A method for smoothing error control of velocity hybrid interpolation trajectory

Abstract

This invention specifically relates to a smoothing error control method for velocity-mixed interpolation trajectories, belonging to the field of five-axis machining trajectory optimization technology. Addressing the problems of conservative estimation and low machining efficiency in existing velocity-mixed smoothing error estimation methods, this invention uses the tangent relationship between the synthesized velocity and the allowable error region to iteratively and accurately find the tangent point position. First, a circular error region is determined based on the tool tip position error limit, and the maximum mixing time satisfying the tool tip constraint is calculated. Then, the tool axis deviation angle error limit is converted into an elliptical error region through inverse kinematics to determine the maximum mixing time satisfying the tool axis constraint. Finally, the minimum of the two values ​​is taken as the mixing time. This invention can make the smoothing error approach the allowable saturation value, maximizing the mixing time while ensuring the accuracy of the tool tip position and tool axis deviation angle, thereby improving five-axis machining efficiency. It is suitable for real-time trajectory smoothing control of five-axis CNC systems.

Description

Technical Field

[0001] This invention relates to the field of five-axis machining trajectory optimization technology, specifically to a method for smoothing error control of velocity hybrid interpolation trajectory. Background Technology

[0002] In five-axis CNC machining, the discrete straight line trajectory generated by the G01 command has problems such as sharp corners and sudden speed changes. It is necessary to achieve trajectory smoothing through speed hybrid interpolation. The smoothing process must strictly constrain the tool tip position error and tool axis deviation angle error to avoid machining out of tolerance.

[0003] Existing error control methods for smoothing corners in speed mixing mostly limit the mixing time by estimating the smoothing error: Some methods use the distance between the midpoint of the mixing time and the inflection point as the error estimate. Although this can constrain the error, the error estimate is significantly scaled down, and the mixing time value is conservative, which reduces processing efficiency.

[0004] Another method uses the distance between the position where adjacent line segments have equal speed and the inflection point as the error estimate, which improves the estimation accuracy. However, from a geometric point of view, there is still error scaling, and the error allowable range is not fully utilized. There is still room for optimization of the mixing time.

[0005] In summary, existing five-axis velocity hybrid interpolation smoothing error control methods generally suffer from inaccurate error estimation and conservative hybridization time, which prevents full utilization of the allowable error range during trajectory smoothing, limiting machining efficiency and making it difficult to meet the engineering requirements of high-precision and high-efficiency five-axis machining.

[0006] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0007] To address the problems of conservative estimation of smoothing error and low processing efficiency in existing velocity hybrid interpolation methods, this invention provides a smoothing error control method for velocity hybrid interpolation trajectories.

[0008] Other features and advantages of the invention will become apparent from the following detailed description, or may be learned in part by practice of the invention.

[0009] According to a first aspect of the present invention, a method for smoothing error control of a velocity hybrid interpolation trajectory is provided, the method comprising: Step 1: Perform velocity planning on the G01 trajectory to be processed to obtain velocity and displacement curves; Step 2: Determine the first allowable error area based on the preset blade tip position error limit, and calculate the first projection length of the point on the boundary of the first allowable error area onto the original blade tip trajectory; Step 3: Based on the first projection length and the displacement curve and velocity curve, calculate the corresponding first duration and first velocity, and synthesize the first displacement vector and the first velocity vector; Step 4: Determine whether the current point determined by the first displacement vector and the first velocity vector is the tangent point between the smooth trajectory and the first error allowable area. If not, adjust the projection direction and repeat steps 2 to 4 until the tangent point is found. Step 5: Calculate the first mixed duration that satisfies the blade tip position error limit based on the second duration determined by the projection length corresponding to the cutting point; Step 6: Based on the preset tool axis deviation angle error limit, transform it into the second error allowable region in the machine tool coordinate system through inverse kinematic transformation, and calculate the second projection length of the point on the boundary of the second error allowable region onto the original tool axis trajectory; Step 7: Based on the second projection length and the displacement curve and velocity curve, calculate the corresponding third duration and second velocity, and synthesize the second velocity vector. At the same time, calculate the tangential vector at the corresponding intersection point on the boundary of the second error allowable region. Step 8: Determine whether the second velocity vector is parallel to the tangential vector. If they are not parallel, adjust the projection direction and repeat steps 6 to 8 until the second velocity vector is parallel to the tangential vector. Step 9: Calculate the second mixing time that satisfies the tool axis deviation error limit based on the fourth duration determined by the projection length corresponding to the parallel time, and take the minimum value between the first mixing time and the second mixing time as the final mixing time to generate a smooth tool path.

