Modelling of grinding gap macro geometry and workpiece kinematics

in throughfeed centreless grinding

R. Drazumerica, P. Krajnik

a, R. Vrabic

a, B. Meyer

b, P. Butala

a, F. Kosel

a, J. Kopac

a

aUniversity of Ljubljana, Faculty of Mechanical Engineering, Slovenia

bRWTH Aachen University, Laboratory for Machine Tools and Production Engineering

WZL, Germany

� � � � � � � � � � � � � � � � � � � � � � �

Corresponding author:

Postal address:

Radovan Drazumeric

University of Ljubljana, Faculty of Mechanical Engineering

Askerceva 6, 1000 Ljubljana, Slovenia

Tel.: +386 1 4771 517

Fax: +386 1 2518 567

E-mail: radovan.drazumeric@fs.uni-lj.si

Co-authors a: P. Krajnik, R. Vrabic, P. Butala, F. Kosel, J. Kopac

Postal address:

University of Ljubljana, Faculty of Mechanical Engineering

Askerceva 6, 1000 Ljubljana, Slovenia

Co-authorb: Bernd Meyer

Postal address:

RWTH Aachen University, Laboratory for Machine Tools and Production Engineering WZL

Steinbachstrasse 19, 52074 Aachen, Germany

1

Abstract

The paper discusses the simulation of a throughfeed centreless grinding process in a virtual

environment (VE). The developed simulations are based on an analytical grinding gap model

describing the grinding gap macro geometry and workpiece kinematics. First of all, the model

is embedded in a desktop application (Cegris), which facilitates regulating wheel truing and

the determination of set-up variables, both of which yield an optimal grinding gap macro

geometry in a reduced set-up time. Finally, the Cegris is ported to a CAVE (CAVE Automatic

Virtual Environment) for an interactive visualisation of the process, an application used to

train machine tool operators.

Keywords: Grinding; Centreless; Modelling; Simulation; Virtual Reality

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2

1. Introduction

Centreless grinding is commonly employed for the mass-finish machining of

rotationally symmetrical workpieces. On the shop floor, where different workpiece

geometries are ground with the same machine tool, the set-up adjustments, usually based on

trial and error, may lead to significant machine tool downtime. For this reason the set-up is

the key issue determining process efficiency. Due to the tendency towards a decrease in batch

sizes, end users direct research initiatives towards flexible, small, or even single batch

centreless grinding, which can be economical only if set-up times are drastically reduced.

The process ability to grind workpieces with acceptable roundness mainly depends on

geometric stability [1], dynamic stability [2-4], workpiece kinematic stability [5], and cycle

length [6]. A more detailed review of process stability issues is given in [7]. Different

computer simulations can be used to predict workpiece roundness and to assist in the selection

of set-up conditions either in plunge [8-12] or throughfeed centreless grinding [13].

For improving throughfeed centreless grinding accuracy it is also necessary to ensure

a grinding gap macro geometry that suppresses variation of the grinding depth [14]. This can

be achieved by appropriate truing of the regulating wheel and grinding gap set-up. Up to now

truing possibilities have been limited. In conventional truing systems, a single point diamond

tool is traversed across the regulating wheel in a straight line, which induces the contact

interference between the regulating wheel and the workpiece. Moreover, such systems do not

consider the possibility of swivelling the regulating wheel [15]. However, the employment of

CNC truing systems can impart an arbitrary shape of the regulating wheel, determined by its

diameter function, and eliminate interference problems [16]. This indicates the need for

further investigation into the grinding gap macro geometry. The first research objective was

therefore not focused on process stability, but was undertaken to develop an analytical model

3

of the grinding gap, which incorporates the grinding gap macro geometry and workpiece

kinematics. The application of the model in the Cegris provides for CNC regulating wheel

truing and adequate adaptation of set-up variables. The second research objective was to

develop virtual centreless grinding that integrates innovative simulation and transfers process

know-how through fully-immersive VE. With its 3D interaction, a CAVE application

(CegrisCAVE) is used for training machine tool operators. There are three main issues that

make training in CAVE relevant: the high cost of training with physical machine tools, the

low availability of these machine tools, and safety concerns.

