangential feed of cutter to obtain tracking error E y And will track error E y Multiplying by a scaling factor K cy Obtaining the compensation delta E of the Y axis of tangential feeding of the cutter y ；
ΔE y ＝K cy E y (4)
In the formula (4): ΔE y The compensation quantity of the Y axis of tangential feeding of the cutter is in mm; e (E) y Y-axis tracking error for tangential feeding of the cutter is in mm; k (K) cy The proportional coefficient of the Y-axis tracking error for tangential feeding of the cutter is dimensionless;
(4.4) the compensation amount ΔE to be followed by the axis C c Compensation delta E of X-axis of radial feeding of cutter x And Y-axis compensation delta E for tangential feed of the tool y Adding to obtain the total compensation quantity E ccc ；
E ccc ＝(ΔE c +ΔE x +ΔE y ) (5)
In formula (5): e (E) ccc The total compensation amount is in mm; ΔE c The unit is mm for the compensation quantity following the axis C; ΔE x The compensation quantity of the X axis for radial feeding of the cutter is in mm; ΔE y The compensation quantity of the Y axis for tangential feeding of the cutter is in mm;
(4.5) the total compensation amount E ccc Multiplying by a scaling factor K eccc Obtaining the final compensation value delta E' c ；
ΔE′ c ＝K eccc E ccc +σ′ c (6)
In formula (6): ΔE' c The final compensation value is in mm; e (E) ccc The unit is mm for the total compensation quantity; k (K) eccc The proportional coefficient is the total compensation quantity, and the dimensionless is realized; sigma'. c The correction amount is taken as a value according to actual conditions, and the unit is mm;
(4.6) adding the final compensation value ΔE' c And tracking error E of the following axis C c Subtracting to obtain the following shaftInput position signal delta E' for C-axis auto-disturbance rejection controller " c The tracking error compensation of the active disturbance rejection controller following the C axis of the shaft is realized, and the control precision of the flexible electronic gear box is improved;
ΔE″ c ＝ΔE′ c -E c (7)
in the formula (7): ΔE' c The unit is mm for the input position signal of the following axis C-axis auto-disturbance rejection controller; ΔE' c The unit is mm for the final compensation value following the axis C; e (E) c The tracking error of the C axis of the follow-up axis is in mm;
(5) Calculating a machining error value
Three evaluation indexes of machining errors are established by the relative position relation of a cutter and a workpiece in the gear hobbing process and are respectively tooth profile deviation F α See formula (8); tooth pitch deviation F p See formula (9); deviation of tooth direction F β See formula (10);
in formula (8): f (F) α Tooth profile deviation is given in mm; z is Z c The number of teeth of the workpiece is zero; m is m n The normal modulus of the workpiece is dimensionless; alpha is the workpiece pressure angle in degrees; beta is the helix angle of the workpiece, and the unit is degree; e (E) c The tracking error of the C axis for the rotation of the workpiece is in mm; e (E) x An X-axis tracking error for radial feeding of the cutter is shown in mm; e (E) y Y-axis tracking error for tangential feeding of the cutter is in mm; e (E) a The A-axis tracking error for adjusting the installation angle of the cutter is measured in degrees; k (K) αc The value of the proportionality coefficient of the C axis of the follow-up axis is 1 or-1, and the proportionality coefficient is dimensionless; k, K αx The proportional coefficient of the X axis for radial feeding of the cutter is 1 or-1, and is dimensionless; k (K) αy The proportional coefficient of the Y axis for tangential feeding of the cutter is 1 or-1, and the value is dimensionless; sigma (sigma) α The tooth profile deviation correction is determined by the processing technological parameters and the characteristic parameters of a machine tool, and the unit is mm;
in the formula (9): f (F) p The tooth pitch deviation is in mm; z is Z c The number of teeth of the workpiece is zero; m is m n The normal modulus of the workpiece is dimensionless; alpha is the workpiece pressure angle in degrees; beta is the helix angle of the workpiece, and the unit is degree; e (E) c The tracking error of the C axis for the rotation of the workpiece is in mm; e (E) x An X-axis tracking error for radial feeding of the cutter is shown in mm; e (E) y Y-axis tracking error for tangential feeding of the cutter is in mm; e (E) a The A-axis tracking error for adjusting the installation angle of the cutter is measured in degrees; k (K) pc The value of the proportionality coefficient of the C axis of the follow-up axis is 1 or-1, and the proportionality coefficient is dimensionless; k (K) px The proportional coefficient of the X axis for radial feeding of the cutter is 1 or-1, and is dimensionless; k (K) py The proportional coefficient of the Y axis for tangential feeding of the cutter is 1 or-1, and the value is dimensionless; sigma (sigma) p The tooth pitch deviation correction is determined by the processing technological parameters and the characteristic parameters of a machine tool, and the unit is mm;