[0010] In some exemplary embodiments, the expressions for the velocity curve and the displacement curve are as follows:

[0011]

[0012] in, Let be the duration of each interval of the piecewise function. For local time parameters, Let be the velocity at each segment point of the piecewise function. This represents the displacement at the segmentation point. The initial velocity, These represent maximum speed, acceleration, and jerk, respectively.

[0013] In some exemplary embodiments, step two specifically includes: The allowable area for the tool tip position error can be determined as: radius is The circle; among which, It is a pre-set tool tip position error limit; take a point on the boundary of the error allowable area and project it onto the original trajectory. First, assume that this point is located relative to the first... i The deflection angle of the segment trajectory is On the straight line; then project onto the first... i Section and the i +1 length of the original blade tip trajectory They are respectively:

[0014] in, The initial values ​​for each angle are calculated as follows: (The angle is the angle between adjacent tool tip paths.)

[0015] in, and respectively along the first i Section and the i +1 unit vector of the blade tip trajectory, Used to store angle values.

[0016] In some exemplary embodiments, step three specifically includes: First, based on the projection length determined in step two and the displacement expression obtained in step one, the duration corresponding to that length is calculated. and Then, the corresponding speed is obtained according to the speed expression. and Therefore, the combined displacement and velocity vectors are:

[0017] in, and These represent the composite velocity and composite displacement, respectively.

[0018] In some exemplary embodiments, step four specifically includes: Based on the set calculation precision ,judge and Whether it is perpendicular, i.e., whether the current point is the tangent point between the smooth trajectory and the error-allowed region; first let , Scenario 1: like ,illustrate and It forms an acute angle, at this time To reduce; then let Then, jump to step two to recalculate the projected length, synthesize the displacement and velocity, and make another judgment; Scenario 2: like ,illustrate and It forms an obtuse angle, at this time If it needs to be increased, then let Then, jump to step two to recalculate the projected length, synthesize the displacement and velocity, and make another judgment; Scenario 3: like Then it is considered as and If they are perpendicular, then the point of tangency has been found, and the next step can be performed.

[0019] In some exemplary embodiments, step five specifically includes: After determining the cutting point position, the maximum mixing time that satisfies the blade tip position error limit can be determined as follows:

[0020] in, and The duration corresponding to the projected length at the tangent point.

[0021] In some exemplary embodiments, step six specifically includes: First, the tool axis offset angle error limit in the workpiece coordinate system needs to be determined. Error limits converted to machine tool coordinate system According to the inverse kinematics transformation of the machine tool, we can obtain:

[0022] in, The tool axis vector, For machine tool rotary axis movement commands; then the tool axis deviation... Represented as:

[0023] This deviation must meet the following conditions:

[0024] This inequality can be further transformed into:

[0025] With the i The deflection angle of the segment trajectory is The slope of a line segment can be determined by the angular relationship. kThe coordinates of the intersection point of the line segment and the allowable error zone can then be calculated by combining the expressions for the ellipse and the line.

[0026] In some exemplary embodiments, step seven specifically includes: The corresponding duration can be determined based on the projection length and the displacement expression. and Then, the corresponding speed is obtained according to the speed expression. and The synthesis rate is then:

[0027] Furthermore, based on the coordinates of the intersection point and the formula for the tangent line of an ellipse, the expression for the tangent line of the ellipse at the intersection point is:

[0028] So, the tangential vector Represented as:

[0029] Here, it's important to pay attention to the choice of sign; the vector should point to the direction that makes the vector... The direction in which the angle increases.

[0030] In some exemplary embodiments, step eight specifically includes: First, the vector is expanded, such as by... Expanded to , A - C in plane Similarly, it can be expanded to According to the set calculation precision ,judge and Whether it is parallel, that is, whether the current point is the tangent point between the smooth trajectory and the error-allowable region; first let , Scenario 1: like Then it is considered as and If they are parallel, then the point of tangency has been found, and the next step can be performed. Scenario 2: If condition one is not met and ,Right now Compared to Rotation direction and angle If the directions of increase are the same, then the angle Need to be reduced; make Then proceed to step six; Scenario 3: If condition one is not met and ,Right now Compared to Rotation direction and angle If the direction of increase is opposite, then the angle Need to be increased; make Then proceed to step six.

[0031] According to a second aspect of the present invention, a storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the smooth error control method for velocity hybrid interpolation trajectory described in the first aspect above.

[0032] According to a third aspect of the present invention, a computer program product is provided, on which a computer program is stored, wherein when the computer program is executed by a processor, the smooth error control method for the velocity hybrid interpolation trajectory described in the first aspect is implemented.

