sensors
Article
A Bevel Gear Quality Inspection System Based on
Multi-Camera Vision Technology
Ruiling Liu *, Dexing Zhong, Hongqiang Lyu and Jiuqiang Han
School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China;
bell@xjtu.edu.cn (D.Z.); hongqianglv@xjtu.edu.cn (H.L.); jqhan@xjtu.edu.cn (J.H.)
* Correspondence: meggie@xjtu.edu.cn; Tel.: +86-29-8266-8665 (ext. 175)
Academic Editor: Gonzalo Pajares Martinsanz
Received: 6 July 2016; Accepted: 23 August 2016; Published: 25 August 2016
Abstract: Surface defect detection and dimension measurement of automotive bevel gears by
manual inspection are costly, inefficient, low speed and low accuracy. In order to solve these
problems, a synthetic bevel gear quality inspection system based on multi-camera vision technology
is developed. The system can detect surface defects and measure gear dimensions simultaneously.
Three efficient algorithms named Neighborhood Average Difference (NAD), Circle Approximation
Method (CAM) and Fast Rotation-Position (FRP) are proposed. The system can detect knock damage,
cracks, scratches, dents, gibbosity or repeated cutting of the spline, etc. The smallest detectable defect
is 0.4 mm × 0.4 mm and the precision of dimension measurement is about 40–50 µm. One inspection
process takes no more than 1.3 s. Both precision and speed meet the requirements of real-time online
inspection in bevel gear production.
Keywords: multi-camera vision; bevel gear; defect detection; dimension measurement
1. Introduction
The bevel gear, also called the automobile shift gear, is an important part in an automobile
transmission. Its quality directly affects the transmission system and the running state of the whole
vehicle [1]. According to statistics, about one third of automobile chassis faults are transmission
faults, in which gear problems account for the largest proportion [2]. Although the bevel gear’s
design, material and manufacturing technique are quite mature and standard, in today’s high-speed
production lines there are still inevitably defects such as dimension deviations, surface scratches,
crushing, dents or insufficient filling, etc. Defective gears will not only reduce the performance of the
car, but also cause security risks and potentially huge losses to manufacturers [3].
Figure 1a shows some kinds of bevel gears. The shape and structure of bevel gears are complicated
and the types of defects various, so bevel gear quality inspection is very difficult. At present it is mainly
completed manually, which is tedious and inefficient. It is hard to guarantee the quality stability and
consistency. Recently Osaka Seimitsu Precision Machinery Corporation in Japan developed a high
precision gear measuring instrument as shown in Figure 1b, but the inspection speed is very slow and
cannot meet the requirements of high-speed production lines. There has been gear defect detection
technology based on machine vision, but it’s mainly used in the inspection of broken teeth and flat
surfaces of general gears [4]. There is no precedent research for bevel gears with complicated shape
and structure [5]. Because of the multiple measurement tasks and diverse defects, the traditional single
vision system cannot obtain enough information. To measure the multiple dimensions quickly and
accurately, to detect and classify the defects completely and precisely, a more efficient vision system
is needed.
Machine vision is such an advanced quality inspection technology which uses intelligent cameras
and computers to detect, identify, judge and measure objects [6–14]. To solve the above problems,
Sensors 2016, 16, 1364; doi:10.3390/s16091364
www.mdpi.com/journal/sensors
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Sensors
2016, 16,
1364
this
paper
develops
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a multi-vision bevel gear quality inspection device which combines defect
detection
and
dimension
measurement
in
one
system.
Three
efficient
image
processing
algorithms
defect detection and dimension measurement in one system. Three efficient image processing
defect detection
and dimension
measurement
in Circle
one system.
Three efficient
processing
named
Neighborhood
Average Difference
(NAD),
Approximation
Methodimage
(CAM)
and
Fast
algorithms
named Neighborhood
Average Difference
(NAD),
Circle Approximation
Method
(CAM)
algorithms
named
Neighborhood
Average
Difference
(NAD),
Circle
Approximation
Method
(CAM)
Rotation-Position
(FRP)
are
proposed.
The
system
successfully
solves
the
problem
of
bevel
gear
defect
and Fast Rotation-Position (FRP) are proposed. The system successfully solves the problem of bevel
and Fast Rotation-Position
(FRP)
proposed.
The system
successfully
solves the article
problem
of bevel
detection
and
measurement
at highare
speed
and
accuracy.
find a short
describing
gear
defect
detection
and measurement
at
high
speed One
and can
accuracy.
One Chinese
can find a short
Chinese
gear
defect
detection
and
measurement
at
high
speed
and
accuracy.
One
can
find
a
short
Chinese
this system
in [15].this system in [15].
article
describing
article describing this system in [15].
(a)
(a)
(b)
(b)
Figure
1. (a)
Samples of
bevel gear;
(b) Gear
measuring instrument
of Osaka
Osaka Seimitsu Precision
Precision
Figure
Figure 1.
1. (a)
(a) Samples
Samples of
of bevel
bevel gear;
gear; (b)
(b) Gear
Gear measuring
measuring instrument
instrument of
of Osaka Seimitsu
Seimitsu Precision
Machinery
Corporation.
Machinery
Machinery Corporation.
Corporation.
2. System Design
2.
System Design
Design
2. System
2.1.
Inspection Project
and Requirement
Analysis
2.1.
2.1. Inspection
Inspection Project
Project and
and Requirement
Requirement Analysis
Analysis
The
defect detection
detection anddimension
dimension measurementsystem
system
developed
this
paper
is designed
The
developed
in in
this
paper
is designed
for
The defect
defect detectionand
and dimensionmeasurement
measurement system
developed
in this
paper
is designed
for
two
specific
types
of
bevel
gears,
A
4
and
F
6
,
as
shown
in
Figure
2.
two
specific
types
of bevel
gears,
A4 and
F6 , as
in Figure
2. 2.
for two
specific
types
of bevel
gears,
A4 and
F6,shown
as shown
in Figure
(a)
(a)
(b)
(b)
(c)
(c)
(d)
(d)
Figure 2. Samples of gear A4 and F6: (a) Top surface of gear A4; (b) Bottom surface of gear A4; (c) Top
Figure 2.
2. Samples
ofofgear
4 and F6: (a) Top surface of gear A4; (b) Bottom surface of gear A4; (c) Top
Figure
Samples
gearAA
(a) Top
4 and Fof
6 : gear
Bottom
surface
F6. surface of gear A4 ; (b) Bottom surface of gear A4 ;
surface
of gear
F6; (d)
6; (d) Bottom surface of gear F6.
surface
of
gear
F
(c) Top surface of gear F6 ; (d) Bottom surface of gear F6 .
(1)
(1)
(1)
(2)
(2)
(2)
(3)
(3)
(3)
The requirements of defect detection and measurement are as follows:
The requirements of defect detection and measurement are as follows:
The requirements of defect detection and measurement are as follows:
Defect detection of tooth end surface, spherical surface and mounting surface, including knock
Defect detection of tooth end surface, spherical surface and mounting surface, including knock
damage,
cracks, of
insufficient
filling, folding,
scratches,
dents
or gibbosity,
repeated spline
Defect detection
tooth end surface,
surface and
mounting
surface, including
damage,
cracks, insufficient
filling, spherical
folding, scratches,
dents
or gibbosity,
repeated knock
spline
broaching,
etc.
As
shown
in
Figure
3.
Defects
greater
than
0.5
mm
×
0.5
mm should
be
damage, cracks,
scratches,
or gibbosity,
spline
broaching,
etc. Asinsufficient
shown in filling,
Figure folding,
3. Defects
greater dents
than 0.5
mm × 0.5 repeated
mm should
be
detected.
broaching,
etc.
As
shown
in
Figure
3.
Defects
greater
than
0.5
mm
×
0.5
mm
should
be
detected.
detected.
Measurement of bevel gear’s height, diameters of two circumcircles, spline’s big and small
Measurement of bevel gear’s height, diameters of two circumcircles, spline’s big and
and small
small
diameters, end rabbet’s diameter. Measurement accuracy is 80–100 μm.
diameters, end rabbet’s diameter. Measurement accuracy is 80–100 µm.
μm.
Defect detection speed is about 1 s for each surface.
Defect detection speed is about 1 s for each surface.
2.2.
Hardware Design
2.2.
2.2. Hardware
Hardware Design
Design
Bevel
gears
have many
many teeth and
and each tooth
tooth has different
different lateral surfaces.
surfaces. For example,
example, gear A
A4
Bevel
Bevel gears
gears have
have many teeth
teeth and each
each tooth has
has differentlateral
lateral surfaces.For
For example,gear
gear A44
has
13 teeth
teeth and 26
26 surfaces; gear
gear F6 has 14
14 teeth and
and 28 surfaces.
surfaces. The defects
defects are diverse.
diverse. How to
has
has 13
13 teeth and
and 26 surfaces;
surfaces; gear FF66 has
has 14 teeth
teeth and 28
28 surfaces. The
The defects are
are diverse. How
How to
to
realize the real-time online inspection of all the teeth and surfaces is a big challenge. One approach
realize the real-time online inspection of all the teeth and surfaces is a big challenge. One approach
is using a single camera and rotational shooting mode, but it requires a high-precision rotary
is using a single camera and rotational shooting mode, but it requires a high-precision rotary
positioning system. The inspection speed is too low to meet the requirements. Because the bevel
positioning system. The inspection speed is too low to meet the requirements. Because the bevel
Sensors 2016, 16, 1364
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realize the real-time online inspection of all the teeth and surfaces is a big challenge. One approach is
using a2016,
single
camera and rotational shooting mode, but it requires a high-precision rotary positioning
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16, 1364
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system.
