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The influence of material stiffness and damping on machining stability in boring tool–workpiece systems using finite element simulation to implement digital twin

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Abstract

Regenerative chatter is a prominent form of vibration in any machining process caused by the waviness of the workpiece surface. During internal turning processes, regenerative chatter constitutes a significant concern due to the highly flexible nature of boring bars and workpieces. As a result, the surface finish is poor, tool wear is accelerated, and machining at a high depth of cut is challenging. Typically, stability lobe diagrams (SLDs), plots of spindle speeds versus depth of cuts, are employed to select stable machining parameters. In the present work, a numerical linear stability analysis of a two-degree-of-freedom finite element model of a boring tool–workpiece system is carried out in the frequency domain to construct SLDs that are utilized to investigate how changing dynamics of the workpiece affect machining stability. The numerical model is validated using an analytical model, and the results of both models are found to be in agreement. Moreover, the results show that the depth of cut of a tool–workpiece system with moderately low and high workpiece stiffness is 11.8% and 16.2% lower than that of a single degree-of-freedom (DOF) system that does not take the workpiece into account. The SLDs of two DOF systems with workpieces of high and very high stiffness are observed to overlap with that of a single DOF system. It is also inferred that the damping ratio of the workpiece has no significant effect on the stability lobes. The machining experiments are conducted on a boring tool–workpiece system, and it is found that the experimental results align with the analytical and numerical findings. Additionally, a digital twin framework based on the computational model is suggested to facilitate the real-time monitoring and optimization of boring processes.

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Abbreviations

A:

Cross-sectional area, (m2)

b:

Width of the chip, (m)

bc :

The critical value of depth of cut, (m)

D:

Shank diameter of boring tool, (m)

Di :

Inner diameter of workpiece, (m)

Do :

Outer diameter of workpiece, (m)

E:

Young’s modulus, (N/m2)

f:

Natural frequency, (Hz)

F(s):

Feed force, (N)

Ff(t):

Dynamic feed force, (N)

Glm,I :

Imaginary part of the elements of the matrix, (G(jω)); l, m represent row and column numbers respectively.

Glm,R :

Real part of the elements of the matrix, (G(jω)); l, m represent row and column numbers respectively.

h(t):

Dynamic depth of cut, (m)

ho :

Nominal depth of cut, (m)

I:

Moment of inertia, (m4)

K:

Stiffness, (N/m)

kf :

Feed force coefficient, (N/m2)

L:

Length of boring tool, (m)

m:

Effective mass of boring tool, (Kg)

m1 :

Effective mass of the boring tool, (Kg)

m2 :

Effective mass of the workpiece, (Kg)

n:

The lobe number

N:

Spindle speed, (rpm)

y:

Displacement, (m)

y1 :

Displacement of the boring tool, (m)

y2 :

Displacement of the workpiece, (m)

ξ:

Damping ratio

ξ1 :

Damping ratio of the boring tool

ξ2 :

Damping ratio of the workpiece

ρ:

Density, (Kg/m3)

τ:

Time delay, (s)

ψ:

The phase angle, (°)

ω1 :

Natural frequency of the boring tool, (Hz)

ω2 :

Natural frequency of the workpiece, (Hz)

ωc :

Chatter frequency, (Hz)

[C]:

Damping matrix

[D]:

Dynamic chip thickness matrix

[G(s)]:

Transfer function matrix

[I]:

Identity matrix

[K]:

Stiffness matrix

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Authors and Affiliations

  1. Department of Mechanical Engineering, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, India

    Saravanamurugan Sundaram, Viswajith S. Nair & Rameshkumar Krishnaswamy

  2. Department of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester, United Kingdom

    Fawas Puthenveetil

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  1. Saravanamurugan Sundaram
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Sundaram, S., Puthenveetil, F., Nair, V.S. et al. The influence of material stiffness and damping on machining stability in boring tool–workpiece systems using finite element simulation to implement digital twin. Int J Interact Des Manuf (2024). https://doi.org/10.1007/s12008-024-01757-7

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