Kinematics constraint planning method and equipment for twelve-axis series-parallel connection structure mirror image milling equipment

Abstract

The invention belongs to the related technical field of numerical control machining, and discloses a kinematics constraint planning method and device for twelve-axis series-parallel connection structure mirror image milling equipment, and the method comprises the steps: (1) enabling a supporting end seven-axis series-parallel connection mechanism to be equivalent to a virtual six-axis series connection machine tool; (2) according to the C3 continuous smooth tool path, a C3 continuous supporting head movement path is obtained according to mirror image machining vertex geometric constraint conditions, and then machining end kinematics constraints, needing to be met, of each sampling point on the tool path are constructed so as to calculate limit values of the feeding speed and the acceleration of the tool; (3) extending the supporting height of the supporting head to obtain a virtual supporting head, then constructing a supporting end kinematics constraint, and further utilizing the supporting end kinematics constraint to calculate limit values of the feeding speed and the acceleration of the virtual supporting head; and (4) obtaining a final cutter feeding speed limit value and an acceleration limit value based on the obtained limit values. The efficiency and the precision are improved at the same time.

Description

Technical Field

[0001] The present invention belongs to the technical field related to numerical control machining, and more specifically, relates to a kinematic constraint planning method and device for a twelve-axis series-hybrid structure mirror milling device. Background Technique

[0002] Mirror milling is carried out by arranging milling and supporting mechanisms symmetrically at both sides of the workpiece. While the milling cutter moves along the cutting trajectory, the supporting mechanism makes a mirror synchronous following movement to complete the machining of the part. Such a machining method can ensure the stiffness at any supporting position. Therefore, mirror milling is usually used for machining thin-walled and low-stiffness parts with large sizes and easy deformation, such as rocket boxes and aircraft skins. Considering the selection of machine tools for the machining end and the supporting end of the mirror milling device: The hybrid machine tool is composed of a parallel mechanism and drive shafts in other directions in series. The 3-RCU+(TX, TY, Y, C) hybrid machine tool with a 3-RCU parallel head combines the advantages of a series machine tool with a large working space and high machining speed, and a parallel structure with high stiffness, small cumulative error and flexibility, which well meets the needs of flexible support for mirror machining and can be used as the supporting end in the mirror milling system, while the traditional five-axis CA double swing head machine tool is used for the supporting end.

[0003] The goal of feed speed planning in numerical control machining is basically to find an ideal feed speed curve along a fixed tool path under predefined constraints such as path geometric features, interpolation period, process constraints, and machine tool kinematic performance (maximum speed, acceleration, and jerk). Therefore, establishing reasonable predefined constraints is the premise for speed planning of the tool motion trajectory. Among these constraints, the machine tool kinematic performance constraint is the safety guarantee for high-speed and high-precision machining. For the above-mentioned twelve-axis series-hybrid structure mirror milling device (the machining end is a five-axis double swing head machine tool, and the supporting end is a seven-axis hybrid structure with a 3-RCU parallel head), since the mapping relationships between the tool and the supporting head movements in the workpiece coordinate system and the movements of each drive shaft in the machine tool coordinate system all have strong non-linear characteristics. For the machining end, not only it is necessary to consider whether its feed movement will cause the movement of its own drive shafts to exceed the physical constraint limits of the machine tool, but also it is necessary to consider whether the feed movement of the supporting end making mirror following will cause the movements of the drive shafts at the supporting end to exceed the limits. Therefore, it is necessary to constrain the feed movement of the tool and the mirror following movement of the supporting head in the workpiece coordinate system according to the kinematic performance of each drive shaft at both ends of the machine tool, including the speed and acceleration limits of the drive shafts, to ensure that the relevant kinematic parameters during the movement of the tool and the supporting head, namely speed, acceleration, jerk, etc., are within the safe allowable range, and to avoid damage to the machine tool structure and decline in transmission accuracy during actual production, resulting in the inability to complete part machining.

[0004] In the current research on kinematic constraint methods for multi-axis numerical control machining such as five-axis machining, when establishing the relationship between the tool feed motion and the speed, acceleration, and even jerk constraints of the drive axes, simplification and approximation are generally carried out or offline optimization methods are adopted. The former has insufficient calculation accuracy and is prone to over-constraint or under-constraint, while applying optimization methods in the numerical control system will make the speed planning process time-consuming and affect the machining efficiency, that is, it is difficult to balance the calculation efficiency and accuracy. To sum up, there is currently a lack of a kinematic constraint planning method suitable for a twelve-axis series-hybrid structure mirror milling device. Summary of the Invention

[0005] In view of the above defects or improvement requirements of the prior art, the present invention provides a kinematic constraint planning method and device for a twelve-axis series-hybrid structure mirror milling device, aiming to solve the problem that the planning methods of existing multi-axis mirror milling devices cannot balance efficiency and accuracy.