The
inspection speed is too low to meet the requirements. Because the bevel gear’s 3teeth
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2016,
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surfaces
are
uniformly
distributed
and
rotationally
symmetric,
we
propose
a
solution
which
can
gear’s teeth surfaces are uniformly distributed and rotationally symmetric, we propose a solution
gear’s
teeth
surfaces
are
uniformly
distributed
and
rotationally
symmetric,
we
propose
a
solution
complete
image
acquisition
and
processing
synchronously
by
using
multiple
high-speed
cameras.
which can complete image acquisition and processing synchronously by using multiple high-speed
which
canThe
complete
image
acquisition
and processing
synchronously
by
using multiple
The
speed
was
an order
of
faster
thanfaster
single
camera
rotary
positioning
system.high-speed
cameras.
speed
was
anmagnitude
order of magnitude
than
single
camera
rotary
positioning
system.
cameras. The speed was an order of magnitude faster than single camera rotary positioning system.
Figure
Figure 3.
3. Examples
Examples of
of defects
defects on
on bevel
bevel gear
gear surface.
surface.
Figure 3. Examples of defects on bevel gear surface.
Figure 4 shows the total plan of our inspection system. Nine high speed USB cameras are used
Figure 44 shows
plan
of
inspection
system.
speed
cameras
areare
used
to
Figure
shows the
the total
total
plan
ofour
our
inspection
system.Nine
Ninehigh
high
speedUSB
cameras
used
to capture
different
parts
of the
bevel
gear
simultaneously.
The
top
camera
isUSB
the core
of the
whole
capture
different
parts
of
the
bevel
gear
simultaneously.
The
top
camera
is
the
core
of
the
whole
image
to
capture
differentsystem.
parts ofItthe
bevel gearthe
simultaneously.
The
camera
is the
coredetection
of the whole
image
acquisition
undertakes
positioning of
thetop
bevel
gear,
defect
and
acquisition
system. system.
It undertakes
the positioning
of the bevel
gear,
defect
detection
anddetection
measurement
image
acquisition
It
undertakes
the
positioning
of
the
bevel
gear,
defect
and
measurement of the top and bottom surfaces.
of the top and of
bottom
surfaces.
measurement
the top
and bottom surfaces.
Figure 4. Diagram of bevel gear inspection system.
Figure
Figure 4.
4. Diagram
Diagram of
of bevel
bevel gear
gear inspection
inspection system.
system.
Seven side-view cameras are emplaced evenly around the bevel gear, with a 45° tilt angle with
Seven
side-view
cameras
emplaced
evenly to
around
the bevel
gear,detecting
with a 45°◦ tiltlateral
angle with
respect
to the
horizontal
planeare
and
perpendicular
gear tooth
groove,
Seven
side-view
cameras
are
emplaced
evenly around
the bevel
gear, with a 45the
tilt angle teeth
with
respect
to
the
horizontal
plane
and
perpendicular
to
gear
tooth
groove,
detecting
the
lateral
teeth
surfaces
omni-directionally.
In
addition,
one
more
camera
with
a
horizontal
view
is
located
on
the
respect to the horizontal plane and perpendicular to gear tooth groove, detecting the lateral teeth
surfaces
Ingear’s
addition,
oneAfter
morethe
camera
with
a horizontal
viewgives
is located
on the
platformomni-directionally.
to measure the bevel
height.
gear is
loaded,
the operator
a command
platform
to the
measure
the bevel
gear’s
height.
the gear
loaded,
the operator
givesreceives
a command
that all of
cameras
acquire
images
at After
the same
time.is An
industrial
computer
and
that
all
of
the
cameras
acquire
images
at
the
same
time.
An
industrial
computer
receives
and
processes the images one by one and gives control signals according to the detected results. To meet
processes
theaccuracy
images one
by one andof
gives
control
signalsdetection,
accordingthree
to the
detected
results. To
meet
the different
requirements
bevel
gear defect
types
of industrial
cameras
the
requirements
gear defect
detection, and
three1.3
types
of industrial
cameras
are different
adopted accuracy
in this system.
They areof3bevel
megapixels,
2 megapixels
megapixels,
respectively.
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surfaces omni-directionally. In addition, one more camera with a horizontal view is located on the
platform to measure the bevel gear’s height. After the gear is loaded, the operator gives a command
that all of the cameras acquire images at the same time. An industrial computer receives and processes
the images one by one and gives control signals according to the detected results. To meet the different
accuracy requirements of bevel gear defect detection, three types of industrial cameras are adopted in
this system. They are 3 megapixels, 2 megapixels and 1.3 megapixels, respectively. We can calculate
Sensors
2016, represents
16, 1364
that one
pixel
40–50 µm according to the gear’s actual size and image size. That4 of
is17to say,
the accuracy in the bevel gear’s height and diameter measurements is 40–50 µm.
We can calculate that one pixel represents 40–50 μm according to the gear’s actual size and image
The
includes
four
modules,
whichand
arediameter
camerameasurements
module, control
andμm.
process
size. system
That is tohardware
say, the accuracy
in the
bevel
gear’s height
is 40–50
module, I/O
module
and
gear
rotary
module,
as
shown
in
Figure
5.
The
camera
module
consists
The system hardware includes four modules, which are camera module, control and process
of nine
high I/O
speed
industrial
cameras
and a top
ring light.
The
ringcamera
light illuminates
the of
whole
module,
module
and gear
rotary module,
as shown
in Figure
5. The
module consists
system.
capturecameras
every and
partaof
bevel
Thelight
control
and processing
module is
nineThe
highcameras
speed industrial
topthe
ring
light.gear.
The ring
illuminates
the whole system.
The cameras
captureprocessing
every part ofand
the output
bevel gear.
control and
processing
module
is responsible
responsible
for image
of The
instructions
and
inspection
results.
I/O module
for
image
processing
and
output
of
instructions
and
inspection
results.
I/O
module
includes monitor, keyboard, mouse and pedal. The monitor displays the results. Theincludes
software is
monitor,
keyboard,
and pedal.
Thepedal
monitor
displays
the results.ofThe
software
is operated
operated
by mouse
andmouse
keyboard.
The foot
starts
the inspection
each
surface.
Softwareby
button
mouse and keyboard. The foot pedal starts the inspection of each surface. Software button starter
starter and automatically trigger are also provided in this system. The gear rotation module is made up
and automatically trigger are also provided in this system. The gear rotation module is made up of
of a stepping motor and a reducer. It rotates the bevel gear precisely in the defect detection of special
a stepping motor and a reducer. It rotates the bevel gear precisely in the defect detection of special
partsparts
and template
acquisition
section.
and template
acquisition
section.
Figure 5. Hardware structure of the bevel gear inspection system.
Figure 5. Hardware structure of the bevel gear inspection system.
Figure 6 shows the prototype of this multi-camera bevel gear quality inspection system. In
order to6 adapt
various
inspection
tasks
and objects,bevel
a series
ofquality
positioninspection
adjusting elements
areorder
Figure
showstothe
prototype
of this
multi-camera
gear
system. In
designed.
The height
of top tasks
camera
andobjects,
illumination
canofbeposition
adjusted.adjusting
Each camera
can be are
adjusted
to adapt
to various
inspection
and
a series
elements
designed.
slightlyofintop
thecamera
horizontal
For side-view
cameras, Each
the tiltcamera
angle and
to theslightly
gear arein the
The height
anddirection.
illumination
can be adjusted.
candistance
be adjusted
adjustable
in
a
large
range,
so
the
system
can
detect
and
measure
the
vast
majority
of
bevel
gears in
horizontal direction. For side-view cameras, the tilt angle and distance to the gear are adjustable
and other gears or parts of similar structure.
a large range, so the system can detect and measure the vast majority of bevel gears and other gears or
parts2.3.
of similar
Softwarestructure.
Design
Based
on above hardware, a fast and multifunctional bevel gear inspection software is
2.3. Software
Design
developed under the MFC and OpenCV platforms. The inspection includes two steps, top and
Based
aboverespectively.
hardware, aThe
fastsoftware
and multifunctional
bevel
gear inspection
is developed
bottomon
surface
can automatically
identify
the currentsoftware
inspection
is the
undertop
the
and OpenCV
The inspection
top and
surface
orMFC
the bottom
of a bevelplatforms.
gear, and whether
the bevelincludes
gear is intwo
the steps,
right place.
Topbottom
inspection
respectively.
can automatically
the current
is of
thesize
topmeasurement
or the bottom of
includesThe
two software
sub-modules,
top surface andidentify
lateral surface,
each inspection
one compose
and
defect
detection.
flowchart
is shown
in Figure
a bevel
gear,
and
whetherThe
thesoftware
bevel gear
is in the
right place.
Top7.inspection includes two sub-modules,
top surface and lateral surface, each one compose of size measurement and defect detection.
The software flowchart is shown in Figure 7.
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Figure 6. Prototype of multi-camera bevel gear inspection system.
Figure 6. Prototype of multi-camera bevel gear inspection system.
Figure 6. Prototype of multi-camera bevel gear inspection system.
Figure 7. Software flowchart of bevel gear inspection system.
Figure 7. Software flowchart of bevel gear inspection system.
Figure 7. Software flowchart of bevel gear inspection system.
For a new inspection
task, the software runs in order of top →lateral→bottom surface
inspection.
any fault
is found,
thethe
program
marks
at order
once and
outputs
the defects and
size
For aIf new
inspection
task,
software
runsit in
of top
→lateral→bottom
surface
For
a
new
inspection
task,
the
software
runs
in
order
of
top
→
lateral
→
bottom
surface
inspection.
measurement
andis then
Themarks
software
theand
bevel
gearthe
inspection
system
inspection. Ifresults,
any fault
found,terminates.
the program
it at of
once
outputs
defects and
size
If any
fault is found,
the and
program
it at once
and outputs
thebevel
defects
and
size measurement
measurement
results,
then marks
terminates.