[0033] According to a fourth aspect of the present invention, an electronic device is provided, comprising: Processor; and Memory for storing the executable instructions of the processor; The processor is configured to implement the smooth error control method for the velocity hybrid interpolation trajectory described in the first aspect above by executing the executable instructions.

[0034] The smoothing error control method for velocity hybrid interpolation trajectory provided in the embodiments of the present invention, based on the definition of smoothing error, utilizes the location where the maximum smoothing error occurs to synthesize the tangent relationship between the velocity vector and the error allowable region, and iteratively calculates the maximum mixing time that meets the error constraints of the tool tip and tool axis. Compared with existing error control methods, the method of the present invention can make the actual smoothing error approach saturation, fully utilize the given geometric error limit range, maximize the mixing time, and improve machining efficiency. Compared with the prior art, it has the following beneficial effects: 1. More precise error control: Based on the tangent relationship between the synthesis speed and the error allowable range, the maximum error point is directly located. The error estimation has no redundant scaling, which allows the actual smoothing error to accurately approach the preset saturation limit and make full use of the error allowable range.

[0035] 2. Higher processing efficiency: Under the dual constraints of tool tip position and tool axis deflection angle, the maximum feasible mixing time is calculated, avoiding conservative values, significantly improving the corner feed speed of five-axis machining, and shortening the processing time.

[0036] 3. Enhanced applicability: It is compatible with both tool tip position error and tool axis deviation angle error control, adapts to the inverse kinematic transformation of five-axis machine tools, and can be directly used for real-time interpolation and trajectory smoothing in five-axis CNC systems, making it highly practical for engineering applications.

[0037] 4. Superior trajectory smoothness: Continuous and smooth feed curves are generated based on precise error control, effectively suppressing sudden speed changes and improving the quality of the machined surface and the stability of the motion.

[0038] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0039] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0040] Figure 1 This is a flowchart of an embodiment of the method of the present invention.

[0041] Figure 2 This refers to the tool path that needs to be smoothed in the embodiments of the method of the present invention.

[0042] Figure 3 This is a schematic diagram of the blade tip position error control method in an embodiment of the present invention.

[0043] Figure 4 This is a schematic diagram of the tangent point finding method in an embodiment of the present invention.

[0044] Figure 5 This is a schematic diagram illustrating the principle of mixed duration calculation in the embodiment of the method of the present invention.

[0045] Figure 6 This is a schematic diagram of the tool axis deviation angle error control method in an embodiment of the present invention.

[0046] Figure 7 These are the smoothing error results controlled by different methods in the embodiments of the present invention.

[0047] Figure 8 This is a feed rate curve obtained by mixing different methods in the embodiments of the present invention. Detailed Implementation

[0048] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the invention will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0049] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0050] In related technologies, reference 1, “S. Tajima, B. Sencer, Accurate real-time interpolation of 5-axis tool-paths with local corner smoothing, International Journal of Machine Tools and Manufacture 142 (2019) 1–15,” discloses a method to control smoothing error by limiting the mixing time of adjacent line segments. It uses the distance between the sampling point corresponding to the midpoint of the mixing time and the inflection point as a constraint on the smoothing error estimate, which can effectively control the smoothing error. However, this method involves scaling in the estimation of the smoothing error, making the determination of the mixing time too conservative, resulting in a loss of processing efficiency.

[0051] Reference 2, “Z. Shi, W. Zhang, Y. Ding, Real-time interpolation with low-pass filtering for five-axis hybrid machining robots, Mechanical Systems and Signal Processing 209 (2024) 111080,” discloses a relatively accurate method for estimating smoothing error. It uses the distance between the position where adjacent line segments have equal velocities and the inflection point as a constraint on the smoothing error estimate, further improving the accuracy of the error estimation. However, from a geometrical perspective, this method still has some scaling limitations and room for optimization.

[0052] The typical characteristics of the above literature are: when using the speed mixing method to smooth the corners of the five-axis trajectory, it is necessary to constrain the smoothing error. However, the existing methods all have certain scaling in the estimation of the smoothing error, which makes the determination of the maximum mixing time more conservative, ultimately resulting in a loss of processing efficiency.

[0053] To address the shortcomings and deficiencies of existing technologies, this example embodiment provides a smoothing error control method for velocity hybrid interpolation trajectories. Based on the definition of smoothing error, it utilizes the tangential relationship between the synthesized velocity and the error allowable region, and through simple iteration, calculates the mixing time that makes the geometric error approach saturation, thereby achieving effective utilization of smoothing error and improving processing efficiency.

