A Sewing Trace Curve Interpolation Method Based on Sag Error Compensation

Abstract

The present invention discloses a sewing trace curve interpolation method based on bow height error compensation. First, the initial feed step is set, and the starting point of the ideal sewing trace curve is used as the initial actual interpolation point; then the second-order Runge-Kutta method is used to calculate the next estimated interpolation point; then the bow height error between the current actual interpolation point and the next estimated interpolation point is calculated using the osculating circle approximation method. If the current bow height error does not exceed the maximum bow height error, the next estimated interpolation point is used as the next actual interpolation point and updated; otherwise, the interpolation point estimation and calculation are repeated until the bow height error between the current interpolation point and the next estimated interpolation point does not exceed the maximum bow height error, until all actual interpolation points are obtained; finally, the feed speed constraint of the machine needle is set, and the feed speed curve is fitted for all actual interpolation points to obtain the actual sewing trace curve. The present invention can improve the accuracy of interpolation and reduce the speed fluctuation during the sewing process, thereby improving the accuracy of the sewing trace.

Description

Technical Field

[0001] The invention belongs to the field of sewing equipment error compensation control and relates to a sewing trace curve interpolation method, in particular to a sewing trace curve interpolation method based on bow height error compensation. Background Art

[0002] With the advancement of electrical and computer technologies, mechatronic sewing equipment is becoming increasingly important in the industry. To meet diverse customer needs, complex sewing curves must be planned prior to machining. The traditional method involves decomposing the machining path into a large number of short straight lines or arcs, followed by linear and circular interpolation. This approach only accommodates relatively simple sewing curves. For complex sewing curves, it introduces significant bow height errors and causes the system to frequently accelerate and decelerate, resulting in significant fluctuations and reduced machining accuracy and efficiency.

[0003] NURBS curves can be used to express various complex curves using a unified mathematical method, eliminating the need for frequent acceleration and deceleration during machining, saving significant processing time. During NURBS curve interpolation, the calculation of control points is cumbersome, and curvature constraints must be met to improve accuracy while reducing speed fluctuations. Therefore, a curve interpolation method is needed to calculate interpolation point parameters and perform speed planning. Summary of the Invention

[0004] In order to solve the problems and needs existing in the background technology, the present invention provides a sewing trace curve interpolation method based on bow height error compensation, which is used to calculate the parameters of the interpolation points and perform speed planning, improve the accuracy of interpolation and reduce speed fluctuations during the sewing process, thereby improving the accuracy of the sewing trace.

[0005] The technical solution adopted in the present invention is:

[0006] Step 1: Set the initial feed step length and use the starting point of the ideal sewing curve as the initial actual interpolation point;

[0007] Step 2: Based on the current actual interpolation point and the current feed step size, the next estimated interpolation point is calculated using the second-order Runge-Kutta method;

[0008] Step 3: Use the osculating circle approximation method to calculate the bow height error between the current actual interpolation point and the next estimated interpolation point. If the current bow height error does not exceed the maximum bow height error, the next estimated interpolation point is used as the next actual interpolation point and updated. Otherwise, proceed to step 4.

[0009] Step 4: Calculate the new feed step length based on the current bow height error, the maximum bow height error, and the current feed step length. Repeat steps 2 and 3 to estimate and calculate the interpolation points until the bow height error between the current interpolation point and the next estimated interpolation point does not exceed the maximum bow height error. Obtain the next actual interpolation point and update it.

[0010] Step 5: Repeat steps 2-4 until the end point of the ideal sewing curve is interpolated and all actual interpolation points are obtained;

[0011] Step 6: Set the feed speed constraint of the needle, fit the feed speed curve for all actual interpolation points, and obtain the actual sewing trace curve.

[0012] In step 3, the osculating circle approximation method is used to generate an osculating arc passing through the current actual interpolation point P. The current actual interpolation point P and the point on the osculating arc The straight-line distance between the current actual interpolation point P and the next estimated interpolation point Q0 is equal to the straight-line distance between the current actual interpolation point P and the next estimated interpolation point Q0, which will close the arc. The actual interpolation point P and the point on the osculating arc The maximum distance between the composed chords is taken as the bow height error between the current actual interpolation point P and the next estimated interpolation point Q0. The calculation formula is:

[0013]

[0014] Among them, r i is an osculating arc The radius, The current actual interpolation point P and the point on the osculating arc The length of the chord.