The software
of the
gear
inspection
system
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results,
then terminates.
The software
of thefour
bevel
gear inspection
system
employs
a multi-thread
employsand
a multi-thread
technique.
It includes
modules,
which are
defect
detection,
equipment
technique.
It
includes
four
modules,
which
are
defect
detection,
equipment
calibration,
calibration, template acquisition and parameter setting. The equipment calibration template
module
acquisition
and
parameter
setting.
The
equipment
calibration
module
calibrates
the
position,
apertures
calibrates the position, apertures and focuses of the nine cameras. The template acquisition module
and
focusesthe
of the
nine collection
cameras. The
acquisition
completes
the parameter
sample collection
completes
sample
andtemplate
size calibration
of amodule
standard
gear. The
setting
and
size
calibration
of
a
standard
gear.
The
parameter
setting
module
adjusts
the
related
parameters
module adjusts the related parameters for different kinds of inspection tasks. The defect
detection
for
different
kinds
inspection
defect
detection
marks
thestatistical
faults in the
gear
image,
module
marks
theoffaults
in thetasks.
gearThe
image,
and
shows module
all the size
and
data.
Figure
8
and
shows
all
the
size
and
statistical
data.
Figure
8
shows
the
appearance
of
the
software.
shows the appearance of the software.
(a)
(b)
(c)
(d)
Figure 8.8.Soft
Softinterface
interface
of bevel
gear inspection
(a)detection;
Defect detection;
(b) Equipment
Figure
of bevel
gear inspection
system:system:
(a) Defect
(b) Equipment
calibration;
calibration;
(c)
Template
acquisition;
(d)
Parameter
setting.
(c) Template acquisition; (d) Parameter setting.
3. Key Algorithms in Defect Detection
3. Key Algorithms in Defect Detection
Because the defects of the bevel gears are complex and various, and the inspection time is short,
Because the defects of the bevel gears are complex and various, and the inspection time is
the general algorithms cannot meet the requirements. In this system, we use multi-threading
short, the general algorithms cannot meet the requirements. In this system, we use multi-threading
technology and propose several efficient image processing algorithms, which are NAD, CAM and
technology and propose several efficient image processing algorithms, which are NAD, CAM and FRP.
FRP. The following introduces these key algorithms in detail.
The following introduces these key algorithms in detail.
3.1. Neighborhood
Average Difference
Difference Method
Method
3.1.
Neighborhood Average
From the
thepoint
point
texture,
all kinds
of defects
are shown
astwists,
waves,
twists, undulations
or
From
of of
texture,
all kinds
of defects
are shown
as waves,
undulations
or roughness
roughness
of
the
surface,
thus
defects
can
be
detected
by
analyzing
gear
texture.
Texture
of the surface, thus defects can be detected by analyzing gear texture. Texture description operators
description
operators
based include
on gray-scale
includesmoothness,
average, standard
based
on gray-scale
histograms
average, histograms
standard deviation,
third orderdeviation,
moment,
smoothness,
third
order
moment,
consistency
and
entropy,
etc.
A
large
number
of
experiments
consistency and entropy, etc. A large number of experiments show that the combination of third order
show thatand
thesmoothness
combination
third
order gear
moment
and
smoothness
do best
in bevelare
gear
defect
moment
doofbest
in bevel
defect
detection,
but these
operators
sensitive
detection, but these operators are sensitive to outside interference. The threshold setting is
complicated and based on massive numbers of experiments and the results cannot show the
Sensors 2016, 16, 1364
7 of 17
to outside interference. The threshold setting is complicated and based on massive numbers of
experiments and the results cannot show the characteristics of defects directly and comprehensively
(such as area). In our system, we present an algorithm called Neighborhood Average Difference (NAD),
which can extract the defects entirely and define larger ones as faults, ignoring tiny ones. The steps are
as follows:
Sensors 2016, 16, 1364
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
7 of 17
Count the number of nonzero pixels in a neighborhood, denoted by N, given the
characteristics
of defects
comprehensively
(such as area). In our system, we present an
neighborhood
rangedirectly
is L ×and
L pixels,
here L = 30.
algorithm called Neighborhood Average Difference (NAD), which can extract
the defects entirely
Calculate the sum of gray values in the neighborhood: S = ∑iL=−01 ∑ Lj=−01 p (i, j), in which p(i,j)
and define larger ones as faults, ignoring tiny ones. The steps are as follows:
is the pixel value of point (i,j).
Step 1: Count the number of nonzero pixels in a neighborhood, denoted by N, given the
Calculate the average pixel value in a neighborhood: M = S/N.
neighborhood range is L × L pixels, here L = 30.
For
pointthe
p(i,j)
inofthe
neighborhood,
if |p(i,j) − M| =
> δ,
then p(i,j)
the point is
∑ δ is∑a threshold,
Step
2: each
Calculate
sum
gray
values in the neighborhood:
( , ), in which
marked
by
setting
p(i,j)
=
255.
is the pixel value of point (i,j) .
Step
3: the
Calculate
the average
value
in a neighborhood:
M connected
= S/N.
Scan
marked
points pixel
in the
image.
If they are in
region and the size of the
Step
4:
For
each
point
p(i,j)
in
the
neighborhood,
if

p(i,j)
–
M
>
δ, δ is aSingle
threshold,
then the
pointand tiny
region is greater than a threshold, then the region is a defect.
marked
points
is marked by setting p(i,j) = 255.
connected regions are ignored.
Step 5:
Scan the marked points in the image. If they are in connected region and the size of the
region is greater than a threshold, then the region is a defect. Single marked points and
In addition, interference such as the impurities, dust and dirt on the surface can be removed
tiny connected regions are ignored.
partly by image dilation and erosion processing.
In addition, interference such as the impurities, dust and dirt on the surface can be removed
partly
by image dilation
and erosion processing.
3.2. Circle Approximation
Method
3.2. Circle
Approximation
Method
Circle
detection
is a classical
problem in image processing [16–19]. To detect the actual and virtual
circles on the
bevel
gear fast
accurately,
named[16–19].
CAM isTopresented.
The main
Circle
detection
is aand
classical
problemaninalgorithm
image processing
detect the actual
and idea is:
on the bevelcenter
gear fast
and
accurately,
algorithm
CAMit is
presented.
Draw avirtual
circle circles
with initialized
and
radius,
thenan
expands
ornamed
contracts
slowly
and The
moves the
main
idea
is:
Draw
a
circle
with
initialized
center
and
radius,
then
expands
or
contracts
it
slowly
center continuously until it is tangent to the circle to be detected. Then keep adjusting its radius and
and moves the center continuously until it is tangent to the circle to be detected. Then keep
center on
condition that they remain tangent. The drawn circle will move closer and closer to the circle
adjusting its radius and center on condition that they remain tangent. The drawn circle will move
to be detected until they match perfectly. Figure 9 shows this process.
closer and closer to the circle to be detected until they match perfectly. Figure 9 shows this process.
Figure 9. Circle Approximation Method: Each row shows an example of circle fitting process. The
Figure 9.
Circle
Approximation
Method:
Eachcircles
row shows
an example
ofthe
circle
solid
circles
are to be detected
and the dash
are regulated
to match
solidfitting
ones. process. The solid
circles are to be detected and the dash circles are regulated to match the solid ones.
Circle center, radius and rotation angle step are three initial inputs of this method. The center
and radius can be approximated only asking the drawn and the target circles have some common
Circle center, radius and rotation angle step are three initial inputs of this method. The center and
area. The more accurate the initial parameters are, the faster the method gets an idea result. It
radius can
be the
approximated
onlyinasking
themeasurement,
drawn and and
the the
target
have some common area.
utilizes
positioning result
dimension
stepscircles
are as follows:
The more accurate the initial parameters are, the faster the method gets an idea result. It utilizes the
Step 1: Extract the edge of the circle (actual or virtual) to be detected by threshold segmentation
positioning result in dimension measurement, and the steps are as follows:
Step 1:
Step 2:
Step 3:
Step 4:
of the original image. Store the edge in target pixel set C.
Step 2: Set the initial center (x0, y0) and radius r0 of the drawn circle. Set the rotation angle step θ.
Extract the edge of the circle (actual or virtual) to be detected by threshold segmentation of
Step 3: Increase or decrease radius r0, r0 = r0 + δr, or r0 = r0 – δr, δr is the change value in each
the original
image. Store the edge in target pixel set C.
adjustment.
Step
4: theCalculate
the pixel
on the
drawnr0circle
with
the current
androtation
radius. Find
thestep θ.
Set
initial center
(x0set
, y0C’) and
radius
of the
drawn
circle.center
Set the
angle
intersection
of C and
C’, record
is empty,
Increase
or decrease
radius
r0 , as
r0 X.
= Ifr0X +
δr , or return
r0 = rto0 Step
− δ3.
,
δ
is
the
change
value in
r
r
Step 5: If X is non-empty and the number of its elements is Xnum, judge whether Xnum satisfies the
each adjustment.
matching condition. If satisfies, output the center and radius information, otherwise move
Calculate
the pixel
C’neighborhoods
on the drawn
circle
with
the current
the center
in its set
eight
and
find the
position
where Xcenter
has theand
leastradius.
elements,Find the
intersection
of Creturn
and C’,
record
record and
to step
3. as X. If X is empty, return to Step 3.
Sensors 2016, 16, 1364
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Step 5:
If X is non-empty and the number of its elements is Xnum , judge whether Xnum satisfies the
matching condition. If satisfies, output the center and radius information, otherwise move
Sensors 2016, 16, 1364
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the center in its eight neighborhoods and find the position where X has the least elements,
and return
to step
3.
