A method of circular interpolation with variable synchronization ratio considering the synchronous establishment transition process

Abstract

The present invention discloses a method for circular interpolation with variable synchronization ratio considering the synchronous establishment transition process, wherein a rectangular coordinate system is established with the center of the circular arc to be interpolated as the coordinate origin, and the unit angle increment corresponding to each interpolation cycle step is calculated; a virtual axis G is created as a guide axis for synchronous motion, and a synchronous motion relationship between the virtual axis and the physical axis is established; the synchronous establishment transition process time required for the physical axis X and axis Y to reach a new synchronous state from the original synchronous state through an acceleration or deceleration process is calculated; the center angle corresponding to the virtual axis G when the synchronization ratio is changed in advance in each interpolation cycle is obtained; the virtual axis G is activated to move, and when the virtual axis G reaches the center angle corresponding to the change in synchronization ratio in advance, the synchronization ratio of the current interpolation cycle is updated, so that the physical axis X and axis Y move with the updated synchronization ratio, and when the virtual axis G moves to the center angle corresponding to the end point, the interpolation is completed, and the circular interpolation ends. The above method effectively reduces the interpolation error and improves the accuracy of circular interpolation.

Description

Technical Field

[0001] The invention relates to the field of motion control technology, and in particular to a method for circular interpolation with variable synchronization ratio taking into account a synchronous establishment transition process. Background Art

[0002] As a key technology of motion control, motion interpolation algorithm directly affects the accuracy of motion trajectory and operation efficiency. Circular interpolation is one of the basic forms of interpolation motion and the basis for realizing complex curve motion. Its accuracy and efficiency have a decisive influence on the accuracy of complex curve motion trajectory. Existing circular interpolation algorithms can generally be divided into two categories: pulse incremental interpolation and data sampling interpolation. Among them, pulse incremental interpolation controls the axis to move in unit increments by outputting pulse increments. Among these methods, the point-by-point comparison method and digital differential analyzer (DDA) are the most representative, but these methods cannot achieve multi-axis linkage during the entire interpolation motion process, resulting in large interpolation errors, and complex quadrant transformations need to be considered, making the algorithm difficult to implement; the output form of data sampling interpolation is no longer a pulse increment, which can effectively reduce the feed speed fluctuation at the line segment connection. Its interpolation accuracy is higher than that of pulse incremental interpolation, but when the step length is not an integer multiple of the expected speed, a zero distance will be generated, resulting in error accumulation, affecting the interpolation accuracy. Although the above-mentioned prior art can realize circular interpolation, each axis is controlled as an independent axis, and the interpolation error caused by the asynchronous movement process of each axis is not considered, which restricts the further improvement of the circular interpolation accuracy.

[0003] In recent years, some scholars have proposed a variable synchronization ratio circular interpolation method to address the problem of large interpolation errors caused by asynchronous axis motion. The method uses synchronous motion control to ensure that the position and speed of each physical axis are strictly synchronized. By continuously changing the synchronization ratio, the physical axis is adjusted from the original synchronization state to the new synchronization state, thereby realizing circular interpolation with high interpolation accuracy and operation efficiency. The essence of this method is to continuously adjust the speed of the physical axis by continuously changing the synchronization ratio, that is, the physical axis changes from the speed corresponding to the original synchronization state to the speed corresponding to the new synchronization state. However, since the speed cannot change suddenly during the actual motion process, when the synchronization ratio changes, the axis needs to follow a certain acceleration and deceleration control strategy and go through an acceleration or deceleration process to reach a new synchronization state. This process is called the transition process of synchronization establishment. The traditional variable synchronization ratio circular interpolation method ignores the transition process of synchronization establishment and does not consider the movement of the axis during the transition process of axis synchronization establishment, which causes the actual motion trajectory to be offset as a whole relative to the target trajectory, resulting in a large interpolation error, affecting the application of this method in high-speed and high-precision occasions. Summary of the invention

