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Cutting model considering damage layer thickness for ultra-precision turning of quartz glass

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Abstract

Quartz glasses have been extensively used for many fields. However, quartz glass is a typical brittle material so that a certain thickness of damage layer appears after conventional mechanical machining. Single point diamond turning (SPDT) is usually employed in the non-ferrous metal machining to achieve nanoscale surface. Recently, there has been an increasing interest in research on the machining of brittle materials SPDT. This paper aims to study the process of turning quartz glass with diamond tools with certain edge radius (several micrometers), in which tool wear is practically taken into consideration. The cutting model is established to estimate the damaged layer thickness on the machined surface through volume of extrusion area. The undeformed chips shape considering the strain rate in this model is obtained by numerical simulation method, which is used to solve the above volume. Then, the experiments of turning quartz glass with different cutting depth, feed rate, and cutting speed are carried out. The experimental results show that the lateral crack depth calculated by the model has the same variation pattern as the surface roughness Sk value, and show good consistence when the feed rate is ranging 1–4 μm/r with the cutting depth which is 2 μm. In addition, the calculation results of the model show that the depth of median crack less than the depth of lateral crack can be achieved with cutting depth ranging 0.2–2 μm while feed rate is 1 μm/r. The research is useful to optimize the turning parameters to reduce the damage layer in quartz glass.

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Data availability

The datasets used or analyzed during the current study are available from the corresponding author or the first author on reasonable request.

Code availability

The code used during the current study is available from the corresponding author or the first author on reasonable request.

Abbreviations

α(P 2):

The difference between the cutting vertex P2 and the cutting vertex of the tool in the cutting depth direction in the normal plane

α p :

Actual cutting depth

α r :

Thickness of unmachinable area after cutting

b :

Depth of lateral crack/depth of lateral crack in the normal plane

c :

Depth of median crack/depth of median crack in the normal plane

D b :

Thickness of damage layer by lateral crack after cutting

D b1 , D b2 , ⋯ , D bn :

Thickness of damage layer caused by lateral crack corresponding to broken chips

D bα :

\(\delta {V}_{sa}\) Corresponding to \({D}_{b}\)

D c :

Thickness of damage layer by median crack after cutting

D c1 , D c2 , ⋯ , D cn :

Thickness of damage layer caused by median crack corresponding to broken chips

D cα :

\(\delta {V}_{sa}\) Corresponding to \({D}_{c}\)

E :

Elastic modulus of workpiece

F n :

Indentation load

f :

Cutting feed rate (per rotation)

H :

Hardness of workpiece

K c :

Static fracture toughness of workpiece

k :

Elastic recovery rate

l 1 :

Arc length of the cutting area on the tool

m :

A parameter

R :

Tool nose radius

R s :

Radius of spherical indenter

r :

Tool edge radius

r a :

Radius of contact area by spherical indenter

r b :

Depth of lateral crack/radius of equivalent hemispherical plastic area

S s :

Area of extrusion area in normal plane

SSD :

Thickness of damage layer caused by median crack in normal plane

t :

Undeformed chips thickness in normal plane

t a :

Undeformed chips thickness in the normal plane at \(a({P}_{2})=a\)

t max :

Maximum undeformed chips thickness

t r :

Thickness of residual part of workpiece after cutting due to elastic recovery

α :

Angle between principal stress direction and tool reference plane

α α :

A compensation coefficient

β :

A parameter

δ V :

Volume of indentation area/volume of extrusion area

δ V 1 , δ V 2 , ⋯ δ V n :

Volume of extrusion area corresponding to broken chips

δ V sa :

Volume of extrusion area at \(a({P}_{2})=a\)

θ :

Angle between normal plane and cutting depth direction

θ s :

Included angle of extrusion area in normal plane

θ sum :

Included angle of total pressed volume in normal plane

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Funding

This research is supported by Engineering Science and Comprehensive Cross Key Projects (grant number 2021YFF0500201, 2021YFF0500202).

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Authors and Affiliations

  1. State Key Laboratory of Tribology in Advanced Equipment (SKLT), Tsinghua University, Beijing, 100084, China

    Yujie Liu, Hao Tong, Guodong Liu, Yong Li & Qifeng Tan

  2. Beijing Key Lab of Precision/Ultra-Precision Manufacturing Equipments and Control, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China

    Yujie Liu, Hao Tong, Guodong Liu, Yong Li & Qifeng Tan

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  1. Yujie Liu
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Contributions

All authors contributed to the investigation, study conception, design, and editing. Material preparation, data collection, and analysis were performed by Yujie Liu and Guodong Liu. Software were performed by Yujie Liu and Qifeng Tan. The first draft of the manuscript was written by Yujie Liu and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Yong Li.

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Liu, Y., Tong, H., Liu, G. et al. Cutting model considering damage layer thickness for ultra-precision turning of quartz glass. Int J Adv Manuf Technol 126, 4087–4100 (2023). https://doi.org/10.1007/s00170-023-11366-5

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