The record
parameter
θ is used
in calculation
of set X. Figure 10 shows how it is defined. R is the
radius. A and B are the starting and ending point of a rotation. Line segment L connects A and B.
The parameter θ is used in calculation of set X. Figure 10 shows how it is defined. R is the
For computational convenience, the center coordinate is set to (0, 0), B is set to (R, 0), A is set to (x1,
radius. A and B are the starting and ending point of a rotation. Line segment L connects A and B.
y1), then:
For computational convenience, the center coordinate is set to (0, 0), B is set to (R, 0), A is set to
(x1 , y1 ), then:
x1  R cos , y1  R sin
(1)
x1 = Rcosθ, y1 = Rsinθ
(1)
L2  (R  R cos )2  R2 sin2 
(2)
L2 = ( R − Rcosθ )2 + R2 sin2 θ
(2)
2 L22) /2R22 ]
θ = arccos
[(2R2R−
 arccos[(2
 L ) / 2R ]
2 Because the image is discrete, L ≥ 1, then across 2R2R−2 1 ≤ θ ≤ π.
Because the image is discrete, L ≥ 1, then across
≤ ≤ .
(3)
(3)
Figure 10.
10. The calculation of rotation
rotation angle
angle step
step θθin
inCAM.
CAM.
Figure
The method
method counts
counts target
target pixels
pixels on
on the
the drawn
drawn circle
circle based
based on
on the
the parameter
parameter θ,
θ, itit searches
searches step
step
The
by
step
like
the
second
hand
of
a
clock.
The
value
of
θ
is
closely
related
to
the
cost
of
computation.
by step like the second hand of a clock. The value of θ is closely related to the cost of computation.
Theoretically,the
thegreater
greaterthe
theθ is,
θ is,
faster
algorithm
is, but
the robustness
ofalgorithm
the algorithm
Theoretically,
thethe
faster
thethe
algorithm
is, but
the robustness
of the
will
will
be
decreased
and
the
detection
accuracy
will
be
reduced
at
the
same
time,
so
the accuracy,
detection
be decreased and the detection accuracy will be reduced at the same time, so the detection
accuracy,
the speed
execution
and the robustness
of the algorithm
beinto
all taken
into
the
execution
andspeed
the robustness
of the algorithm
should be should
all taken
account
toaccount
set the
to set step
the angle
θ. In addition,
θ can
be set dynamically.
In the
early
of the algorithm
is
angle
θ. In step
addition,
θ can be set
dynamically.
In early of
algorithm
a bigger aθ bigger
is usedθto
used
to
approach
the
detected
circle
quickly.
θ
becomes
smaller
as
soon
as
the
drawn
circle
touches
approach the detected circle quickly. θ becomes smaller as soon as the drawn circle touches the detected
the detected
is then
fitted
in aThe
small
range. The
algorithm
efficientwith
and
circle
which iscircle
thenwhich
searched
and searched
fitted in aand
small
range.
algorithm
is efficient
andisaccurate
accurate
with
a
dynamic
theta.
a dynamic theta.
Similar to
to Hough
Hough Transform,
inin
virtue
of
Similar
Transform, our
our method
methodisisrobust
robusttotoimage
imagenoise
noiseand
anddisturbance
disturbance
virtue
cumulative
sum.
It It
has
a asimple
preprocessing of
of threshold
threshold
of
cumulative
sum.
has
simplesearching
searchingidea
ideaand
andonly
only requires
requires aa preprocessing
segmentation.
While
in
Hough
Transform,
preprocessing
of
edge
detection
or
skeleton
extraction
is
segmentation. While in Hough Transform, preprocessing of edge detection or skeleton extraction is
very
time
consuming.
very time consuming.
In order
order to
to verify
verify the
the detection
detection results
results of
of our
our algorithm,
algorithm, we
we compare
compare itit with
with Hough
Hough transform
transform
In
by
fitting
the
moon
in
Figure
11.
The
results
of
the
two
methods
are
almost
identical
and
cannot be
be
by fitting the moon in Figure 11. The results of the two methods are almost identical and cannot
distinguished by
by naked
naked eye.
eye. Details
Details of
of the
the comparison
comparison are
are shown
shown in
in Table
Table 1.1. The
The data
data show
show that
that
distinguished
CAM
is
about
50
times
faster
than
Hough
Transform,
with
little
difference
in
initial
parameter
CAM is about 50 times faster than Hough Transform, with little difference in initial parameter setting.
setting.
In addition,
the Hough
classical
Hough Transform
cannot
used
in highimages
resolution
images
In
addition,
the classical
Transform
cannot be used
in be
high
resolution
because
the
because thespace
parameter
matrix will
increase dramatically
with of
thethe
increase
theresulting
image size,
parameter
matrixspace
will increase
dramatically
with the increase
imageof
size,
in
in a large
amount ofand
computation
and However,
storage space.
However,
our circlealgorithm
approximation
aresulting
large amount
of computation
storage space.
our circle
approximation
is not
algorithministhis
notaspect.
restricted
this aspect.
is simple
and fast withand
less
andthe
is high
very
restricted
It isin
simple
and fastItwith
less computation,
is computation,
very suitable for
suitable for
thedetection
high precision
circle detection situation.
precision
circle
situation.
CAM is suitable for fitting circles when a good initialization is available. Hough is suitable for
fitting circles in the presence of noise and multiple models (multiple circle arcs). A solution from
Hough transform will generally require refinement using an iterative method like CAM.
Our method is more suitable for detection of circles which have been positioned approximately.
In actually, with the auxiliary system composed by sensors and cameras, the location of bevel gear
won’t deviate greatly. The gross location of the circle can be determined by software in advance. So
Sensors 2016, 16, 1364
9 of 17
CAM is suitable for fitting circles when a good initialization is available. Hough is suitable for
fitting circles in the presence of noise and multiple models (multiple circle arcs). A solution from
Hough transform will generally require refinement using an iterative method like CAM.
Our method is more suitable for detection of circles which have been positioned approximately.
In
actually,
with the auxiliary system composed by sensors and cameras, the location of bevel9gear
Sensors 2016, 16, 1364
of 17
won’t deviate greatly. The gross location of the circle can be determined by software in advance. So our
method
can be
successfully
applied
to mosttoofmost
the industrial
circle detection
occasions.occasions.
The detection
our method
can
be successfully
applied
of the industrial
circle detection
The
and
production
efficiency efficiency
can be improved
significantly
with its speed
detection
and production
can be improved
significantly
withadvantage.
its speed advantage.
Sensors 2016, 16, 1364
9 of 17
our method can be successfully applied to most of the industrial circle detection occasions. The
detection and production efficiency can be improved significantly with its speed advantage.
Figure 11.
11. Moon
Moon picture
picture (952
(952 ×
× 672
Figure
672pixels)
pixels) and
and circle
circle fitting
fitting result.
result. Red
Red cross
cross is
is the
the center.
center.
Table 1. Compare Circle Approximation Method with Hough Transform in moon fitting.
Table 1. Compare Circle Approximation Method with Hough Transform in moon fitting.
Min
Max
Step Size of
Step Aize of
fitting result. Red cross is the center.
Method Figure 11. Moon picture (952 × 672 pixels) and circle
Center
Radius/pixel
Radius/pixel
Angle/rad
Radius/pixel
Min
Max
Step
Size of
Step
Aize of
Method
Center
Hough Transform
150
250
Null
0.1
Radius/pixel
Radius/pixel
Angle/rad
Radius/pixel
Table 1. Compare Circle Approximation Method with Hough Transform in moon fitting. 1
CAM
150
250
Image center
0.006
0.5
Hough Transform
Method
CAM
150
Null Step Size of0.1 Step Aize of 1
Min
Max250
Center
Time/s
Radius/pixel
Radius/pixel
150
250
Image centerAngle/rad0.006 Radius/pixel 0.5
detection
methods,
solid circles and
arcs.5.6623
But it
150
250 our method
Null can detect0.1
1
150
250
Image center
0.006
0.5
0.1189
Time/s
Time/s
5.6623
0.1189
5.6623
0.1189
Like
other
circle
can also
Hough
Transform
CAM
detect virtual
circles such as gear spline circle, inscribed circle and circumscribed circle of a polygon.
Like
other
circle
detection
methods,
ourvirtual
method
can detect
circles
and arcs. But it can also
Figure
12 Like
shows
the
fitting
results
of spline
circles
onsolid
gearsolid
F6 by
our method.
other
circle
detection
our method
can detect
circles
and arcs. Butcircle
it can also
detect virtual
circles
such
as gearmethods,
spline circle,
inscribed
circle
and
circumscribed
of a polygon.
detect virtual circles such as gear spline circle, inscribed circle and circumscribed circle of a polygon.
Figure 12 shows the fitting results of spline virtual circles on gear F6 by our method.
Figure 12 shows the fitting results of spline virtual circles on gear F6 by our method.
(a)
(a)
(b)
(b)
Figure
12. Fitting the spline circles by CAM: (a) Image of spline; (b) Detection results of inscribed and
Figure 12. Fitting the spline circles by CAM: (a) Image of spline; (b) Detection results of inscribed and
Figure
12.
Fitting
the spline
circles by CAM:
(a) Image
of spline; (b) Detection results of inscribed and
circumscribed
circles
of of
spline
bygreen
green
circles).
circumscribed
circles
spline(denoted
(denoted by
circles).
circumscribed circles of spline (denoted by green circles).
3.3.Rotation-Position
Fast Rotation-Position
3.3. Fast
3.3. Fast Rotation-Position
In order to carry out accurate inspection of the bevel gear, the position of the workpiece should
In order
to carry out accurate inspection of the bevel gear, the position of the workpiece should
be determined quickly after loading. It includes horizontal, vertical and rotational position. This
In order to carry
outafter
accurate
inspection
of the bevel
gear, the
position
the workpiece
should
be
be determined
quickly
loading.