[0004] The purpose of the present invention is to provide a method for circular interpolation with a variable synchronization ratio that takes into account a synchronous establishment transition process. The method takes into account a synchronous establishment transition process between a virtual axis G and physical axes X and Y. According to an acceleration and deceleration control strategy, the synchronous establishment transition process time required for the physical axes X and Y to reach a new synchronous state after an acceleration or deceleration process is calculated. The center angle of the virtual axis G corresponding to the synchronous ratio is calculated and set when the synchronous ratio is changed in advance, so as to ensure that when the physical axes X and Y move onto the arc, they just reach a new synchronous state with the virtual axis G, thereby effectively reducing the interpolation error and improving the circular interpolation accuracy.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] A method for circular interpolation with variable synchronization ratio considering a synchronous establishment transition process, the method comprising:

[0007] Step 1: Establish a rectangular coordinate system with the center of the arc to be interpolated as the origin, and calculate the unit angle increment corresponding to each interpolation cycle step according to the starting position, end position and center angle of the arc interpolation;

[0008] Step 2: Create a virtual axis G as the leading axis of synchronous motion, use the actual physical axis X and axis Y as the following axes of synchronous motion, and establish the synchronous motion relationship between the virtual axis and the physical axis;

[0009] Step 3: According to the acceleration and deceleration control strategy, the synchronization establishment transition process time required for the physical axis X and axis Y to reach the new synchronization state from the original synchronization state through the acceleration or deceleration process is calculated;

[0010] Step 4, using the synchronization establishment transition process time calculated in step 3 and the speed of the virtual axis G, calculate the position advance amount of the virtual axis G when the synchronization ratio is changed in advance in each interpolation cycle, and then obtain the center angle of the virtual axis G corresponding to the synchronization ratio when the synchronization ratio is changed in advance in each interpolation cycle;

[0011] Step 5: According to the positional relationship between the virtual axis G and the physical axis X and axis Y during the synchronous motion, the synchronous motion relationship between the physical axis X and axis Y following the virtual axis G is obtained respectively, and then the synchronization ratio of each interpolation cycle is calculated using the unit angle increment obtained in step 1;

[0012] Step 6, activate the virtual axis G movement. When the virtual axis G reaches the center angle corresponding to the advance change of the synchronization ratio, update the synchronization ratio of the current interpolation cycle, so that the physical axis X and axis Y move with the updated synchronization ratio. When the virtual axis G moves to the center angle corresponding to the end point, the interpolation is completed and the circular interpolation ends.

[0013] It can be seen from the technical solution provided by the present invention that the method takes into account the transition process of the virtual axis G and the physical axis X and axis Y being synchronously established, and calculates the synchronization establishment transition process time required for the physical axis X and axis Y to reach a new synchronization state after the acceleration or deceleration process according to the acceleration and deceleration control strategy, and calculates and sets the center angle corresponding to the virtual axis G when the synchronization ratio is changed in advance, to ensure that when the physical axis X and axis Y move to the arc, they just reach a new synchronization state with the virtual axis G, thereby effectively reducing the interpolation error and improving the arc interpolation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0015] Figure 1 A schematic flow chart of a method for circular interpolation with variable synchronization ratio considering a synchronous establishment transition process provided by an embodiment of the present invention;

[0016] Figure 2 This is a schematic diagram of the relationship between the physical axis position and θ during the full circular motion interpolation according to the embodiment of the present invention;

[0017] Figure 3 A schematic diagram of an S-curve acceleration / deceleration control strategy for synchronously establishing a transition process according to an embodiment of the present invention;

[0018] Figure 4 A schematic diagram of coordinates of sampling points of the interpolation trajectory according to an embodiment of the present invention;

[0019] Figure 5 This is a schematic diagram of the MSE results of various methods at different radii under the conditions of speed v=10mm / s and interpolation step length of 1mm in the example of the present invention;

[0020] Figure 6 This is a schematic diagram of the δ variation curve obtained by different methods under the condition of speed v=10mm / s in the example of the present invention. DETAILED DESCRIPTION

[0021] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments, which does not constitute a limitation of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0022] like Figure 1 The figure is a flow chart of a method for circular interpolation with variable synchronization ratio considering the synchronous establishment transition process provided by an embodiment of the present invention, the method comprising:

[0023] Step 1: Establish a rectangular coordinate system with the center of the arc to be interpolated as the origin, and calculate the unit angle increment corresponding to each interpolation cycle step according to the starting position, end position and center angle of the arc interpolation;

[0024] In this step, the center O of the arc to be interpolated is set as the coordinate origin, the line connecting the arc starting point P0 and the center O is defined as the vertical axis of the rectangular coordinate system, and the rectangular coordinate system is constructed. Then, the coordinates of the arc starting point P0 are (0, R), and R is the radius of the arc to be interpolated.

