CN103606156A - One-dimensional non-uniform gear morphology point cloud precise registration method - Google Patents

Abstract

The invention discloses a one-dimensional non-uniform gear morphology point cloud precise registration method, and relates to the field of data processing. The one-dimensional non-uniform gear morphology point cloud precise registration method is used for solving the problem that a discrete sequence registration error is large because sample intervals of corresponding points are different when an ICP registration algorithm is adopted to carry out registration on the corresponding points of an actually-measured gear sequence and a virtual gear sequence. The method comprises the steps that first, quantity registration is carried out on the actually-measured gear sequence and the virtual gear sequence; second, initial phase registration is carried out on the actually-measured sequence and the virtual gear sequence; third, corresponding-point registration is carried out on the actually-measured sequence and the virtual gear sequence. The one-dimensional non-uniform gear morphology point cloud precise registration method is based on the actually-measured gear sequence, regenerates virtual gear sequence with the same sample intervals of the corresponding points as the actually-measured gear sequence, and further improves the accuracy of the gear one-dimensional non-uniform point cloud data registration. The one-dimensional non-uniform gear morphology point cloud precise registration method can achieve one-dimensional non-uniform gear morphology point cloud precise registration, and is high in registration accuracy, simple to calculate and reliable.

Description

One-dimensional Inhomogeneous gear pattern point cloud Precision Registration

Technical field

The present invention relates in a kind of gear pattern reverse-engineering, One-dimensional Inhomogeneous gear pattern point cloud Precision Registration, can realize the accuracy registration of gear One-dimensional Inhomogeneous pattern point cloud, belongs to data processing field.

Background technology

Gear variance analysis has great importance for processing and manufacturing and the raising transmission system performance of gear, traditional contact gear deflection method of measurement, and measuring speed is slow, and data sampling rate is low.By laser scanning gear, obtain actual measurement gear sequence, calculate actual measurement gear sequence and virtual gear sequence difference and obtain gear deviation, avoided the problems referred to above.Here, actual measurement gear sequence refers to the gear pattern one-dimensional point cloud data that laser continuous sweep gear obtains, and virtual gear sequence refers to the gear pattern one-dimensional point cloud data that generate according to design of gears parameter.

If want, by calculating, survey gear sequence and virtual gear sequence difference obtains gear deviation, must realize the accuracy registration of actual measurement gear sequence and virtual gear sequence corresponding point.Paper < < cloud data registration and surface subdivision technical research > > have proposed the method for a kind of ICP of employing registration Algorithm to two groups of cloud data registrations.First this method uses the method for how much Hash to two groups of cloud data initial registration, using the result after initial registration as new initial position; Recycling ICP algorithm carries out meticulous registration, meticulous registration process is to each point in first point cloud, in second point cloud, the nearest point of detection range is as corresponding point, obtain the optimum three-dimension varying that all corresponding point of registration are right, and be applied on first point cloud, algorithm is set certain convergence criterion conventionally, carries out this operation iteratively until meet this convergence criterion.Adopt ICP registration Algorithm can effectively solve actual measurement gear sequence that laser scanning reference position uncertainty causes and the phase differential between virtual gear sequence has this problem of randomness.But during due to laser scanning gear, its scanning position error has randomness, having caused actual measurement gear sequence is One-dimensional Inhomogeneous discrete series.And virtual gear sequence is the even discrete series of one dimension, the two number of samples is identical, corresponding point sampling interval is different, and ICP registration Algorithm is applicable to the discrete series registration that corresponding point sampling interval is identical, and the discrete series registration error different for corresponding point sampling interval is larger.

Summary of the invention

The present invention carries out registration for solving existing employing ICP registration Algorithm to the corresponding point of actual measurement gear sequence and virtual gear sequence, existence causes because corresponding point sampling interval is different the problem that discrete series registration error is larger, and a kind of One-dimensional Inhomogeneous gear pattern point cloud Precision Registration is provided.