2. Grinding gap model

In order to model the grinding gap, the grinding gap macro geometry and workpiece

kinematics have to be analytically described. The grinding wheel is of cylindrical shape with

diameter sd . The workpiece diameter function w wd z determines the material removal rate

along the grinding gap. For continuous material removal and undisturbed workpiece passage

to the spark out zone, a polynomial w wd z , shown in Fig. 1, is introduced:

2

1 0 1 3

2 2

2

w s sa w s sa

w w w w w

s sa

z b b z b bd z d d d

b b; 0 w s saz b b , (1)

1w w wd z d ; w s saz b b , (2)

where 0wd is the diameter of a blank, 1wd is the final workpiece diameter, sb is the grinding

wheel width, and sab is the width of the spark out zone. The introduced w wd z is important

due to the fact that an interfered spark out can deteriorate workpiece roundness [17].

2.1. The grinding gap macro geometry

4

Fig. 2 shows the four centreless grinding gap objects: the grinding wheel, the workrest

blade, the workpiece, and the regulating wheel. The material removal process takes place

between the grinding wheel and the workpiece. The workrest blade is used to support the

workpiece at a given centre height h , which has a significant influence on geometric stability

[1]. The regulating wheel is inclined by an angle r to generate an axial force component so

that workpieces can be fed across the width of the grinding wheel as they rotate [6]. The

swivelling angle r is a set-up variable that affects regulating wheel truing cycle time.

It has been shown that process nonlinearity can arise because of the contact loss

between the workpiece-regulating wheel and the workpiece-workrest blade [17]. Furthermore,

if the workpiece loses contact with the grinding wheel in the spark out zone, the workpiece

will not be ground round [2]. Besides contact loss, process stability is dependent on contact

filtering. It has been found that the effectiveness of contact filtering is improved if the

workpiece-regulating wheel contact length is increased [4]. Consequently, modelling is based

on a demand for simultaneous line contact of the workpiece with the grinding wheel, the

workrest blade, and the regulating wheel along the length of the grinding gap. It is supposed

that this modelling demand assures optimal grinding gap macro geometry.

In the following calculations all grinding gap contacts are presumed to be ideally stiff.

First of all, the workpiece-grinding wheel contact is determined as:

2 2

2 0w w s w w s w wd z d h y z x x z , (3)

where w wx z is the horizontal and w wy z is the vertical workpiece centre displacement,

shown in Fig. 3. The horizontal distance between workpiece-grinding wheel centres sx is

shown in Fig. 4.

Secondly, the workpiece-workrest blade contact is determined as follows:

5

0 2 sin cos 0w w w w w w wd z d x z y z , (4)

where the workrest blade angle is shown in Fig. 4.

Thirdly, the workpiece-regulating wheel contact is determined as follows:

2

2 2 02

w w

x w y w

d zA z A z ; (5)

costan

2 cos 2

r w r w rx w r w w w r

r

d z z bA z x x z z , (6)

sin tantan tan cos

2 cos 2 cos

r w r w r ry w r r r w w w w

r r

d z z bA z z h y z z , (7)

where rb refers to regulating wheel width, r wd z represents the regulating wheel diameter

function, while r wz is the regulating wheel contact angle with the workpiece, shown in

Fig. 3. The horizontal distance between workpiece-regulating wheel centres rx is shown in

Fig. 4. To ensure the required workpiece-regulating wheel line contact, the contact has to have

a single point of tangency at any workpiece position along the grinding gap, which is

achieved by setting rw

r

ddz

dto zero:

cos sin cos cos sin sin sin 0x w r r w y w r r w r r r wA z z A z z z . (8)

Quantities x wA z and y wA z have been introduced exclusively in order to shorten the

above formulations.