[0025] Define the end point of the i-th interpolation cycle as P i (P Xi ,P Yi );P Xi , P Yi Respectively represent the end positions of the physical axis X and axis Y at the i-th interpolation cycle, i = 1, 2, ..., n; n is the number of interpolation steps;

[0026] Define θ as the arc starting point P0 and the interpolation point P i The corresponding central angle is θ i =∠P0OP i , when θ n =2π, it means the arc to be interpolated is a complete circle;

[0027] The unit angle increment Δθ corresponding to each interpolation cycle step is calculated using the following formula (1):

[0028] Δθ=θ i -θ i-1 =(θ n -θ0) / n (1).

[0029] Step 2: Create a virtual axis G as the leading axis of synchronous motion, use the actual physical axis X and axis Y as the following axes of synchronous motion, and establish the synchronous motion relationship between the virtual axis and the physical axis;

[0030] In this step, the physical axis X and axis Y of the actual motion are moved to the starting position of the arc, and the arc interpolation speed is set to v, where v is a constant; the characteristic that the center angle of the interpolation point changes uniformly with time is used to construct a virtual axis G with the center angle of the interpolation point as the position output; the virtual axis G is used as the leading axis of the synchronous motion, and the physical axis X and axis Y are used as the following axes of the synchronous motion; the synchronous motion relationship between the virtual axis G and the physical axis X and axis Y is established according to formula (2);

[0031] like Figure 2The figure shows the relationship between the physical axis position and the center angle θ during the full circular motion interpolation according to the embodiment of the present invention. According to the parametric equation of the circle, the positions of the physical axis X and axis Y are calculated using the following formula (2): With θ i The change relationship:

[0032]

[0033] Step 3: According to the acceleration and deceleration control strategy, the synchronization establishment transition process time required for the physical axis X and axis Y to reach the new synchronization state from the original synchronization state through the acceleration or deceleration process is calculated;

[0034] In this step, we can take the typical S-curve acceleration and deceleration control strategy as an example, and assume that the axis needs to go through the following steps to reach the new synchronization state from the original synchronization state. Figure 3 The acceleration process shown.

[0035] According to the S-type acceleration and deceleration control strategy, the time of the physical axis X and axis Y in the acceleration section, uniform acceleration section, and deceleration section is calculated using the following formula (3):

[0036]

[0037] In the formula, · corresponds to the physical axis name; t ·1 ,t ·2 and t ·3 Respectively represent the time of acceleration section, uniform acceleration section and deceleration section; A ·max Indicates the maximum acceleration; J · represents the acceleration; v ·sta 、v ·end They represent the initial speed and final speed of the current synchronous transition process respectively. The corresponding relationship between the arc interpolation speed and the speed components of each physical axis is calculated by formula (4):

[0038]

[0039] In the formula, v is a constant, which represents the circular interpolation speed;

[0040] The above process is that the axis is accelerated from the original synchronous state to the new synchronous state;

[0041] When it is necessary to decelerate to reach a new synchronous state, let t ·1 ,t ·2 and t ·3 They represent the time of acceleration / deceleration section, uniform deceleration section and deceleration / acceleration section respectively. ·max Indicates the maximum deceleration, J · represents the acceleration, and the time of different deceleration sections is calculated using equations (3) and (4) respectively;

[0042] Then, the following formula (5) is used to obtain the synchronization establishment transition process time t required for the physical axis X and axis Y to reach the new synchronization state from the original synchronization state: ·total :

[0043] t ·total =t ·1 +t ·2 +t ·3 (5).