One-dimensional Inhomogeneous gear pattern point cloud Precision Registration, comprises that the data memory format of setting actual measurement One-dimensional Inhomogeneous gear pattern point cloud is { k, x (k) }, k is actual measurement gear sequential sampling position, k=n Δ t (n) wherein, and Δ t (n) represents sampling interval, n is number of samples, and Δ t (n) is the function about n, n=1,2,3 ... N, N represents to survey the total number of samples of gear sequence, take number of samples n as independent variable, obtain surveying gear sequence x (n); The method can be divided into following steps:

Step 1, actual measurement gear sequence and virtual gear sequence number amount registration;

Gear pattern is divided into four sections of descriptions, usings the starting point of the left profile of tooth of gear as the initial point that generates gear virtual sequence, according to design of gears parameter, generate gear equation as follows:

$Q\left(t\right)=\left\{\begin{array}{cc}{Q}_1\left(t\right)& (t_1\&le;t<t_2)\\ Q_2\left(t\right)& (t_2\&le;t<t_3)\\ Q_3\left(t\right)& (t_3\&le;t<t_4)\\ Q_4\left(t\right)& (t_4\&le;t<t_5)\end{array}\right.---\left(1\right)$

Q ₁(t) represent the left profile of tooth equation of gear, Q ₂(t) represent gear teeth tips equation, Q ₃(t) represent the right profile of tooth equation of gear, Q ₄(t) represent Gear Root equation, t ₁represent the left profile of tooth starting point of gear, t ₂the separation that represents the left profile of tooth of gear and gear teeth tips, t ₃represent the right profile of tooth starting point of gear, t ₄the separation that represents the right profile of tooth of gear and Gear Root, t ₅represent Gear Root terminating point; According to actual measurement gear sequential sampling position k, to t discretize, setting sampling interval Δ t (n)=Δ t is uniformly, presses

calculate k _maxfor the maximal value of sampling location k, make t=n Δ t, obtain virtual gear sequence equation q (n):

$q\left(n\right)=\left\{\begin{array}{cc}{Q}_1\left(\mathrm{n\&Delta;t}\right)& (t_1\&le;\mathrm{n\&Delta;t}<t_2)\\ Q_2\left(\mathrm{n\&Delta;t}\right)& (t_2\&le;\mathrm{n\&Delta;t}<t_3)\\ Q_3\left(\mathrm{n\&Delta;t}\right)& (t_3\&le;\mathrm{n\&Delta;t}<t_4)\\ Q_4\left(\mathrm{n\&Delta;t}\right)& (t_4\&le;\mathrm{n\&Delta;t}<t_5)\end{array}\right.---\left(2\right)$

By formula (2) generating virtual gear sequences y (n).

Step 2, actual measurement gear sequence and virtual gear sequence initial phase registration;

According to actual measurement gear sequential sampling position k, through step 1 to formula (1) discretize after, completed the registration of surveying gear sequence and virtual gear sequential sampling quantity, but there is phase differential in the two.X (n) and y (n) substitution (3) formula, the cross correlation function R of realistic survey gear sequence and virtual gear sequence _xy(r), r represents that sky moves ordinal number.

$R_{\mathrm{xy}}\left(r\right)=\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}x\left(n\right)y(n+r),r=\mathrm{0,1,2},\&CenterDot;\&CenterDot;\&CenterDot;,m<N---\left(3\right)$

In formula, m is that maximum sky moves ordinal number, establishes and works as R _xy(r) while obtaining maximal value, to move ordinal number be n to corresponding sky ₀, according to the character of cross correlation function, n ₀be the actual measurement gear sequence sky corresponding with phase differential between virtual gear sequence and move ordinal number, the phase differential of correspondence is k ₀.

Step 3, actual measurement gear sequence and virtual gear sequence Image matching;

The sky of trying to achieve according to step 2 moves ordinal number n ₀, after virtual gear sequence phase sky is moved, realized the initial phase registration with actual measurement gear sequence.But during due to laser scanning gear, its scanning position error has randomness, i.e. sampling interval Δ t (n) inequality, actual measurement gear sequence is One-dimensional Inhomogeneous discrete series, actual measurement gear sequence and virtual gear sequence corresponding point are difficult to exact matching.Formula (1) is carried out to phase shift k ₀, then according to actual measurement gear sequential sampling position k, the virtual gear sequence regenerating, its growth equation q ' (k):

$q^{\&prime;}\left(k\right)=\left\{\begin{array}{cc}{Q}_1(k+k_0)& (t_1\&le;k+{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA0000426861050000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_0<t_2)\\ Q_2(k+k_0)& (t_2\&le;k+{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA0000426861050000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_0<t_3)\\ Q_3(k+k_0)& (t_3\&le;k+{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA0000426861050000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_0<t_4)\\ Q_4(k+k_0)& (t_4\&le;k+{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA0000426861050000021.png"\; state="\{\{state\}\}">k</figure-callout>}}_0<t_5)\end{array}\right.---\left(4\right)$

The amplitude q ' that obtains virtual gear sequence by formula (4) (k), if take number of samples n as independent variable, obtains virtual gear sequences y ' (n), virtual gear sequences y ' (n) and actual measurement gear sequence x (n) corresponding point accuracy registration.