[0015] In step 4, according to the current bow height error Maximum bow height error δ max , Current feed step Calculate the new feed step size The calculation formula is as follows:

[0016]

[0017] In step 6, the feed speed constraint of the needle is:

[0018]

[0019] Among them, v is the feed speed of the needle, min{} represents the minimum value, T is the interpolation period, δ max is the maximum bow height error, ρ is the curvature radius of the NURBS curve, a nmax is the maximum normal acceleration, jnmax is the maximum normal acceleration.

[0020] In step 6, a seven-segment S-shaped speed planning algorithm with an initial and final speed of 0 is used to fit the feed speed curve of all actual interpolation points to obtain the actual sewing trace curve.

[0021] The beneficial effects of the present invention are:

[0022] The present invention uses NURBS curves for interpolation, iteratively adjusts the control points according to the bow height error, and limits the feed speed for speed planning based on the bow height error, normal acceleration, and normal jerk, thereby improving the accuracy of interpolation and reducing speed fluctuations during the sewing process, thereby improving the accuracy of sewing stitches. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Flowchart of the present invention.

[0024] Figure 2 This is the bow height error result of curve interpolation in the embodiment of the present invention.

[0025] Figure 3 It is the speed fluctuation rate of the speed planning result in the embodiment of the present invention. DETAILED DESCRIPTION

[0026] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0027] like Figure 1 As shown, the present invention includes the following steps:

[0028] Step 1: Set the initial feed step length and use the starting point of the ideal sewing curve as the initial actual interpolation point;

[0029] Step 2: Based on the current actual interpolation point and the current feed step, the parameters of the interpolation point are the point coordinates, and the estimated initial value of the next estimated interpolation point is calculated using the second-order Runge-Kutta method;

[0030] Using the second-order Runge-Kutta method, the parameter of the current actual interpolation point P is recorded as u i , the estimated initial parameters of the next estimated interpolation point Q0 are Both satisfy the following formula:

[0031]

[0032]

[0033] Where T is the interpolation period, n1 and n2 are the first and second intermediate parameters respectively, and u′i and u″ i They represent the first-order derivative and second-order derivative of the NURBS curve at the current actual interpolation point P respectively.

[0034] Step 3: Use the osculating circle (OC) approximation method to calculate the bow height error between the current actual interpolation point and the next estimated interpolation point. If the current bow height error does not exceed the maximum bow height error δ max , then the next estimated interpolation point is used as the next actual interpolation point and updated, otherwise go to step 4;

[0035] In step 3, the osculating circle (OC) approximation method is used to generate an osculating arc passing through the current actual interpolation point P. The current actual interpolation point P and the point on the osculating arc The straight-line distance between the current actual interpolation point P and the next estimated interpolation point Q0 is equal to the straight-line distance between the current actual interpolation point P and the next estimated interpolation point Q0, which will close the arc. The actual interpolation point P and the point on the osculating arc The maximum distance between the composed chords is taken as the bow height error between the current actual interpolation point P and the next estimated interpolation point Q0. The calculation formula is:

[0036]

[0037] Among them, r i is an osculating arc The radius, The current actual interpolation point P and the point on the osculating arc The length of the chord.

[0038] Step 4: Calculate the new feed step length based on the current bow height error, the maximum bow height error, and the current feed step length. Repeat steps 2 and 3 to estimate and calculate the interpolation point until the bow height error between the current interpolation point and the next estimated interpolation point does not exceed the maximum bow height error, and obtain the next actual interpolation point.

[0039] In step 4, in order to reduce the amount of calculation, according to the current bow height error Maximum bow height error δ max , Current feed step Calculate the new feed step size The calculation formula is as follows:

[0040]

[0041] like Figure 2 As shown in FIG. 1 , the bow height error result of the curve interpolation in this embodiment is shown. As can be seen from the figure, the bow height error does not exceed 10 μm, which meets the maximum bow height error limit of 12 μm.

[0042] Step 5: Repeat steps 2-4 until the end point of the ideal sewing curve is interpolated and all actual interpolation points are obtained;

[0043] Step 6: Set the feed speed constraint of the needle, use the seven-segment S-type speed planning algorithm with the initial and final speeds of 0 to fit the feed speed curve of all actual interpolation points, complete the curve interpolation, and obtain the actual sewing trace curve.