[0044] Step 4, using the synchronization establishment transition process time calculated in step 3 and the speed of the virtual axis G, calculate the position advance amount of the virtual axis G when the synchronization ratio is changed in advance in each interpolation cycle, and then obtain the center angle of the virtual axis G corresponding to the synchronization ratio when the synchronization ratio is changed in advance in each interpolation cycle;

[0045] In this step, since the position output of the virtual axis G is the center angle corresponding to the interpolation point, the center angle corresponding to the virtual axis G when the synchronization ratio is changed in advance in the i-th interpolation cycle is Calculate using the following formula (6)

[0046]

[0047] In the formula, is the position advance amount of the virtual axis G when the synchronization ratio is changed in advance during the i-th interpolation cycle, which is calculated using the following formula (7):

[0048]

[0049] In the formula, v G is the speed of the virtual axis G, calculated using equations (8) and (9); It indicates the average time for physical axes X and Y to reach a new synchronization state from the original synchronization state after acceleration or deceleration;

[0050] Let t G Indicates that the virtual axis moves from θ0 to θ n Time, t G Calculated by the following formula (8):

[0051] t G =n×l / v (8)

[0052] In the formula, l = 2Rsin (Δθ / 2) is the step length corresponding to the unit angle increment; n is the number of interpolation steps; v is a constant, indicating the arc interpolation speed; R is the radius of the arc to be interpolated; θ is the distance between the arc starting point P0 and the interpolation point P i The corresponding central angle of the circle;

[0053] Substituting the above equation (8) into the following equation (9), the velocity v of the virtual axis G is calculated: G :

[0054] v G =(θ n -θ0) / t G (9).

[0055] Step 5: According to the positional relationship between the virtual axis G and the physical axis X and axis Y during the synchronous motion, the synchronous motion relationship between the physical axis X and axis Y following the virtual axis G is obtained respectively, and then the synchronization ratio of each interpolation cycle is calculated using the unit angle increment obtained in step 1;

[0056] In this step, during the synchronous motion, the virtual axis G and the physical axis X and axis Y have the following positional relationship (10):

[0057]

[0058] In the formula, They represent the end positions of the virtual axis G at the i-1th and i-th interpolation cycles respectively; They respectively represent the synchronization ratios of the physical axis X and axis Y following the virtual axis G in the ith interpolation cycle;

[0059] According to formula (10), the synchronization ratio with the virtual axis G and the physical axis X and axis Y positions as intermediate parameters is obtained:

[0060]

[0061] Substituting equation (2) into equation (11), we can obtain the synchronization ratio of the i-th interpolation cycle:

[0062]

[0063] Then use equation (1) to convert θ i and θ i-1 Expressed as Δθ, the synchronization ratio of each interpolation cycle is calculated according to the following formula (13):

[0064]

[0065] Step 6, activate the virtual axis G movement. When the virtual axis G reaches the center angle corresponding to the advance change of the synchronization ratio, update the synchronization ratio of the current interpolation cycle, so that the physical axis X and axis Y move with the updated synchronization ratio. When the virtual axis G moves to the center angle corresponding to the end point, the interpolation is completed and the circular interpolation ends.

[0066] In this step, define the variable θ GIt is used to store the center angle of the virtual axis G corresponding to the change of synchronization ratio in advance in each interpolation cycle. The center angle of the virtual axis G corresponding to the change of synchronization ratio in advance in the first interpolation cycle calculated in step 4 is Assign the value to variable θ G ;

[0067] Define the variable k X , k Y Store the synchronization ratios of the physical axis X and axis Y respectively, and the synchronization ratio of the first interpolation cycle calculated in step 5 Assign values ​​to variables k respectively X , k Y ;

[0068] Activate the virtual axis G motion, so that the virtual axis G moves at a speed v G From the starting point corresponding to the center angle θ0 to the end point corresponding to the center angle θ n Movement; when the virtual axis G reaches the center angle θ corresponding to the change of synchronization ratio in advance G When θ G Whether the end point is reached corresponds to the central angle θ n ;

[0069] If θ G ≠θ n , then let i++, that is, the i+1th interpolation cycle, and update the center angle and synchronization ratio of the virtual axis G when the current interpolation cycle changes the synchronization ratio in advance, that is, the center angle θ of the virtual axis G when the i+1th interpolation cycle changes the synchronization ratio in advance calculated in step 4 Gi+1 Assign the value to variable θ G At the same time, the synchronization ratio k of the i+1th interpolation cycle calculated in step 5 is Xi+1 , k Yi+1 Assign values ​​to variables k respectively X , k Y , so that the physical axis X and axis Y move at the updated synchronization ratio;

[0070] If θ G =θ n , it indicates that the virtual axis G moves to the end point of the arc and the circular interpolation process ends.

