Study of a hollow laser beam for cladding

Abstract

Laser cladding, as a promising manufacturing technology, has been widely used in industry for component recovery and surface modification. In this paper, a hollow laser beam was proposed to optimize the laser intensity distribution. A three-dimensional (3-D) finite element (FE) model was developed using ANSYS to investigate the thermal field in the clad deposited by a hollow laser beam. The thermal results, such as the temperature distribution and the cooling rate, were investigated. The effect of the hollow ratio between the inner and outer radius of the hollow beam on the molten pool shape was also studied. The temperature at the boundary of the molten pool was higher than at the center. A clad with a flat metallurgical bonding was formed. The microstructure in the clad was mainly consisted of fine dendrites except the large columnar structures along the bonding. The hardness distribution of the clad was associated with the grain size distribution and the dilution by the substrate. The molten pool was not able to be generated with a high hollow ratio, while overheated at the center with a low hollow ratio. Based on the comparison with the Gaussian laser beam, the hollow laser beam could effectively alleviate the overheating at the center of the clad.

Appendix

A cylindrical laser beam with the intensity I₀ irradiates a 45° mirror and is reflected onto a parabolic ring mirror, forming a hollow laser beam which is symmetrical to the focal plane, as shown in Fig. 3a. The laser beam profile is characterized by two parts: one is the straight propagation part of the laser (regions I and V) and the other is the Rayleigh range (regions II, III, and IV) when the laser beam is close to the focal point. In the Rayleigh range, the laser beam can be subdivided into two sections: one without intersections of the laser beam (regions II and IV) and one with intersections of laser beam (region III) [20].

In the straight propagation part (regions I and V), the distribution of the laser intensity I is written as [20]

$$ I=2p\frac{\sqrt{2}{H}_1\left({a}_1\hbox{--} H\right){a}_1^2}{r\left|h\right|\left({a}_1^2+2{p}^2\right)}{I}_1 $$

(8)

where $r\in \left(\frac{p^2-{\left(H-\frac{d}{2}\right)}^2}{2p\left(H-\frac{d}{2}\right)}|h\left|,\frac{D}{2H}|h\right|\right),\kern0.5em {a}_1=\frac{p\left(r+\sqrt{r^2+{h}^2}\right)}{\left|h\right|}$, p is the characteristic parameter of the parabolic mirror, h is the axis distance, H ₁ is the Rayleigh length, and H ₂ is the intersection length.

In the Rayleigh region without intersections of laser beam (regions ІІ and IV), the distribution of laser intensity I yields as described in [20]

$$ I=2p\frac{\sqrt{2}{H}_1\left({a}_1\hbox{--} H\right){a}_1^2}{r\left|h\right|\left({a}_1^2+2{p}^2\right)\left[\left(\sqrt{2}-1\right)\left|h\right|+{H}_1\right]}{I}_1 $$

(9)

where $r\in \left(-\frac{d_{\min }}{2}+\frac{\left({H}_1D+H{d}_{\min}\right)\left|h\right|}{2H{H}_1},\frac{d_{\min }}{2}+\frac{\left[{H}_1\left({p}^2-{\left(H\hbox{--} \frac{d}{2}\right)}^2\right)-p\left(H\hbox{--} \frac{d}{2}\right){d}_{\min}\right]\left|h\right|}{2p\left(H\hbox{--} \frac{d}{2}\right){H}_1}\right),\kern0.5em {a}_1=\frac{p\left({b}_1+\sqrt{b_1^2+{H}_1^2}\right)}{\left|{H}_1\right|},\kern0.75em {b}_1=\frac{\sqrt{2}{H}_1r+\left(\frac{\sqrt{2}}{2}{d}_{\min }+\frac{D}{2H}{H}_1\right)\left(\left|h\right|-{H}_1\right)}{\left(\sqrt{2}-1\right)\left|h\right|+{H}_1}$

In the Rayleigh region with intersections of laser beam (region III), the distribution of laser intensity I of the nonintersection part and intersection part are described as [20]

$$ I=2p\left(\frac{\sqrt{2}{H}_1\left({a}_1\hbox{--} H\right){a}_1^2}{r\left|h\right|\left({a}_1^2+2{p}^2\right)\left[\left(\sqrt{2}-1\right)\left|h\right|+{H}_1\right]}+\frac{\sqrt{2}{H}_1\left({a}_2\hbox{--} H\right){a}_2^2}{r\left|h\right|\left({a}_2^2+2{p}^2\right)\left[\left(\sqrt{2}-1\right)\left|h\right|+{H}_1\right]}\right){I}_1 $$

(10)

where

$$ r\in \left(0,\frac{d_{\min }}{2}-\frac{\left({H}_1D+H{d}_{\min}\right)\left|h\right|}{2H{H}_1}\right),\kern0.5em {a}_1=\frac{p\left({b}_1+\sqrt{b_1^2+{H}_1^2}\right)}{\left|{H}_1\right|},\kern0.75em {b}_1=\frac{\sqrt{2}{H}_1r+\left(\frac{\sqrt{2}}{2}{d}_{\min }+\frac{D}{2H}{H}_1\right)\left(\left|h\right|-{H}_1\right)}{\left(\sqrt{2}-1\right)\left|h\right|+{H}_1},\kern0.5em {a}_1=\frac{p\left({b}_2+\sqrt{b_2^2+{H}_1^2}\right)}{\left|{H}_1\right|},\kern0.5em {b}_2=\frac{-\sqrt{2}{H}_1r+\left(\frac{\sqrt{2}}{2}{d}_{\min }+\frac{D}{2H}{H}_1\right)\left(\left|h\right|-{H}_1\right)}{\left(\sqrt{2}-1\right)\left|h\right|+{H}_1} $$