2.2. Workpiece kinematics

In order to determine workpiece kinematics, a nonsliding workpiece-regulating wheel

contact at every point of the grinding gap is assumed [18]. The mechanism of spinner

6

occurrence and regulating wheel friction characteristics are not taken into consideration [11].

The workpiece kinematics consists of the workpiece rotational frequency w wn z and

feedrate fa wv z :

cos cos cos cos sin sin

sin sin cos sin

r w

w w r r r w w w r r w w w

w w

r r r w w w

d zn z n z z z z

d z

z z

, (9)

sin cos cos sin sin60

r w

fa w r r r r w r r w

d zv z n z z , (10)

where rn is the regulating wheel rotational frequency and w wz is the workpiece contact

angle with the regulating wheel, shown in Fig. 3.

The workpiece kinematics provides for the calculation of the grinding cycle time ct

and the specific material removal rate w wQ z , which are the most important estimates of

process productivity:

0

sb

wc

fa w

dzt

v z, (11)

2

ww w w w w fa w

w

ddQ z z d z v z

dz. (12)

2.3. Model verification

The grinding gap model was experimentally verified prior to its application in

simulation. As the model of the grinding gap macro geometry is included in the workpiece

kinematics model, only the latter is directly verified. For this, grooved workpieces were

ground. The w wn z was monitored by measuring groove passage frequency while the

7

fa wv z was monitored by measuring the gap between successive workpieces. Monitoring

employed noncontact eddy current sensors mounted on coolant nozzles, as shown in Fig. 5.

Grinding experiments were conducted on a Studer Mikrosa Kronos L centreless

grinder. The workpieces were bearing rings made of 100Cr6 bearing steel. The workpieces

were turned to diameter 0 50wd mm and length 25wl mm. For grinding of bearing rings

the end user required a continuous reduction of workpiece feedrate towards the spark out zone

in order to prevent their tipping over. This was achieved by inputting referential variables so

that the entry regulating wheel diameter 0rd was larger than the exit regulating wheel

diameter 1rd .

During measurements no gap between the successive workpieces was detected, which

proves the reduction of workpiece feedrate along the grinding gap. In terms of workpiece

rotational frequency w wn z , the calculated results agree well with the experimental results,

as shown in Fig. 6.

3. Applications of the model

A Cegris non-immersive VE and a CegrisCAVE fully-immersive VE are used for the

model application, where the process is simulated and visualised before its physical

utilisation. VE is classified according to the spatiality of interaction and representation. VE

with 2D interaction and 3D representation is considered non-immersive, whereas VE with 3D

interaction and 3D representation is considered fully-immersive [21].

3.1. Parameterisation of the grinding gap objects

For the visualisation of the process in a VE, a parameterisation of the grinding gap

objects is required. The objects are described as parametric surfaces with two parameters as

given in [19].

8

3.2. Cegris application

The Cegris application creates a non-immersive VE on a personal computer. The

simulation is written in the C# programming language for the .NET platform and uses the

OpenGL graphics library. The .NET framework is used for the graphical user interface (GUI)

and for variable loading and saving, screenshot acquisition, and charting. The OpenGL library

is used for 3D visualisation.

The role of the Cegris with regard to the process is presented in Fig. 7. Referential

variables are the inputs to the simulation. The simulation outputs assist in the set-up of the

optimal grinding gap macro geometry, which consists of two parts.

Firstly, the regulating wheel diameter function r wd z is calculated. For regulating

wheel truing a CNC converts the r wd z related data into a G-code [16]. Prior to truing, the

machine tool operator manually swivels the regulating wheel by the calculated angle r ,

which can significantly reduce the truing cycle time and consequently the set-up time. For

example, let us consider a distinctive change in the grinding gap referential variables.

Namely, the workpiece centre height is changed from 3h mm to 18h mm and the

regulating wheel inclination angle is changed from 2r to 4r . In the case of truing

with a non-swivelling regulating wheel {A}, the truing allowance equals ,max 6.8rd mm.

