The objective of the work is providing design criteria for surface grinding machine structures, in order to prevent the onset on undesired vibrations during grinding, vibrations that are often due to a specific dynamic instability that can affect these kind of machines.

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Design criteria for grinding
machine dynamic stability
Marco Leonesioa, Giacomo Bianchia, Nicola Lussorio Caub
aInstitute of Intelligent Industrial Technologies and Systems for Advanced Manufacturing
National Research Council of Italy (STIIMA – CNR)
bPhiDrive s.r.l.

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Objective
Chatter issue in grinding machines
Steps to obtain an improvement of grinding machine structural design
Leonesio M. et al., Design criteria for grinding machine dynamic stability

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Leonesio M. et al., Design criteria for grinding machine dynamic stability
Surface grinding machine
Typical work defect: wavy
surface due to dynamic
instability onset (chatter)
How should the machine
structure be designed in
order to limit chatter
onset?

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Leonesio M. et al., Design criteria for grinding machine dynamic stability
Objective
 Stability analysis of grinding process based on target process parameters and machine structural
dynamics by design (FEM);
 Identification of the critical eigenmode and its characteristics (geometry and modal parameters);
 Guidelines on how the critical eigenmode should be modified to match the target grinding operation.
The stability analysis exploits the Nyquist criterion for MIMO systems, taking into account both regenerative
chatter and a particular kind of force-field instability analysed by the authors*.
*Leonesio, M., Parenti, P., Cassinari, A., & Bianchi, G. (2014). Force-field instability in surface grinding. The International
Journal of Advanced Manufacturing Technology, 72(9-12), 1347-1360, doi: 10.1007/s00170-014-5725-7
The objective is pursued through the following steps:

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Grinding model
2 Dofs linear grinding force model
Leonesio M. et al., Design criteria for grinding machine dynamic stability

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Leonesio M. et al., Design criteria for grinding machine dynamic stability
Grinding model
sgnx
t
y s
f MRR
k
f V
      
      
       
     w w w w wMRR b V x a y y aD baV b a x V z z aD            
a: actual infeed
b: width of cut
Ω: wheel velocity
kt: tangential grinding coefficient
µ: force ratio between normal and tangential component of grinding force
fx: grinding force in tangential direction
fy: grinding force in normal direction
Vw: workpiece feed velocity
ẋ, x: velocity and displacement perturbation along feed direction
ẏ, y: velocity and displacement perturbation along normal direction
fx , δx , Vw
a
fy , δy
+
b
Ω
with
0
0
x x
vel pos
y y
f f x x
f f y y
          
         
          
P P
 
 
sgn sgn0 sgn
: ; :
0
eqt w t
pos vel
s s eq
a aDbk V bk
V V a aD  
            
P Pwith

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Leonesio M. et al., Design criteria for grinding machine dynamic stability
Grinding model
τ: wheel revolution period (1/Ω)
Gr: one-rev. grinding ratio
[Hw]: wheel compliance matrix
kc: contact stiffness
Wheel regeneration
(initial focus on surface grinding)
Process
Compliance at wheel
     , : (s, ) pos vels s s  L R P P H   det , 0  I L
Open-loop Transfer Function Stability limit according to Nyquist criterion

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Stability analysis
Distinction between regenerative and non-regenerative chatter
Relationship between non-regenerative chatter and eigenmode characteristics
Necessary condition for non-regenerative instability
Leonesio M. et al., Design criteria for grinding machine dynamic stability

9. Space for VideoClick to edit Master title style Space for VideoStability analysis
Leonesio M. et al., Design criteria for grinding machine dynamic stability
    , : det , 0a a ak k k      I L
    ˆ: det 0b b bk k k   I L 
Actual stability limit (with wheel regeneration) depending on
wheel speed:
Fictitious stability limit (canceling out wheel regeneration)
independent on wheel speed:
 ( , )s R I
 min
min
: 1,0a
b
k
Q
k
 
