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Mechanistic cutting force model for rotary ultrasonic machining of rocks

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Abstract

Cutting force is the predominant output variable in rotary ultrasonic machining (RUM). It dictates other output variables, such as tool wear, cutting temperature, edge chipping, etc. It is desirable to develop a mechanistic model to predict cutting force and reveal the underlying cutting tool-workpiece interaction in RUM. Numerous researchers have developed theoretical approaches to predict cutting force in RUM; nevertheless, the combined effects of material removal on cutting force model have not been investigated. RUM has been used for machining rocks in several recent experimental investigations. However, there are no reports on cutting force model for RUM of rocks. This work bridges the gap and reports an improved mechanistic cutting force model. The model is derived based on the ductile mode removal and brittle fracture mode removal of rock under the indentation of a single abrasive particle. The cutting force model for RUM of rocks is then developed by aggregating the effects of all active abrasive particles bonded to the tool end face. Based on this model, the relationships between input variables (tool rotation speed, feedrate, ultrasonic vibration amplitude, abrasive size, abrasive concentration, and tool size) and cutting force are predicted. Experiments have been conducted and the experimental results agree well with the model predicted trends.

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Abbreviations

A :

Ultrasonic vibration amplitude (m)

A 0 :

Area of the tool end face (m2)

C a :

Abrasive concentration

C h :

Lateral crack depth (m)

C L :

Lateral crack length (m)

\( {d}_a^1 \) and \( {d}_a^2 \) :

Abrasive sizes related to the pore sizes of sieves (m)

d c :

Critical depth of cut for brittle-to-ductile transition (m)

do and di :

Outer and inner diameters of the tool (m)

E :

Elastic modulus of the rock

F :

Cutting force measured during RUM of rock (N)

F i :

Maximum impact force applied by one abrasive particle (N)

F m :

Maximum impact force (N)

f :

Ultrasonic vibration frequency (Hz)

f r :

Feedrate (m/s)

h max :

Maximum protrusion height (m)

H v :

Vickers hardness of the rock (Pa)

k :

Proportionality parameter

K IC :

Fracture toughness of the rock (Pa‧m1/2)

K Id :

Dynamic fracture toughness (Pa‧m1/2)

L :

Effective cutting distance (m)

L b :

Brittle fracture mode cutting distance (m)

L d :

Ductile mode cutting distance (m)

MRR a :

Material removal rate of one abrasive particle (m3/s)

MRR c :

Material removal rate of the tool (m3/s)

N :

Number of abrasive particles on the tool end face

N a :

Number of effective abrasive particles on the tool end face

R d :

Distance of an abrasive particle to the center of the tool (m)

S :

Tool rotation speed (rpm)

S1 and S2 :

Standard mesh numbers

S a :

Abrasive size (mm)

t :

Time (s)

V :

Actual volume of material removed by one abrasive particle during one ultrasonic vibration cycle (m3)

V b :

Volume of brittle mode material removal (m3)

V d :

Volume of ductile mode material removal (m3)

V Δt :

Volume of material removed by one abrasive particle during effective cutting time (m3)

v :

Poisson’s ratio of the rock

z 0 :

Penetration depth (m)

α :

Geometric factor of the shape of the abrasive particle

β :

Semi-angle between two opposite edges of an abrasive particle (Degree)

β 0 :

Half-top angle of an abrasive particle (Degree)

λ 0 :

Integrative factor

μ :

Mean value of abrasive protrusion height

ρ :

Density of the abrasive material (g/mm3)

σ :

Standard deviation of protrusion heights

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Acknowledgments

The authors would like to thank Dr. Christopher Jones (Department of Civil Engineering at Kansas State University) for his assistance with nano-dynamic mechanical analysis.

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Authors and Affiliations

  1. Department of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, KS, 66506, USA

    P. K. S. C Fernando & Meng Zhang

  2. Department of Industrial and Systems Engineering, Texas A & M University, College Station, TX, 77843, USA

    Z. J. Pei

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Contributions

Palamandadige Fernando analyzed the rock material removal mechanisms, developed the model, conducted the experiments, collected and analyzed the data, and wrote the manuscript. The conception and the design of experiments were discussed by all authors. Meng Zhang and Zhijian Pei provided critical revision.

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Correspondence to Meng Zhang.

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Fernando, P.K.S.C., Pei, Z.J. & Zhang, M. Mechanistic cutting force model for rotary ultrasonic machining of rocks. Int J Adv Manuf Technol 109, 109–128 (2020). https://doi.org/10.1007/s00170-020-05624-z

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