However, in the case of truing with a swivelled regulating wheel, where the swivelling angle

is calculated with Cegris {B}, the truing allowance equals ,max 2rd mm, as shown in Fig. 8.

This reduces the regulating wheel truing cycle time by 70% if the same truing feedrate

and infeed are used. It has to be noted that the changes in referential variables are not as

drastic in normal production. The average reduction in regulating wheel truing cycle time

reported by end users using the Cegris is 30% [20]. In addition to the reduction of the

regulating wheel truing cycle time, the Cegris enables the calculation of r wd z so that

9

fa wv z can be increasing or decreasing. Secondly, the set-up variables rx and sx provide for

a precise positioning of the workpiece centre height. In this way simulation-based workpiece

centre height adjustments are performed that are independent of the machine tool operator.

This leads to an average reduction of the grinding gap set-up by 20%, as reported by end users

[20]. Hence it follows that the industrial application of the Cegris enabled the end users to

reduce the set-up time by 50% on average, which has an effect on machining costs depending

on the batch size and workpiece length. In the case study involving grinding 20000 bearing

rings, the total machining costs decreased by 7%, while in the case study involving grinding

1500 piston rods, the total machining costs decreased by 20% [20].

The Cegris can be also used to predict key process variables such as the geometric

stability index [18], the grinding cycle time (Eq. 11), and the specific material removal rate

(Eq. 12). Another important feature of the Cegris is that it visually depicts different types of

set-up errors. In this way, the integration of safety into the process set-up is achieved.

3.3. CegrisCAVE application

A CegrisCAVE creates a fully-immersive VE by projecting images on the inner walls

of a room-sized cube. The projected views are calculated in real time and respond to trainee

motion and data manipulation. The employed CAVE system consists of passive stereo

technology with circular polarisation for image generation, optoelectronic motion tracking

with infrared video cameras, and head mounted reflection surfaces, interaction devices, and an

underlying computer system, which is responsible for projection synchronisation and for

handling data from the hardware devices. The CegrisCAVE is written in C++ using the

ViSTA toolkit for interactive visualisations in a VE. ViSTA utilises the OpenSG open source

scenegraph library for rendering and supports OpenGL.

10

The CegrisCAVE is used in the training process. The simulation offers trainees a wide

range of different interactions by using human computer interfaces. Trainees can interact with

the VE via a pointer, which enables zooming, panning, and rotating the visualised grinding

gap objects, as shown in Fig. 9. The interactions are divided into the set-up and the process. In

the set-up interaction, grinding gap errors occur as in physical machining and are visualised to

show trainees the results of an incorrect set-up. Yet the simulation eliminates the risk of

accidents during training. Furthermore, in the process interaction, the simulation enables the

visualisation of workpiece kinematics and major process variables in real time. Training with

CegrisCAVE can therefore improve the competence of machine tool operators via enhanced

process understanding. Consequently, better process performance and an additional reduction

in set-up time can be indirectly achieved.

4. Conclusions

The throughfeed centreless grinding adding value largely depends on having an

underlying simulation that can make the set-up more efficient. Another important value-

adding issue refers to training, which is often limited by cost, availability, and safety

concerns. A grinding gap model was developed for the simulation of the process. A novel

approach based on analytical geometry was used to describe grinding gap macro geometry at

any instant. The workpiece-regulating wheel contact conditions vary significantly along the

grinding gap. The progressive variations of contact conditions as well as the variation of

workpiece and regulating wheel diameters were included in the workpiece kinematics model.

In this way some of the limitations of previous work were overcome. The workpiece

kinematics model was experimentally verified.

The Cegris application creates a non-immersive VE. The simulation inputs referential

variables which determine the workpiece position, the kinematics, and the material removal

rate in such a way as to achieve the targeted productivity and the desired workpiece feedrate

11

variation along the grinding gap. The simulation outputs both the regulating wheel diameter

function and set-up variables that ensure the optimal grinding gap macro geometry. The

regulating wheel truing process is far from optimum if a conventional truing system is used.