Effect of the present invention: the present invention proposes a kind of One-dimensional Inhomogeneous gear pattern point cloud Precision Registration, the actual measurement gear sequence of take is benchmark, regenerate one group of virtual gear sequence identical with actual measurement gear sequence corresponding point sampling interval, and then improved the precision of gear One-dimensional Inhomogeneous cloud data registration.The present invention specifically adopts related operation to ask for the phase differential between actual measurement gear sequence and virtual gear sequence.Related operation has traversed actual measurement gear sequence and all cloud datas of virtual gear sequence, realized the two phase place registration on the whole, the registration accuracy that is better than ICP registration Algorithm pointwise optimizing, simultaneously, in step 3, sampling location according to actual measurement gear sequence regenerates virtual gear sequence, eliminates the registration error causing due to sampling interval inequality.The present invention can realize One-dimensional Inhomogeneous gear pattern point cloud accuracy registration, and registration accuracy is high, and calculating is simple, method is reliable.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of One-dimensional Inhomogeneous gear pattern point cloud Precision Registration of the present invention;

Fig. 2 is quantity registration results schematic diagram in One-dimensional Inhomogeneous gear pattern point cloud Precision Registration of the present invention;

Fig. 3 is initial phase registration results schematic diagram in One-dimensional Inhomogeneous gear pattern point cloud Precision Registration of the present invention;

Fig. 4 is Image matching result schematic diagram in One-dimensional Inhomogeneous gear pattern point cloud Precision Registration of the present invention.

In figure: * is actual measurement gear sequence, and zero is virtual gear sequence, and is the virtual gear sequence regenerating.

Embodiment

In conjunction with Fig. 1 to Fig. 4, present embodiment is described, One-dimensional Inhomogeneous gear pattern point cloud Precision Registration, by following steps, realized:

Step 1: actual measurement gear sequence and virtual gear sequence number amount registration;

If one week total number of samples N of the straight annular wheel of certain laser scanning involute urve is 2519, sampling interval Δ t (n) is non-homogeneous, take number of samples n as independent variable, obtains surveying gear sequence x (n), in conjunction with Fig. 2;

Known gears number of teeth z is 85, and modulus m is 3.27742, and the pressure angle α of reference circle place is 25 °, addendum coefficient h _a ^*be 0.8, tip clearance coefficient c ^*be 0.3.According to this design of gears parameter, generate gear equation as follows:

$Q\left(t\right)=\left\{\begin{array}{ccc}2r-r_b/\cos {\mathrm{\&alpha;}}_k& {\mathrm{\&alpha;}}_k=\sqrt[3]{3\left(t\right)}-{\left(\sqrt[3]{3\left(t\right)}\right)}^{2.9268}/8.185& (0\&le;t<0.00672\mathrm{\&pi;})\\ 2r-r_{\max }& & (0.00672\mathrm{\&pi;}\&le;t<0.01037\mathrm{\&pi;})\\ 2r-r_b/\cos {\mathrm{\&alpha;}}_k& {\mathrm{\&alpha;}}_k=\sqrt[3]{3{\mathrm{\&theta;}}^{\&prime;}}-{\left(\sqrt[3]{3{\mathrm{\&theta;}}^{\&prime;}}\right)}^{2.9268}/8.185& \\ & {\mathrm{\&theta;}}^{\&prime;}=2(\tan \frac{5\mathrm{\&pi;}}{36}-\frac{5\mathrm{\&pi;}}{36})+\frac{\mathrm{\&pi;}}{85}-t& (0.01037\mathrm{\&pi;}\&le;t<0.01709\mathrm{\&pi;})\\ 2r-r_{\min }& & (0.01709\mathrm{\&pi;}\&le;t<0.02352\mathrm{\&pi;})\end{array}\right.---\left(5\right)$

According to actual measurement gear sequential sampling position k, to t discretize, setting sampling interval Δ t (n)=Δ t is that sampling interval Δ t is uniformly

make t=n Δ t, obtain virtual gear sequence equation q (n) as shown in (6) formula.

