Coupling evaluation for material removal and thermal control on precision milling machine tools

Abstract

Machine tools are one of the most representative machining systems in manufacturing. The energy consumption of machine tools has been a research hotspot and frontier for green low-carbon manufacturing. However, previous research merely regarded the material removal (MR) energy as useful energy consumption and ignored the useful energy consumed by thermal control (TC) for maintaining internal thermal stability and machining accuracy. In pursuit of energy-efficient, high-precision machining, more attention should be paid to the energy consumption of TC and the coupling relationship between MR and TC. Hence, the cutting energy efficiency model considering the coupling relationship is established based on the law of conservation of energy. An index of energy consumption ratio of TC is proposed to characterize its effect on total energy usage. Furthermore, the heat characteristics are analyzed, which can be adopted to represent machining accuracy. Experimental study indicates that TC is the main energy-consuming process of the precision milling machine tool, which overwhelms the energy consumption of MR. The forced cooling mode of TC results in a 7% reduction in cutting energy efficiency. Regression analysis shows that heat dissipation positively contributes 54.1% to machining accuracy, whereas heat generation negatively contributes 45.9%. This paper reveals the coupling effect of MR and TC on energy efficiency and machining accuracy. It can provide a foundation for energy-efficient, high-precision machining of machine tools.

Graphical abstract

Keywords

machine tools / cutting energy efficiency / thermal stability / machining accuracy / coupling evaluation

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Nomenclature

a_{\mathrm{e}}	Cutting width
a_{\mathrm{f}}	Feed rate per tooth
a_{\mathrm{p}}	Depth of cut
c_{\mathrm{A}}	Specific heat capacity of compressed air
c_{\mathrm{l}\mathrm{i}}	Specific heat capacity of auxiliary liquid
CF, xF, yF, uF, qF, wF, and k_{F_{\mathrm{c}}}	Cutting coefficients
CO{P}^j	Coefficient of performance of the jth TC unit
d_0	Diameter of cutting tool
E_{\mathrm{b}}	Energy consumed by basic functional units
E_{\mathrm{c}}	Cutting energy
E_{\mathrm{f}}	Energy requirements of feed motors during noncutting stage
E_{\mathrm{m}\mathrm{s}}	Energy requirement of the main spindle during noncutting stage
E_{\mathrm{M}\mathrm{R}}	Energy consumed by MR units
E_{\text{MR-c}}	Constant energy requirement of main spindle and feed axes during noncutting stage
E_{\mathrm{t}\mathrm{c}}	Energy requirement of the tool change system
E_{\mathrm{t}}	Total energy consumption of machine tool
E_{\mathrm{T}\mathrm{C}}	Energy consumed by TC units
E_{\text{TC-u}}^j	Electricity consumption of the jth TC unit
F_{\mathrm{c}}	Cutting force
G_{\mathrm{w}}	Machining accuracy
\mathrm{\Delta }L	Thermal deformation of a certain component
{\dot{m}}_{\mathrm{A}}	Mass flow rate of compressed air
{\dot{m}}_{\mathrm{l}\mathrm{i}}	Mass flow rate of auxiliary liquid
{\dot{m}}_{\mathrm{h}\mathrm{a}}	Mass flow rate of the hot air flowing into the electrostatic air filter
n	Rotation speed of the main spindle
n_1	Number of nozzles
P_{\mathrm{b}}	Power of basic operation
P_{\mathrm{c}}	Cutting power
P_i	Power of the ith MR unit
P_k	Power consumption of the kth basic unit
P_{\mathrm{l}}	Power loss related to MR
P_{\mathrm{l}}^{\mathrm{a}}	Power loss of amplifier
P_{\mathrm{l}}^{\mathrm{i}\mathrm{m}}	Power loss of inner motor
P_{\mathrm{l}}^{\mathrm{m}\mathrm{f}}	Power loss of mechanical transmission chains
P_{\mathrm{M}\mathrm{R}}	Power consumed by MR
P_{\text{MR-c}}	Power consumed by MR units during noncutting operation
P_{\mathrm{T}\mathrm{C}}	Power consumed by TC
P_{\text{TC-c}}	Power consumed by TC units during cooling operation
P_{\text{TC-s}}	Power consumed by TC units during standby operation
Q_{\mathrm{c}}	Cutting heat
Q_{\mathrm{c}\mathrm{h}}	Heat transferred to chips
Q_{\mathrm{d}}	Heat dissipation of machine tool
Q_{\mathrm{d}}^{\mathrm{c}\mathrm{a}}	Heat taken away by compressed air
Q_{\mathrm{d}}^{\mathrm{h}\mathrm{a}}	Heat dissipation of hot air
Q_{\mathrm{d}}^j	Heat taken away by the jth TC unit
Q_{\mathrm{d}}^{\mathrm{l}\mathrm{i}}	Heat taken away by auxiliary liquid
Q_{\mathrm{g}}	Heat generation of all heat sources
{\dot{Q}}_{\mathrm{g}}^{\mathrm{m}\mathrm{s}}	Heat generation of main spindle system
Q_{\mathrm{t}}	Heat transferred to cutting tool
Q_{\mathrm{w}\mathrm{p}}	Heat transferred to workpiece
t_{\mathrm{c}}	Cutting time
t_{\mathrm{h}\mathrm{a}}	Duration time of hot air
t_i	Operating time of the ith MR unit
t_k	Operating time of the kth basic-unit
t_{\mathrm{l}\mathrm{i}}	Duration time of auxiliary liquid
t_{\mathrm{A}}	Usage time of compressed air
T_{\mathrm{a}}	Ambient temperature
T_{\mathrm{h}\mathrm{a}}	Temperature of hot air
T_{\mathrm{l}\mathrm{i},\mathrm{i}\mathrm{n}}	Input temperature of auxiliary liquid
T_{\mathrm{l}\mathrm{i},\mathrm{o}\mathrm{u}\mathrm{t}}	Output temperature of auxiliary liquid
T_{\mathrm{o}\mathrm{u}\mathrm{t}}	Air temperature at corresponding nozzle
T_{\mathrm{s}}	Temperature inside machine tool
\mathrm{\Delta }T	Temperature rise of a certain component
v_{\mathrm{c}}	Cutting speed
z	Tooth number of milling cutter
\eta	Convert efficiency of mechanical energy to heat
{\eta }_{\mathrm{m}}	Spindle motor efficiency
{\eta }_{\mathrm{M}\mathrm{R}}	Cutting energy efficiency
{\eta }_{\mathrm{T}\mathrm{C}}	Energy consumption ratio of TC
{\delta }_{\mathrm{F}\mathrm{E}}	Flatness error

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51975076 and 52105533). The authors gratefully acknowledge the reviewers and the editors for their insightful comments.

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