[0006] To achieve the above object, according to one aspect of the present invention, there is provided a kinematic constraint planning method for a twelve-axis series-hybrid structure mirror milling device, the method comprising the following steps:

[0007] (1) Construct the motion transfer relationship from the tool pose and the support head pose satisfying the mirror machining opposite geometric constraints in the workpiece coordinate system of the twelve-axis series-hybrid structure mirror milling device to the machining end and the support end in their respective machine coordinate systems; and equivalent the seven-axis hybrid mechanism (L1, L2, L3, Y2, TY, TX, C2) at the support end to a virtual six-axis serial machine tool (X2, Y2, Z2, A2, B2, C2);

[0008] (2) According to the C3 continuous smooth tool path, obtain the C3 continuous support head motion path from the mirror machining opposite geometric constraint conditions, and construct the kinematic constraints of the machining end that each sampling point pair (P T , R T ) on the tool path needs to satisfy based on the smoothed tool path and the mapping relationship between the tool feed motion and the speed and acceleration of the corresponding drive axes (X1, Y1, Z1, A1, C1). Furthermore, use the kinematic constraints of the machining end to calculate the limit values v T,max and a T,max of the tool feed speed and acceleration at each sampling point pair;

[0009] (3) After extending the support height of the support head to obtain a virtual support head, construct the kinematic constraints of the support end based on the mapping relationship between the mirror following motion of the support head and the speed and acceleration of the corresponding drive axes (L1, L2, L3, Y2, TY, TX, C2). Furthermore, use the kinematic constraints of the support end to calculate the limit values v Smax and a Smax of the virtual support head feed speed and acceleration on each segment of the tool path;

[0010] (4) Based on the limit values v T,max and a T,max of the tool feed speed and acceleration, as well as the limit values v Smax and a Smax of the virtual support head feed speed and acceleration, the final tool feed speed limit value is obtained as v max = min(v T,max , v S,max ), and the acceleration limit value is a max = min(a T,max , a S,max ).

[0011] Furthermore, the top geometric constraints include: (1) The tool center point TCP and the support point SCP are both on the straight line where the normal vector n T of the workpiece surface is located, and the distance between the two points is the expected wall thickness H of the thin-walled part; (2) The tool axis vector V T and the support direction vector V S of the support head satisfy collinearity and opposite directions, and V T coincides with the normal vector n T of the workpiece surface.

[0012] Furthermore, the C3 continuous smooth tool path includes the tool tip point path C T (u) and the tool axis vector path O T (u); the C3 continuous support head movement path includes the support point path C S (u) and the support direction vector O S (u); the support point path C S (u) and the support direction vector path O S (u) are expressed as:

[0013]

[0014] Furthermore, P T = (x T , y T , z T ) is a point on C T (u), and R T = (A1, C1) is the corresponding tool axis vector. According to the geometric characteristics of the path C T (u) and the structural parameters of the machining end five-axis machine tool, the relationship between the speeds of each drive axis and the tool feed speed v T is:

[0015] V p = μ tp · v T (p = X1, Y1, Z1, A1, C1)

[0016] The proportionality coefficient μ in the formula tp Through analytical calculation, the relationship between the speeds of each drive shaft and the tool feed speed v is also obtained T as follows:

[0017] A p = λ tp ·(v T ) 2 + σ tp ·a T (p = X1, Y1, Z1, A1, C1)

[0018] If the speed and acceleration limit values of the drive shaft at the machining end are V pmax and A pmax , then for any point P T on the trajectory C T,i (u), the feasible region of the tool feed motion parameters v T and a T is determined by the following inequality group:

[0019]

[0020] where i is the serial number of the sampling point, p = (X1, Y1, Z1, A1, C1) is the drive shaft, μ tp,i , λ tp,i , σ tp,i are the relationship coefficients of the drive shaft p with respect to v T and a T at the i-th sampling point. N points are sampled on the trajectory C T (u), and the corresponding v T,i and a T,i for each point are obtained. The minimum value among them is taken as v T,max and a T,max .

[0021] Furthermore, the support height of the support head is extended to obtain a virtual support head, and the support point of the virtual support head is made to coincide with the tool tip point. At this time, C T (u) and O S (u) are the motion trajectories of the virtual support head, corresponding to the sampling point pairs (P T , R T ). While sampling the tool trajectory, (P T , R S ) is obtained, where R S = (A2, B2) is the support direction vector corresponding to the point P T . Then, the limit values v S,max and a S,max of the feed speed and acceleration of the virtual support point are obtained

[0022] Furthermore, the mapping relationship between the follow-up movement of the support head and the speeds and accelerations of the drive shafts (L1, L2, L3, Y2, TY, TX, C2) has been obtained. Combining this with the geometric characteristics of the trajectory C T (u), the relationship between the speeds of the drive shafts at each support end and the feed speed v of the virtual support head is obtained as follows: S The relationship is:

[0023] V q = μ sq ·v S (q = (L1, L2, L3, Y2, TY, TX, C2))

[0024] The relationship between the speeds of the drive shafts and the feed speed v of the virtual support head S and the tangential acceleration a S is:

[0025] A q = λ sq ·(v S ) 2 + σ sq ·a S (q = (L1, L2, L3, Y2, TY, TX, C2))

[0026] If the speed and acceleration limit values of the drive shafts at the machining end are V qmax and A qmax , for any point P T on the trajectory C T,i (u), the feasible region of the feed motion parameters v S and a S of the virtual support head is determined by the following inequality group:

[0027]

[0028] q = (L1, L2, L3, Y2, TY, TX, C2) is the drive shaft at the support end, and μ sq,i , λ sq,i , σ sq,i are the relationship coefficients of the drive shaft q with respect to v S and a S at the i-th sampling point. Corresponding to the N points sampled on the trajectory C T (u), calculate the corresponding v S,i and a S,i for each point, and take the minimum value among them as v S,max and a S,max .

