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299
OPTIMIZED AUTOMATION THROUGH INNOVATIVE
ROBOT SYSTEMS
Detelina Ignatova
Abstract: Grinding and polishing are standard operations in material
processing which are nowadays automated with the help of industrial robots in order
to relieve human labour and optimize the profitability of production. However, it is
expensive to adapt present systems to the production of other part geometries and
operation cycles, and therefore adaptations are economically applicable only for
large batch sizes.
In this paper an analysis of a robot system for beltgrinding will be presented.
Key words: beltgrinding operations, robotic grinding, optimized automation.
1. Introduction
A special challenge is posed in this context by the automation of “seeing and
evaluating” processing errors on highly shiny surfaces, which are even difficult for
the untrained human eye to detect. Furthermore, errors in the workpiece material in
the process chain of rough grinding, finish grinding and polishing can often be
detected only after a part, or all, of the processing has been done. This results in
greater cooperation among what are now single machines, which are only interlinked
due to the material flow in order to enable complete or partial reworking of
inadequate workpieces. To account for these problems, the following developments
have been made:
• The development of a software system in the vicinity of the workshop for
demanding robot processing applications such as grinding and polishing [1]. This
software system closes the gap between multifunctional, but complex offline
programming systems used in the planning department, on the one hand, and
inefficient possibilities of robot control used by the operator for optimizing the
program on the other hand – Fig 1.
Fig. 1. Userorientated offlineprogramming and real grinding process.
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300
• The development of a fully automatic working process chain for industrial
robotaided grinding and polishing that, on the basis of the measurements of an image
processing system, modifies a given machining course. The focus lies here on
industrial robotaided processes like grinding and polishing of complex free forming
geometries with high demands on the optical quality of the resulting surface.
2. Belt grinding processes
2.1 Belt grinding process simulation
Two questions have to be solved during the implementation of the grinding
process simulation. One is the representation of the workpiece and cutter model, and
the other is the determination of material removal. The workpiece is discretized into
elements and the grinding tool is represented by polygons. The second one is to
determine how much material is removed on each grinding point. The whole
simulation system is driven by incrementally removing material from the workpiece
stock. As mentioned above, it can not use Boolean set operations between the tool
envelop and
workpiece like turning or milling processes. Instead, the calculation
should based on an experience model integrating many influential parameters.
2.2 Removal determination
In the freeform surface grinding process, the linear global grinding model given
by Hammann [2] is not applicable anymore. Particularly, the local nonuniform force
distribution in the contact area must be considered and the influence of other
manufacturing parameters also needs to be investigated. Generally, the procedure to
estimate the removal rate can be divided into three steps: contact situation
determination, force distribution calculation and removal computation – Fig. 2. The
first one describes the geometric information about the intersection between the
grinding belt and workpiece, which will be used to obtain the pressure in the contact
area in the second phase. Then other parameters are included to get the final removal
in the last stage [3].
Fig.2. Removal calculation of one contact point. (a) The contact point in a grinding path; (b)
Contact situation of that point; (c) Force distribution computed from the contact situation; (d)
The final removal distribution in that contact area
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3. Analysis of the technological contact at the robotized grinding of the
parts with complex shapes
The process of the finishing operations of the parts with complex shapes consists
of complicated motions. The aim of the modeling is the process of treatment to be
described by means of geometrical and kinematics relations. On the Fig. 3 is shown a
Robotized Technological Module for beltgrinding and polishing for parts with
complex space surfaces.
Fig.3. Robotized Technological Module for beltgrinding and polishing
for parts with complex space surfaces
On the Fig. 4 and Fig. 5 main structural and kinematical schemes of this
robotized grinding module are presented. The main structural scheme is a closed
monocontour kinematics chain with a technological pair (
Σ
Σ
k k
−
+1
). Furthermore,
with this pair the geometrical limits are considered. This complex consists of two
independent opened monocontour mechanisms: I. The Grinding station
Σ
k
, which
puts in motion a tool (grid, belt or etc.). II. The Robot
Σ
k +1
which carries a part. A
robot at a complicated motion actuates this part.