[0054] This method first uses a preset tool tip position error limit and the tangent relationship between the synthesized velocity and the allowable error range to iteratively find the tangent point position and determine the maximum mixing time that satisfies the tool tip error constraint. Then, based on the tool axis deflection angle error limit in the workpiece coordinate system and the inverse kinematics transformation formula, the allowable error range in the machine tool coordinate system is derived, and the tangent relationship is used again to find the tangent point, determining the maximum mixing time that satisfies the tool axis error constraint. Finally, the maximum mixing time that simultaneously satisfies both the tool tip and tool axis error constraints is determined.

[0055] refer to Figure 1 As shown, the specific steps may include: Step 1: Perform velocity planning on the G01 trajectory to be processed to obtain velocity and displacement curves; Step 2: Determine the first allowable error area based on the preset blade tip position error limit, and calculate the first projection length of the point on the boundary of the first allowable error area onto the original blade tip trajectory; Step 3: Based on the first projection length and the displacement curve and velocity curve, calculate the corresponding first duration and first velocity, and synthesize the first displacement vector and the first velocity vector; Step 4: Determine whether the current point determined by the first displacement vector and the first velocity vector is the tangent point between the smooth trajectory and the first error allowable area. If not, adjust the projection direction and repeat steps 2 to 4 until the tangent point is found. Step 5: Calculate the first mixed duration that satisfies the blade tip position error limit based on the second duration determined by the projection length corresponding to the cutting point; Step 6: Based on the preset tool axis deviation angle error limit, transform it into the second error allowable region in the machine tool coordinate system through inverse kinematic transformation, and calculate the second projection length of the point on the boundary of the second error allowable region onto the original tool axis trajectory; Step 7: Based on the second projection length and the displacement curve and velocity curve, calculate the corresponding third duration and second velocity, and synthesize the second velocity vector. At the same time, calculate the tangential vector at the corresponding intersection point on the boundary of the second error allowable region. Step 8: Determine whether the second velocity vector is parallel to the tangential vector. If they are not parallel, adjust the projection direction and repeat steps 6 to 8 until the second velocity vector is parallel to the tangential vector. Step 9: Calculate the second mixing time that satisfies the tool axis deviation error limit based on the fourth duration determined by the projection length corresponding to the parallel time, and take the minimum value between the first mixing time and the second mixing time as the final mixing time to generate a smooth tool path.

[0056] The specific steps described above are as follows: Step 1: Complete velocity planning and obtain the displacement-velocity curve.

[0057] First, velocity planning is performed based on the input G01 trajectory and pre-set motion constraints to obtain the velocity. Displacement The expression is as follows:

[0058]

[0059] in, Let be the duration of each interval of the piecewise function. For local time parameters, Let be the velocity at each segment point of the piecewise function. This represents the displacement at the segmentation point. The initial velocity, These represent maximum speed, acceleration, and jerk, respectively.

[0060] For specific speed planning methods, refer to "X. Du, J. Huang, L.-M. Zhu, A complete S-shape feed rate scheduling approach for NURBS interpolator, Journal of Computational Design and Engineering 2 (4) (2015) 206–217."

[0061] Step 2: Determine the allowable error area based on the given tool tip position error limit and project it onto the original trajectory.

[0062] The allowable area for the tool tip position error can be determined as: radius is A circle. Among them, This is a pre-set error limit for the tool tip position. A point is taken at the boundary of the error-allowed region and projected onto the original trajectory. First, it is assumed that this point is located relative to the... i The deflection angle of the segment trajectory is On the straight line. Then project onto the first. i Section and the i +1 length of the original blade tip trajectory They are respectively:

[0063] in, The initial values ​​for each angle are calculated as follows: (The angle is the angle between adjacent tool tip paths.)

[0064] in, and respectively along the first i Section and the i +1 unit vector of the blade tip trajectory, Used to store angle values.

[0065] Step 3: Synthesize the displacement vector and velocity vector.

[0066] First, based on the projection length determined in step two and the displacement expression obtained in step one, the duration corresponding to that length is calculated. and Then, the corresponding speed is obtained according to the speed expression. and Therefore, the combined displacement and velocity vectors are:

[0067] in, and These represent the composite velocity and composite displacement, respectively.

[0068] Step 4: Determine if it is a tangent point and perform iteration.

[0069] Based on the set calculation precision ,judge and Whether it is perpendicular, i.e., whether the current point is the tangent point between the smooth trajectory and the error-allowed region. First, let... , Scenario 1: like ,illustrate and It forms an acute angle, at this time It needs to be reduced. Therefore, let... Then, jump to step two to recalculate the projected length, synthesize the displacement and velocity, and make another judgment.

[0070] Scenario 2: like ,illustrate and It forms an obtuse angle, at this time It needs to be increased. Then let... Then, jump to step two to recalculate the projected length, synthesize the displacement and velocity, and make another judgment.