[0029] Furthermore, taking (x s , y s , z s , is , j s , k s ) represents the pose of the support head in the workpiece coordinate system, where (x s , y s , z s ) represents the position coordinates of the support point, and (i s , j s , k s ) represents the support direction vector. Then, the forward kinematics of the hybrid mechanism is expressed as:

[0030] (L1, L2, L3, Y2, TY, TX, C2) → (x s , y s , z s , i s , j s , k s )

[0031] Solving for the pose of the support head in the workpiece coordinate system from the position coordinates of each drive axis, after real and virtual transformation, the forward kinematics is further expressed as:

[0032] (L1, L2, L3, Y2, TY, TX, C2) → (x s , y s , z s , i s , j s , k s ) → (x s , y s , i s , A2, B2)

[0033] Where (i s , j s , k s ) has the following relationship with the rotation angle of the virtual rotation axis:

[0034]

[0035] Furthermore, for the support end, the relationship between the support point velocity and the velocities of each drive axis at the support end of the hybrid structure is determined by the following formula:

[0036]

[0037] In the formula, J VI is a 7-row 6-column Jacobian matrix, v sq (q = x, y, z) is the linear velocity v of the support point S in the x, y, z three directions, and ω sq (q = x, y, z) is the angular velocity of the support point.

[0038] The present invention also provides a kinematic constraint planning system for a twelve-axis series-hybrid structure mirror milling device. The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it executes the kinematic constraint planning method for the twelve-axis series-hybrid structure mirror milling device as described above.

[0039] The present invention also provides a computer-readable storage medium. The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions cause the processor to implement the kinematic constraint planning method for the twelve-axis series-hybrid structure mirror milling device as described above.

[0040] Generally speaking, compared with the prior art through the above technical solutions conceived by the present invention, the kinematic constraint planning method and device for the twelve-axis series-hybrid structure mirror milling device provided by the present invention mainly have the following beneficial effects:

[0041] 1. The kinematic constraint planning method adopts a C3 continuous (third derivative continuous) tool path and a support head follow-up path, so that the kinematic constraint parameters involved (such as speed and acceleration) all have analytical expressions. In this way, C3 continuity suppresses sudden changes in acceleration, reduces mechanical vibration, and the analytical expressions can be directly called, avoiding the computational time-consuming of online iteration, realizing the optimization of dynamic performance and the reduction of computational time-consuming, and improving the computational efficiency. At the same time, the seven-axis hybrid mechanism at the support end is equivalent to a virtual six-axis serial machine tool, and a virtual support head is constructed, transforming the non-linear kinematic problem of the hybrid mechanism into a standardized processing process of the serial structure, reducing the computational complexity of the kinematic constraint parameters at the support end, being able to adapt to mainstream numerical control systems (such as FANUC, SIEMENS), without modifying the underlying code, and being able to directly reuse the code library and function modules of the existing numerical control system to a certain extent, standardizing the control logic, simplifying the debugging and upgrading process, improving compatibility, reducing costs and computational complexity, and thus improving accuracy.

[0042] 2. According to the kinematic performance constraints of the driving shafts at the machining end and the support end of the twelve-axis series-hybrid structure mirror milling device and planning the mirror synchronous motion at both ends, it can ensure that when the tool and the support head mill along a predetermined trajectory, the speeds and accelerations of the tool and the support head are within the safe allowable range, solving the problem of over-limit of the moving axes.

[0043] 3. The motion characteristics such as the speeds and accelerations of the tool and the support head in the workpiece coordinate system are constrained by the performance of the driving shafts at both ends, ensuring a consistent acceleration and deceleration process at the machining end and the support end, realizing speed synchronization, avoiding tremor phenomena when machining large thin-walled parts, and ensuring that the wall thickness error is within the allowable range when mirror machining large thin-walled parts such as aircraft skins.

[0044] 4. Define a virtual support head in the workpiece coordinate system, and forcefully bind its movement to the tool path; directly derive the support end constraints through geometric mirroring relationships, thus eliminating the need for redundant independent support path planning, and achieving strict pose coupling between the machining end and the support end through mirror mapping, reducing the computational complexity while ensuring synchronization. Description of the Drawings

[0045] Figure 1 Figures (a) and (b) in [the figure] are respectively schematic diagrams of the five-axis serial machine tool at the machining end and the seven-axis hybrid machine tool at the support end of the twelve-axis serial-hybrid structure mirror milling equipment involved in the present invention;

[0046] Figure 2 is a flowchart of a kinematic constraint planning method for a twelve-axis serial-hybrid structure mirror milling equipment provided by an embodiment of the present invention;

[0047] Figure 3 is a schematic diagram of the mirror machining opposed geometric constraints constructed according to the preferred embodiment of the present invention;

[0048] Figure 4 is a schematic diagram of the motion transfer relationship from the tool pose and the support head pose satisfying the mirror machining opposed geometric constraints in the workpiece coordinate system to the respective machine tool coordinate systems at both ends according to the preferred embodiment of the present invention;