It includes
horizontal,
vertical
andofrotational
position.
This
system uses a mechanical device to realize the horizontal and vertical position. Due to the complex
determined
quickly
after
loading.
It
includes
horizontal,
vertical
and
rotational
position.
This
system
system
uses
a mechanical
to realize
vertical
position.
to the
gear
structure
and the device
short feeding
time, the
it ishorizontal
difficult to and
achieve
effective
rotary Due
position
by complex
uses
mechanical
device
to realize
thetime,
horizontal
and
vertical
position.
Due
therotary
complex
gear astructure
and
thethis
short
feeding
it is difficult
to achieve
effective
rotary
positiongear
by
hardware.
We
solve
problem
by image
processing
method.
Taking
into account
the to
center
structure
and
short
feeding
time,
it is difficult
to divided
achieve
effective
rotary
position
by
hardware.
symmetry
of the
bevel
gear, the
position
is
into
three steps
which
arethe
center
hardware.
We the
solve
this
problem
byrotation
image
processing
method.
Taking
into
account
center
rotary
positioning,
image
acquisition
of
tooth
surface
and the rotary
angle
We
solve
this
bygear,
imagethe
processing
method.
Taking
intocalculation:
account
the steps
centerwhich
rotary are
symmetry
symmetry
of problem
the
bevel
rotation
position
is divided
into three
center
of
the(1)
bevel
gear,
the
rotation
position
divided
into
three
steps
which
are
positioning,
image
Center
positioning.
To cut
theisimage
of the
inner
circle,
first
segment
thecenter
top camera
image
positioning,
image
acquisition
ofout
tooth
surface
and
the
rotary
angle
calculation:
with
a certain
threshold,
then
remove
interference
of impurity and inherent defects by
acquisition
of tooth
surface
and the
rotary
angle
calculation:
(1) Center
positioning.
To cut outarea
the filting.
imageThe
of the
inner
circle,
first segment
the top
image
foreground
and background
circle
center
and diameter
are extracted
bycamera
area
with statistics
a certain
threshold,
then
remove
interference
of
impurity
and
inherent
defects
by
and coordinates averaging. Figure 13a–c show this process.
(2)
Teeth-end
image
extraction.
Segment
Figure
13a
again
with
a
smaller
threshold
value
and
cut
foreground and background area filting. The circle center and diameter are extracted by area
out the
teeth-endaveraging.
image. Remove
interference
of impurity
and inherent defects by
statistics
andentire
coordinates
Figure
13a–c show
this process.
foreground and background area filtering. Then draw two circles with the center calculated
(2) Teeth-end image extraction. Segment Figure 13a again with a smaller threshold value and cut
above and proper radiuses, extract only the teeth-end surface, as shown in Figure 13d–f.
out the entire teeth-end image. Remove interference of impurity and inherent defects by
Sensors 2016, 16, 1364
10 of 17
(1)
Center positioning. To cut out the image of the inner circle, first segment the top camera image
with a certain threshold, then remove interference of impurity and inherent defects by foreground
and background area filting. The circle center and diameter are extracted by area statistics and
coordinates averaging. Figure 13a–c show this process.
(2) Teeth-end image extraction. Segment Figure 13a again with a smaller threshold value and cut out
the entire teeth-end image. Remove interference of impurity and inherent defects by foreground
and background area filtering. Then draw two circles with the center calculated above and proper
Sensors 2016, 16, 1364
10 of 17
radiuses, extract only the teeth-end surface, as shown in Figure 13d–f.
(3) (3)
Calculate
the16,rotation
implementtemplate
templatematching
matching
algorithm
in defect
Calculate
rotationangle.
angle. In
In order
order to
to implement
algorithm
Sensors 2016,the
1364
10 ofin
17 defect
detection,
thethe
original
shouldbe
betransformed
transformed
a standard
position
detection,
originalimage
imageof
ofthe
thebevel
bevel gear
gear should
to to
a standard
position
to to
(3) the
Calculate
the temple.
rotation
angle.
In
order to shows
implement
template
matching
algorithm
in defect
 . α.
extract
the
matched
temple.
Thefollowing
following
how
totocalculate
thethe
rotary
angle
extract
matched
The
shows
how
calculate
rotary
angle
detection, the original image of the bevel gear should be transformed to a standard position to
13following
teeth, which
evenly.
angle
For example,
gear A4 has
 . between two
extract thebevel
The
showsare
howdistributed
to calculate the
rotaryThe
angle
For example,
bevelmatched
gear Atemple.
4 has 13 teeth, which are distributed evenly. The angle between two teeth
teeth
is
360°/13
=
27.69°,
as
shown
in
Figure
14.
O
is
the
center
of
the
gear
and
P
i is the geometric
◦ , as shown
13 teeth,
are distributed
evenly.
two center of
For example,
bevel in
gear
A4 has 14.
is 360◦ /13 = 27.69
Figure
O is which
the center
of the gear
andThe
Piangle
is thebetween
geometric
center teeth
of aistooth.
angleas between
x-axis 14.
and
line
i is defined as αi. For each tooth, αi is
360°/13The
= 27.69°,
shown in Figure
O is
the OP
center
of the gear and Pi is the geometric
a tooth.
The angle
between
x-axis and
line OPi 0°–27.69°.
is definedFor
as αgear
each
tooth,
αi is
converted into the
i . For
converted
firstThe
quadrant
and within
A4, α
, α1,…,
αtooth,
13. Weαeliminate
centerinto
of athe
tooth.
angle between
x-axis and line OP
i is defined
asi =αiα
. 1For
each
i is
◦ –27.69◦ . For gear A , α = α , α , . . . , α . We eliminate any α that has great
first any
quadrant
and
within
0
40°–27.69°.
1 For
1 the
icalculate
into the
first quadrant
withinand
gearmean
A4,13αi =ofα1the
, α1,…,
α13which
. We eliminate
αi converted
that has great
difference
withand
others,
rest,
isi defined as
difference
with
and
calculate
thedetected.
mean
the
rest, which
is defined
as
the rotation
α of the
any
αi others,
that
hasα great
difference
others,of
and
calculate
the show
mean
of
thethe
rest,
which
is definedangle
as
the rotation
angle
of the
gear to with
be
Experiments
that
rotation-position
method
rotation angle
α of theThe
gear
to bethat
detected.
Experiments
show
the rotation-position
method
gearprovides
to be the
detected.
Experiments
show
the rotation-position
method
excellent
excellent
accuracy.
error
is about
0.005°, which
canthat
meet
the provides
requirements
of theaccuracy.
gear
provides excellent
The error is about 0.005°, which can meet the requirements of the gear
The position
error is
about
0.005◦ , accuracy.
which can
meet the requirements of the gear position determination.
determination.
position determination.
(a)
(a)
(b)
(c)
(b)
(d)
(e)
(c)
(f)
Figure 13. The image preprocess of FRP method: (a) Top surface image; (b) Segmentation for inner
Figure 13.circle
The(d)
image
preprocess
of FRP
method:
(a) Top (d)
surface
image;for
(b)teeth
Segmentation
(with
a larger
threshold);
(c) Inner
circle(e)
detected;
Segmentation
end(f)
(with a for inner
circle (withsmaller
a larger
threshold);
(c) of
Inner
circle (f)
detected;
Segmentation for teeth end (with a smaller
threshold);
(e) Result
area filting;
Teeth end(d)
image.
Figure 13. The image preprocess of FRP method: (a) Top surface image; (b) Segmentation for inner
threshold); (e) Result of area filting; (f) Teeth end image.
circle (with a larger threshold); (c) Inner circle detected; (d) Segmentation for teeth end (with a
smaller threshold); (e) Result of area filting; (f) Teeth end image.
Figure 14. Calculation of gear rotation angle.
Figure 14. Calculation of gear rotation angle.
Figure 14. Calculation of gear rotation angle.
Sensors 2016, 16, 1364
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Sensors 2016, 16, 1364
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2016, 16, Matching
1364
3.4. Template
Template
and Collection
Collection
3.4.
Matching and
11 of 17
In machine
vision,
wewe
often
compare
an input
imageimage
with awith
standard
image toimage
find the
3.4. Template
Matching
and
Collection
In
machine
vision,
often
compare
an input
a standard
todifference
find the
or
target,
which
is
called
template
matching.
It’s
fast
and
efficient.
In
this
system
we
use
difference or target, which is called template matching. It’s fast and efficient. In this systemtemplate
we use
In machine vision, we often compare an input image with a standard image to find the
matching matching
a lot to extract
thetoarea
to be detected,
eliminating
the interference
of non-inspection
areas
template
a
lot
extract
the
area
to
be
detected,
eliminating
the
interference
difference or target, which is called template matching. It’s fast and efficient. In this system we useof
and
improving
the
inspection
speed.
non-inspection
areas aand
inspection
template matching
lotimproving
to extractthe
the
area to speed.
be detected, eliminating the interference of
Figure 15a
15a isisthe
thetop
topsurface
surfaceimage
imageofofbevel
bevelgear
gear
Figure
is the
matching
template.
4 and
Figure
A4Aand
Figure
15b15b
is the
matching
template.
In
non-inspection areas and improving the inspection
speed.
In Figure
15b,
the
value
of background
and
edge
of
the
gear
are
set
to
150,
which
means
they
are
Figure
15b,
the
value
of
background
and
edge
of
the
gear
are
set
to
150,
which
means
they
are
Figure 15a is the top surface image of bevel gear A4 and Figure 15b is the matching template. In a
a
non-inspection
area. Black,
white
and
some
other
gray
colorsindicate
indicatedifferent
differentparts
partstotobebedetected.
detected.
non-inspection
white
and
some
other
colors
Figure 15b, the area.
valueBlack,
of background
and
edge
ofgray
the gear
are set to 150,
which means
they are a
The
templates
are
collected
from
a
standard
and
perfect
gear.