[0071] Scenario 3: like Then it is considered as and If they are perpendicular, then the point of tangency has been found, and the next step can be performed.

[0072] Step 5: Calculate the mixing time that meets the tool tip position error limit.

[0073] After determining the cutting point position, the maximum mixing time that satisfies the blade tip position error limit can be determined as follows:

[0074] Here and The duration corresponding to the projected length at the tangent point.

[0075] Step 6: Determine the allowable error range of the tool axis trajectory and calculate the projected length.

[0076] First, the tool axis offset angle error limit in the workpiece coordinate system needs to be determined. Error limits converted to machine tool coordinate system According to the inverse kinematics transformation of the machine tool, we can obtain:

[0077] in, The tool axis vector, This is the machine tool rotary axis movement command. Therefore, the tool axis deviation... It can be represented as:

[0078] This deviation must meet the following conditions:

[0079] This inequality can be further transformed into:

[0080] It can be observed that the allowable error range is... A - C An ellipse in a coordinate system. (The last part is incomplete and likely refers to a specific coordinate system or ellipse i Taking the corner at +1 trajectory point as an example, the center of the ellipse is... The length of the major axis is The length of the minor axis is Therefore, the error limit of rotation commands in the machine tool coordinate system It is no longer a fixed value.

[0081] With the i The deflection angle of the segment trajectory is The slope of a line segment can be determined by the angular relationship.k The coordinates of the intersection point of the line segment and the allowable error zone can then be calculated by combining the expressions for the ellipse and the line.

[0082]

[0083] The calculated coordinates of the intersection point are:

[0084] The error limit can be determined based on the coordinates of the intersection point. for:

[0085] The length projected onto the original trajectory is:

[0086] in, The angle between adjacent tool axis paths. and respectively along the first i Section and the i +1 unit vector of the tool axis path, and They are respectively In the i Section and the i +1 is the projected length on the original tool axis path.

[0087] Step 7: Combine the velocity vectors and calculate the elliptical tangential vector. The corresponding duration can be determined based on the projection length and the displacement expression. and Then, the corresponding speed is obtained according to the speed expression. and The synthesis rate is then:

[0088] Furthermore, based on the coordinates of the intersection point and the formula for the tangent line of an ellipse, the expression for the tangent line of the ellipse at the intersection point is:

[0089] So, the tangential vector Represented as:

[0090] Here, it's important to pay attention to the choice of sign; the vector should point to the direction that makes the vector... The direction in which the angle increases.

[0091] Step 8: Determine if it is a tangent point and perform iteration.

[0092] First, the vector is expanded, such as by... Expanded to , A - C in plane Similarly, it can be expanded to Based on the set calculation precision. ,judge and Whether it is parallel, that is, whether the current point is the tangent point between the smooth trajectory and the error-allowable region. First let , Scenario 1: like Then it is considered as and If they are parallel, then the point of tangency has been found, and the next step can be performed.

[0093] Scenario 2: If condition one is not met and ,Right now Compared to Rotation direction and angle If the directions of increase are the same, then the angle It needs to be reduced in size. (Order) Then proceed to step six.

[0094] Scenario 3: If condition one is not met and ,Right now Compared to Rotation direction and angle If the direction of increase is opposite, then the angle It needs to be increased. (Order) Then proceed to step six.

[0095] Step 9: Calculate the mixing time that meets the cutter axis offset angle error limit and determine the final mixing time.

[0096] After determining the tangent position, the maximum mixing time that satisfies the cutter axis offset angle error limit can be determined as follows:

[0097] Finally, the mixing time that simultaneously satisfies the error limits of the tool tip and tool axis is determined as follows:

[0098] By superimposing the motion curves of adjacent line segments based on the final determined mixing time, a continuous feed rate curve can be obtained. Integrating the rate curve yields a smooth tool path.

[0099] The steps in this exemplary embodiment will now be described in more detail with reference to the accompanying drawings and embodiments.

[0100] Example 1 In this embodiment of the invention, the toolpath that needs to be smoothed is as follows: Figure 2 The fan-shaped trajectory shown has a preset blade tip position error limit of [value missing]. The cutter shaft offset angle error limit is .

[0101] The specific implementation steps of the smoothing error control method for velocity hybrid interpolation trajectory proposed in this invention are as follows: Step 1: Complete velocity planning and obtain the displacement-velocity curve.

[0102] Taking the first two line segments of the sector trajectory as an example, the input G01 trajectory points are: , , , , , First, based on the input G01 trajectory and pre-set motion constraints, velocity planning is performed to obtain the velocity. Displacement The expression is as follows:

[0103]

[0104] in, Let be the duration of each interval of the piecewise function. For local time parameters, Let be the velocity at each segment point of the piecewise function. This represents the displacement at the segmentation point. The initial velocity, These represent maximum speed, acceleration, and jerk, respectively.