[0049] Figure 5 is a schematic diagram of equivalently transforming the seven-axis hybrid structure at the support end into a six-axis serial machine tool according to the preferred embodiment of the present invention, where (a) is the seven-axis hybrid structure at the support end, and (b) is the transformed six-axis serial machine tool, and the drive shaft of this six-axis machine tool is called the virtual axis;

[0050] Figure 6 is a schematic diagram of obtaining a C3 continuous support head motion trajectory from the mirror machining opposed geometric constraint conditions based on the existing C3 continuous smooth tool path according to the preferred embodiment of the present invention;

[0051] Figure 7 is a schematic diagram of the process of establishing a virtual support head when establishing the kinematic constraints at the support end according to the preferred embodiment of the present invention, where (a) is a schematic diagram of the mirror synchronous movement of the tool and the support head during the actual machining process, and (b) is a schematic diagram of the mirror synchronous movement at both ends under the virtual support head;

[0052] Figure 8 is a schematic diagram of the process of performing speed planning on the tool tip motion trajectory and then interpolating to obtain the reference positions of the drive shafts at the machining end and the support end provided by an embodiment of the present invention;

[0053] Figure 9It is a flowchart of the synchronous segment G-code execution of the mirror machining system constructed according to the embodiments of the present invention. Detailed implementation manners

[0054] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0055] The present invention provides a kinematic constraint planning method for a twelve-axis series-hybrid structure mirror milling device. The method constrains and plans the mirror synchronous motion of the driving shafts at the machining end and the support end of the mirror milling device according to the kinematic performance, and ensures that when the tool and the support head mill along a predetermined trajectory, the motion of each driving shaft at the machining end and the support end does not exceed the physical constraint limits of the machine tool.

[0056] Please refer to Figure 1 and Figure 2 , the method mainly includes the following steps:

[0057] S1, construct the motion transfer relationship from the tool pose and the support head pose that satisfy the mirror machining opposite geometric constraints in the workpiece coordinate system of the twelve-axis series-hybrid structure mirror milling device to the respective machine tool coordinate systems at the machining end and the support end.

[0058] Among them, the tool pose includes the tool tip point and the tool axis direction, and the support head pose includes the support point and the support direction. Please refer to Figure 3 , during the mirror milling process, the milling and support mechanisms are arranged symmetrically on both sides of the workpiece. While the milling cutter moves along the cutting trajectory, the support mechanism performs mirror synchronous following motion to complete the milling process. The whole process needs to ensure that the machining end and the support end meet the opposite geometric constraint conditions.

[0059] The opposite geometric constraints include: (1) The tool center point TCP (Tool Center Point) and the support center point SCP (Support Center Point) are both on the straight line where the normal vector n of the workpiece surface T is located, and the distance between the two points is the expected wall thickness H of the thin-walled part; (2) The tool axis vector V T and the support direction vector V of the support head S satisfy collinearity and opposite directions, and V T coincides with the normal vector n of the workpiece surface T .

[0060] Please refer to Figure 4 , O w -X w Y w Zw is the workpiece coordinate system, that is, the part programming coordinate system. The machining end is a five-axis CA double swivel head gantry machine tool, O M1 -X M1 Y M1 Z M1 is its machine tool coordinate system. For the machining end, its motion transmission relationship is:

[0061] The support end is a seven-axis hybrid structure, which consists of a bottom turntable C2, a horizontal moving guide rail (Y2), an inclined cross slide (TX + TY) at a 45° angle to the horizontal guide rail, and a 3-RCU parallel module. The fixed platform of the parallel module is fixedly connected to the parallel connection frame and moves with the TX axis. The moving platform is connected to the parallel machine frame through three identical branch chains, and the angle between these branch chains is 120°. Each branch chain includes joints such as a revolute joint, a cylindrical joint, and a universal joint, as well as connecting rods connecting these joints. O M2 -X M2 Y M2 Z M2 is its machine tool coordinate system, and its origin O M2 coincides with the center of the bottom turntable. For the support end, its motion transmission relationship is:

[0062] S2, the seven-axis hybrid mechanism (L1, L2, L3, Y2, TY, TX, C2) of the support end is equivalent to a virtual six-axis serial machine tool (X2, Y2, Z2, A2, B2, C2).

[0063] The hybrid mechanism of the support end can not only produce the effect of translational motion along the virtual X2, Y2, and Z2 axes, but also produce the effect of rotational motion around the (virtual) X2 axis and (virtual) Y2 axis directions (the positive directions of the X2, Y2, and Z2 axes are the same as those of the X M2 、Y M2 、Z M2 of the machine tool coordinate system of the support end). Adding the rotation of the bottom turntable C2, this mechanism can be equivalent to a six-axis CAB triple swivel head machine tool. The drive axes (L1, L2, L3, Y2, TY, TX, C2) before transformation are called real axes, and the drive axes (X2, Y2, Z2, A2, B2, C2) after transformation are called virtual axes.

