Abstract
Laser cladding is a complex manufacturing process involving more than 19 variables related to laser source, workpiece movement, powder-substrate material combinations, clad geometry, powder flow dynamics, shrouding gas flow and so on. Significant research efforts have been directed to analytical-numerical-empirical modelling of laser cladding and also in-process monitoring and control of the process. Still, due to complicated physics there is a dearth of simple analytical model for estimation of dilution in laser cladding. Its experimental measurement requires suitable micrographs of the clad cross section perpendicular to the clad path. This is a time-consuming and destructive way of measurement. Numerical models are time consuming to evaluate and hence not suitable for fast decision making or real-time control implementation. The analytical models available, despite having many approximations, are a little complicated, require fair amount computer programming and often need suitable prior guessing of range of output parameters for adjustment of constant values in the models. This poses some challenges for use and having an intuitive guidance, for a beginner/unskilled operator. Besides, their complexity may erect barrier in the way of their implementation for real time monitoring and control. This work proposes a simple linear regression model, formed based on energy balance approach, to estimate dilution in laser cladding. After fitting to a set of data, within a suitable process parameter-window, for a particular clad-substrate material combination, this model can estimate dilution as a function of input/easily measureable parameters, viz. laser power, scan speed, clad width and clad height. The model fitted well to the experimental data taken from literature.
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Abbreviations
- \( \lambda \) :
-
dilution (fraction)
- \( A_{\text{c}} \) :
-
clad cross sectional area above initial substrate surface
- \( A_{\text{s}} \) :
-
cross sectional area of clad layer dilution below initial substrate surface
- \( h_{\text{c}} \) :
-
clad height above initial substrate surface
- \( h_{\text{s}} \) :
-
clad layer dilution depth below initial substrate surface
- \( w_{\text{p}} \) :
-
width of the clad pass (perpendicular to the clad velocity vector)
- \( l_{\text{c}} \) :
-
length of the clad pass (along the clad velocity vector)
- \( \eta_{1} \) :
-
fraction of the laser energy being coupled into the cladding process
- \( P \) :
-
laser power
- \( v \) :
-
laser scan speed
- \( \rho^{\text{c}} \) :
-
density of the clad material in solid state
- \( C_{\text{p}}^{\text{c}} \) :
-
specific heat of the clad material in solid state
- \( \rho^{\text{c'}} \) :
-
density of the clad material in liquid state
- \( C_{\text{p}}^{{{\text{c}}{\prime }}} \) :
-
specific heat of the clad material in liquid state
- \( T_{\text{m}}^{\text{c}} \) :
-
melting temperature of the clad material
- \( T_{0}^{\text{c}} \) :
-
initial temperature of the clad material
- \( \rho^{\text{s}} \) :
-
density of the substrate material in solid state
- \( C_{\text{p}}^{\text{s}} \) :
-
specific heat of the substrate material in solid state
- \( T_{\text{m}}^{\text{s}} \) :
-
melting temperature of the substrate material
- \( T_{0}^{\text{s}} \) :
-
initial temperature of the substrate material
- \( \eta_{2} \) :
-
fraction of input energy being conducted into the substrate
- \( C_{1} \), \( C_{2} \), and \( C_{3} \) :
-
constants of regression
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Chakraborty, S.S., Dutta, S. Estimation of dilution in laser cladding based on energy balance approach using regression analysis. Sādhanā 44, 150 (2019). https://doi.org/10.1007/s12046-019-1134-9
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DOI: https://doi.org/10.1007/s12046-019-1134-9