[0105] The values ​​for the first and second segments of the trajectory are as follows:

[0106] For specific speed planning methods, refer to "X. Du, J. Huang, L.-M. Zhu, A complete S-shape feed rate scheduling approach for NURBS interpolator, Journal of Computational Design and Engineering 2 (4) (2015) 206–217."

[0107] Step 2: Determine the allowable error area based on the given tool tip position error limit and project it onto the original trajectory.

[0108] like Figure 3 As shown, the allowable area for the tool tip position error can be determined as: a radius of... A circle. Among them, This is a pre-defined error limit for the tool tip position. A point is taken at the boundary of the error-allowed region and projected onto the original trajectory. First, it is assumed that this point is located at an angle of θ relative to the i-th segment of the trajectory. On the straight line. Then project onto the first. i Section and the i +1 length of the original blade tip trajectory They are respectively:

[0109] in, The initial values ​​for each angle are calculated as follows: (The angle is the angle between adjacent tool tip paths.)

[0110] in, and respectively along the first i Section and the i +1 unit vector of the blade tip trajectory, Used to store angle values.

[0111] Step 3: Synthesize the displacement vector and velocity vector.

[0112] First, based on the projection length determined in step two and the displacement expression obtained in step one, the duration corresponding to that length is calculated. and Then, the corresponding speed is obtained according to the speed expression. and Therefore, the combined displacement and velocity vectors are:

[0113] in, and These represent the composite velocity and composite displacement, respectively.

[0114] Step 4: Determine if it is a tangent point and perform iteration.

[0115] like Figure 4 As shown, based on the set calculation precision ,judge and Whether it is perpendicular, i.e., whether the current point is the tangent point between the smooth trajectory and the error-allowed region. First, let... , Scenario 1: like ,illustrate and It forms an acute angle, at this time It needs to be reduced. Therefore, let... Then, jump to step two to recalculate the projected length, synthesize the displacement and velocity, and make another judgment.

[0116] Scenario 2: like ,illustrate and It forms an obtuse angle, at this time It needs to be increased. Then let... Then, jump to step two to recalculate the projected length, synthesize the displacement and velocity, and make another judgment.

[0117] Scenario 3: like Then it is considered as and If they are perpendicular, then the point of tangency has been found, and the next step can be performed.

[0118] If we meet condition three, we can proceed directly to the next step.

[0119] Step 5: Calculate the mixing time that meets the tool tip position error limit.

[0120] like Figure 5 As shown, after determining the tangent position, the maximum mixing time that satisfies the blade tip position error limit can be determined as follows:

[0121] Here and The duration corresponding to the projected length at the tangent point.

[0122] Step 6: Determine the allowable error range of the tool axis trajectory and calculate the projected length.

[0123] First, the tool axis offset angle error limit in the workpiece coordinate system needs to be determined. Error limits converted to machine tool coordinate system According to the inverse kinematics transformation of the machine tool, we can obtain:

[0124] in, The tool axis vector, This is the machine tool rotary axis movement command. Therefore, the tool axis deviation... It can be represented as:

[0125] This deviation must meet the following conditions:

[0126] This inequality can be further transformed into:

[0127] It can be found that the error tolerance region is an ellipse in the A-C coordinate system. Taking the corner at the i +(1)st trajectory point as an example, the center of this ellipse is , the length of the major axis is , and the length of the minor axis is . Therefore, the rotation instruction error limit in the machine tool coordinate system is no longer a fixed value.

[0128] The slope of the line segment with a deflection angle of i from the th trajectory segment can be determined through the angle relationship to be k = -0.1053. Then the intersection coordinates of this line segment and the error tolerance region can be calculated by联立椭圆与直线表达式计算.

[0129]

[0130] The calculated intersection coordinates are:

[0131] Based on the intersection coordinates, the error limit at this time can be determined as:

[0132] The length projected onto the original trajectory is:

[0133] Among them, is the angle between adjacent cutter axis paths, and are the unit vectors along the i th and the i +(1)st cutter axis paths respectively, and are respectively projected lengths on the i th and the i +(1)st original cutter axis paths.

