pres pmi2012 surface_grinding_model_v2

from research .… to market

A time-domain surface grinding model for dynamic simulation

Marco Leonesio, P. Parenti, A. Cassinari, G. Bianchi, M. Monno

[email protected]

CIRP - PMI 2012 29-30th of October 2012, Nagoya, Japan

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Contents

• motivation and objectives• model description• calibration procedure• dynamic validation• some evidences of a non-regenerative

instability• conclusions and future developments

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On the other side, the quality of a workpiece resulting from a grinding process is strongly influenced by the static and dynamic behavior of the mechanical system, composed by machine tool, wheel, fixture and workpiece; in particular, the dynamic compliance may cause vibrations leading to poor surface quality.

Motivation and objectives

Surface grinding is one of the oldest and most widely used grinding processes: to date there are still few alternatives available for producing perfectly smooth surfaces which are acceptable both technically and from a cost point of view.

For these reason, the comprehension and modeling of grinding process dynamics assume a paramount importance both for end-users and grinder manufacturers.

Example of wavy surface

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Different architectures, different dynamic response, different behaviours ...


How does machine design (reflected in machine dynamics) and/or grinding parameters affect the vibration onset?

Courtesy of Ermando Rosa™

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A simulation model has been developed for fulfilling the afore-mentioned issues.

An effective simulation model should have the following characteristics:

Generality. It must handle any kind of machine tool dynamics - even considering control effect and nonlinearities – and all possible grinding operations;

Easy calibration. The calibration of the model must be as fast as possible to cope with the short industrial timing;

Completeness. The model must represent all and only the phenomena that are relevant in determining process performance;

- Implementation in Matlab/Simulink environment enabling a possible mechatronic simulation machine + process;

- Wheel and workpiece speed as run-time variables;

- Simple force model with only 3 parameters;

- Non linear force model;- General wheel workpiece

engagement condition;- No wheel regeneration as

wheel lobing effect is not the main concern in surface grinding;

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Model description

Input: • Relative wheel-workpiece position in

traverse, feed and normal direction

Output: • Normal and tangential grinding force• Wheel torque• Actual Material Removal Rate (MRR)• Final surface geometry• Wheel center oscillations

Dynamic compliance

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Model description

• Coarse spacing in traverse direction (Y) (where no forces are exerted); • Fine spacing in feed direction (X);

• Z-buffer approach for workpiece representation;• The wheel is regarded as a perfect disk;

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Model description

Model parameters

Workpiece dimensions and discretization in feed and traverse direction;

Wheel radius Wheel width (Vs) wheel tangent velocity [m/s], or wheel angular velocity [rpm]; Sign of wheel velocity; Nominal specific energy (K) for a reference MRR and wheel

velocity [J/mm3]; n (exponential correction for specific energy (0:1)); Kc (contact stiffness) [N/mm]; µ ratio between tangential and normal components of grinding

force;Process parameters as model input

Vw (worpiece feed velocity) [mm/s] a (infeed) [mm] VT (workpiece traverse velocity) [mm/s]

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Model description

A local force model for tangential and normal cutting forces, needed to remove each volume element of the z-buffer, is introduced. It is based on the definition of an actual specific energy associated to the removal:

; i

i i in t n

s

Ec MRRf f f

V

• Ec: nominal specific energy• MRRi: material removal rate associated to the considered ith volume element• Vs: wheel peripheral velocity• µ: ratio between the normal and tangential force components

niEc hKnowing that , it yields

n

i

s

MRREc K

V

10

tfnf

Wheel

Workpiece

1iz nTOTf

tTOTf

iz

y

O

MRR computation and force integration

Model description

1

2i i iz zV y x

ii V

MRRt

1i

TOT ii f f R

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Model description

c

in

ii K

Frr

2

1

ˆ

1

iic

in

ini

n

rrK

F

FF

Due to normal force, the grinding grits are subject to a displacement that can be modeled by means of a so-called contact stiffness Kc. In this model it is assumed that each grain of the surface of the wheel is supported by a single linear spring.The reduced local infeed can be expressed as it follows:

The corresponding normal force is:

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Model description

Example of result

0 0.05 0.1 0.15 0.20

200

400

600Forces - Par: 10 2 0.02 500 0 600 1

time[s]

No

rmal

Fo

rce[

N]

0 0.05 0.1 0.15 0.20

100

200

300

time[s]

Tan

gen

tial

Fo

rce[

N]

transient beviour due to wheel entrance

[mm]

