阅读说明：本技术 一种柔性电子齿轮箱的多轴同步运动控制方法 (Multi-axis synchronous motion control method of flexible electronic gear box ) 是由 田晓青 李旦 吴雨 于 2019-11-28 设计创作，主要内容包括：本发明涉及一种柔性电子齿轮箱的多轴同步运动控制方法,属于数控机床技术领域。该方法适用于数控滚齿机。根据数控滚齿机加工原理,构建一种齿轮几何误差与机床各个运动轴跟踪误差之间的函数关系；由各个运动轴跟踪误差参数建立每一位置控制时间点的齿廓、齿距、齿向偏差的加工误差数学模型；通过建立一种解耦补偿模型用于计算下一位置控制时间点工件回转轴所需补偿量；通过计算各位置控制时间点的加工误差数值,得到位置控制总时间内不采用同步控制方法和采用同步控制方法的加工误差平均绝对值、加工误差总补偿量,完成多轴同步运动控制。本发明通过多轴同步运动控制方法,可以将加工速度提高20％～30％,机床调试时间缩短10％～30％,从而降低生产成本。(The invention relates to a multi-axis synchronous motion control method of a flexible electronic gear box, and belongs to the technical field of numerical control machines. The method is suitable for the numerical control gear hobbing machine. According to the machining principle of a numerical control gear hobbing machine, a functional relation between a gear geometric error and tracking errors of all movement axes of a machine tool is constructed; establishing a machining error mathematical model of tooth profile, tooth pitch and tooth direction deviation of each position control time point according to the tracking error parameters of each motion axis; calculating the compensation quantity required by the workpiece rotating shaft at the next position control time point by establishing a decoupling compensation model; and (3) calculating the machining error numerical values of all the position control time points to obtain the machining error average absolute value and the machining error total compensation quantity which do not adopt a synchronous control method and adopt the synchronous control method in the total position control time, and finishing the multi-axis synchronous motion control. The invention can improve the processing speed by 20-30% and shorten the debugging time of the machine tool by 10-30% by a multi-axis synchronous motion control method, thereby reducing the production cost.)

1. A multi-axis synchronous motion control method of a flexible electronic gear box is suitable for a numerical control gear hobbing machine; the numerical control gear hobbing machine comprises an A shaft, a B shaft, a C shaft, an X shaft, a Y shaft and a Z shaft, wherein the A shaft is a hob installation angle adjusting shaft, the B shaft is a hob rotating shaft, the C shaft is a workpiece rotating shaft, the X shaft is a hob radial feeding shaft, the Y shaft is a hob tangential feeding shaft, and the Z shaft is a hob axial feeding shaft; wherein the B axis, the X axis, the Y axis and the Z axis are main motion axes; each main motion shaft servo motor is detected by a grating encoder and then used as reference data to be input to a microprocessor, the flexible electronic gear box functional module is used as C-axis working data after being processed and transformed according to a hobbing process mathematical model, and a control theory algorithm is adopted to realize the motion rule specified by the electronic gear box module so as to realize hobbing; the flexible electronic gear box realizes a control function based on an ARM, DSP and FPGA hardware platform, and is characterized in that:

according to the machining principle of a numerical control gear hobbing machine, a functional relation between a gear geometric error and tracking errors of all movement axes of a machine tool is constructed; the individual motion axis tracking errors include: b axis tracking error E_b(Hob rotary shaft tracking error E_b) C-axis tracking error E_c(tracking error of rotating shaft of work E_c) Z axis tracking error E_z(hob axial feed shaft tracking error E_z) Y axis tracking error E_y(Hob tangential feed axis tracking error E_y) X-axis tracking error E_x(Hob radial feed axis tracking error E_x) And hob installation angle error E_a(ii) a Establishing tooth profile deviation F from tracking error parameters of various motion axes_αTooth pitch deviation F_pHelical deviation F_βThe machining error mathematical model is used for evaluating the geometric error of the gear by utilizing the numerical result of the machining error mathematical model; calculating the machining error value, namely the tooth profile deviation F at each position control time point through each motion axis error parameter at each position control time point_αNumerical value, pitch deviation F_pNumerical, helical deviation F_βA numerical value; based on the idea of cross-coupling control, a decoupling compensation model is established for calculating the compensation quantity delta E required by the C axis_c(ii) a Compensating the amount of compensation Δ E at the next position control time point_cCompensating to the C-axisCalculating the compensated machining error value, i.e. the compensated tooth profile deviation F, from the tracking error of each motion axis at that moment_αNumerical, compensated tooth pitch deviation F_pNumerical, post-compensation helix deviation F_βAnd meanwhile, obtaining the average absolute value of the machining errors and the total compensation quantity of the machining errors without adopting a synchronous control method and adopting the synchronous control method in the total time of the position control, and finishing the multi-axis synchronous motion control of the total time of the position control.

