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Input attribute optimization for thermal deformation of machine-tool spindles using artificial intelligence

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Abstract

The heat generated due to internal and external rotating components, electrical parts, and varying ambient temperatures can cause thermal deformations and significantly impact the precision of machine tools (MTs). Thermal error is crucial in industrial processes, corresponding to approximately 60–70% of MT errors. Accordingly, developing an accurate thermal error prediction model for MTs is essential for their high precision. Therefore, this study proposes an artificial neural network (ANN) model to predict the thermal deformation of a high-speed spindle. However, an important feature for the development of a reliable prediction model is the optimization of the input parameters such that the model generates accurate predictions. Hence, the development of an algorithm to determine the optimal input parameters is essential. Therefore, a genetic algorithm (GA)-based optimization model is also developed in this study to select the optimal input combinations (supply coolant temperature, coolant temperature difference between the inlet and outlet of the spindle, and supply coolant flow rate) for different spindle speeds ranging from 10,000 to 24,000 rpm in increments of 2000 rpm. The R2 values of the ANN prediction model are in the range of 0.94 to 0.98 for different spindle speeds. Furthermore, the optimized input parameters are used in single- and dual-spindle systems to verify the accuracy of the developed model as per ISO 230-3. For a single-spindle system, the thermal deformation prediction accuracy of the developed model is in the range of 96.26 to 98.82% and within 1.04 μm compared with the experimental findings. Moreover, when applied to a dual-spindle system, the model’s accuracy is improved by 7.31% compared with that of the variable coolant volume (VCV) method. The maximum deviation of the dual-spindle system can be controlled to within 2.52 μm using the optimized input parameters for a single-spindle system without further optimizing the parameters. The results show that the proposed input attribute optimization (IAO) model can also be adopted for dual-spindle systems to achieve greater prediction accuracy and precision of the machining process, and one industrial cooler can be used for multiple spindles of the same type. In dual-spindle systems operating at different spindle speeds, the power consumption could be reduced by 11% to 34%, and the total lifetime CO2 emissions could be reduced from 72,981 to 52,595.5 kg. These substantial reductions in energy consumption and CO2 emissions highlight the potential of dual-spindle systems to contribute to sustainable manufacturing.

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Data availability

Data will be made available on request.

Abbreviations

ANN:

Artificial neural network

GA:

Genetic algorithm

ISO:

International Organization for Standardization

MT:

Machine tool

VCV:

Variable coolant volume

IAO:

Input attribute optimization

CCV:

Constant coolant volume

PID:

Proportional–integral–derivative

FEM:

Finite element method

FDEM:

Finite difference element method

AI:

Artificial intelligence

BR:

Bayesian regularization

BP:

Backpropagation

IPSO:

Improved particle swarm optimization

SOM:

Self-organizing feature map

FFNN:

Feedforward neural network

MA:

Moving average

LR:

Linear regression

AR:

Autoregression

SGNN:

Serial gray neural network

PGNN:

Parallel gray neural network

BAS:

Beetle antennae search

ANFIS:

Adaptive neuro-fuzzy inference system

SVD-AUKF:

Singular value decomposition-adaptive unscented Kalman filter

LASSO:

Least absolute shrinkage and selection operator

XGBoost:

Extreme Gradient Boosting

RF:

Random forest

SA-PSO-SVR:

Simulated annealing-particle swarm optimization and support vector regression

GPR:

Gaussian process regression

MSE:

Mean squared error

RWS:

Roulette wheel selection

WOA:

Whale optimization algorithm

BOA:

Butterfly optimization algorithm

GS:

Gravitational search

IPO:

Inclined planes system optimization

∆Y :

Overall uncertainty

∆x n :

Individual variable uncertainty

H j :

jth neuron in the hidden layer

i :

Index of neurons in the input layer

j :

Index of neurons in the hidden layer

k :

Index of neurons in the output layer

f :

Transfer function

a j :

Threshold value of the jth neuron in the hidden layer

b k :

Threshold value of the kth neuron in the output layer

Q ij :

Weight between the ith and jth neurons

Q ik :

Weight between the jth and kth neurons

O k :

kth neuron in the output layer

e k :

Error between the predicted and desired outputs

P k :

Predicted output

Y k :

Desired output

N :

Number of samples

P i :

Selection probability of the ith individual

f i :

Fitness value of the ith individual

f j :

Fitness value of the jth individual

n :

Total number of individuals

δ z :

Thermal deformation along the Z-axis

m :

Axis direction

t :

Index of heat sources

l :

Total number of deformational components

δ zt :

Thermal deformation along the Z-axis due to the tth heat source

ε :

Strain

ε zt :

Strain along the Z-axis due to the temperature change of the tth heat source

∆T t :

Temperature difference between the initial and steady states for the tth heat source

∆T base :

Change in the temperature of the base

∆T sp :

Change in the temperature of the spindle

∆T m :

Change in the temperature of the motor

∆T c :

Change in the temperature of the coolant

ε z ,base :

Strain along the Z-axis due to the temperature change of the base

ε z ,sp :

Strain along the Z-axis due to the temperature change of the spindle

ε z ,m :

Strain along the Z-axis due to the temperature change of the motor

ε z ,m,sp :

Strain along the Z-axis due to the temperature changes of the motor and spindle

α :

Thermal expansion coefficient

L :

Length of a system component

A :

Accuracy

AI :

Accuracy improvement

Number of inputs:

3

Number of hidden layers:

14

Number of output layers:

1

Max. number of epochs:

1000

Learning rate:

0.1

Accuracy:

0.001

Population size:

38

Number of generations:

100

Crossover rate:

0.2

Mutation rate:

0.1

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Funding

This work was supported by the National Science and Technology Council (Ministry of Science and Technology), Taiwan, under Grant MOST 109-2622-E-167-015.

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Authors and Affiliations

  1. Graduate Institute of Precision Manufacturing, National Chin-Yi University of Technology, Taichung, 41170, Taiwan

    Swami Nath Maurya, Win-Jet Luo, Prateek Negi & Pei-Tang Wang

  2. Department of Refrigeration, Air Conditioning & Energy Engineering, National Chin-Yi University of Technology, Taichung, 41170, Taiwan

    Bivas Panigrahi

Authors
  1. Swami Nath Maurya
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  2. Win-Jet Luo
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  3. Bivas Panigrahi
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  4. Prateek Negi
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  5. Pei-Tang Wang
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Contributions

Material preparation, data collection, and analysis were performed by Swami Nath Maurya and Win-Jet Luo. Swami Nath Maurya and Win-Jet Luo wrote the first draft of the manuscript; review and editing were done by Swami Nath Maurya, Win-Jet Luo, and Bivas Panigrahi, and all the authors commented on the current version of the manuscript. All the authors have read and approved the final manuscript.

Corresponding author

Correspondence to Win-Jet Luo.

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Maurya, S.N., Luo, WJ., Panigrahi, B. et al. Input attribute optimization for thermal deformation of machine-tool spindles using artificial intelligence. J Intell Manuf (2024). https://doi.org/10.1007/s10845-024-02350-1

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