[0064] Please refer to Figure 5 , and use (x s , y s , z s , i s , j s , k s ) to represent the pose of the support head in the workpiece coordinate system in S1, where (xs , y s , z s ) represents the position coordinates of the support point SCP, while (i s , j s , k s ) represents the support direction vector. Then, the forward kinematics of the hybrid mechanism can be expressed as:

[0065] (L1, L2, L3, Y2, TY, TX, C2) → (x s , y s , z s , i s , j s , k s )(1)

[0066] That is, to solve the pose of the support head in the workpiece coordinate system from the position coordinates of each drive axis. After the real and virtual transformation, the forward kinematics can be further expressed as:

[0067] (L1, L2, L3, Y2, TY, TX, C2) → (x s , y s , z s , i s , j s , k s ) → (x s , y s , i s , A2, B2)(2)

[0068] Where (i s , j s , k s ) has the following relationship with the rotation angles of the virtual rotation axes:

[0069]

[0070] Conversely, if (i s , j s , k s ) is known and the rotation angles A2, B2, C2 of the rotation axes are required, then there are:

[0071] C2 = atan2(-x s , y s )(4)

[0072]

[0073] B2 = -arcsin(i n )

[0074]

[0075] Furthermore, the CNC machining G-codes for the machining end and the support end can be written in a consistent format (combining the programming specifications of mirror machining G-codes. In the machining end G-code, 'G103.1 Q{1,2}' represents enabling the dual-channel synchronous mode. The support end enables mirror following through the 'M130' instruction. 'WAIT P n' is the channel waiting marker, and the number n represents the nth channel waiting marker of this channel. The 'M131' instruction represents closing the channel following), so that the motion control of the seven-axis hybrid mechanism can be achieved by adopting the processing strategy for traditional serial six-axis machine tools.

[0076] S3. Establish the mapping relationships between the tool feed motion and the speeds and accelerations of the corresponding drive axes (X1, Y1, Z1, A1, C1), and between the mirror following motion of the support head and the speeds and accelerations of the corresponding drive axes (L1, L2, L3, Y2, TY, TX, C2).

[0077] For the support end, the relationship between the support point speed and the speeds of the drive axes at the support end of the hybrid structure can be determined by the following expression:

[0078]

[0079] In the above formula, J VI is a 7-row and 6-column Jacobian matrix, and v sq (q = x, y, z) is the linear velocity component of the support point v S in the x, y, and z directions, and ω sq (q = x, y, z) is the angular velocity of the support point.

[0080] Calculate the accelerations of the drive axes at the support end of the hybrid structure from the support point acceleration through the following expression:

[0081]

[0082] In the above formula, H AI is a 7-row and 1-column transformation matrix, α sq (q = x, y, z) is the linear acceleration of the support point, and ω asq (q = x, y, z) is the angular acceleration of the support point. The relationship between the angular velocity of the support point and the virtual rotation axes A2, B2, C2 is:

[0083]

[0084] and are the rotational speeds of the virtual rotation axes. Differentiating both sides of the formula with respect to time can solve the relationship between the angular acceleration ω asq (q = x, y, z) of the support point and the virtual axes A2, B2, C2.

[0085] S4. Based on the C3 continuous smooth tool path, the C3 continuous support head motion path is obtained from the mirror machining anti-top geometric constraint conditions. The C3 continuous smooth tool path includes the tool tip point path C T (u) and the tool axis vector path O T (u); the C3 continuous support head motion path includes the support point path C S (u) and the support direction vector O S .

[0086] Please refer to Figure 6 , the tool path includes the tool tip point path C T (u) and the tool axis vector path O T (u). According to the mirror machining anti-top geometric constraint conditions, the support point path C S (u) and the support direction vector path O S (u) of the support head can be expressed as:

[0087]

[0088] S5. Based on the smoothed tool path and the mapping relationship between the tool feed motion and the speeds and accelerations of the corresponding drive axes (X1, Y1, Z1, A1, C1), the machining end kinematic constraints that each sampling point pair (P T , R T ) on the tool path needs to satisfy are constructed. Then, the limiting values v T,max and a T,max of the tool feed speed and acceleration at each sampling point pair are calculated using these machining end kinematic constraints. Among them, P T = (x T , y T , z T ) is a point on C T (u), and R T = (A1, C1) is the corresponding tool axis vector.

[0089] According to the geometric characteristics of the path C T (u) and the structural parameters of the machining end five-axis machine tool, the relational expressions between the speeds of each drive axis and the tool feed speed v T are as follows:

[0090] V p = μ tp ·v T (p = X1, Y1, Z1, A1, C1)(11)

[0091] The proportionality coefficient μ tp in the above formula can be analytically calculated. Similarly, the relational expressions between the speeds of each drive axis and the tool feed speed v T are as follows:

[0092] A p = λ tp ·(v T ) 2 + σ tp ·a T (p = X1,Y1,Z1,A1,C1)(12)

[0093] The proportionality coefficients λ tp and σ tp can be analytically calculated. If the speed and acceleration limit values of the driving shaft at the machining end are V pmax and A pmax , then for any point P T on the trajectory C T,i (u), the feasible region of the tool feed motion parameters v T and a T is determined by the following system of inequalities:

[0094]

[0095] where i is the serial number of the sampling point, p = (X1,Y1,Z1,A1,C1) is the driving shaft, and μ tp,i , λ tp,i , σ tp,i are the relationship coefficients of the driving shaft p with respect to v T and a T at the i-th sampling point. N points are sampled on the trajectory C T (u) to obtain the corresponding v T,i and a T,i for each point, and the minimum value among them is taken as v T,max and a T,max .