2. The multi-axis synchronous operation control method of the flexible electronic gearbox is characterized by comprising the following specific operation steps of:

(1) determination of gear machining type by' diagonal hobbing method

When the helical cylindrical gear is machined by adopting a diagonal hobbing method, the C shaft generates additional rotation to meet the geometric relationship of generating a spiral line because the cutter moves along the Z shaft; when a tool shifting process is required, the C shaft generates additional rotation to meet the requirement of a generating relationship changed due to tool shifting because the tool moves along the Y shaft;

the generating and differential relation of the processed helical gear is shown as a formula (1),

in formula (1): z_b、λ、n_bThe number of the heads of the hob, the helix angle of the hob, the rotation speed of the hob shaft, Z_c、β、m_n、n_cThe number of the teeth of the workpiece, the helical angle of the workpiece, the normal modulus of the workpiece and the rotating speed of the workpiece are respectively; k_b、K_z、K_yRespectively a first polynomial coefficient, a second polynomial coefficient and a third polynomial coefficient; v. of_zFor axial feed speed of hob, v_yThe tangential feeding speed of the hob is determined, and when the helix angle of the hob is right-handed, β is determined>At 0, K_BHelix angle left hand, i.e. β, 1<At 0, K_BWhen β is equal to-1>0、V_Z<At 0, K_ZWhen β is equal to 1<0、V_Z<At 0, K_ZWhen β is equal to-1>0、V_Z>At 0, K_ZWhen β is equal to-1<0、V_Z>At 0, K_Z1 is ═ 1; when V is_Y>At 0, K_Y1 is ═ 1; when V is_Y<At 0, K_Y＝-1；

When the straight spur gear is machined, namely the workpiece helix angle β is 0;

(2) establishing a machining error mathematical model

Determining the machining types of the numerical control gear hobbing machine to be a left-handed helical gear, a right-handed helical gear and a straight gear by the step (1); establishing a position control time point t of a workpiece_kThe machining error mathematical model of (2), the motion error relates to relevant parameters: b axis tracking error E_bC-axis tracking error E_cZ axis tracking error E_zY axis tracking error E_yX-axis tracking error E_xAnd hob installation angle error E_a(ii) a Position control time t_kRespective motion axis tracking error of

tooth profile deviation of three evaluation indexes for establishing gear geometric error by relative position attitude relation of cutter and workpiece in gear hobbing processPitch offset

in the formulae (2), (3), (4):units are mm, m_nIs the normal modulus, Z, of the workpiece_cWhen the hob rotates rightwards, β is that the number of teeth of the workpiece is α, the pressure angle of the workpiece is α, the unit is DEG, the helix angle of the workpiece is β, the unit is DEG, and the unit is DEG, the gamma is the installation angle of the hob, and the unit is DEG>0, when the hob is in left-hand rotation, β<0；

(3) Establishing decoupling compensation model

According to the machining error mathematical model, a decoupling compensation model based on a cross coupling control idea is provided for reducing the error of multi-axis synchronous motion, so that the accurate control of the multi-axis synchronous motion is realized; in the formula (3)

the relationship between the compensation object and the polynomial parameters influencing the geometric errors of the gear, i.e. the position control time t, is obtained from equation (5)_k+1C axis compensation amount ofAnd position control time t_kError of tracking each axis of motion E_c、E_x、E_yThe obtained decoupling compensation model is as follows:

in formula (6):

in formula (7):

in the formulas (5), (6) and (7), k is 0-n;

(4) calculating the average absolute value of the machining error and the total compensation amount of the machining error

Under the condition of not adopting a synchronous control method, the average absolute values of three processing errors of the total position control time t are respectively as follows:

M_αis the mean absolute value of the error of the tooth profile in mm and M_pIs the mean absolute value of the pitch error in mm and M_βThe unit is mm, k is 0-n;

in the case of the synchronous control method, the method will be

M'_αis the mean absolute value of tooth profile error in mm and M'_pIs mean absolute value of tooth pitch error in mm and M'_βThe unit is mm, k is 0-n;

the total compensation amount of the total position control time t is as follows:

S＝n(M_α+M_p+M_β-M'_α-M'_p-M'_β) (8)

in the formula (8), S is the total compensation amount of the total position control time t, and the unit is mm, thereby completing the multi-axis synchronous motion control of the total position control time t.

