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Active temperature control method based on time grating principle for the feed system of precision machine tool and its application

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Abstract

Variations in running conditions cause fluctuation in the temperature field of precision machine tools, which inevitably results in thermal errors. To meet the demands of dynamic and time-varying temperature control capability, an active temperature control (ATC) method based on time grating principle is proposed, and the ATC system is developed. The ATC system contains main-loop and sub-loops. The oil target temperature in the sub-loop is determined according to the running parameters and the matching principle of the generalized heat generation–dissipation power. In accordance with the time grating principle, dynamic and differential oil temperature control of each sub-loop is achieved via the inlet time regulation of high-temperature (H-t) or low-temperature (L-t) oil in the main-loop. The main-loop H-t and L-t oil target temperatures are determined by the target range of the sub-loop temperature. The dynamic distribution of the refrigeration capacity and proportional heating mode is adopted to control the temperatures of H-t and L-t oil. By focusing on the feed system of precision machine tool, we carry out both dynamic simulation study and verification experiments, and the results show that the ATC method and system can effectively regulate the temperature field of precision machine tools, thus improving the thermal accuracy of the precision machine tool.

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Data availability

All data generated or analysed during this study are included in this article.

Abbreviations

ATC:

Active temperature control

CTC:

Constant temperature cooling

H-t:

High-temperature

L-t:

Low-temperature

RS:

Refrigerated state

PPP:

Volumetric diagonal (positive direction along the three axes)

ZPE:

Z-axis positioning error

c oil :

Oil combining specific heat (J/(kg·°C))

d hf :

Characteristic dimension (m)

e ht :

H-t oil temperature error (°C)

e lt :

L-t oil temperature error (°C)

e st :

Sub-loop oil temperature error (°C)

F N :

Pressure on the guideway (N)

H :

System heating capacity (W)

H f :

Air convection heat transfer coefficient (W/(m2·°C))

h 1 :

Specific enthalpy of the refrigerant vapour at the compressor inlet (J/kg)

h 2 :

Specific enthalpy of the refrigerant at the compressor outlet (J/kg)

h 4 :

Specific enthalpy of the refrigerant vapour at the evaporator inlet (J/kg)

K mhp :

Proportional amplification coefficient of H-t in the main-loop

K mrrh :

Main-loop H-t oil time regulation ratio

K mrrl :

Main-loop L-t oil time regulation ratio

K sp :

Proportional amplification coefficient of the sub-loop

K srr :

Sub-loop time regulation ratio

k mh :

Ratio of the energy transferred to the oil by the H-t oil pump

M b :

Bearing friction torque (N·mm)

M D :

Driving torque (N·mm)

M 1 :

Bearing torque in relation to bearing load (N·mm)

M 0 :

Bearing torque independent of the bearing load (N·mm)

M P :

Ball spiral resistance torque (N·mm)

M T :

Motor output torque (N·mm)

N u :

Nusselt number

n :

Bearing speed (r/min)

n h :

Number of sub-loops through the H-t oil

n l :

Number of sub-loops through the L-t oil

n mn :

Main-loop interval partition value

n sub :

Sub-loop interval partition value

P :

Compressor theoretical motor power (W)

P b :

Bearing heat generation power (W)

P eht :

Electric heater heating power (W)

P env :

Heat dissipation power carried away by the surrounding environment (W)

P fs :

Generalized heat generation power estimation of the feed system (W)

P bs :

Ball screw–nut pair heat generation power (W)

P m :

Motor heat generation power (W)

P ohd :

Oil heat dissipation power (W)

P ph :

H-t oil pump input power (W)

P phg :

The heat-generating power of heat transfer position (W)

P s :

Guide slider heat generation power (W)

P sth :

Sub-loop thermal power (W)

P str :

Power that causes the temperature rise of the feed system structural parts (W)

p mh :

H-t oil pump outlet pressure (Pa)

Q :

System refrigeration capacity (W)

q mh :

H-t oil flow in the main-loop (L/min)

q ml :

L-t oil flow in the main-loop (L/min)

q soil :

Sub-loop oil flow (L/min)

R mt :

Main-loop temperature deviation range

T hre :

H-t return oil temperature (°C)

T in :

Oil temperatures at the ball screw inlet (°C)

T lre :

L-t return oil temperature (°C)

T mha :

Actual oil temperature at the outlet of the H-t oil pump (°C)

T mhd :

Derivative time of H-t in the main-loop (s)

T mhi :

Integral time of H-t in the main-loop (s)

T mhsa :

Main-loop oil simulation temperature value at the outlet of the H-t oil pump (°C)

T mht :

Target temperature of the H-t oil in the main-loop (°C)

T mhtsa :

Oil temperature after refrigeration or heating in the H-t oil tank (°C)

T mla :

Actual oil temperature at the outlet of the L-t oil pump (°C)

T mlsa :

Main-loop oil simulation temperature value at the outlet of the L-t oil pump (°C)

T mlt :

Target temperature of the L-t oil in the main-loop (°C)

T mltsa :

Oil temperature after refrigeration or heating in the L-t oil tank (°C)

T out :

Oil temperatures at the ball screw outlet (°C)

T sa :

Sub-loop oil actual temperature (°C)

T sas :

Actual temperature simulation value of a sub-loop oil (°C)

T sd :

Derivative time of the sub-loop (s)

T si :

Integral time of the sub-loop (s)

T st :

Sub-loop oil target temperature (°C)

t i :

Unit time interval (s)

t mcc :

Main-loop temperature control cycle (s)

t scc :

Sub-loop temperature control cycle (s)

U(t):

Sub-loop control output (°C)

U(t)ul :

Upper limit of the output (°C)

U(t)ll :

Lower limit of the output (°C)

V mt :

Mixed oil tank volume (L)

V oil :

Volume of the oil tank (L)

V sc :

Sub-loop control vector

v s :

Relative velocity of guide slide (m/s)

η :

Motor mechanical efficiency

η e1 :

Electrical efficiency

λ f :

Thermal conductivity between the feeding system components and the air (W/(m•K))

μ :

Friction coefficient between slider and guide rail

ρ oil :

Oil density (kg/m3)

∆T mh :

The temperature rise of the H-t oil through the pump (°C)

∆T oil :

Temperature difference between oil inlet and outlet (°C)

Δt cr :

Refrigeration rate of the oil tank (°C/min)

Δt hr :

Heating rate of the oil tank (°C/min)

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Funding

This work is supported by the Project of Large and Medium-sized CNC Machine Tools Key Manufacturing Equipment for the Machine Tool Industry (Grant numbers TC210H035-008)

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Authors and Affiliations

  1. Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin, 300354, China

    Yingjie Zheng, Weiguo Gao, Dawei Zhang, Tian Huang, Xingyu Zhao & Faze Chen

  2. School of Engineering, University of Warwick, Coventry, CV4 7AL, UK

    Tian Huang

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  1. Yingjie Zheng
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  2. Weiguo Gao
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  4. Tian Huang
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Contributions

Methodology, data collection, and analysis were performed by Yingjie Zheng. Material preparation, data curation, and supervision were performed by Weiguo Gao and Dawei Zhang. Validation and investigation were performed by Tian Huang, Xingyu Zhao, and Faze Chen. The first draft of the manuscript was written by Yingjie Zheng; all authors read and approved the manuscript.

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Correspondence to Weiguo Gao.

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Zheng, Y., Gao, W., Zhang, D. et al. Active temperature control method based on time grating principle for the feed system of precision machine tool and its application. Int J Adv Manuf Technol 124, 1537–1555 (2023). https://doi.org/10.1007/s00170-022-10594-5

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