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Fundamental Cost Analysis of Cold Spray

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Abstract

The cost structure of the cold spray (CS) process is analyzed using a generic cost model applicable to all present types of CS systems (“high pressure,” “low pressure,” KM™, “kinetic spraying,” etc.) and kinds of application (coating, restoration, additive manufacturing, near-net forming). The cost model has originally been developed at SIEMENS and is easy to use, while being sufficiently accurate to support decisions. The dependence of the process costs on the gas stagnation properties is discussed. It is shown (i) that high pressure is generally favorable, (ii) that He-N2 blends possess economic potential, and (iii) that He recovery saves costs in high volume production, even when He-N2 blends are used. The cost model allows for the determination of the cost-optimal He concentration of the propellant gas for a given application. CS is, among others, suited to spray bond coatings on gas turbine blades and offers cost-saving potential, as shown in a case study.

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Abbreviations

a :

Speed of sound, m/s

A thr :

Nozzle throat area, mm2

c :

Helium mass fraction

\( c_p \) :

Isobaric specific heat, kJ/kg K

C elc :

Electrical energy costs, per kg deposited material, EUR

C eqp :

Costs of equipment ownership, per kg deposited material, EUR

C gas :

Gas costs, per kg deposited material, EUR

C pwd :

Powder costs, per kg deposited material, EUR

C tot :

Total costs of 1 kg deposited material, EUR

d p :

Powder particle diameter, μm

F gas :

Inverse gas flow factor, 3600 m/\( \sqrt K \) s

γ:

Specific heat ratio

GL:

Geometric loss factor

h :

Specific enthalpy, kJ/kg

HL:

Heat loss factor

M :

Mach number

m gas :

Amount of gas consumed for deposition of 1 kg material, kg

\( \dot{m}^{*} \) :

Critical mass flow rate, kg/s

\( \dot{m}_{\text{dsi}} \) :

Flow rate of gas injected downstream of the nozzle throat, kg/h

\( \dot{m}_{\text{gas}} \) :

Gas flow rate of heated main gas stream, kg/h

\( m_{\text{pwd}} \) :

Amount of powder consumed for deposition of 1 kg material, kg

\( \dot{m}_{\text{pwd}} \) :

Powder feeding rate, kg/h

μ:

Distribution function of particle size mass fraction, μm−1

P :

Gas stagnation pressure, MPa

Q gas :

Heating energy absorbed by gas, per kg deposited material, kWh

Q los :

Thermal energy loss, per kg deposited material, kWh

R :

Specific gas constant, J/kg K

ρ1 :

Gas density at nozzle exit, kg/m3

ρgas :

Gas density, kg/m3

t :

Gas temperature, K

t off :

Total duration of gas flow without powder flow, per kg deposited material, h

t on :

Total duration of powder flow, per kg deposited material, h

t run :

Total duration of gas flow, per kg deposited material, h

T :

Gas stagnation temperature, K

T amb :

Gas inlet temperature, K

U elc :

Electrical energy price, EUR/kWh

U eqp :

Equipment hourly rate, EUR/h

U gas :

Gas price, EUR/kg

U pwd :

Powder price, EUR/kg

ν1 :

Gas velocity at nozzle exit, m/s

νcr :

Critical velocity, m/s

νgas :

Gas velocity, m/s

νp :

Particle velocity, m/s

νpi :

Particle impact velocity, m/s

w :

Powder-to-gas mass loading ratio

Y DE, \( {{\Upupsilon}} \) :

Deposition efficiency, yield

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Authors and Affiliations

  1. Siemens AG, Corporate Technology, 13623, Berlin, Germany

    O. Stier

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  1. O. Stier
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Correspondence to O. Stier.

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This article is an invited paper selected from presentations at the 2013 International Thermal Spray Conference, held May 13-15, 2013, in Busan, South Korea, and has been expanded from the original presentation.

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Stier, O. Fundamental Cost Analysis of Cold Spray. J Therm Spray Tech 23, 131–139 (2014). https://doi.org/10.1007/s11666-013-9972-1

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