Therefore a CNC truing system was applied. The Cegris outputs the regulating wheel

swivelling angle that minimises the truing cycle time. Furthermore, the simulation alerts the

operator to possible errors in a given set-up. In this way it is possible to test different set-ups

without trial and error, which in turn reduces machine tool downtime and diminishes the risks

of crashes in reality.

The Cegris represented the basis for the CegrisCAVE developed in a fully-immersive

VE, which was employed for the training of machine tool operators by using interactive 3D

graphics. This provided the trainees with enhanced understanding of the process and allowed

them to integrate new knowledge into process planning and operation as quickly and

efficiently as possible. The simulation of centreless grinding in CAVE represents a new

paradigm in the simulation of machining operations.

Acknowledgements

This research was conducted within the NMP2-CT-2005-016547 project, which was

sponsored by the European Commission as part of FP6. The authors would also like to

acknowledge the Centre for Computing and Communication of RWTH Aachen University for

supporting the CegrisCAVE.

12

References

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13

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14

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List of figures

Fig. # Caption

Fig. 1. Workpiece diameter function.

Fig. 2. Throughfeed centreless grinding gap.

Fig. 3. Geometrical functions of the grinding gap model.

Fig. 4. Set-up variables.

Fig. 5. Eddy current sensors mounted on coolant nozzles.

Fig. 6. Workpiece rotational frequency along the grinding gap.

Fig. 7. The Cegris and process integration.

Fig. 8. Regulating wheel truing allowance with respect to the swivelling angle.

Fig. 9. Interaction with the CegrisCAVE.

dw0

dw1

bs

bsazw

dw

& ' ( ) * + ,

Grinding wheel

Workpiece

Regulating wheel

Workrest blade

ns

nw

nr

vfa

zw

ar

dr

- . / 0 1 2 3

jw

dw

zw

jr

dr

xw

yw

4 5 6 7 8 9 :

h

xrxs

ds

dr1

dr0

b

dw0

dw1

; < = > ? @ A

Coolant nozzles

Eddy current sensors

Grindingwheel

Workrest blade

Bearing ring

B C D E F G H

Grinding wheel

= 650 mm

= 660 mm

d

bs

s

Workpiece

Regulating wheel

d

d

l

d

d

n

w0

w1

w

r0

r1

r

= 50 mm

= 49.8 mm

= 25 mm

= 345 mm

= 339 mm

= 48 rpm

ns = 1470 rpm

330

329

328

327

326

325

324

323

0 100 200 300 400 500 600 700

nw

[rpm]

zw [mm]

Roughing zone Finish and spark-out zone

a dr r= 2°, = 3 mm, = 0.29°h

a dr r= 4°, = 18 mm, = 0.63°h

Calculated ( )n zw w

Measured n zw w( )

I J K L M N O

Referentialvariables

Regulatingwheel

Blank

Grindinggap model

Operator CNC truingsystem

Machinetool

Grindingwheel

Workrestblade

Workpiece

Cegris

Regulating wheeltruing

Centreless grindingprocess

h n, ,ar r

h n

z

, ,

( )

ar r

wd d dr0 r1 w, ,

dr r, x , xs

dr ( )zw

P Q R S T U V

Grinding wheel

d

bs

s

= 650 mm

= 660 mm

Workpiece

Regulating wheel

d

d

l

d

d

n

w0

w1

w

r0

r1

r

= 50 mm

= 49.8 mm

= 25 mm

= 345 mm

= 339 mm

= 48 rpm

ns = 1470 rpm

354

350

346

342

3380 100 200 300 400 500 600 700

dr

[mm]

zw [mm]

ar = 2°, = 3 mmh

ar = 4°, = 18 mmh

Ddr,max = 2 mm

Ddr,max = 6.8 mm

dr = 0°

dr = 0°

dr = 0.63°

dr = 0.29°

{A}

{B}

W X Y Z [ \ ]

^ _ ` a b c d