Workpiece surface representation

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wMRR baV

Experimental campaign

Model calibration is performed exploiting stable passes: vibration level is monitored in order to check its negligibility. In such a condition, the MRR is given here below:

lnln ln ln ln

ln ln ln lnln

ni wi si i

t i wi si i

KbF V V a

F V V a

1 0

1 -1

; wn t n

s

VF Kb a F F

V

where b is the width of cut, a the actual infeed and Vw the workpiece velocity. The force model converges to the following well-known expression [Inasaki, 1977]

Exploiting a logarithmic transformation, the model parameters can be identified solving the following linear regression starting from grinding force measurements and process parameters Vw, Vs and ai:

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The experimental campaign for model parameters identification and validation has been conducted on an Ermando Rosa Iron™ (with an aluminum oxide wheel, resin bonded, by Rappold™ (dimension: 400x57x127, code: 7A36IBJ15), characterized by a quite large grit size and a soft grade.

The grinding forces were measured by means of a Kistler™ piezo dynamometer 9255B connected to a National Instrument™ DAQ (NI9215). The workpiece was constituted by a block of low-carbon steel (Fe510 - EN10027) with more or less the same dimensions of the dynamometer (260x210x40mm). The lubricant fluid was a Castrol SYNTILO 81E (5%).

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Machine dynamics in feed and infeed directions (X and Z respectively, including the cross terms) have been characterized by hammer test at wheel hub. Then, a modal parameters identification has been performed using SDTools™ software package, obtaining a MIMO state-space model to be imported in Simulink™ environment.

20 40 60 80 100 120 140 160 180

10-8

mod

Dynamic compliance at spindle hub

20 40 60 80 100 120 140 160 180-200

0

200

deg

Freq. [Hz]

FRF XZFRF ZZFRF XX

The total static compliance is about 30N/µm. This data has been exploited to estimate the actual infeed – that is an input of the identification system – from normal force measurement, instead of measuring it directly. Contact stiffness has been identified via FEM model.

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48 grinding tests

Parameter Name Level 1 Level 2 Level 3 Level 4

Nom. Infeed (mm) 0.005 0.01 0.015 0.02

Table vel. (m/min) 5 10 15 20

Wheel vel. (rpm) 1277 1322 1490 -

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Mea

n nor

mal

Force

Z [N

]

Tests#

Measurement SimulatedMean Normal Force [N]

No

rmal

fo

rce

[N]


Mean Normal Force [N]Some problems are related to the force shape, that exhibits an anomalous

curved behaviour …

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Dynamic validation

An artificial wheel unbalance has been introduced during the cutting tests in order to induce cutting vibrations: three values of unbalance have been tested: 80/160/240 µm

0.5 1 1.5 2 2.5 3

-300

-250

-200

-150

-100

-50

0

Test #1 - Unbalance=0.08mm - Vs=1340rpm Ae=0.02mm Vw=5m/min

time [s]

Forc

e X

(ta

ngentia

l) [N

]

MeasuredSimulationMeasured filtered at 40Hz

Comparison between measured and simulated force with a wheel unbalance (80µm), Vs=1340rpm, anom=0.02mm,Vw=5m/min

The maximum residual error on the 2 force components for all the 3 unbalances is about 10%

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Vibrations @ 22Hz (wheel frequency)

λ=Vw/f=5*(1000/60)/22=3.78mm

Simulated peak-to-peak=2µm

Measured peak-to-peak=1.6µm

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Some evidences of a non-regenerative instability

Let a single pass of surface grinding be considered, after a wheel dressing and balancing. It means:- No wheel regenerative chatter because wheel is ideal;- No wheel unbalance- No workpiece regenerative chatter because a single pass is considered

Dw [mm] b [mm] K [J/mm3] µ Ωwheel [rpm] Vw [m/min] a [mm]

600 100 30 1.51000

(positive)32 0.01

Parameters

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Some evidences of a non-regenerative instability

Vibrations @ 30Hz

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Conclusions and future developments

A surface grinding model has been developed, able to:

• Reproduce grinding process vibrations related to machine-process dynamic interaction (i.e. unbalance and grinding chatter);

• Graphical representation of the workpiece surface finish, directly comparable with the real macro topography, as it appears during visual inspection;

• Easy exploitability in an integrated mechatronic simulation environment to include any possible machine tool (with drives) dynamics;

Some evidences of a non-regenerative instability have been pointed out.

Future developments

An analytical study of a possible phenomenon entailing a non-regenerative chatter occurrence will be undertaken;

Wheel wear model will be introduced, together with a fast experimental procedure to identify G-ratio.

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Thank you for the attention!