Fig.4. Main structural scheme of Fig.5. Kinematical technological scheme
robotized grinding module of the beltgrinding robot
These two kinematics chains are closed geometrically with the pair
Σ
k
(tool)
and
Σ
k +1
(part). The base O is connected to the static coordinates
S X Y Z
0 0 0 0
(,,)
. Each
of links of mechanisms I and II are connected to suitable coordinates
S X Y Z
i i i i
(,,)
. It
is convenient to use these coordinates and the wellknown homogeneous
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transformations of the Denavit and Hartenberg because all real kinematics pairs have
one degree of freedom. In local coordinates
S
k
and
S
k +1
the radiusvectors of the
point
M M
k
(
∈
Σ
k k
M;
+1
∈
Σ
k +1
;
M M M
k k
=
=
+1 0
)
are described as matrix
column:
r x y z
M
i
M
i
M
i
M
i T( ) ( ) ( ) ( )
[,,,]= 1
, (i = k, k+1) (2.1)
It is obvious that in the static coordinates
S
0
the following equality is
performed:
r r
M M
k k
( ) ( )0 0
1
=
+
(2.2)
The transition of the local coordinates
S
k
and
S
k +1
to static coordinates
S
0
is
completed by means of the 4x4 matrix [4] (homogenous transformations) as to make
the round of from
S
k
to
S
0
for the mechanism I and from
S
k +1
to
S
0
for the
mechanism II and then:
T r T r
k
M
k
k
M
k
0 0 1
1
,
( )
,
( )
..=
+
+
(2.3)
This equation is called the "matrix equation of the closed chain". It is written for
the contact point M∈Σ and gives three independent scalar equations, which determine
the position, velocity and acceleration for this point in the static coordinates
S X Y Z
0 0 0 0
(,,)
.
Two matrices
T
k0,
and
T
o k,+1
determine the positions (place and orientation) of
the tool and the part respectively in the static coordinates. If the lefthand side of the
equation is given (the geometry and position of the tool) and the righthand side is
not, then this is referred to as inverse kinematics problem of the position. Conversely,
if the right portion is given and left side is not, then this is referred to as a direct
kinematics problem of the position. The equality (2.2) is necessary, but it is not a
sufficient condition for available contact between the tool and the part. The condition
of colinearity of the normal vectors is:
n n
M M
k k
( ) ( )0 0
1
=
+
(2.4)
The last equation, which provides permanent contact between the tool and the
part is the condition for perpendicularly of the two absolutely velocities
V
M
k
and
V
M
k +1
and the general normally:
( ).V V n
M M M
k k k
−
=
+1
0
(2.5)
Through the contact between the tool and part and the independent relative
motion with the relative velocity
V V V
M M12
1 2
=
−
between them the robotized grinding is
executed.
On the Fig. 5 the kinematicstechnological scheme of the robot and the grinding
station is given. The robotized technological module consists of an industrial robot
with six degrees of freedom and twopositional belt grinding station. Permanent axis
S
1
S
1
of the grinding station represents motions of the tool. Changeable axis of
S
2
S
2
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303
represents a momentary configuration of the robot, which support the contact
between the tool and part and realize the round motions by
V ia ia
s s
1 1
=
=var;var
ω
.
Angular velocity
ω
ω
=
=
=
const V r const
t
(.)
1
1 1
is the main technological velocity of
the tool. It is known that each position of the body is determinate from six
independent parameters: three coordinates of one point of the body and three angles.
If we summarize the three regional (linear) velocities
Σ
V
k
V
=
0
2
and three local
(angular) velocities
Σω
k s
k
=
ω
we get two components of the screwmotion at the
momentary axis
S
2
S
2
(see Fig. 4).
In addition to known theorems for complicated motion of the rigid body for the
absolute velocities of the contact point we have:
V V V
M s t
1 1 1 1
0 1
=
+
×
+
ω
ρ
;
(2.6)
V V
M s
2 2 2
0 2
=
+
×
ω
ρ
.
(2.7)
Where
V
oi
(i = 1, 2) is velocity of some point
O
i
from axis
S
i
S
i
; ρ
i
is radius
vector of the point
M
i
with beginning
O
i
∈
S
i
S
i
;
V r k
t
1
1 1 0
=
ω
⸮
is the relative
technological velocity of the points from grinding belt;
r
1
is the radius of the roller,
which put in motion the belt.
References:
1. Kuhlenkoetter B., Development of a Robot Syatem for Advanced High
Quality Manufacturing Processes, Acta Polytechnika, Vol. 46, No 1, pp 37, (2006)
2.
Hammann, G., 1998. Modellierung des Abtragsverhaltens Elastischer
Robotergefuehrter Schleifwerkzeuge. Ph.D Thesis, University Stuttgart, Stuttgart,
Germany.
3. Ren Xiangyang, Mueller H.,
Kuhlenkoetter B., Surfelbased surface
modeling for robotic belt grinding simulation, Journal of Zhejiang University
SCIENCE A ISSN 10093095; ISSN 18621775.
4. Minkov K., ROBOTICA, SU “St. Kl. Ohridski”, Sofia, 1986.
Data for author:
Detelina Stoyanova Ignatova, assoc. prof., PhD, eng., Department of Mechanics
of Multibody Systems, Institute of Mechanics, Bulgarian Academy of Sciences,
Sofia, Bulgaria, Sofia 1113, “Acad. G. Bonchev Str.”, bl. 4, tel. 029696408, Email:
ignatova@imbm.bas.bg
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