Here
is
the
acquisition
process
of
The templates
collected
a standard
and perfect
gear. Here
is the parts
acquisition
process of
non-inspection
area.are
Black,
whitefrom
and some
other gray
colors indicate
different
to be detected.
top surface
surface template.
template. First extract
extract the
the gear’s
gear’s center
center and
and rotation
rotation angle,
angle, and then
then divide
divide target
target pixels
pixels
top
The templates areFirst
collected from
a standard
and perfect
gear. Here and
is the acquisition
process of
into
different
parts
according
to
their
distance
to
the
center
and
mark
with
different
colors,
remove
into
different
parts according
to their
distance
to the
andangle,
markand
withthen
different
top surface
template.
First extract
the gear’s
center
andcenter
rotation
dividecolors,
target remove
pixels
background pixels
pixels completely.
completely. The
templates
are
numbered
and
saved
in
order
of
rotation
angle.
background
The
templates
are
numbered
and
saved
in
order
of
rotation
angle.
into different parts according to their distance to the center and mark with different colors, remove
background pixels completely. The templates are numbered and saved in order of rotation angle.
(a)
(a)
(b)
(b)
Figure
4; (b) The matching template.
Figure 15.
15. (a)
(a) Top
Top surface
surface of
of gear
gear A
A4;
(b) The matching template.
Figure 15. (a) Top surface of gear A4; (b) The matching template.
The lateral template is collected by the aid of a special gear painted with black and white
The lateral
is collected
bybythethe
aidaid
of aofspecial
geargear
painted
withwith
black and white
matted
The
lateral template
template
collected
a special
painted
and through
white
matted
coating,
shown
in is
Figure
16a. This
ensures
that
a perfect
template
can be black
extracted
coating,
shown
in
Figure
16a.
This
ensures
that
a
perfect
template
can
be
extracted
through
a
simple
shown in Figure
16a.
ensures
that a perfect
template
be extracted
through
amatted
simplecoating,
image processing,
shown
in This
Figure
16b. Figure
16c is an
originalcan
lateral
image and
Figure
image
processing,
shown
in
Figure
16b.
Figure
16c
is
an
original
lateral
image
and
Figure
16d
is the
a simple
processing,
shown
Figure 16b.
Figure 16c is an original lateral image and Figure
16d
is theimage
extracted
teeth surface
byintemplate
matching.
extracted
surface
bysurface
template
16d
is the teeth
extracted
teeth
by matching.
template matching.
(a)
(a)
(b)
(b)
(c)
(c)
(d)
(d)
Figure 16. The collection and use of bevel gear lateral template. (a) Lateral image of template gear;
Figure
16.
collection
use
lateral
(a)(a)Lateral
of of
template
gear;
Figure
16. The
The
collection
and
useof
ofbevel
bevel
gear
lateraltemplate.
template.
Lateral
image
template
gear;
(b)
Extracted
template;
(c)and
Lateral
image
togear
be
detected;
(d) Extracted
imageimage
by
template
matching.
(b)
Extracted
template;
(c)
Lateral
image
to
be
detected;
(d)
Extracted
image
by
template
matching.
(b) Extracted template; (c) Lateral image to be detected; (d) Extracted image by template matching.
In this system the templates collection and processing are completed automatically without
In this system the templates collection and processing are completed automatically without
artificial
participation.
automatically
numberedare
and
saved in order
of rotation
angle
In this
system theTemplates
templatesare
collection
and processing
completed
automatically
without
artificial participation. Templates are automatically numbered and saved in order of rotation angle
and
camera.
After a template
is collected,
the gear is numbered
rotated to another
angle order
by theofstep-motor
and
artificial
participation.
Templates
are automatically
and saved
rotation and
angle
and
camera.
After a template
is collected,
the gear is rotated
to another
angleinby
the step-motor
the
next
collection
begins.
The
angle
interval
is
about
0.01°–0.02°.
The
total
template
image
size
is
as
andnext
camera.
After begins.
a template
collected,
theisgear
is 0.01°–0.02°.
rotated to another
angle
by theimage
step-motor
and
the
collection
The is
angle
interval
about
The total
template
size is as
◦
◦
large
as
25
GB,
that
is
to
say,
the
system
achieves
ideal
inspection
speed
by
sacrificing
storage
the next
begins.
intervalachieves
is aboutideal
0.01 –0.02
. Thespeed
total template
image storage
size is as
large
as collection
25 GB, that
is to The
say, angle
the system
inspection
by sacrificing
space.
large as 25 GB, that is to say, the system achieves ideal inspection speed by sacrificing storage space.
space.
4.
4. Inspection
InspectionResults
Results
4. Inspection Results
The
and methods
methodsare
aredifferent
differentfor
forbevel
bevelgears
gearsvary
varyinin
structure.
Figures
17a,b
The inspection tasks and
structure.
Figure
17a,b
are
The inspection tasks and methods are different for bevel gears vary in structure. Figures 17a,b
are
bottom
surfaces
of
gear
F
6
and
A
4
respectively.
F
6
is
flat
and
defects
are
obvious
in
the
image.
bottom
surfaces
of gear
F6 and
A4Arespectively.
F6 is flat and defects are obvious in the image. It It
is
are
bottom
surfaces
of gear
F6 and
4 respectively. F6 is flat and defects are obvious in the image. It
is easy to detect. A4 is spherical and the image is dark and weak in contrast. The defects are hard to
is easy to detect. A4 is spherical and the image is dark and weak in contrast. The defects are hard to
be found in the image, especially for dints. The inspection algorithm of A4 is much more
be found in the image, especially for dints. The inspection algorithm of A4 is much more
complicated.
complicated.
Sensors 2016, 16, 1364
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easy to detect. A4 is spherical and the image is dark and weak in contrast. The defects are hard to be
found2016,
in the
especially for dints. The inspection algorithm of A4 is much more complicated.
Sensors
16, image,
1364
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Sensors 2016, 16, 1364
12 of 17
(a)
(a)
(b)
(b)
Figure 17.
17. Bottom images
images of FF6 and
and A
A4:: (a)
6; (b) Bottom of A4.
Figure
(a) Bottom
Bottom of
of F
(b)Bottom
Bottomof
ofA
A44. .
Figure 17. Bottom
Bottom images of
of F66
Bottom
of
FF66;;(b)
4 (a)
4.1. Example of Defect Detection and Dimension Measurement
Example of
of Defect
Defect Detection
Detection and Dimension Measurement
4.1. Example
In this section, we illustrate how the system works through a practical example, the inspection
example,
thethe
inspection
of
In this section, we
we illustrate
illustratehow
howthe
thesystem
systemworks
worksthrough
througha apractical
practical
example,
inspection
of bottom surface of bevel gear A4.
bottom
surface
of of
bevel
gear
A4A
. 4.
of
bottom
surface
bevel
gear
4.1.1.
on Bottom
Bottom Surface
4.1.1. Inspection
Inspection of
of Top-Circle
Top-Circle on
4.1.1.
Inspection
of
Top-Circle
on Bottom Surface
Surface
The
top
of
back
surface
is
a
standard
sharp
in image
the image
of a perfect
A4 But
gear. But
it is
The top
sharp
ringring
in the
of a perfect
A4 gear.
fragile
The
top of
ofback
backsurface
surfaceisisa standard
a standard
sharp
ring
in the image
of a perfect
A4 gear.it is
But
it is
fragile
andto
easily
to be damaged
in production
are as
shown
as ring,
broken
ring,
burr or
and easily
be damaged
in production
process.process.
DefectsDefects
are shown
broken
burr
or uneven
fragile
and easily
to be damaged
in production
process.
Defects
are shown
as broken
ring,
burr or
uneven
in theThe
image.
Thewill
system
will
detect
theasdefects
in Figure
18. The
color in color
the image.
system
detect
and
markand
themark
defects
shown as
in shown
Figure 18.
The following
uneven
color
in the image.
The system
will
detect
and
mark
the defects
as
shown
in Figure
18. The
following
illustrate
the
detail
inspection
process.
illustrate
the
detail
inspection
process.
following illustrate the detail inspection process.
Figure 18. Inspection of bottom surface of gear A4, red boxes mark defects and green circle marks
Figure 18. Inspection of bottom surface of gear A4, red boxes mark defects and green circle marks
Figure 18. Inspection of bottom surface of gear A4 , red boxes mark defects and green circle marks
circumcircle.
circumcircle.
circumcircle.
Step 1:
Step 1:
Step 1:
Step 2:
Step 2:
Step 2:
Extract the ring and its neighborhood by threshold segmentation, and then remove small
Extract the ring and its neighborhood by threshold segmentation, and then remove small
noise
around
theand
ring byneighborhood
area filter, the result
is shown
in Figure 19a.
Extract
the ring
threshold
segmentation,
and then remove small
noise
around
the ringits
by area filter, theby
result
is shown
in Figure 19a.
Fitting
the
ring
boundaries.
Generally
the
bevel
gear
is
centrosymmetric,
figure out the
noise around
theboundaries.
ring by areaGenerally
filter, the result
is shown
19a.
Fitting
the ring
the bevel
gear in
is Figure
centrosymmetric,
figure out the
approximate
center
by average
coordinate.
the gear
inner and
outer boundaryfigure
circles of the
Fitting the ring
boundaries.
Generally
the Fit
bevel
centrosymmetric,
the
approximate
center
by average
coordinate.
Fit
the innerisand
outer boundary circlesout
of the
ring
by
CAM.
Red
circles
in
Figure
19b
are
the
fitting
result.
