Author Contributions
Conceptualization, Z.S., Y.F. and P.Z.; methodology, Z.S. and Y.F.; software, Y.F.; validation, Y.F.; formal analysis, Y.F.; investigation, Y.F.; resources, Z.S.; data curation, Z.S. and Y.F.; writing—original draft preparation, Y.F.; writing—review and editing, Z.S., Y.F. and Y.S.; visualization, Y.F.; supervision, Z.S., Y.F. and Y.S.; project administration, Z.S. and Y.F.; funding acquisition, Z.S. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Model of integrated error curve in gear section.
Figure 1.
Model of integrated error curve in gear section.
Figure 2.
A segment on the integrated error curve in gear bidirectional cross-section. (SJZ curve).
Figure 2.
A segment on the integrated error curve in gear bidirectional cross-section. (SJZ curve).
Figure 3.
Any segment on the gear integrated error curve.
Figure 3.
Any segment on the gear integrated error curve.
Figure 4.
Gray distribution in the normal direction at a certain point on the profile.
Figure 4.
Gray distribution in the normal direction at a certain point on the profile.
Figure 5.
Gear sub-pixel contour extraction method based on GTC−Facet model.
Figure 5.
Gear sub-pixel contour extraction method based on GTC−Facet model.
Figure 6.
Circle fitting of the center hole contour on the gear end face.
Figure 6.
Circle fitting of the center hole contour on the gear end face.
Figure 7.
Gradient amplitude and direction of sub-pixel points.
Figure 7.
Gradient amplitude and direction of sub-pixel points.
Figure 8.
Solving pitch deviation from the extracted contour from the image.
Figure 8.
Solving pitch deviation from the extracted contour from the image.
Figure 9.
Theoretical involute at the corresponding profile position.
Figure 9.
Theoretical involute at the corresponding profile position.
Figure 10.
Calculation of profile deviation.
Figure 10.
Calculation of profile deviation.
Figure 11.
Components of profile deviation in the direction of motion.
Figure 11.
Components of profile deviation in the direction of motion.
Figure 12.
Comparison of positioning errors between two algorithms. (a) Measurement setup. (b) Comparison of positioning errors.
Figure 12.
Comparison of positioning errors between two algorithms. (a) Measurement setup. (b) Comparison of positioning errors.
Figure 13.
GVMS. (a) System structure. (b) Collected gear image.
Figure 13.
GVMS. (a) System structure. (b) Collected gear image.
Figure 14.
Gear integrated error curve of gear section (right flank). (a) Gear integrated error curve. (b) Gear integrated error curve and its outer envelope.
Figure 14.
Gear integrated error curve of gear section (right flank). (a) Gear integrated error curve. (b) Gear integrated error curve and its outer envelope.
Figure 15.
Gear integrated error curve of gear section (left flank). (a) Gear integrated error curve. (b) Gear integrated error curve and its outer envelope.
Figure 15.
Gear integrated error curve of gear section (left flank). (a) Gear integrated error curve. (b) Gear integrated error curve and its outer envelope.
Figure 16.
Polar coordinate representation of the gear integrated error curve. (right profile). (a) Gear integrated error curve. (b) Gear integrated error curve and its outer envelope.
Figure 16.
Polar coordinate representation of the gear integrated error curve. (right profile). (a) Gear integrated error curve. (b) Gear integrated error curve and its outer envelope.
Figure 17.
Polar coordinate representation of the gear integrated error curve. (left profile). (a) Gear integrated error curve. (b) Gear integrated error curve and its outer envelope.
Figure 17.
Polar coordinate representation of the gear integrated error curve. (left profile). (a) Gear integrated error curve. (b) Gear integrated error curve and its outer envelope.
Figure 18.
P26 measuring equipment.
Figure 18.
P26 measuring equipment.
Figure 19.
Pitch deviation (GVMS measurement results). (a) Single−pitch deviation (left). (b) Sector pitch deviation (left). (c) Single−pitch deviation (right). (d) Sector pitch deviation (right).
Figure 19.
Pitch deviation (GVMS measurement results). (a) Single−pitch deviation (left). (b) Sector pitch deviation (left). (c) Single−pitch deviation (right). (d) Sector pitch deviation (right).
Figure 20.
Pitch deviation (P26 measurement result): (a) left flank; (b) right flank.
Figure 20.
Pitch deviation (P26 measurement result): (a) left flank; (b) right flank.
Figure 21.
Decomposition of profile form deviation and profile slope deviation in the gear integrated error curve. (a) Total profile deviation. (b) Profile form deviation. (c) Profile slope deviation.
Figure 21.
Decomposition of profile form deviation and profile slope deviation in the gear integrated error curve. (a) Total profile deviation. (b) Profile form deviation. (c) Profile slope deviation.
Figure 22.
Profile deviation. (four teeth, GVMS measurement results).
Figure 22.
Profile deviation. (four teeth, GVMS measurement results).
Figure 23.
Profile deviation (four teeth, P26 measurement result).
Figure 23.
Profile deviation (four teeth, P26 measurement result).
Figure 24.
Integrated measurement method speed comparison.
Figure 24.