[0096] S6. After extending the support height of the support head to obtain a virtual support head, based on the mapping relationship between the mirror following motion of the support head and the speeds and accelerations of the corresponding driving shafts (L1,L2,L3,Y2,TY,TX,C2), kinematic constraints of the support end are constructed, and then the limit values v Smax and a Smax of the feed speed and acceleration of the virtual support head on each tool trajectory are calculated using the kinematic constraints of the support end.

[0097] In one embodiment, first, the support height of the support head is extended to obtain a virtual support head, and the support point of the virtual support head is made to coincide with the tool tip point. At this time, C T (u) and O S (u) are the motion trajectories of the virtual support head, corresponding to the sampling point pairs (P T ,R T ) in S5. While sampling the tool trajectory, (P T,R S ), where R S = (A2, B2) is the corresponding point P T support direction vector. Then, similar to S5, under the speed and acceleration limits of the support end drive shafts (L1, L2, L3, Y2, TY, TX, C2), the limit values v S,max and a S,max .

[0098] Please refer to Figure 7 , the height of the support head is H s , the wall thickness of the part is H, the tool tip point and the support point move along the smooth trajectories C T (u) and C S (u) to complete the machining of the part. If kinematic constraints of the support end are established according to the trajectory C S (u), the calculation amount is increased, and the height H s of the support head is extended to make it equal to H vs , where H vs = H s + H. At this time, the support point trajectory of the virtual support head is C T (u).

[0099] For the sampling point pair (P T,i ,R T,i ) corresponding to S5, the pose of the virtual support head is (P T,i ,R S,i ). The mapping relationship between the following motion of the support head and the speeds and accelerations of the drive shafts (L1, L2, L3, Y2, TY, TX, C2) has been obtained. Combining with the geometric characteristics of the trajectory C T (u), the relational expressions of the speeds of each drive shaft of each support end and the feed speed v S of the virtual support head are as follows:

[0100] V q = μ sq ·v S (q = (L1, L2, L3, Y2, TY, TX, C2))(14)

[0101] The proportionality coefficient μ sq in the above formula can be analytically calculated. Similarly, the relational expressions of the speeds of each drive shaft and the feed speed v S and the tangential acceleration a S of the virtual support head are as follows:

[0102] A q = λ sq ·(v S ) 2 + σ sq ·aS (q = (L1, L2, L3, Y2, TY, TX, C2))(15)

[0103] Proportionality coefficient λ sq and σ sq can be analytically calculated. If the speed and acceleration limit values of the machining end drive shaft are V qmax and A qmax , for any point P T on the trajectory C T,i (u), the feasible region of the feed motion parameters v S and a S of the virtual support head is determined by the following inequality group:

[0104]

[0105] q = (L1, L2, L3, Y2, TY, TX, C2) is the support end drive shaft, μ sq,i , λ sq,i , σ sq,i are the relationship coefficients of the drive shaft q with respect to v S and a S at the i-th sampling point, corresponding to the N points sampled on the trajectory C T (u) in S3. Calculate v S,i and a S,i corresponding to each point, and take the minimum value as v S,max and a S,max .

[0106] S7. Based on the limit values v T,max and a T,max of the tool feed speed and acceleration, as well as the limit values v Smax and a Smax of the feed speed and acceleration of the virtual support head, the final tool feed speed limit value is v max = min(v T,max , v S,max ), and the acceleration limit value is a max = min(a T,max , a S,max ).

[0107] According to the general process of numerical control machining, that is, first input the numerical control machining G code, the numerical control system interprets the G code, performs kinematic constraint processing, speed interval division and speed planning, and finally interpolates and calculates the position coordinates of each drive shaft. Please refer to Figure 8 , in this embodiment, only the speed planning of the tool tip trajectory C T (u) is performed, and the three-dimensional curve C T (u) is tracked to determine the tool along C TThe time-arc length mapping relationship s(t) of (u). During interpolation, the arc length s is mapped to the curve parameter u by numerical methods, and then the tool tip position coordinate P that satisfies the opposite geometric constraints can be calculated by sharing the parameter u. T and the tool axis vector O T and the support point position coordinate P S and the support direction vector O S .

[0108] For any to-be-machined trajectory C T (u), the trajectory segments can be divided according to the curvature of the trajectory, and then the speed limit values of each trajectory segment can be calculated through steps S1 to S7. Thus, the continuous trajectory segments are divided into different speed intervals. After speed planning, the final speed curve can be obtained, and then the arc length s(t) at any time can be obtained. Then interpolation is performed to calculate the displacement increments of each drive axis at the machining end and the support end, and further obtain the speeds and accelerations of each drive axis at the machining end and the support end, and judge whether the speeds and accelerations of the drive axes at any moment exceed the limit values. If the speeds and accelerations of each drive axis are within the limit range and the speed of a certain drive axis is close to the limit value, that is, there is no over-constraint phenomenon, it can be proved that a kinematic constraint planning method for a twelve-axis series-hybrid structure mirror milling device provided by the present invention is effective.

