On the Cooling Rate and Layer Structure in Spray Metallization
Abstract Generated abstract
This paper estimates the cooling rate of steel particles after impact during electric spray metallization and relates it to the expected structure of the deposited layer. Treating the deformed particle as an infinite thin plate, the authors calculate transient cooling from radiation, convection, and heat conduction into the substrate under specified spraying conditions. The computed cooling rate in the transformation interval is found to exceed the critical quenching rate for carbon steel, suggesting formation of martensite with retained austenite or martensite alone. Metallographic examination of very thin sprayed layers is reported to support this conclusion, showing fine needle martensite and, in some cases, structureless martensite.
Full Text
ON THE COOLING RATE AND LAYER STRUCTURE IN METALLIZATION BY SPRAYING
A. F. Krupin, G. P. Boikov
Presented by Prof. A. N. Dobrovidov and Prof. G. I. Fuks
The calculation carried out for the temperature of particles in the spray cone during electric metallization by spraying [1] with steel shows that the particles reach the metallized surface at a temperature somewhat below the crystallization temperature. Further cooling of the particles takes place on the surface of the product being metallized. Depending on the rate at which the particles cool on the surface, a coating of different hardness may be obtained and, consequently, with other properties associated with it. Calculation of the cooling rate of particles on the surface is of not only theoretical interest, but also great practical importance from the standpoint of comparing it with the critical quenching rate and, consequently, estimating the structure of the droplet in the metallized layer.
It is known that the cooling rate in the temperature interval \(A_1—M\) has a substantial effect on the temperature at which martensitic transformation begins. When steel is cooled from the temperature of the point \(A_1\) at a rate lower than the critical one, partial decomposition of austenite occurs, which leads to an increase in the martensitic point \(M\), or else complete decomposition of austenite occurs with the formation of a ferrite-carbide mixture of varying degree of dispersion. At a cooling rate equal to or greater than the critical rate, a martensite structure is obtained.
Cooling of particles on the surface of the product occurs through heat transfer by radiation, convection, and thermal conduction. Upon impact with the metallized surface, the particles, which have the shape of a sphere, are deformed and take the form of plates with a thickness \(2R = 0.001—0.002\) mm [2]. Since the other dimensions of such a plate are large in comparison with the thickness, from the standpoint of the theory of heat conduction the plate may be regarded as infinite. At the moment of impact, the temperature of the particle rises (according to our estimates by approximately \(20—25^\circ\)C) as a result of the conversion of a certain fraction of the kinetic energy into heat. After impact, the particles begin to cool rapidly. Below, an attempt is made to give an approximate calculation of the cooling rate of a particle on the metallized surface.
For calculating the cooling of particles arranged in a single layer on the product, we adopt the following conditions and assumptions: a) the particles fall onto a steel cylinder and have, after impact, a thickness of 0.001 mm; b) the velocity of motion of the air jet washing over the cylinder is \(w = 170\) m/sec [3]; c) the temperature of the air jet in the spray cone is \(t_{\text{air}} = 85^\circ\)C [4];
the heat removed into the metallized article and the heat given up by the particle through convection are approximately equal [5]; d) the initial temperature of the particle is 1436°C (the temperature of the particle at the instant of impact, plus the increase in the particle temperature due to the conversion of part of the kinetic energy into heat).
In calculating the cooling of particles on the surface, the following thermophysical characteristics were adopted: \(\lambda = 25\ \dfrac{\mathrm{kcal}}{\mathrm{m}\cdot\mathrm{hour}\cdot\mathrm{deg}}\); \(a = 0.025\ \dfrac{\mathrm{m}^2}{\mathrm{hour}}\);
\[ C_{\mathrm{rad}} = 4.2\ \dfrac{\mathrm{kcal}}{\mathrm{m}^2\,\mathrm{hour}\,\mathrm{deg}\,K^4}; \qquad \alpha = 220\ \dfrac{\mathrm{kcal}}{\mathrm{m}^2\,\mathrm{hour}\,\mathrm{deg}}; \]
[6]. We carry out the calculation by the formula for an infinite plate [7], which, for the case of cooling, may be represented as:
\[ t_n = t_0 - \frac{a\tau_1}{\lambda R}\cdot \sum_{i=1}^{i=n} q_{ci}, \qquad \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \quad (1), \]
where
\[ q_{ci} = \frac{q'_{ci} + q''_{ci} + q'''_{ci}}{2} \]
is the effective heat flux removed from the body.