Technical Field

The invention belongs to the technical field of numerical control machines, and particularly relates to a multi-shaft synchronous operation control method for a numerical control gear hobbing machine with a coupling relation.

Background

For realizing multi-axis motion control of a common numerical control gear processing machine tool, a set of direct current speed regulating device is generally used for driving two direct current motors, armatures of the two motors are connected in series, and excitation coils are connected in parallel. In order to maintain speed synchronization, the two motor shafts must be rigidly connected, and only one of the two motors provides speed feedback data; two sets of AC variable frequency speed regulating systems are used to control two AC variable frequency or servo motors as main and auxiliary shafts, and the two motors provide their own speed feedback data. In order to keep the speed synchronous, the two motor shafts also need to be rigidly connected, but the situation that the speed ring is continuously adjusted can occur due to the clearance, so that the control system is extremely unstable, and the oscillation generated by the adjustment static error of the control system can be obviously observed at the shaft end of the motor; if the system is arranged at the end of the motor, although the system is stable, the control precision is difficult to guarantee due to transmission clearance. In addition, numerically controlled gear cutting machines have extremely stringent requirements between the two or more relative speeds of motion associated with the inline transmission during the machining process. The traditional numerical control system obtains linkage motion instructions of a plurality of coordinates by using an interpolation algorithm, but the dynamic precision and the static precision of each coordinate axis cannot be consistent, so that the requirement of inline transmission cannot be met.

As the numerical control system for machining the medium-high grade gear in the independent intellectual property rights is blank, foreign medium-high grade gear machining numerical control systems, such as German SIEMENS, Japan FANUC, Japan Mitsubishi, French NUM and the like, have to be purchased. The foreign gear numerical control systems are expensive and have a strict market admission system, and the development of the gear processing equipment manufacturing industry in China is severely restricted. Therefore, the method promotes the research and development and industrialization of the domestic gear machining numerical control system, improves the technical level, the matching capacity and the market competitiveness of domestic high-grade gear numerical control system products, breaks the situation that the market of the high-grade numerical control system in the gear machine tool is monopolized by foreign enterprises, improves the complete machine matching capacity of the domestic high-grade gear numerical control machine tool, and has great significance in promoting the development of the domestic gear equipment manufacturing industry.

In addition, under the condition of obtaining the same processing quality, the independently developed medium-high-grade gear processing numerical control system device with the electronic gear box function has the price less than 50% of the price of imported products, so that the device has great cost performance advantage.

Disclosure of Invention

The invention provides a multi-axis synchronous motion control method of a flexible electronic gear box, aiming at realizing multi-axis linkage high-precision control based on the flexible electronic gear box in the hobbing process.

A multi-axis synchronous motion control method of a flexible electronic gear box is suitable for a numerical control gear hobbing machine; the numerical control gear hobbing machine comprises an A shaft, a B shaft, a C shaft, an X shaft, a Y shaft and a Z shaft, wherein the A shaft is a hob installation angle adjusting shaft, the B shaft is a hob rotating shaft, the C shaft is a workpiece rotating shaft, the X shaft is a hob radial feeding shaft, the Y shaft is a hob tangential feeding shaft, and the Z shaft is a hob axial feeding shaft; wherein the B axis, the X axis, the Y axis and the Z axis are main motion axes; each main motion shaft servo motor is detected by a grating encoder and then used as reference data to be input to a microprocessor, the flexible electronic gear box functional module is used as C-axis working data after being processed and transformed according to a hobbing process mathematical model, and a control theory algorithm is adopted to realize the motion rule specified by the electronic gear box module so as to realize hobbing; the flexible electronic gearbox realizes a control function based on an ARM, DSP and FPGA hardware platform;