This
is
preparatory
work
for
approximate
by average
coordinate.
inner
and outer
circles
of the
ring
by CAM.center
Red circles
in Figure
19b are Fit
thethe
fitting
result.
This isboundary
preparatory
work
for
Step
3
and
the
following
dimension
measurement.
ring
by
CAM.
Red
circles
in
Figure
19b
are
the
fitting
result.
This
is
preparatory
work
for
Step 3 and the following dimension measurement.
Step 3: Defect
detection.
The pixels
of the top
ring are highlighted for a qualified gear, so the dark
Step
3
and
the
following
dimension
measurement.
Step 3: Defect detection. The pixels of the top ring are highlighted for a qualified gear, so the dark
circles
aretop
marked
defects. For
inside and
Step 3: pixels
Defect between
detection.two
Thered
pixels
of the
ring areas
forthe
a qualified
gear,outside
so the
pixels
between
two
red
circles
are marked
ashighlighted
defects. For
the
inside and
outside
neighborhood
of the two
ring,red
defects
areare
located
by as
thedefects.
combination
of fixed
and
dynamic
dark
pixels
between
circles
marked
For
the
inside
and
outside
neighborhood of the ring, defects are located by the combination of fixed and dynamic
threshold
segmentation.
The
merged
is shown
the white pixel
groups
Figure
neighborhood
of the ring,
defects
areresult
located
by the as
combination
of fixed
and in
dynamic
threshold
segmentation.
The
merged
result
is shown
as
the white pixel
groups
in
Figure
19c.
Then
eliminate
additional
arc
by
image
open-operation
and
extract
bigger
defects
by
threshold
segmentation.
The
merged
result
is
shown
as
the
white
pixel
groups
in
Figure
19c. Then eliminate additional arc by image open-operation and extract bigger defects19c.
by
area filtering,
asadditional
shown in Figure
The
end result is marked
by red
boxesdefects
in Figure
18.
Then
eliminate
arc by 19d.
image
open-operation
and extract
bigger
by area
area filtering,
as shown in Figure
19d.
The
end result is marked
by red
boxes in Figure
18.
filtering, as shown in Figure 19d. The end result is marked by red boxes in Figure 18.
4.1.2. Inspection of Spherical Surface
4.1.2. Inspection of Spherical Surface
The defects on spherical surface are not obvious in the top camera image and should be
The defects on spherical surface are not obvious in the top camera image and should be
detected from lateral camera images. Figure 20a shows such an image. The region just facing the
detected from lateral camera images. Figure 20a shows such an image. The region just facing the
camera is highly lit and both sides are darker and darker. Experiments show that defects in the
camera is highly lit and both sides are darker and darker. Experiments show that defects in the
Sensors 2016, 16, 1364
transition
region
Sensors
2016, 16,
1364
13 of 17
are the most obvious, so the main inspection area is between the high light and13the
of 17
darkest regions.
Sensors
Sensors 2016,
2016, 16,
16, 1364
1364
13
13 of
of 17
17
transition
transition region
region are
are the
the most
most obvious,
obvious, so
so the
the main
main inspection
inspection area
area is
is between
between the
the high
high light
light and
and the
the
darkest
regions.
darkest regions.
(a)
(b)
(c)
(d)
Figure19.
19. Defect
Defect detection
detection of
(b)(b)
Top
ring
fitting
Figure
of top
top ring
ring on
onbottom
bottomsurface:
surface:(a)
(a)Top
Topring
ringextraction;
extraction;
Top
ring
fitting
(red
circles);
(c)
Result
of
defect
detection;
(d)
Defects
after
open-operation.
(red circles); (c) Result of defect detection; (d) Defects after open-operation.
To extract the target region fast, the system creates a template for each lateral camera, as
4.1.2. Inspection of Spherical Surface
shown in Figure 20b. Gray indicates the inspection region and black/white is the non-inspection
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
The The
defects
on spherical
surface
not obvious
in the
topavoiding
camera
image
and should
be detected
region.
white
stripe is used
forare
device
calibration
and
erroneous
inspections.
The
whole
sphere
surface
cannot Figure
betop
covered
by
seven
cameras
at
a The
time.extraction;
To ensure
the
defects
can be is
from
lateral
camera
images.
20a
shows
such
an
image.
region
just
facing
the
camera
Figure
19.
Defect
detection
of
ring
on
bottom
surface:
(a)
Top
ring
(b)
Top
ring
fitting
Figure 19. Defect detection of top ring on bottom surface: (a) Top ring extraction; (b) Top ring fitting
detected
at any
angle,
theofgear
is rotated
3 to
5 times
by
a stepper
highly
litcircles);
and
both
darker
and darker.
Experiments
showmotor.
that defects in the transition region
(red
(c)
Result
detection;
(d)
after
(red
circles);
(c) sides
Resultare
of defect
defect
detection;
(d) Defects
Defects
after open-operation.
open-operation.
are the most obvious, so the main inspection area is between the high light and the darkest regions.
To
extract
the
target
region
fast,
system
creates
aa template
for
each
camera,
as
fast,
thethe
system
creates
a template
for each
camera,
as shown
To extract
extractthe
thetarget
targetregion
region
fast,
the
system
creates
template
for lateral
each lateral
lateral
camera,
as
shown
in
Figure
20b.
Gray
indicates
the
inspection
region
and
black/white
is
the
non-inspection
in
Figure
20b.
Gray
indicates
the
inspection
region
and
black/white
is
the
non-inspection
region.
shown in Figure 20b. Gray indicates the inspection region and black/white is the non-inspection
region.
The
white
stripe
used
device
calibration
and
avoiding
erroneous
inspections.
The
The white
stripe
is used
calibration
avoiding
erroneous
inspections.
whole sphere
region.
The
white
stripeforis
isdevice
used for
for
device and
calibration
and
avoiding
erroneous The
inspections.
The
whole
sphere
surface
cannot
be
covered
by
seven
cameras
at
a
time.
To
ensure
the
defects
can
be
surface
cannot
be
covered
by
seven
cameras
at
a
time.
To
ensure
the
defects
can
be
detected
at
whole sphere surface cannot be covered by seven cameras at a time. To ensure the defects canany
be
detected
at
any
angle,
the
gear
is
rotated
3
to
5
times
by
a
stepper
motor.
angle, theatgear
rotated
to 5 is
times
by a3stepper
motor.
detected
any is
angle,
the3gear
rotated
to 5 times
by a stepper motor.
(a)
(b)
Figure 20. (a) The lateral image of sphere surface; (b) The template of sphere surface.
The motor rotation is time-consuming. The motor begins to rotate just at the end of a single
image acquisition. The rotation completes when the image processing finishes, then the next image
acquisition begins. Inspection time is saved greatly by this process. The defects are detected by the
NAD method. Figure 21a
shows an image with defects in it and Figure 21b
shows the inspection
(a)
(b)
(a)
(b)
result.
Figure
20. (a)
The lateral
image of
sphere surface;
(b) The
template of
sphere surface.
Figure
Figure 20.
20. (a)
(a) The
The lateral
lateral image
image of
of sphere
sphere surface;
surface; (b)
(b) The
The template
template of
of sphere
sphere surface.
surface.
The
The motor
motor rotation
rotation is
is time-consuming.
time-consuming. The
The motor
motor begins
begins to
to rotate
rotate just
just at
at the
the end
end of
of aa single
single
The
motor rotation
is time-consuming.
Thethe
motor
begins
to rotate
just atthen
the end
of a image
single
image
acquisition.
The
rotation
completes
when
image
processing
finishes,
the
next
image acquisition. The rotation completes when the image processing finishes, then the next image
image acquisition. The
rotation completes
when theby
image process.
processing finishes,
thendetected
the next image
acquisition
acquisition begins.
begins. Inspection
Inspection time
time is
is saved
saved greatly
greatly by this
this process. The
The defects
defects are
are detected by
by the
the
acquisition
begins.
Inspection
time
is
saved
greatly
by
this
process.
The
defects
are
detected
by the
NAD
method.
Figure
21a
shows
an
image
with
defects
in
it
and
Figure
21b
shows
the
inspection
NAD method. Figure 21a shows an image with defects in it and Figure 21b shows the inspection
NAD method. Figure 21a shows an image with defects in it and Figure 21b shows the inspection result.
result.
result.
(a)
(b)
Figure 21. (a) A lateral image of the sphere surface; (b) Inspection result of Figure 21a.
4.1.3. Measurement of End Rabbet Diameter
Size measurement includes the diameters of large and small circumcircles and end rabbets.
The two circumcircles are relatively easy to fit by threshold segmentation and CAM. The fitting
results are shown as green
circular groove on the
(a)
(b)
(a) circles in Figure 22a. The end rabbet is a shallow
(b)
Figure
Figure
21.
(a)
A
lateral
image
of
the
sphere
surface;
(b) Inspection
Inspection result
result of
of Figure
Figure 21a.
21a.
Figure 21.
21. (a)
(a) A
A lateral
lateral image
image of
of the
the sphere
sphere surface;
surface; (b)
4.1.3.
4.1.3. Measurement
Measurement of
of End
End Rabbet
Rabbet Diameter
Diameter
Size
Size measurement
measurement includes
includes the
the diameters
diameters of
of large
large and
and small
small circumcircles
circumcircles and
and end
end rabbets.
rabbets.
The
two
circumcircles
are
relatively
easy
to
fit
by
threshold
segmentation
and
CAM.
The two circumcircles are relatively easy to fit by threshold segmentation and CAM. The
The fitting
fitting
results
are
shown
as
green
circles
in
Figure
22a.
The
end
rabbet
is
a
shallow
circular
groove
on
results are shown as green circles in Figure 22a. The end rabbet is a shallow circular groove on the
the
Sensors 2016, 16, 1364
14 of 17
4.1.3. Measurement of End Rabbet Diameter
Size measurement includes the diameters of large and small circumcircles and end rabbets.