Regeneration merit factor

10. Space for VideoClick to edit Master title style Space for VideoStability analysis
Leonesio M. et al., Design criteria for grinding machine dynamic stability
Eigenmode analysis for force field instability
Let the case Q1 be considered. In this case, the instability is due to particular properties of the process force field, which is
not conservative and allows closed path integrals associated to energy accumulation. Let the energy transferred from the
wheel to the process be expressed:
2
0
:
c
TOT pos vel pos velW W W d dt

      P p p P p p


& &Ñ  
coscos sin
sinsin cos
 
 
I c
J c
A tx
t
A ty
     
     
     
p
Total energy exchange:
WTOT>0  The process dissipates energy (stable process)
WTOT<0  Energy accumulation (instability could occur if
dissipation in the structure is small)
x
y
AIAJ 
Elliptical wheel orbit according
to a given eigenvector

11. Space for VideoClick to edit Master title style Space for VideoStability analysis
Leonesio M. et al., Design criteria for grinding machine dynamic stability
Eigenmode analysis for force field instability
x
y
AIAJ 
WTOT depends on:
1. Process parameters;
2. ellipse axes ratio (AJ/AI);
3. inclination angle .
kt
[J/mm3]
b
[mm]
Vw
[m/s]
Ω
[rpm]
Dw
[m] G a
[mm] μ
30 1 0.53 -1000 600 2.6 0.01 1.4
Example
A necessary conditon for
instability can be established,
that depends only on (AJ/AI)
and .
RESULT:
- There exists a worst  value
- Higher (AJ/AI) ratio increases stability

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Design suggestions
Suggestions for critical eigenmode modification
Application example
Leonesio M. et al., Design criteria for grinding machine dynamic stability

13. Space for VideoClick to edit Master title style Space for VideoDesign suggestions
Leonesio M. et al., Design criteria for grinding machine dynamic stability
Surface grinding machine model
x
y
AIAJ 
Eigenvector
analysis
 AJ/AI
 
Critical mode
Dynamic compliance
at wheel
Strokes specifications are:
- 5500mm for the longitudinal axis X
- 2000mm for the traverse axis Y
- 1025mm for the vertical axis Z

14. Space for VideoClick to edit Master title style Space for VideoDesign suggestions
Leonesio M. et al., Design criteria for grinding machine dynamic stability
Process
parameters
Critical mode
Q is
low?
 Increase dynamic stiffness
 Use a wheel with high G-ratio
yes
Chatter merit factor
(Q)
no
Evaluate necessary condtion
with (AJ/AI) and 
(AJ/AI)
is low?
 Try to increase lumped dampings to
have a more «complex» mode
yes
no  Change inclination  by
displacing mass and
wheel position

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Leonesio M. et al., Design criteria for grinding machine dynamic stability
Stability limit(=0)
Max. poles real part
Stability analysis on a reduced analytical representation of
FEM dynamics and coupling it with the grinding process
model (example of slide 11) without the regenerative
loop
Growth rate of the fastest unstable pole vs (AJ/AI) and .
The necessary condition for instability is satisfied
Analytical verification of necessary condition
Growth rate

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Conclusions
Leonesio M. et al., Design criteria for grinding machine dynamic stability

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Leonesio M. et al., Design criteria for grinding machine dynamic stability
• A stability analysis for grinding operations that relates the stability characteristics of the process to the geometrical
properties of the eigenmodes of the closed loop machine-process system is proposed;
• In case regenerative phenomenon can be neglected, a necessary condition for instability has been identified,
expressed in terms of principal axes ratio and inclination the elliptical trajectory associated to the most critical
eigenmode;
• Suggestions can be provided to machine designer for improving structural dynamic characteristics;
LIMITS
The approach is valid only if the influence of grinding process on wheel open-loop dynamics is negligible. In some
extreme cases, this condition could be not satisfied.

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THANK YOU!
Design criteria for grinding
machine dynamic stability
Marco Leonesioa, Giacomo Bianchia, Nicola Lussorio Caub
aInstitute of Intelligent Industrial Technologies and Systems for Advanced Manufacturing
National Research Council of Italy (STIIMA – CNR)
bPhiDrive s.r.l.