[0109] In another embodiment of the present invention, a kinematic constraint planning method for a twelve-axis series-hybrid structure mirror milling device described in the present invention is integrated in a numerical control system, and then actual machining verification is carried out. The mirror milling system of this embodiment includes:

[0110] A twelve-axis series-hybrid structure mirror milling device: the machining end is a five-axis CA double swing head machine tool, and the support end is a seven-axis hybrid structure including a 3-RCU parallel head;

[0111] And a numerical control system. This numerical control system includes machining end and support end channels. Each channel corresponds to a process of the operating system, and a process includes an interpreter module, a trajectory smoothing module, a speed planning module, and an interpolation module. The machining end channel is the main channel, and the support end channel is the slave channel. The kinematic constraint planning method for the twelve-axis series-hybrid structure mirror milling device described above is integrated in the speed planning module. For the slave channel, due to the transformation from the real axes (L1, L2, L3, Y2, TY, TX, C2) to the virtual axes (X2, Y2, Z2, A2, B2, C2), the corresponding support end G code can be programmed by using the programming method for serial machine tools, that is, the programming formats of the main and slave channels are the same.

[0112] According to the mirror machining principle and in connection with the actual mirror machining scenario, the G-code programming specification for mirror machining can be formulated. The G-codes of the master and slave channels are divided into synchronous segments and asynchronous segments. The asynchronous segments mainly involve the feed and retract processes of the machining end and the support end. For the synchronous segments, under the condition of opposing geometric constraints, the relevant position coordinates of the support end can be obtained by offsetting the relevant position coordinates of the machining end. Therefore, only the start or end marks of the synchronous segments need to be set in the slave channel, and there is no need to write the G-codes of the synchronous segments in the slave channel.

[0113] For the asynchronous segments of the mirror machining G-codes, that is, it is not required that the cutting tool at the machining end and the support head at the support end perform mirror synchronous movement. The G-code execution processes of the master and slave channels are the same as those of traditional multi-axis numerical control machining. The G-code execution process of the synchronous segments is as Figure 9 shown. The M130 instruction in the slave channel enables channel synchronization. Then the master channel interprets the G-codes of the synchronous segments at the machining end. After trajectory smoothing, speed planning, and interpolation modules, the reference positions of the two driving axes are obtained. The movement of each driving axis is realized through the servo system and PLC control. After the machining of the synchronous segments is completed, the M131 instruction in the slave channel disables channel synchronization. The speed planning module includes three steps: calculation of kinematic constraint parameters, division of speed intervals, and acceleration and deceleration control. The kinematic constraint calculation part is a kinematic constraint planning method for a twelve-axis series-hybrid structure mirror milling device as described above.

[0114] The present invention also provides a kinematic constraint planning system for a twelve-axis series-hybrid structure mirror milling device. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it executes the kinematic constraint planning method for the twelve-axis series-hybrid structure mirror milling device as described above.

[0115] The present invention also provides a computer-readable storage medium. The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions cause the processor to implement the kinematic constraint planning method for the twelve-axis series-hybrid structure mirror milling device as described above.

[0116] It is easy for those skilled in the art to understand that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A kinematic constraint planning method for a twelve-axis series-hybrid structure mirror milling device, characterized in that The method comprises the following steps: (1) Construct the motion transfer relationship from the tool pose and the support head pose that satisfy the mirror machining anti-top geometric constraints in the workpiece coordinate system of the twelve-axis series-hybrid structure mirror milling equipment to the machining end and the support end in their respective machine coordinate systems; and equivalent the seven-axis hybrid mechanism (L1, L2, L3, Y2, TY, TX, C2) at the support end to a virtual six-axis serial machine tool (X2, Y2, Z2, A2, B2, C2); (2) Based on the C3 continuous smooth tool path, the C3 continuous support head motion path is obtained from the mirror machining opposite geometric constraint conditions. Based on the smoothed tool path and the mapping relationship between the tool feed motion and the speeds and accelerations of the corresponding drive axes (X1, Y1, Z1, A1, C1), the machining end kinematic constraints to be satisfied by each sampling point pair (P T , R T ) are constructed. Furthermore, the limiting values v T,max and a T,max of the tool feed speed and acceleration at each sampling point pair are calculated using the machining end kinematic constraints; (3) After obtaining the virtual support head by extending the support height of the support head, a kinematic constraint of the support end is constructed based on the mapping relationship between the mirror following motion of the support head and the speeds and accelerations of the corresponding drive shafts (L1, L2, L3, Y2, TY, TX, C2), and then the limit values v Smax and a Smax ; (4) Based on the limit values v T,max and a T,max of the tool feed speed and acceleration, as well as the limit values v Smax and a Smax of the virtual support head feed speed and acceleration, the final tool feed speed limit value is obtained as v max = min(v T,max , v S,max ), and the acceleration limit value is a max = min(a T,max , a S,max ).

2. The kinematic constraint planning method of the twelve-axis series-parallel structure mirror milling equipment according to claim 1, characterized in that: The opposite geometric constraints include: (1) Both the tool center point TCP and the support center point SCP are on the straight line where the normal vector n of the workpiece surface is located, and the distance between the two points is the expected wall thickness H of the thin-walled part; (2) The tool axis vector V T and the support direction vector V T of the support head satisfy collinearity and opposite directions, and V S coincides with the normal vector n of the workpiece surface T . T ​ 3. The kinematic constraint planning method of the twelve-axis series-hybrid structure mirror milling equipment according to claim 1, characterized in that: The C3 continuous smooth tool path includes the tool tip point path C T (u) and the tool axis vector path O T (u); The C3 continuous support head motion path includes the support point path C S (u) and the support direction vector O S (u); The support point path C S (u) and the support direction vector path O S (u) is expressed as:

4. The kinematic constraint planning method for the twelve-axis series-hybrid structure mirror milling equipment according to claim 3, characterized in that: P T =(x T , y T , z T ) is a point on C T (u), and R T =(A1, C1) is the corresponding cutter axis vector. According to the geometric characteristics of the trajectory C T (u) and the structural parameters of the machining end five-axis machine tool, the relationship between the speeds of each drive axis and the cutter feed speed v T is as follows: V p = μ tp ·v T (p = X1, Y1, Z1, A1, C1) The proportionality coefficient μ in the formula tp Through analytical calculation, the relationships between the speeds of each drive shaft and the tool feed speed v T are as follows: A p = λ tp ·(v T ) 2 + σ tp ·a T (p = X1, Y1, Z1, A1, C1) If the speed and acceleration limit values of the processing end drive shaft are V pmax and A pmax , then for any point P T on the trajectory C T,i (u), the feasible region of the tool feed motion parameters v T and a T is determined by the following system of inequalities: where i is the serial number of the sampling point, p = (X1, Y1, Z1, A1, C1) is the drive shaft, μ tp,i , λ tp,i , σ tp,i is the relationship coefficient of the drive shaft p relative to v T and a T at the i-th sampling point. N points are sampled on the trajectory C T (u), and the corresponding v T,i and a T,i of each point are obtained. The minimum value among them is taken as v T,max and a T,max .

5. The kinematic constraint planning method for the twelve-axis series-hybrid structure mirror milling equipment according to claim 1, characterized in that: The support height of the extended support head is increased to obtain a virtual support head, and the support point of the virtual support head is made to coincide with the tool tip point. At this time, C T (u) and O S (u) is the movement trajectory of the virtual support head, corresponding to the sampling point pair (P T , R T ). While sampling the tool path, (P T , R S ) is obtained, where R S = (A2, B2) is the support direction vector corresponding to the point P T . Furthermore, the limit values v S,max and a S,max of the feed speed and acceleration of the virtual support point are obtained.

6. The kinematic constraint planning method of the twelve-axis series-hybrid structure mirror milling equipment according to claim 1, characterized in that: The mapping relationship between the following motion of the support head and the speeds and accelerations of the drive shafts (L1, L2, L3, Y2, TY, TX, C2) has been obtained, and combined with the geometric characteristics of the trajectory C T (u), the relationship between the speeds of the drive shafts at each support end and the feed speed v of the virtual support head is obtained S The relationship formula is as follows: V q = μ sq ·v S (q = (L1, L2, L3, Y2, TY, TX, C2)) The relationship between the speeds of each drive shaft and the feed speed v of the virtual support head S and the tangential acceleration a S is as follows: A q = λ sq ·(v S ) 2 + σ sq ·a S (q = (L1, L2, L3, Y2, TY, TX, C2)) If the speed and acceleration limit values of the processing end drive shaft are V qmax and A qmax , for any point P T on the trajectory C T,i (u), the feasible region of the feed motion parameters v S and a S of the virtual support head is determined by the following set of inequalities: q = (L1, L2, L3, Y2, TY, TX, C2) is the support end drive shaft, μ sq,i , λ sq,i , σ sq,i is the relationship coefficient of the drive shaft q relative to v at the i-th sampling point S and a S . Corresponding to the N points sampled on the trajectory C T (u), calculate v S,i and a S,i corresponding to each point, and take the minimum value among them as v S,max and a S,max .

7. The kinematic constraint planning method for the twelve-axis series-parallel hybrid structure mirror milling equipment according to any one of claims 1-6, characterized in that: Denote the pose of the support head in the workpiece coordinate system as (x s , y s , z s , i s , j s , k s ), where (x s , y s , z s ) represents the position coordinates of the support point, and (i s , j s , k s ) represents the support direction vector. Then the forward kinematics of the hybrid mechanism is expressed as: (L1,L2,L3,Y2,TY,TX,C2) → (x s , y s , z s , i s , j s , k s ) Solve the support head pose in the workpiece coordinate system from the position coordinates of each drive axis. After real-virtual transformation, the forward kinematics is further expressed as: (L1, L2, L3, Y2, TY, TX, C2) → (x s , y s , z s , i s , j s , k s ) → (x s , y s , i s , A2, B2), where (i s , j s , k s ) has the following relationship with the rotation angle of the virtual rotation axis:

8. The kinematic constraint planning method of the twelve-axis series-hybrid structure mirror milling equipment according to any one of claims 1-6, characterized in that: For the support end, the relationship between the support point velocity and the velocities of each drive axis at the support end of the hybrid structure is determined by the following formula: Where J VI is a 7-row and 6-column Jacobian matrix, and v sq (q = x, y, z) is the linear velocity v S of the support point in the components in the three directions of x, y, and z, and ω sq (q = x, y, z) is the angular velocity of the support point.

9. A kinematic constraint planning system for a twelve-axis series-hybrid structure mirror milling device, characterized in that: The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it executes the kinematic constraint planning method of the twelve-axis series-hybrid structure mirror milling equipment according to any one of claims 1-8.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions cause the processor to implement the kinematic constraint planning method of the twelve-axis series-hybrid structure mirror milling equipment according to any one of claims 1-8.

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