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Thermal network-based compensation model for a vertical machining center subjected to ambient temperature fluctuations

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Abstract

Thermal influences, on and by the machine tool are one of the main reasons for the machining error. Although both the internal and the external heat sources lead to the thermal error, their relative proportion is typically dependent on the operating conditions such as machining parameters, the duration of machining and availability of temperature-controlled space to name a few. Literature survey reveals that a significant portion of the research either addresses the effects of internal heat sources or a combination of internal and external heat sources since the de-facto standard is to commission the machine tool in a temperature-controlled space. However, in this work, only the influence of external heat sources, predominantly caused by ambient temperature variations onto the distortions observed at the Tool Center Point (TCP) is considered. Smart sensory device such as Resistance Temperature Detector (RTD) sensor data is used for the modelling of thermal distortion due to external heat sources. The model is inherently based on the development of a thermal network using a lumped system approach for the estimation of temperatures of machine tool components and then the TCP distortion using the construction relation. Further, the model is modified through the introduction of two aspects: first is the addition of thermal contact conductance as the machine tool components are practically connected; and the second is the parameterization of free convection heat coefficient from being a stationary value to a function of the ambient temperature. The proposed method is then applied to predict the thermal error on a vertical machining center subjected to environmental temperature variation. The results show that the model considering a combination of the thermal contact conductance and parameterized free convection coefficient leads to a closer agreement with the experimental data. The strategy along with a thermal compensation technique presented in this research successfully lead to the improved machining precision (approximately 70% of the original thermal error is addressed across the combinations) without a need of a conditioned environment for C-frame type vertical machining centers.

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Abbreviations

α :

Thermal expansion coefficient (m/mK)

l, u :

Lower and upper bound

δ xe, δ ye, δ ze :

Measured thermal distortion in X-, Y-, Z-axes respectively (μm)

δ xp, δ yp, δ zp :

Predicted thermal distortion in X-, Y-, Z-axes respectively (μm)

δ y(error), δ z(error) :

Residual thermal distortion, i.e., error after compensation in Y-, Z-axes respectively (μm)

γ xe, γ ye :

Measured angular distortion about X- and Y-axes respectively (μrad)

ρ :

Density of component (kg/m3)

σ :

Equivalent root mean square surface roughness (m)

C p :

Specific heat of component (J/kgK)

D a, ... , D e :

Measured thermal displacement from sensors Sa, ..., Se respectively (μm)

\(E^{\prime }\) :

Equivalent elastic modulus (N/m2)

h :

Thermal convection coefficient (W/m2K)

h ∗ :

Scalar multiplier (W/m2K2)

k s :

Equivalent thermal conductivity (W/mK)

k :

Thermal conductivity (W/mK)

L c :

Characteristic length (m)

P :

Contact pressure (N/m2)

r ij, A ij :

TCC and contact area at the interface of components i and j respectively (W/m2K, m2)

T e :

Ambient temperature (°C)

T i :

Temperature of ith component (°C)

V, A s :

Volume (m3) and effective convective heat transfer area (m2) respectively

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Acknowledgements

MNK and HAS acknowledge the Advanced Machine Tool Testing Facility (AMTTF) for providing a thermal chamber to perform experiments. Further, they thank Mr. Srinivas N. Grama and Mr. Ashvarya Mathur of Dr. Kalam Centre for Innovation, Bharat Fritz Werner Ltd., for their help with the coding, conduction of experiments, manuscript preparation as well as proof-reading of the manuscript.

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  1. Dr. Kalam Centre for Innovation, Bharat Fritz Werner Ltd., Off Tumkur Road, Bengaluru, Karnataka, 560022, India

    Mallinath N. Kaulagi & Harshad A. Sonawane

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  1. Mallinath N. Kaulagi
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Correspondence to Mallinath N. Kaulagi.

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Kaulagi, M.N., Sonawane, H.A. Thermal network-based compensation model for a vertical machining center subjected to ambient temperature fluctuations. Int J Adv Manuf Technol 124, 3973–3994 (2023). https://doi.org/10.1007/s00170-021-08241-6

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