in the formula (10): f (F) β The tooth direction deviation is in mm; z is Z c The number of teeth of the workpiece is zero; m is m n The normal modulus of the workpiece is dimensionless; alpha is the workpiece pressure angle in degrees; beta is the helix angle of the workpiece, and the unit is degree; e (E) c The tracking error of the C axis for the rotation of the workpiece is in mm; e (E) y Y-axis tracking error for tangential feeding of the cutter is in mm; e (E) z Z-axis tracking error for axial feeding of the cutter is in mm; k (K) βc The value of the proportionality coefficient of the C axis of the follow-up axis is 1 or-1, and the proportionality coefficient is dimensionless; k (K) βy The proportional coefficient of the Y axis for tangential feeding of the cutter is 1 or-1, and the value is dimensionless; k (K) βz The proportional coefficient of the Z axis for axial feeding of the cutter is 1 or-1, and the value is dimensionless; sigma (sigma) β For the tooth direction deviation correction quantity, by addingDetermining technical parameters and characteristic parameters of a machine tool, wherein the unit is mm;
the calculation method of maximum value, average value and root mean square value is introduced to realize the evaluation index tooth profile deviation F of the machining error α Deviation of tooth pitch F p Deviation of tooth direction F β Is calculated quantitatively;
under the condition of adopting a self-compensating interference control method of the flexible electronic gear box, the maximum values of the tooth profile deviation, the tooth pitch deviation and the tooth direction deviation are shown in a formula (11); average values of tooth profile deviation, tooth pitch deviation and tooth direction deviation are shown in formula (12); root mean square values of tooth profile deviation, pitch deviation and tooth direction deviation, see formula (13);
M α ＝max(|F α |)；M p ＝max(|F p |)；M β ＝max(|F β |) (11)
In the formula (11): m is M α The unit is mm and the maximum value of tooth profile deviation is shown; m is M p The unit is mm and the maximum value of the tooth pitch deviation is shown; m is M β The unit is mm and the maximum value of the tooth direction deviation is the unit;
in the formula (12): a is that α The mean value of tooth profile deviation is given in mm; a is that p The mean value of the tooth pitch deviation is given in mm; a is that β The average value of the tooth direction deviation is given in mm; n is the number of data points collected in the total period, k is 1-n and is a positive integer, and dimensionless;
in the formula (13): r is R α The tooth profile deviation is root mean square value, and the unit is mm; r is R p The unit is mm, which is the root mean square value of the tooth pitch deviation; r is R β The root mean square value of the tooth direction deviation is in mm; n is the number of data points collected in the total period, k is 1-n and is a positive integer, and dimensionless.
2. A self-compensating disturbance control method for a flexible electronic gearbox in accordance with claim 1, wherein: the specific implementation process of the motion law in the step (3) is as follows:
(3.1) the motion rule of the B axis of the cutter rotation is that the cutter rotates at a constant rotating speed, and the first position signal is a straight line with a slope of 0.8-1 rising at a constant speed;
(3.2) the X axis of the radial feeding of the cutter does not participate in the cutting process, the motion rule is that the motion is increased at a constant speed within 0-5s, and the slope is 1-1.2; the gradient is 0 after being kept unchanged within 5-10 s; the constant speed is reduced to 0 within 10-15s, and the slope is-1.2 to-1; the slope is 0 after being kept unchanged for 15-20 s;
(3.3) the Y axis of tangential feeding of the cutter participates in the cutting process, wherein the motion rule is kept unchanged within 0-5s, and the slope is 0; the gradient is 2 to 2.2 after the constant speed is increased within 5 to 10 seconds; the slope is 0 after being kept unchanged within 10-15 s; the constant speed is reduced to 0 within 15-20s, and the slope is-2.2 to-2;
(3.4) the Z axis of the axial feeding of the cutter participates in the cutting process, wherein the motion rule is kept unchanged within 0-5s, and the slope is 0; the gradient is 4 to 4.2 after the constant speed is increased within 5 to 10 seconds; the slope is 0 after being kept unchanged within 10-15 s; the constant speed is reduced to 0 within 15-20s, and the slope is-4.2 to-4.
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