The two circumcircles are relatively easy to fit by threshold segmentation and CAM. The fitting results
Sensors 2016, 16, 1364
14 of 17
are shown as green circles in Figure 22a. The end rabbet is a shallow circular groove on the gear.
Sensors 22b
2016,shows
16, 1364its location and 22c is an amplified image. The division of two regions of different
14 of 17
Figure
gear.
Figure
22b shows its location and 22c is an amplified image. The division of two regions
of
gray
values
in
Figure
22c
is
the
rabbet
circle.
It
is
dark
in
the
image
and
hard
to
identify.
different gray values in Figure 22c is the rabbet circle. It is dark in the image and hard to identify.
gear.
Figurethe
22brabbet
showscircle
its location
and 22c in
is the
an amplified
image.
The division
of two regions
Because
notdistinct
distinct
image,
fixed
dynamic
thresholding
such
asof
Because the
rabbet circle
isisnot
in the
image,
fixed
or or
dynamic
thresholding
such
as the
different
gray
values
in
Figure
22c
is
the
rabbet
circle.
It
is
dark
in
the
image
and
hard
to
identify.
the
algorithm
or the
interactive
method
notapplicable
applicable[20–22].
[20–22].Figure
Figure23a
23a shows
shows the
the gray
OtsuOtsu
algorithm
or the
interactive
method
areare
not
gray
Because
therabbet
rabbet
circle
is not
distinctpixels.
in theWe
image,
fixed
or pixels
dynamic
thresholding
such
the
histogram
of
the
circle
and
its
nearby
find
that
the
on
the
rabbet
circle
areasthe
histogram of the rabbet circle and its nearby pixels. We find that the pixels on the rabbet circle
are
Otsu
algorithm
or
the
interactive
method
are
not
applicable
[20–22].
Figure
23a
shows
the
gray
darkest.
They
are the
of the
about
3000–5000
pixels.
We extract
thesethese
pixels
and
the darkest.
They
are left
the part
left part
of histogram,
the histogram,
about
3000–5000
pixels.
We extract
pixels
histogram
of
the rabbet
circle
and
its as
nearby
pixels.
We find
that the pixels on the rabbet circle are
then
get
the
outline
of
the
rabbet
circle,
shown
in
Figure
23b.
and then get the outline of the rabbet circle, as shown in Figure 23b.
the We
darkest.CAM
They are
therabbet
left part
of the
histogram,
about
3000–5000
pixels.
We circle
extract these
pixels
fit fit
the
circle
in Figure
23b. The
shown
the red
Figure
We use
use CAMtoto
the rabbet
circle
in Figure
23b.result
The isresult
isas
shown
as the in
red
circle22a.
in
and
then
get
the
outline
of
the
rabbet
circle,
as
shown
in
Figure
23b.
We
prove
again
that
our
method
is
much
faster
than
the
Hough
Transform
and
least-squares
method
Figure 22a. We prove again that our method is much faster than the Hough Transform and
We use CAM
to fit the rabbet circle in Figure 23b. The result is shown as the red circle in
while
ensuring
the accuracy.
least-squares
method
while ensuring the accuracy.
Figure 22a. We prove again that our method is much faster than the Hough Transform and
least-squares method while ensuring the accuracy.
(a)
(b)
(c)
Figure 22.
22. Size
Size
measurement of
of circumcircles
circumcircles and
and (b)
end rabbet:
rabbet: (a)
circles are
are circumcircles
circumcircles
and
(a)measurement
(c)
Figure
end
(a) Green
Green circles
and
red
is
end
rabbet
circle.
(b)
Location
of
end
rabbet;
(c)
Extracted
rabbet
and
its
amplified
image.
red
is end22.
rabbet
circle. (b) Location
of end rabbet;
Extracted
andcircles
its amplified
image. and
Figure
Size measurement
of circumcircles
and(c)
end
rabbet: rabbet
(a) Green
are circumcircles
red is end rabbet circle. (b) Location of end rabbet; (c) Extracted rabbet and its amplified image.
(a)
(b)
Figure 23. (a) Histogram
(a) of End rabbet and nearby pixels; (b) Extract the outline
(b) of rabbet circle.
Figure 23. (a) Histogram of End rabbet and nearby pixels; (b) Extract the outline of rabbet circle.
Figure 23.
(a) Histogram
of End
rabbet and nearby pixels; (b) Extract the outline of rabbet circle.
4.2. Statistical
Results
of Bevel Gear
Inspection
the Results
inspection
system
4.2. Using
Statistical
of Bevel
Geardeveloped
Inspection in this paper, 84 bevel gears of type A4 and 84 of type
4.2. Statistical Results of Bevel Gear Inspection
F6 are tested. Tables 2–4 are the inspection results of A4. Tables 5–7 are the inspection results of F6.
Using the inspection system developed in this paper, 84 bevel gears of type A4 and 84 of type
the inspection
system
developedofin our
this paper,
gears
of typeunder
A4 andthe
84 current
of type
The Using
data shows
that size
measurement
system84isbevel
100%
accurate
F6 are tested. Tables 2–4 are the inspection results of A4. Tables 5–7 are the inspection results of F6.
F
2–4 are the
inspection
results
. Tables
5–7 are
theisinspection
F6 .
requirements.
Measurement
accuracy
is about
45 of
μmA4and
repeated
error
no more results
than 90ofμm.
6 are tested. Tables
The data shows that size measurement of our system is 100% accurate under the current
The data
shows
that
size
measurement
of
our
system
is
100%
accurate
under
the
current
requirements.
minimum detectable defect is 0.4 mm × 0.4 mm. Inspection time of one surface is less than 1.3 s.
requirements. Measurement accuracy is about 45 μm and repeated error is no more than 90 μm.
Measurement
accuracy
about
45 are
µm suitable
and repeated
error
is no more
thaninspection
90 µm. The
Both the accuracy
and isthe
speed
for the
real-time
on-line
in minimum
automatic
The minimum detectable defect is 0.4 mm × 0.4 mm. Inspection time of one surface is less than 1.3 s.
production lines.
Both the accuracy and the speed are suitable for the real-time on-line inspection in automatic
production lines.
Sensors 2016, 16, 1364
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detectable defect is 0.4 mm × 0.4 mm. Inspection time of one surface is less than 1.3 s. Both the
accuracy and the speed are suitable for the real-time on-line inspection in automatic production lines.
Table 2. Top surface inspection of gear A4 .
Top Circle
Results
Teeth Surface
Teeth Edge
Connected Fault
Knock
Dent
Knock
Insufficient Filling
Knock
Insufficient Filling
1
1
100
7
7
100
10
10
100
15
12
80
1
1
100
13
11
84.6
10
10
100
Number of defects
Detected defects
Accuracy/%
Table 3. Lateral surface inspection of gear A4 .
Results
Knock
Scratch
Dent
Gibbosity
Roughness
Peeling off
Number of defects
Detected defects
Accuracy/%
30
28
93.3
23
19
82.6
18
16
88.9
1
1
100
6
6
100
1
1
100
Table 4. Bottom surface inspection of gear A4 .
Bottom Ring
Results
Spherical Surface
Spline
Knock
Scratch
Knock
Scratch
Dent
Duplicated Broaching
41
39
95.1
12
12
100
15
15
100
23
22
95.6
19
19
100
6
6
100
Number of defects
Detected defects
Accuracy/%
Table 5. Top surface inspection of gear F6 .
Results
Number of defects
Detected defects
Accuracy/%
Top Ring
Top Teeth Surface
Teeth Edge
Chamfer Lack
Knock
Dent
Knock
Dent
Knock
Insufficient Filling
2
2
100
7
7
100
8
8
100
17
16
94.1
9
9
100
34
30
88.2
18
18
100
Table 6. Lateral surface inspection of gear F6 .
Results
Number of defects
Detected defects
Accuracy/%
Lateral Teeth Surface
Lateral Teeth Small Surface
Knock
Dent
Scratch
Insufficient Filling
Knock
Dent
Scratch
42
37
88.1
8
8
100
11
8
72.7
3
3
100
13
11
84.6
5
5
100
4
3
75
Table 7. Bottom surface inspection of gear F6 .
Results
Number of defects
Detected defects
Accuracy/%
Bottom Ring
Mounting Surface
Spline
Knock
Rough
Knock
Scratch
Size Error
Duplicated Broaching
3
3
100
3
3
100
2
2
100
5
4
80
4
4
100
3
3
100
5. Discussion
The presented multi-camera automobile bevel gear quality inspection system adopts advanced
machine vision technology. It solves the problem of difficult inspection of complicated gears at high
Sensors 2016, 16, 1364
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speed and with high precision. The research shows that machine vision can substitute most manual
work in bevel gear inspection, improving the efficiency of production and the degree of automation.
The prototype of this system has been realized and applied in bevel gear production. There are
still some technical problems to be solved. The edge of the gear is a non-detectable area in our system
and some defects in low contrast images cannot be detected reliably. We are seeking better illumination
schemes and new inspection ideas to solve these problems.
Acknowledgments: The work was supported by Natural Science Foundation of Shaanxi, China (No. 2012JQ8042)
and the grants from National Natural Science Foundation of China (No. 61105021).
Author Contributions: All authors contributed extensively to the work presented in this paper and wrote the
manuscript. Ruiling Liu reviewed the state-of-the-art and wrote the initial version of the paper. Dexing Zhong and
Hongqiang Lyu participated the analysis of the vision techniques. Jiuqiang Han instructed the whole development
of the system.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
NAD
CAM
FRP
Neighborhood Average Difference
Circle Approximation Method
Fast Rotation-Position
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