Integrated measurement method speed comparison.
Figure 25.
Judging the burr position through the gear integrated error curve. (a) Image of tooth 6 with burrs. (b) Gear integrated error (left profile, cartesian coordinates). (c) Gear integrated error (left profile, polar coordinates).
Figure 25.
Judging the burr position through the gear integrated error curve. (a) Image of tooth 6 with burrs. (b) Gear integrated error (left profile, cartesian coordinates). (c) Gear integrated error (left profile, polar coordinates).
Figure 26.
Schematic diagram of measured eccentricity of gears.
Figure 26.
Schematic diagram of measured eccentricity of gears.
Figure 27.
Analysis of gear eccentricity using the SJZ curve.
Figure 27.
Analysis of gear eccentricity using the SJZ curve.
Figure 28.
Analysis of profile modification using the gear integrated error curve.
Figure 28.
Analysis of profile modification using the gear integrated error curve.
Table 1.
CVMS parameters.
Table 1.
CVMS parameters.
Component | Parameters |
---|
Camera | CMOS, GigE interface, 5472 × 3648 px, 1″ target surface |
Lens | Magnification: 0.5; distortion: <0.006%; resolution: 7.9 μm |
Light source | LED surface light source |
Pixel equivalent | 4.76 μm/pixel |
Gear parameters | Powder metallurgy spur gears; number of teeth: 17; modulus: 0.5 mm; pressure angle: 20° |
Table 2.
Comparison of error results decomposed from the gear integrated error curve (unit: μm).
Table 2.
Comparison of error results decomposed from the gear integrated error curve (unit: μm).
Items | Right-Hand Tooth Flank | Left-Hand Tooth Flank |
---|
| GVMS | P26 | Error | GVMS | P26 | Error |
| 20.8 | 15.5 | 5.3 | 22.7 | 18.8 | 3.9 |
| 4.5 | 3.3 | 1.2 | 6.3 | 3.4 | 2.9 |
| 5.5 | 7.3 | −1.8 | 6.2 | 5.7 | 0.5 |
| 2.5 | 1.5 | 1.0 | 2.9 | 1.2 | 1.7 |
| 3.5 | −7.3 | −10.8 | 3.7 | −5.8 | 9.5 |
| 15.1 | 12.9 | 2.2 | 15.2 | 14.9 | 0.3 |
| 7.0 | 7.4 | −0.4 | 9.5 | 11.1 | −1.6 |
| 0.2 | 0.1 | 0.1 | 0.3 | 0.1 | 0.2 |
| 10.1 | 10.3 | −0.2 | 11.5 | 10.6 | 0.9 |
| 0.3 | 0.1 | 0.2 | 0.2 | 0.1 | 0.1 |
Table 3.
Comparison of pitch deviation (taking the absolute value of the maximum deviation).
Table 3.
Comparison of pitch deviation (taking the absolute value of the maximum deviation).
Items | Tooth Flank | GVMS | P26 | Error |
---|
(μm) | left | 9.5 | 11.1 | −1.6 |
right | 7.0 | 7.4 | −0.4 |
(μm) | left | 15.2 | 14.9 | 0.3 |
right | 15.1 | 12.9 | 2.2 |
Table 4.
Comparison of total profile deviation (four teeth).
Table 4.
Comparison of total profile deviation (four teeth).
Tooth Number | Tooth Flank | GVMS | P26 | Error |
---|
1 | left | 2.4 | 3.5 | −1.1 |
right | 2.0 | 3.4 | −1.4 |
6 | left | 3.2 | 5.7 | −2.5 |
right | 3.0 | 7.3 | −3.3 |
10 | left | 2.6 | 4.5 | −1.9 |
right | 2.8 | 6.4 | −3.6 |
14 | left | 3.2 | 3.5 | −0.3 |
right | 2.1 | 1.2 | 0.9 |
Table 5.
Comparison of profile form deviation (four teeth).
Table 5.
Comparison of profile form deviation (four teeth).
Tooth Number | Tooth Flank | GVMS | P26 | Error |
---|
1 | left | 2.5 | 1.5 | 1.0 |
right | 2.3 | 1.5 | 0.8 |
6 | left | 3.1 | 1.2 | 1.9 |
right | 1.5 | 0.9 | 0.6 |
10 | left | 2.2 | 1.1 | 1.1 |
right | 0.9 | 1.2 | −0.3 |
14 | left | 3.4 | 1.7 | 1.7 |
right | 1.3 | 1.2 | 0.1 |
Table 6.
Comparison of profile slope deviation (four teeth).
Table 6.
Comparison of profile slope deviation (four teeth).
Tooth Number | Tooth Flank | GVMS | P26 | Error |
---|
1 | left | −0.3 | −3.1 | 2.8 |
right | −2.2 | −3.6 | 1.4 |
6 | left | 3.8 | −5.8 | 2.0 |
right | −3.4 | −7.6 | 3.2 |
10 | left | −1.2 | −3.9 | 2.7 |
right | −2.1 | −6.0 | 3.9 |
14 | left | −3.2 | −2.1 | −1.1 |
right | 2.5 | −0.4 | 2.9 |