$q\left(n\right)=\left\{\begin{array}{ccc}2r-r_b/\cos {\mathrm{\&alpha;}}_k& {\mathrm{\&alpha;}}_k=\sqrt[3]{3\left(\mathrm{n\&Delta;t}\right)}-{\left(\sqrt[3]{3\left(\mathrm{n\&Delta;t}\right)}\right)}^{2.9268}/8.185& (0\&le;\mathrm{n\&Delta;t}<0.00672\mathrm{\&pi;})\\ 2r-r_{\max }& & (0.00672\mathrm{\&pi;}\&le;\mathrm{n\&Delta;t}<0.01037\mathrm{\&pi;})\\ 2r-r_b/\cos {\mathrm{\&alpha;}}_k& {\mathrm{\&alpha;}}_k=\sqrt[3]{3{\mathrm{\&theta;}}^{\&prime;}}-{\left(\sqrt[3]{3{\mathrm{\&theta;}}^{\&prime;}}\right)}^{2.9268}/8.185& \\ & {\mathrm{\&theta;}}^{\&prime;}=2(\tan \frac{5\mathrm{\&pi;}}{36}-\frac{5\mathrm{\&pi;}}{36})+\frac{\mathrm{\&pi;}}{85}-\mathrm{n\&Delta;t}& (0.01037\mathrm{\&pi;}\&le;\mathrm{n\&Delta;t}<0.01709\mathrm{\&pi;})\\ 2r-r_{\min }& & (0.01709\mathrm{\&pi;}\&le;\mathrm{n\&Delta;t}<0.02352\mathrm{\&pi;})\end{array}\right.---\left(6\right)$

By (6) formula generating virtual gear sequences y (n), get the data of front 50 points of y (n);

(1,139.0086), (2,139.7567), (3,140.5246) ..., (49,137.0064), (50,136.3164) } and mapping, in conjunction with Fig. 2, in figure, number of samples n=50, sky moves ordinal number n ₀=12: wherein, * is actual measurement gear sequence, and zero is virtual gear sequence, and is the virtual gear sequence regenerating.

Step 2: actual measurement gear sequence and virtual gear sequence initial phase registration;

By formula (2), calculate sky and move ordinal number n ₀=12, survey the phase differential k of gear sequence and virtual gear sequence ₀be 0.00953 π, realize the initial phase registration of actual measurement gear sequence and virtual gear sequence, initial phase registration results is in conjunction with shown in Fig. 3;

Step 3: actual measurement gear sequence and virtual gear sequence Image matching;

According to phase differential k ₀regenerate the virtual gear sequence with x (n) with identical Δ t (n), its growth equation is as shown in the formula shown in (7).

$q^{\&prime;}\left(k\right)=\left\{\begin{array}{ccc}2r-r_b/\cos {\mathrm{\&alpha;}}_k& {\mathrm{\&alpha;}}_k=\sqrt[3]{3(k+0.00953\mathrm{\&pi;})}-{\left(\sqrt[3]{3(k+0.00953\mathrm{\&pi;})}\right)}^{2.9268}/8.185& (0\&le;k+0.00953\mathrm{\&pi;}<0.00672\mathrm{\&pi;})\\ 2r-r_{\max }& & (0.00672\mathrm{\&pi;}\&le;k+0.00953\mathrm{\&pi;}<0.01037\mathrm{\&pi;})\\ 2r-r_b/\cos {\mathrm{\&alpha;}}_k& {\mathrm{\&alpha;}}_k=\sqrt[3]{3{\mathrm{\&theta;}}^{\&prime;}}-{\left(\sqrt[3]{3{\mathrm{\&theta;}}^{\&prime;}}\right)}^{2.9268}/8.185& \\ & {\mathrm{\&theta;}}^{\&prime;}=2(\tan \frac{5\mathrm{\&pi;}}{36}-\frac{5\mathrm{\&pi;}}{36})+\frac{\mathrm{\&pi;}}{85}-(k+0.00953\mathrm{\&pi;})& (0.01037\mathrm{\&pi;}\&le;k+0.00953\mathrm{\&pi;}<0.01709\mathrm{\&pi;})\\ 2r-r_{\min }& & (0.01709\mathrm{\&pi;}\&le;k+0.00953\mathrm{\&pi;}<0.02352\mathrm{\&pi;})\end{array}\right.$

The amplitude q ' that obtains virtual gear sequence by formula (7) (k), be take number of samples n as independent variable, obtains virtual gear sequences y ' (n), and its image is in conjunction with Fig. 4, has realized the accuracy registration of virtual gear sequence and actual measurement gear sequence corresponding point.