according to the machining principle of a numerical control gear hobbing machine, a functional relation between a gear geometric error and tracking errors of all movement axes of a machine tool is constructed; the individual motion axis tracking errors include: b axis tracking error E_b(Hob rotary shaft tracking error E_b) C-axis tracking error E_c(tracking error of rotating shaft of work E_c) Z axis tracking error E_z(hob axial feed shaft tracking error E_z) Y axis tracking error E_y(Hob tangential feedAxis tracking error E_y) X-axis tracking error E_x(Hob radial feed axis tracking error E_x) And hob installation angle error E_a(ii) a Establishing tooth profile deviation F from tracking error parameters of various motion axes_αTooth pitch deviation F_pHelical deviation F_βThe machining error mathematical model is used for evaluating the geometric error of the gear by utilizing the numerical result of the machining error mathematical model; calculating the machining error value, namely the tooth profile deviation F at each position control time point through each motion axis error parameter at each position control time point_αNumerical value, pitch deviation F_pNumerical, helical deviation F_βA numerical value; based on the idea of cross-coupling control, a decoupling compensation model is established for calculating the compensation quantity delta E required by the C axis_c(ii) a Compensating the amount of compensation Δ E at the next position control time point_cCompensating to C axis, calculating compensated machining error value, i.e. compensated tooth profile deviation F, according to tracking error of each motion axis at the moment_αNumerical, compensated tooth pitch deviation F_pNumerical, post-compensation helix deviation F_βAnd meanwhile, obtaining the average absolute value of the machining errors and the total compensation quantity of the machining errors without adopting a synchronous control method and adopting the synchronous control method in the total time of the position control, and finishing the multi-axis synchronous motion control of the total time of the position control.

The technical scheme for further limiting is as follows:

the specific operation steps of the multi-axis synchronous operation control based on the flexible electronic gearbox are as follows:

(1) determination of gear machining type by' diagonal hobbing method

When the helical cylindrical gear is machined by adopting a diagonal hobbing method, the C shaft generates additional rotation to meet the geometric relationship of generating a spiral line because the cutter moves along the Z shaft; when a tool shifting process is required, the C shaft generates additional rotation to meet the requirement of a generating relationship changed due to tool shifting because the tool moves along the Y shaft;

the generating and differential relation of the processed helical gear is shown as a formula (1),

in the formula Z_b、λ、n_bThe number of the heads of the hob, the helix angle of the hob, the rotation speed of the hob shaft, Z_c、β、m_n、n_cThe number of the teeth of the workpiece, the helical angle of the workpiece, the normal modulus of the workpiece and the rotating speed of the workpiece are respectively; k_b、K_z、K_yRespectively a first polynomial coefficient, a second polynomial coefficient and a third polynomial coefficient; v. of_zFor axial feed speed of hob, v_yThe tangential feeding speed of the hob is determined, and when the helix angle of the hob is right-handed, β is determined>At 0, K_BHelix angle left hand, i.e. β, 1<At 0, K_BWhen β is equal to-1>0、V_Z<At 0, K_ZWhen β is equal to 1<0、V_Z<At 0, K_ZWhen β is equal to-1>0、V_Z>At 0, K_ZWhen β is equal to-1<0、V_Z>At 0, K_Z1 is ═ 1; when V is_Y>At 0, K_Y1 is ═ 1; when V is_Y<At 0, K_Y＝-1；

When the straight spur gear is machined, namely the workpiece helix angle β is 0;

(2) establishing a machining error mathematical model

Determining the machining types of the numerical control gear hobbing machine to be a left-handed helical gear, a right-handed helical gear and a straight gear by the step (1); establishing a position control time point t of a workpiece_kThe machining error mathematical model of (2), the motion error relates to relevant parameters: b axis tracking error E_bC-axis tracking error E_cZ axis tracking error E_zY axis tracking error E_yX-axis tracking error E_xAnd hob installation angle error E_a(ii) a Position control time t_kRespective motion axis tracking error ofWherein

The unit is mm, and the unit is,

the unit is the rad,

the unit is degree, k is 0-n;

tooth profile deviation of three evaluation indexes for establishing gear geometric error by relative position attitude relation of cutter and workpiece in gear hobbing processPitch offset

