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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 belt-grinding will be presented.

Key words: belt-grinding 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 multi-functional, 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. User-orientated offline-programming and real grinding process.

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• The development of a fully automatic working process chain for industrial

robot-aided 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 robot-aided 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 free-form surface grinding process, the linear global grinding model given

by Hammann [2] is not applicable anymore. Particularly, the local non-uniform 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 belt-grinding and polishing for parts with

complex space surfaces.

Fig.3. Robotized Technological Module for belt-grinding 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 belt-grinding 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 co-ordinates and the well-known homogeneous

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transformations of the Denavit and Hartenberg because all real kinematics pairs have

one degree of freedom. In local co-ordinates

S

k

and

S

k +1

the radius-vectors 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 co-ordinates

S

0

the following equality is

performed:

r r

M M

k k

( ) ( )0 0

1

=

+

(2.2)

The transition of the local co-ordinates

S

k

and

S

k +1

to static co-ordinates

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 co-ordinates

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 co-ordinates. If the left-hand side of the

equation is given (the geometry and position of the tool) and the right-hand 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 kinematics-technological 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 two-positional 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 co-ordinates 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 screw-motion 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 3-7, (2006)

2.

Hammann, G., 1998. Modellierung des Abtragsverhaltens Elastischer

Robotergefuehrter Schleifwerkzeuge. Ph.D Thesis, University Stuttgart, Stuttgart,

Germany.

3. Ren Xiang-yang, Mueller H.,

Kuhlenkoetter B., Surfel-based surface

modeling for robotic belt grinding simulation, Journal of Zhejiang University

SCIENCE A ISSN 1009-3095; ISSN 1862-1775.

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, E-mail:

ignatova@imbm.bas.bg

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