[0071] The implementation process of the above method is illustrated below with a specific example. In this example, two physical axes are defined as axis X and axis Y, and the initial arc interpolation speed v=10mm / s, and the maximum acceleration is 100mm / s. 2 , the maximum deceleration is -100mm / s 2 , acceleration j = 50000 mm / s 3; First, select the center O of the arc to be interpolated as the origin of the coordinate system, establish a rectangular coordinate system, set the radius R of the arc to be interpolated to 20mm, then the coordinates of the starting point P0 of the arc to be interpolated are (0,20), and define the line connecting the center of the arc to be interpolated and the starting point P0 of the interpolation motion as the vertical axis of the coordinate system; the starting position of the central angle is θ0=0, and the end position is θ n =2π, the interpolation step length is set to 1mm, and the total number of interpolation steps n=126;

[0072] First, use the above formula (1) to calculate the unit angle increment Δθ:

[0073] Δθ=(360-0) / 126=2.857

[0074] Before circular interpolation, move the physical axis X and axis Y to the starting position, create a virtual axis G, and establish a synchronous relationship between the virtual axis G and the physical axis X and axis Y;

[0075] Using the above formula (5), the synchronization establishment transition process time required for the X axis to reach the new synchronization state from the original synchronization state in the first interpolation cycle is calculated:

[0076] t Xtotal =0.002-0.002+0.002=0.002

[0077] Among them, t X1 ,t X2 ,t X3 Calculated from the above formula (3):

[0078] t X1 =t X3 =100 / 50000=0.002

[0079] t X2 =(9.99-10) / 100-100 / 50000=-0.002

[0080] Using the above formula (5), the synchronization establishment transition process time required for the Y axis to reach the new synchronization state from the original synchronization state in the first interpolation cycle is calculated:

[0081] t Ytotal =0.002-0.003+0.002=0.001

[0082] Among them, t Y1 ,t Y2 ,t Y3 Calculated from the above formula (3):

[0083] t Y1 =t Y3 =100 / 50000=0.002

[0084] t Y2 =(-0.498-0) / -100-100 / 50000=0.003

[0085] Using the above formula (6), we can calculate that the center angle of the virtual axis G corresponding to the first interpolation cycle when the synchronization ratio is changed in advance is θ G1 :

[0086] θ G1 =2.857-0.071=2.786

[0087] Among them, the above formula θ be1 Calculation: First, use the above formula (8) to calculate the time t of the virtual axis G movement G , and then use the above formula (9) to calculate the speed v of the virtual axis G , then use Calculate

[0088] t G =126×1 / 10=12.6

[0089] v G =360 / 12.6=28.57

[0090]

[0091] Then, using the above formula (10), the position relationship between axis X and axis Y in the first interpolation cycle is obtained:

[0092]

[0093] Then, the synchronization ratio of the first interpolation cycle is calculated using the above equations (11), (12), and (13):

[0094]

[0095] When the calculated first interpolation cycle is changed in advance, the center angle of the virtual axis G Assign the value to variable θ G ; The first interpolation cycle synchronization ratio calculated Assign values ​​to variables k respectively X , k Y ; Activate the virtual axis G movement, so that the virtual axis G moves at the calculated speed v G From the starting point corresponding to the center angle θ0 to the end point corresponding to the center angle θ n Movement, while the physical axis X and axis Y move at a synchronization ratio of 0.350 and -0.009 respectively. When the virtual axis G reaches the synchronization ratio in advance, the corresponding center angle θ G When it is 2.786, it is determined that θG The corresponding central angle θ does not reach the end point n , update the center angle and synchronization ratio of the virtual axis G when the current interpolation cycle changes the synchronization ratio in advance, that is, the center angle of the virtual axis G corresponding to the i-th interpolation cycle calculated in step 4 when the synchronization ratio is changed in advance Assign the value to variable θ G At the same time, the synchronization ratio of the i-th interpolation cycle calculated in step 5 is Assign values ​​to variables k respectively X , k Y , so that the physical axis X and axis Y move at the updated synchronization ratio until the circular interpolation is completed.