Next we determine:
- The radiant heat flux given up by the particle:
\[ q'_{c1} = C\left(\frac{T_0}{100}\right)^4 = 4.2\left(\frac{1436+273}{100}\right)^4 = 363\cdot 10^3\ \frac{\mathrm{kcal}}{\mathrm{m}^2\,\mathrm{hour}}. \]
- The convective heat flux:
\[ q''_{c1} = \alpha\left(T_0 - T_{\mathrm{air}}\right) = 220(1436 - 85) = 298\cdot 10^3\ \frac{\mathrm{kcal}}{\mathrm{m}^2\,\mathrm{hour}}. \]
On the basis of the adopted assumption:
\[ q'''_{c1} = q''_{c1} \]
Consequently,
\[ q_{c1} = \frac{q'_{c1} + q''_{c1} + q'''_{c1}}{2} = 479.5\cdot 10^3\ \frac{\mathrm{kcal}}{\mathrm{m}^2\,\mathrm{hour}} \]
- The approximate calculated time interval is found from the formula [7]:
\[ \tau_1 = \frac{0.03\cdot T_0\lambda R}{q_{c1}\cdot a} = 538\cdot 10^{-10}\ \text{hours}. \]
For greater accuracy of the calculation we adopt:
\[ \tau_1 = 350\cdot 10^{-10}\ \text{hours}. \]
- The particle temperature after the first calculated time interval, according to formula (1):
\[ t_1 = t_0 - \frac{a\cdot \tau_1}{\lambda R}\cdot q_{c1} = 1403^\circ\mathrm{C}. \]
Knowing the particle temperature after the first calculated time inter-
the time interval, we determine the effective heat flux for the next step:
\[ q_{c2}=\frac{q'_{c2}+q''_{c2}+q'''_{c2}}{2} =459\cdot 10^3\ \frac{\mathrm{kcal}}{\mathrm{m}^2\cdot \mathrm{h}} \]
Here
\[ q'_{c2}=C\left(\frac{T_1}{100}\right)^4 \quad \text{and} \quad q''_{c2}=\alpha\left(T_1-T_{\mathrm{air}}\right). \]
- We estimate the actual error of the calculation using the inequality:
\[ \varphi_m< \frac{3(q_{c1}-q_{c2})} {q_{c1}\left(1+2\cdot\displaystyle\sum_{n=1}^{\infty} e^{-\mu_n^2\frac{a\tau_1}{R^2}}\right)} =0.128. \]
Thus, the calculation error for the specified calculated time interval is less than 12.8 percent.
Finally accepting this calculated time interval, we have
\[ t_2=t_0-\frac{a\tau_1}{\lambda R}(q_{c1}+q_{c2})=1371^\circ\mathrm{C}, \]
where \(t_2\) represents the temperature of the particle at the end of the second calculated time interval. Continuing analogous calculations, we find \(t_3, t_4\), etc., which, for convenience, we plot on the graph of the function \(t=f(\tau)\) (Fig. 1).
Fig. 1. Change in the temperature of a particle on the metallized surface.
Examination of the curve shows that the cooling rate of a particle on the metallized surface in the interval \(A_1-M\) is considerably higher than the critical quenching rate, which for carbon steel lies within the range \(150\text{–}350^\circ/\mathrm{sec}\) [8]. Therefore, it should be expected that the structure of the droplet in the layer will be martensite and retained austenite, or pure martensite.
We carried out special investigations of the structure of thin metallization layers (1–2 deformed particles thick) obtained under normal conditions of electric metallization. The results of the metallographic analysis are shown in Fig. 2, where the structure of fine-needle martensite is expressed quite clearly. In many cases a structure of structureless martensite is observed.
Fig. 2. Droplet structure—fine-needle martensite. (U12A steel.) ×400.
LITERATURE
- A. F. Krupin, G. P. Boikov—“Cooling of particles in a spray cone during electric metallization by spraying.” Izvestiya TPI, vol. 85, 1957.
- Operation of metallization apparatus, Mashgiz, 1955.
- N. V. Kats, E. M. Linnik—Electric metallization, Selkhozgiz, 1953.
- Electric metallization in the repair of worn automobile parts (brief manual), Voenizdat of the People’s Commissariat of Defense, 1945.
- S. S. Shteinberg—Cooling media for hardening, GONTI, Leningrad, 1939.
- S. N. Shorin—Heat Transfer, Moscow, 1952, GISL.
- G. P. Boikov—Heating of bodies under the action of radiant heat. Dissertation, Tomsk Polytechnic Institute named after S. M. Kirov, 1955.
- A. P. Gulyaev—Heat Treatment of Steel, Mashgiz, 1953.