[0134] Step 7: Synthesize the velocity vectors and calculate the elliptical tangential vectors According to the projected length and the displacement expression, the corresponding time durations and can be determined, and then the corresponding velocities and It should be noted that the "联立椭圆与直线表达式计算" in the original text seems to be an incomplete or incorrect expression. It might need to be further clarified in the original context for a more accurate translation. Also, there are some tags like <0000...> which are likely specific to a certain system or format and might not be directly translatable in a meaningful way other than preserving them as is. If there are specific instructions or meanings associated with these tags in your actual work, more appropriate handling might be required. The synthesis rate is then:

[0135] Furthermore, based on the coordinates of the intersection point and the formula for the tangent line of an ellipse, the expression for the tangent line of the ellipse at the intersection point is:

[0136] So, the tangential vector Represented as:

[0137] Here, it's important to pay attention to the choice of sign; the vector should point to the direction that makes the vector... The direction in which the angle increases.

[0138] Step 8: Determine if it is a tangent point and perform iteration.

[0139] First, the vector is expanded, such as by... Expanded to In the AC plane Similarly, it can be expanded to Then according to Figure 6 The cases shown are categorized according to the set calculation precision. ,judge and Whether it is parallel, that is, whether the current point is the tangent point between the smooth trajectory and the error-allowable region. First let , Scenario 1: like Then it is considered as and If they are parallel, then the point of tangency has been found, and the next step can be performed.

[0140] Scenario 2: If condition one is not met and ,Right now Compared to Rotation direction and angle If the directions of increase are the same, then the angle It needs to be reduced in size. (Order) Then proceed to step six.

[0141] Scenario 3: If condition one is not met and ,Right now Compared to Rotation direction and angle If the direction of increase is opposite, then the angle It needs to be increased. (Order) Then proceed to step six.

[0142] Step 9: Calculate the mixing time that meets the cutter axis offset angle error limit and determine the final mixing time.

[0143] After determining the tangent position, the maximum mixing time that satisfies the cutter axis offset angle error limit can be determined as follows:

[0144] Finally, the mixing time that simultaneously satisfies the error limits of the tool tip and tool axis is determined as follows:

[0145] By superimposing the motion curves of adjacent line segments based on the final determined mixing time, a continuous feed rate curve can be obtained. Integrating the rate curve yields a smooth tool path.

[0146] After the above steps of calculating the mixing time and superimposing the motion curves, the final smoothing error result of this embodiment is as follows: Figure 7 As shown in the figure, the smoothing error controlled by this method is closer to its limit value without exceeding the preset limit, indicating that the error control accuracy of this method is higher. The feed rate curve planned in this embodiment is shown in the figure. Figure 8 As shown, the feed rate curve obtained by the method of this invention has a shorter total time, indicating higher machining efficiency. This is because the accurate estimation of the error makes the smoothing error approach saturation, allowing the tool to pass through corners at a faster speed, ultimately improving efficiency and verifying the effectiveness of the method of this invention.

[0147] In summary, this invention can precisely control smoothing error, bringing geometric error as close to saturation as possible without exceeding limits. Compared to existing smoothing error control methods, this invention utilizes the maximum error location, the tangent relationship between the synthesized velocity vector and the allowable error region, and precisely controls smoothing error by limiting the mixing time, making the actual smoothing error closer to saturation, thereby improving processing efficiency.

[0148] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0149] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims.

[0150] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is defined only by the appended claims.

Claims

1. A method for smoothing error control of velocity hybrid interpolation trajectory, characterized in that, The method includes: Step 1: Perform velocity planning on the G01 trajectory to be processed to obtain velocity and displacement curves; Step 2: Determine the first allowable error area based on the preset blade tip position error limit, and calculate the first projection length of the point on the boundary of the first allowable error area onto the original blade tip trajectory; Step 3: Based on the first projection length and the displacement curve and velocity curve, calculate the corresponding first duration and first velocity, and synthesize the first displacement vector and the first velocity vector; Step 4: Determine whether the current point determined by the first displacement vector and the first velocity vector is the tangent point between the smooth trajectory and the first error allowable area. If not, adjust the projection direction and repeat steps 2 to 4 until the tangent point is found. Step 5: Calculate the first mixed duration that satisfies the blade tip position error limit based on the second duration determined by the projection length corresponding to the cutting point; Step 6: Based on the preset tool axis deviation angle error limit, transform it into the second error allowable region in the machine tool coordinate system through inverse kinematic transformation, and calculate the second projection length of the point on the boundary of the second error allowable region onto the original tool axis trajectory; Step 7: Based on the second projection length and the displacement curve and velocity curve, calculate the corresponding third duration and second velocity, and synthesize the second velocity vector. At the same time, calculate the tangential vector at the corresponding intersection point on the boundary of the second error allowable region. Step 8: Determine whether the second velocity vector is parallel to the tangential vector. If they are not parallel, adjust the projection direction and repeat steps 6 to 8 until the second velocity vector is parallel to the tangential vector. Step 9: Calculate the second mixing time that satisfies the tool axis deviation error limit based on the fourth duration determined by the projection length corresponding to the parallel time, and take the minimum value between the first mixing time and the second mixing time as the final mixing time to generate a smooth tool path.