[0096] In order to further verify the effectiveness of the above method, the results of the method of this embodiment are compared with the results of the commonly used methods in the prior art: data sampling method and traditional variable synchronization ratio circular interpolation method.

[0097] The mean squared error (MSE) is used as the interpolation accuracy evaluation index, and MSE is defined as:

[0098]

[0099] Where N is the number of sampling points; m is the serial number of the sampling point; x′m, y′ m Denotes the interpolation trajectory sampling point d′ m Coordinate, x m ,y m Denotes the theoretical sampling point d of the interpolation trajectory m Coordinates, point d′ m and d m The central angles are equal; δ m is d m and d′ m The deviation distance, like Figure 4 FIG. 4 is a schematic diagram showing the coordinates of the sampling points of the interpolation trajectory according to an embodiment of the present invention.

[0100] like Figure 5 The figure shows the MSE results of various methods at different radii under the conditions of speed v=10mm / s and interpolation step length of 1mm in the example of the present invention. Figure 5It can be seen that: since the scheme of this embodiment is based on the acceleration and deceleration control strategy, the synchronization establishment transition process time required for the physical axis X and axis Y to reach a new synchronization state after the acceleration or deceleration process is calculated, and the center angle corresponding to the virtual axis G when the synchronization ratio is changed in advance is calculated and set, to ensure that when the physical axis X and axis Y move to the arc, they just reach a new synchronization state with the virtual axis G, effectively reducing the interpolation error caused by not considering the synchronization establishment transition process, and having a smaller MSE under different interpolation step sizes and different interpolation speeds, and a higher interpolation accuracy.

[0101] like Figure 6 The figure shows a schematic diagram of the δ variation curve obtained by different methods under the condition of speed v=10mm / s in the example of the present invention. It can be clearly seen that the data sampling method generates a zero distance during the interpolation process, which leads to the accumulation of errors. Therefore, in the data sampling method, the δ value gradually increases. In contrast, the variable synchronization ratio interpolation algorithm effectively reduces the error, so that its δ value is maintained at a lower level. The method described in the embodiment of the present invention fully considers the transition process of the axis from the original synchronization state to the new synchronization state during the variable synchronization ratio on the basis of the variable synchronization ratio interpolation algorithm, further reducing the error, so the δ value is smaller.

[0102] It is worth noting that the contents not described in detail in the embodiments of the present invention belong to the prior art known to professional and technical personnel in the field.

[0103] In summary, the method described in the embodiment of the present invention fully considers the transition process of the axis from the original synchronization state to the new synchronization state during the change of the synchronization ratio, and calculates the synchronization establishment transition process time required for the physical axis X and axis Y to reach the new synchronization state after the acceleration or deceleration process, and then obtains the center angle corresponding to the virtual axis G when the synchronization ratio is changed in advance. By changing the synchronization ratio in advance, it is ensured that when the physical axis X and axis Y move to the arc, they just reach a new synchronization state with the virtual axis G, which effectively reduces the interpolation error, thereby achieving higher precision arc interpolation.

[0104] In addition, a person skilled in the art can understand that all or part of the steps in the above-mentioned embodiment method can be implemented by instructing related hardware through a program, and the corresponding program can be stored in a computer-readable storage medium. The above-mentioned storage medium can be a read-only memory, a disk or an optical disk, etc.

[0105] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed in the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims. The information disclosed in the background technology section of this article is only intended to deepen the understanding of the overall background technology of the present invention, and should not be regarded as an admission or in any form that the information constitutes prior art known to those skilled in the art.