Claims (1)

1. One-dimensional Inhomogeneous gear pattern point cloud Precision Registration, the data memory format that comprises setting actual measurement One-dimensional Inhomogeneous gear pattern point cloud is { k, x (k) }, k is actual measurement gear sequential sampling position, described k=n Δ t (n), Δ t (n) represents sampling interval, n is number of samples, and Δ t (n) is the function about n, n=1,2,3 ... N, N is the total number of samples of actual measurement gear sequence, take number of samples n as independent variable, obtain the process of actual measurement gear sequence x (n);

It is characterized in that, the method is realized by following steps:

Step 1, actual measurement gear sequence and virtual gear sequence number amount registration;

Gear pattern is divided into four sections, usings the starting point of the left profile of tooth of gear as the initial point that generates gear virtual sequence, according to design of gears parameter, generate gear equation, with formula one, be expressed as:

Formula one, $Q\left(t\right)=\left\{\begin{array}{cc}{Q}_1\left(t\right)& (t_1\&le;t<t_2)\\ Q_2\left(t\right)& (t_2\&le;t<t_3)\\ Q_3\left(t\right)& (t_3\&le;t<t_4)\\ Q_4\left(t\right)& (t_4\&le;t<t_5)\end{array}\right.$

In formula: Q ₁(t) represent the left profile of tooth equation of gear, Q ₂(t) represent gear teeth tips equation, Q ₃(t) represent the right profile of tooth equation of gear, Q ₄(t) represent Gear Root equation, t ₁represent the left profile of tooth starting point of gear, t ₂the separation that represents the left profile of tooth of gear and gear teeth tips, t ₃represent the right profile of tooth starting point of gear, t ₄the separation that represents the right profile of tooth of gear and Gear Root, t ₅represent Gear Root terminating point; According to actual measurement gear sequential sampling position k, to t discretize, setting sampling interval Δ t (n)=Δ t is uniformly, presses calculate k _maxfor the maximal value of sampling location k, make t=n Δ t, obtain virtual gear sequence equation, described virtual gear sequence equation q (n) is expressed as with formula two:

Formula two, $q\left(n\right)=\left\{\begin{array}{cc}{Q}_1\left(\mathrm{n\&Delta;t}\right)& (t_1\&le;\mathrm{n\&Delta;t}<t_2)\\ Q_2\left(\mathrm{n\&Delta;t}\right)& (t_2\&le;\mathrm{n\&Delta;t}<t_3)\\ Q_3\left(\mathrm{n\&Delta;t}\right)& (t_3\&le;\mathrm{n\&Delta;t}<t_4)\\ Q_4\left(\mathrm{n\&Delta;t}\right)& (t_4\&le;\mathrm{n\&Delta;t}<t_5)\end{array}\right.$

According to virtual gear sequence equation q (n) generating virtual gear sequences y (n);

Step 2, actual measurement gear sequence and virtual gear sequence initial phase registration;

Root will be surveyed gear sequence x (n) and virtual gear sequences y (n) substitution formula three, obtain the cross correlation function R of actual measurement gear sequence and virtual gear sequence _xy(r), described r is that sky moves ordinal number;

Formula three, $R_{\mathrm{xy}}\left(r\right)=\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}x\left(n\right)y(n+r),r=\mathrm{0,1,2},\&CenterDot;\&CenterDot;\&CenterDot;,m<N;$

In formula: m is that maximum sky moves ordinal number, set and work as R _xy(r), while getting maximal value, it is n that corresponding sky moves ordinal number ₀, described n ₀be the actual measurement gear sequence sky corresponding with phase differential between virtual gear sequence and move ordinal number;

Step 3, actual measurement gear sequence and virtual gear sequence Image matching;

Formula one is carried out to phase shift k ₀, described k ₀for the actual measurement gear sequence phase differential corresponding with virtual gear sequence, according to actual measurement gear sequential sampling position k, the virtual gear sequence regenerating, growth equation q ' (k), is expressed as with formula four:

Formula four, $q^{\&prime;}\left(k\right)=\left\{\begin{array}{cc}{Q}_1(k+k_0)& (t_1\&le;k+k_0<t_2)\\ Q_2(k+k_0)& (t_2\&le;k+k_0<t_3)\\ Q_3(k+k_0)& (t_3\&le;k+k_0<t_4)\\ Q_4(k+k_0)& (t_4\&le;k+k_0<t_5)\end{array}\right.$

The amplitude q ' that obtains virtual gear sequence according to formula four (k), be take number of samples n as independent variable, obtains virtual gear sequences y ' (n), described virtual gear sequences y ' (n) and actual measurement gear sequence x (n) corresponding point accuracy registration.

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