Deviation in tooth direction

Position control time t_kThe machining error mathematical model of (a) is as follows:

in the formulae (2), (3), (4):

units are mm, m_nIs the normal modulus, Z, of the workpiece_cWhen the hob rotates rightwards, β is that the number of teeth of the workpiece is α, the pressure angle of the workpiece is α, the unit is DEG, the helix angle of the workpiece is β, the unit is DEG, and the unit is DEG, the gamma is the installation angle of the hob, and the unit is DEG>0, when the hob is in left-hand rotation, β<0；

(3) Establishing decoupling compensation model

According to the machining error mathematical model, a decoupling compensation model based on the cross coupling control idea is provided for reducingSmall multi-axis synchronous motion error, thereby realizing the accurate control of multi-axis synchronous motion; in the formula (3)

The item is set as

Obtaining the formula (5) and setting the pitch error

Is 0;

the relationship between the compensation object and the polynomial parameters influencing the geometric errors of the gear, i.e. the position control time t, is obtained from equation (5)_k+1C axis compensation amount ofAnd position control time t_kError of tracking each axis of motion E_c、E_x、E_yThe obtained decoupling compensation model is as follows:

in formula (6):is C-axis compensation quantity, and the unit is mm and m_nIs the gear normal module, Z_cGear tooth number α is gear pressure angle, unit is degree, β is gear helix angle, unit is degree, gamma is hob installation angle, unit is degree;

in formula (7):

for controlling the time t_k+1C-axis tracking error controlled by synchronous motion is adopted, and the unit is rad;

in the formulas (5), (6) and (7), k is 0-n;

(4) calculating the average absolute value of the machining error and the total compensation amount of the machining error

Under the condition of not adopting a synchronous control method, the average absolute values of three processing errors of the total position control time t are respectively as follows:

M_αis the mean absolute value of the error of the tooth profile in mm and M_pIs the mean absolute value of the pitch error in mm and M_βThe unit is mm, k is 0-n;

in the case of the synchronous control method, the method will be

Substituting the equations (2), (3) and (4) to obtain the position control time t_kIs/are as follows

The three average absolute values of the processing error of the total position control time t are respectively as follows:

M'_αis the mean absolute value of tooth profile error in mm and M'_pIs mean absolute value of tooth pitch error in mm and M'_βThe unit is mm, k is 0-n;

the total compensation amount of the total position control time t is as follows:

S＝n(M_α+M_p+M_β-M'_α-M'_p-M'_β) (8)

in the formula (8), S is the total compensation amount of the total position control time t, and the unit is mm, thereby completing the multi-axis synchronous motion control of the total position control time t.

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

(1) according to the invention, by the multi-axis synchronous motion control method of the flexible electronic gear box, the machining error of the gear can be compensated and corrected in the process of machining the gear by using the numerical control gear hobbing machine, so that the geometric error of the gear is reduced.

(2) The multi-axis synchronous motion control method of the flexible electronic gear box can improve the processing speed by 20-30 percent and shorten the debugging time of a machine tool by 10-30 percent, thereby reducing the production cost.

(3) According to the multi-shaft synchronous motion control method of the flexible electronic gear box, the numerical control gear hobbing machine can be used for flexibly processing different types of gears such as a left-handed helical gear, a right-handed helical gear and a straight-tooth cylindrical gear, a multi-shaft synchronous motion control method for a workpiece gear is not required, and the multi-shaft synchronous motion control method has wide adaptability.

Drawings

FIG. 1 is a schematic view showing the distribution of the motion axes of a gear hobbing machine;

FIG. 2 is a diagram of a flexible electronic gear box multi-axis synchronous motion control principle.

Detailed Description

In order to more specifically describe the technical means and the innovative features of the present invention, the technical solutions of the present invention are further described in detail by embodiments with reference to the accompanying drawings.

A multi-axis synchronous motion control method of a flexible electronic gear box is suitable for a numerical control gear hobbing machine, and is shown in figure 1; the numerical control gear hobbing machine comprises an A shaft, a B shaft, a C shaft, an X shaft, a Y shaft and a Z shaft; the axis A is a hob installation angle adjusting shaft, the axis B is a hob rotating shaft, the axis C is a workpiece rotating shaft, the axis X is a hob radial feeding shaft, the axis Y is a hob tangential feeding shaft, and the axis Z is a hob axial feeding shaft.