Claims

1. A method for circular interpolation with variable synchronization ratio considering the synchronous establishment transition process, characterized in that: The method comprises: Step 1: Establish a rectangular coordinate system with the center of the arc to be interpolated as the origin, and calculate the unit angle increment corresponding to each interpolation cycle step according to the starting position, end position and center angle of the arc interpolation; Step 2: Create a virtual axis G as the leading axis of synchronous motion, use the actual physical axis X and axis Y as the following axes of synchronous motion, and establish the synchronous motion relationship between the virtual axis and the physical axis; Step 3: According to the acceleration and deceleration control strategy, the synchronization establishment transition process time required for the physical axis X and axis Y to reach the new synchronization state from the original synchronization state through the acceleration or deceleration process is calculated; Step 4, using the synchronization establishment transition process time calculated in step 3 and the speed of the virtual axis G, calculate the position advance amount of the virtual axis G when the synchronization ratio is changed in advance in each interpolation cycle, and then obtain the center angle of the virtual axis G corresponding to the synchronization ratio when the synchronization ratio is changed in advance in each interpolation cycle; Step 5: According to the positional relationship between the virtual axis G and the physical axis X and axis Y during the synchronous motion, the synchronous motion relationship between the physical axis X and axis Y following the virtual axis G is obtained respectively, and then the synchronization ratio of each interpolation cycle is calculated using the unit angle increment obtained in step 1; Step 6, activate the virtual axis G movement. When the virtual axis G reaches the center angle corresponding to the advance change of the synchronization ratio, update the synchronization ratio of the current interpolation cycle, so that the physical axis X and axis Y move with the updated synchronization ratio. When the virtual axis G moves to the center angle corresponding to the end point, the interpolation is completed and the circular interpolation ends.

2. The method of circular interpolation with variable synchronization ratio considering the synchronous establishment transition process according to claim 1, characterized in that: The process of step 1 is specifically as follows: Set the center O of the arc to be interpolated as the coordinate origin, define the line connecting the arc starting point P0 and the center O as the vertical axis of the rectangular coordinate system, and construct a rectangular coordinate system. Then the coordinates of the arc starting point P0 are (0, R), and R is the radius of the arc to be interpolated. Define the end point of the i-th interpolation cycle as P i (P Xi ,P Yi );P Xi , P Yi Respectively represent the end positions of the physical axis X and axis Y at the i-th interpolation cycle, i = 1, 2, ..., n; n is the number of interpolation steps; Define θ as the arc starting point P0 and the interpolation point P i The corresponding central angle is θ i =∠P0OP i , when θ n =2π, it means the arc to be interpolated is a complete circle; The unit angle increment Δθ corresponding to each interpolation cycle step is calculated using the following formula (1): Δθ=θ i -θ i-1 =(θ n -θ0) / n (1).

3. The method of circular interpolation with variable synchronization ratio considering the synchronous establishment transition process according to claim 2, characterized in that: The process of step 2 is specifically as follows: Move the physical axis X and axis Y of the actual motion to the starting position of the arc, and set the arc interpolation speed to v, where v is a constant; using the characteristic that the center angle of the interpolation point changes uniformly over time, construct a virtual axis G with the center angle of the interpolation point as the position output; use the virtual axis G as the leading axis of the synchronous motion, and the physical axis X and axis Y as the following axis of the synchronous motion; establish the synchronous motion relationship between the virtual axis G and the physical axis X and axis Y according to formula (2); According to the parametric equation of the circle, the positions of the physical axis X and axis Y are calculated using the following formula (2): With θ i The change relationship:

4. The method of circular interpolation with variable synchronization ratio considering the synchronous establishment transition process according to claim 2, characterized in that: The process of step 3 is specifically as follows: According to the S-type acceleration and deceleration control strategy, the time of the physical axis X and axis Y in the acceleration section, uniform acceleration section, and deceleration section is calculated using the following formula (3): In the formula, · corresponds to the physical axis name; t ·1 ,t ·2 and t ·3 Respectively represent the time of acceleration section, uniform acceleration section and deceleration section; A ·max Indicates the maximum acceleration; J · represents the acceleration; v ·sta 、v ·end They represent the initial speed and final speed of the current synchronous transition process respectively. The corresponding relationship between the arc interpolation speed and the speed components of each physical axis is calculated by formula (4): In the formula, v is a constant, which represents the circular interpolation speed; The above process is that the axis is accelerated from the original synchronous state to the new synchronous state; When it is necessary to decelerate to reach a new synchronous state, let t ·1 ,t ·2 and t ·3 They represent the time of acceleration / deceleration section, uniform deceleration section and deceleration / acceleration section respectively. ·max Indicates the maximum deceleration, J · represents the acceleration, and the time of different deceleration sections is calculated using equations (3) and (4) respectively; Then, the following formula (5) is used to obtain the synchronization establishment transition process time t required for the physical axis X and axis Y to reach the new synchronization state from the original synchronization state: ·total : t ·total =t ·1 +t ·2 +t ·3 (5)。 5. The method of circular interpolation with variable synchronization ratio considering the synchronous establishment transition process according to claim 4, characterized in that: The process of step 4 is specifically as follows: Assume that in the i-th interpolation cycle, the center angle of the virtual axis G corresponding to the change of synchronization ratio in advance is Calculate using the following formula (6) In the formula, is the position advance amount of the virtual axis G when the synchronization ratio is changed in advance during the i-th interpolation cycle, which is calculated using the following formula (7): In the formula, v G is the speed of the virtual axis G, calculated using equations (8) and (9); Indicates the average time it takes for the physical axes X and Y to reach a new synchronization state from the original synchronization state after acceleration or deceleration; Let t G Indicates that the virtual axis moves from θ0 to θ n Time, t G Calculated by the following formula (8): t G =n×l / v (8) Where, l = 2Rsin (Δθ / 2) is the step length corresponding to the unit angle increment; n is the number of interpolation steps; v is a constant, indicating the arc interpolation speed; R is the radius of the arc to be interpolated; θ is the arc starting point P0 and the interpolation point P i The corresponding central angle of the circle; Substituting the above equation (8) into the following equation (9), the velocity v of the virtual axis G is calculated: G : v G =(θ n -θ0) / t G (9)。 6. The method of circular interpolation with variable synchronization ratio considering the synchronous establishment transition process according to claim 3, characterized in that: The process of step 5 is specifically as follows: During synchronous motion, the virtual axis G and the physical axis X and axis Y have the following positional relationship (10): In the formula, They represent the end positions of the virtual axis G at the i-1th and i-th interpolation cycles respectively; They respectively represent the synchronization ratios of the physical axis X and axis Y following the virtual axis G in the ith interpolation cycle; According to formula (10), the synchronization ratio with the virtual axis G and the physical axis X and axis Y positions as intermediate parameters is obtained: Substituting equation (2) into equation (11), we can obtain the synchronization ratio of the i-th interpolation cycle: Then use equation (1) to convert θ i and θ i-1 Expressed as Δθ, the synchronization ratio of each interpolation cycle is calculated according to the following formula (13):

7. The method of circular interpolation with variable synchronization ratio considering the synchronous establishment transition process according to claim 2, characterized in that: The process of step 6 is specifically as follows: Define the variable θ G It is used to store the center angle of the virtual axis G corresponding to the change of synchronization ratio in advance in each interpolation cycle. The center angle θ corresponding to the virtual axis G when the synchronization ratio is changed in advance in the first interpolation cycle calculated in step 4 is G1 Assign the value to variable θ G ; Define the variable k X , k Y Store the synchronization ratios of the physical axis X and axis Y respectively, and the synchronization ratio of the first interpolation cycle calculated in step 5 Assign values ​​to variables k respectively X , k Y ; Activate the virtual axis G motion, so that the virtual axis G moves at a speed v G From the starting point corresponding to the center angle θ0 to the end point corresponding to the center angle θ n Movement; when the virtual axis G reaches the center angle θ corresponding to the change of synchronization ratio in advance G When θ G Whether the end point is reached corresponds to the central angle θ n ; If θ G ≠θ n , then let i++, that is, the i+1th interpolation cycle, and update the center angle and synchronization ratio of the virtual axis G when the current interpolation cycle changes the synchronization ratio in advance, that is, the center angle of the virtual axis G when the i+1th interpolation cycle changes the synchronization ratio in advance calculated in step 4 Assign the value to variable θ G At the same time, the synchronization ratio of the i+1th interpolation cycle calculated in step 5 is Assign values ​​to variables k respectively X , k Y , so that the physical axis X and axis Y move at the updated synchronization ratio; If θ G =θ n , it indicates that the virtual axis G moves to the end point of the arc and the circular interpolation process ends.

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