[0044] In step 6, to ensure the accuracy of the stitches during sewing, the feed speed needs to be limited according to the maximum bow height error. The feed speed v is limited under the maximum bow height error:

[0045]

[0046] During the sewing process, the needle will generate normal acceleration and normal jerk when moving along the curve, and the feed speed also needs to be limited based on the two.

[0047] The feed rate limit under the maximum normal acceleration limit is:

[0048]

[0049] The feed rate limit under the maximum normal jerk limit is:

[0050]

[0051] In summary, the feed speed constraint of the needle during sewing is:

[0052]

[0053] Among them, v is the feed speed of the needle, min{} represents the minimum value, T is the interpolation period, δ max is the maximum bow height error, ρ is the curvature radius of the NURBS curve, a nmax is the maximum normal acceleration, j nmax is the maximum normal acceleration.

[0054] Under this feed rate constraint, a seven-segment S-shaped speed model with an initial and final speed of 0 is used for speed planning, so that the acceleration can be continuously changed and a reasonable S-shaped feed rate curve is obtained.

[0055] According to the seven-segment S-shaped speed planning algorithm, a series of speed control points are obtained. Assuming the feed speed at the previous speed control point is v1 and the feed speed at the next speed control point is v2, the speed fluctuation rate U at each point is:

[0056]

[0057] The speed fluctuation rate of the speed planning result in this embodiment is as follows: Figure 3 As shown in the figure, the speed fluctuation rate is within the range of ±0.06%, achieving a good speed planning effect.

[0058] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, or improvements made within the scope of the present invention are intended to be included within the scope of protection of the present invention. Any matters not described in detail in this specification constitute prior art known to those skilled in the art.

Claims

1. A sewing trace curve interpolation method based on bow height error compensation, characterized in that: The following steps are involved: Step 1: Set the initial feed step length and use the starting point of the ideal sewing curve as the initial actual interpolation point; Step 2: Based on the current actual interpolation point and the current feed step size, the next estimated interpolation point is calculated using the second-order Runge-Kutta method; Step 3: Use the osculating circle approximation method to calculate the bow height error between the current actual interpolation point and the next estimated interpolation point. If the current bow height error does not exceed the maximum bow height error, the next estimated interpolation point is used as the next actual interpolation point and updated. Otherwise, proceed to step 4. Step 4: Calculate the new feed step length based on the current bow height error, the maximum bow height error, and the current feed step length. Repeat steps 2 and 3 to estimate and calculate the interpolation points until the bow height error between the current interpolation point and the next estimated interpolation point does not exceed the maximum bow height error. Obtain the next actual interpolation point and update it. In step 4, according to the current bow height error Maximum bow height error δ max , Current feed step Calculate the new feed step size The calculation formula is as follows: Step 5: Repeat steps 2-4 until the end point of the ideal sewing curve is interpolated and all actual interpolation points are obtained; Step 6: Set the feed speed constraint of the needle, fit the feed speed curve for all actual interpolation points, and obtain the actual sewing trace curve.

2. The method for sewing trace curve interpolation based on bow height error compensation according to claim 1, characterized in that: In step 3, the osculating circle approximation method is used to generate the osculating arc at the current actual interpolation point P. The current actual interpolation point P and the point on the osculating arc The straight-line distance between the current actual interpolation point P and the next estimated interpolation point Q0 is equal to the straight-line distance between the current actual interpolation point P and the next estimated interpolation point Q0, which will close the arc. The actual interpolation point P and the point on the osculating arc The maximum distance between the composed chords is taken as the bow height error between the current actual interpolation point P and the next estimated interpolation point Q0. The calculation formula is: Among them, r i is an osculating arc The radius, The current actual interpolation point P and the point on the osculating arc The length of the chord.

3. The method for sewing trace curve interpolation based on bow height error compensation according to claim 1, characterized in that: In step 6, the feed speed constraint of the needle is: Among them, v is the feed speed of the needle, min{} represents the minimum value, T is the interpolation period, δ max is the maximum bow height error, ρ is the curvature radius of the NURBS curve, a nmax is the maximum normal acceleration, j nmax is the maximum normal acceleration.

4. The method for sewing trace curve interpolation based on bow height error compensation according to claim 1, characterized in that: In step 6, a seven-segment S-shaped speed planning algorithm with an initial and final speed of 0 is used to fit the feed speed curve of all actual interpolation points to obtain the actual sewing trace curve.

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