2. The method according to claim 1, characterized in that, The expressions for the velocity curve and the displacement curve are as follows: in, Let be the duration of each interval of the piecewise function. For local time parameters, Let be the velocity at each segment point of the piecewise function. This represents the displacement at the segmentation point. The initial velocity, These represent maximum speed, acceleration, and jerk, respectively.

3. The method according to claim 2, characterized in that, Step two specifically involves: The allowable area for the tool tip position error can be determined as: radius is The circle; among which, It is a pre-set tool tip position error limit; take a point on the boundary of the error allowable area and project it onto the original trajectory. First, assume that this point is located relative to the first... i The deflection angle of the segment trajectory is On the straight line; then project onto the first... i Section and the i +1 length of the original blade tip trajectory They are respectively: in, The initial values ​​for each angle are calculated as follows: (The angle is the angle between adjacent tool tip paths.) in, and respectively along the first i Section and the i +1 unit vector of the blade tip trajectory, Used to store angle values.

4. The method according to claim 3, characterized in that, Step three specifically involves: First, based on the projection length determined in step two and the displacement expression obtained in step one, the duration corresponding to that length is calculated. and Then, the corresponding speed is obtained according to the speed expression. and Therefore, the combined displacement and velocity vectors are: in, and These represent the composite velocity and composite displacement, respectively.

5. The method according to claim 4, characterized in that, Step four specifically involves: Based on the set calculation precision ,judge and Whether it is perpendicular, i.e., whether the current point is the tangent point between the smooth trajectory and the error-allowed region; first let , Scenario 1: like ,illustrate and It forms an acute angle, at this time To reduce; then let Then, jump to step two to recalculate the projected length, synthesize the displacement and velocity, and make another judgment; Scenario 2: like ,illustrate and It forms an obtuse angle, at this time If it needs to be increased, then let Then, jump to step two to recalculate the projected length, synthesize the displacement and velocity, and make another judgment; Scenario 3: like Then it is considered as and If they are perpendicular, then the point of tangency has been found, and the next step can be performed.

6. The method according to claim 5, characterized in that, Step five specifically involves: After determining the cutting point position, the maximum mixing time that satisfies the blade tip position error limit can be determined as follows: in, and The duration corresponding to the projected length at the tangent point.

7. The method according to claim 6, characterized in that, Step six specifically involves: First, the tool axis offset angle error limit in the workpiece coordinate system needs to be determined. Error limits converted to machine tool coordinate system According to the inverse kinematics transformation of the machine tool: in, The tool axis vector, For machine tool rotary axis movement commands; then the tool axis deviation... Represented as: This deviation must meet the following conditions: This inequality can be further transformed into: With the i The deflection angle of the segment trajectory is The slope of a line segment can be determined by the angular relationship. k Then the coordinates of the intersection point of the line segment and the error allowable area can be calculated by combining the expressions of the ellipse and the line. The calculated coordinates of the intersection point are: The error limit can be determined based on the coordinates of the intersection point. for: The length projected onto the original trajectory is: in, The angle between adjacent tool axis paths. and respectively along the first i Section and the i +1 unit vector of the tool axis path, and They are respectively In the i Section and the i +1 is the projected length on the original tool axis path.

8. The method according to claim 7, characterized in that, Step seven specifically involves: The corresponding duration can be determined based on the projection length and the displacement expression. and Then, the corresponding speed is obtained according to the speed expression. and The synthesis rate is then: Furthermore, based on the coordinates of the intersection point and the formula for the tangent line of an ellipse, the expression for the tangent line of the ellipse at the intersection point is: So, tangential vector Represented as: Here, it's important to pay attention to the choice of sign; the vector should point to the direction that makes the vector... The direction in which the angle increases.

9. The method according to claim 8, characterized in that, Step eight specifically involves: First, the vector is expanded, such as by... Expanded to , A - C in plane Similarly, it can be expanded to According to the set calculation precision ,judge and Whether it is parallel, that is, whether the current point is the tangent point between the smooth trajectory and the error-allowable region; first let , Scenario 1: like Then it is considered as and If they are parallel, then the point of tangency has been found, and the next step can be performed. Scenario 2: If condition one is not met and ,Right now Compared to direction and angle of rotation If the directions of increase are the same, then the angle Need to be reduced; make Then proceed to step six; Scenario 3: If condition one is not met and ,Right now Compared to direction and angle of rotation If the direction of increase is opposite, then the angle Need to be increased; make Then proceed to step six.

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