**3. Design and optimization**

Thermal Spraying is an indirect process, where only the basic conditions can be controlled by altering the process parameters. A deterministic control of the transfer of heat and kinetic energy to the feedstock particle is not possible. Due to the vast variety of process parameters some time said to be more than one hundred (Lugscheider & Bach, 2002) - sophisticated approaches of designed experiments are a good tool to both understand the complex interdependencies between the parameters and to optimize coatings properties due to the demands. In the following the basic considerations and the proof of suitability of statistical design of experiments are given for controlling and optimization of thermal spraying processes.

Thermal Spraying of Oxide Ceramic and Ceramic Metallic Coatings 177

sufficient coating qualities in specified tolerance regions. Besides the gathering of the relevant know-how regarding the spraying of certain feedstock etc., the processes must be insensitive against deviations over longer periods of time to reach this goal. For example, in **Figure 7** a quadratic functional correlation between the deposition efficiency of feedstock

Fig. 7. Assumed correlation between applied amperage and relative deposition efficiency

The sketch shows, that the same magnitude of deviation of the applied amperage from the chosen control value results in two different deviation spans of the resulting DE (Ry1 and Ry2). Another point is the influence of noise factors, which also can disturb the known relation between process parameters and the expected result. Following the approach after G. Taguchi, the effects of the control factors (i.e. process parameters) are extended by the

Fig. 8. Scheme of the effects of control, noise and signal factors on the coating process (after

The basic tools of the method are the so called orthogonal arrays. Like the conventional matrices of designing experiments for factorial designs, the levels of the parameters to be investigated are arranged by given plans. But unlike the methods of DoE, the functional correlation between factors and the measured results are expressed in terms of a signal-to-

and the applied amperage in the APS process is assumed.

effects of noise and signal factors (see **Figure 8**).

Phadke, 1989)

### **3.1 Basic considerations**

The goal of conducting experiments is to get information about the functional relation between the process conditions and the resulting coatings properties determining both the economical effectiveness of the coating process as well as the coatings behaviour under operational conditions. For example the deposition efficiency (DE) of the feedstock material in case of plasma spraying of oxide ceramics, i.e. the percentage of the inset feedstock contributing to the coating buildup, is dependent of the chosen federate as well as the achievable heat transfer from the plasma to the feedstock particles. Therefore it can be assumed, that there is a functional correlation between the powder feedrate, the applied amperage to the plasma and the chosen plasma and secondary gas mixture (species, total flow and ratio) controlling the specific heat and therefore the capacity of heat transfer of the plasma. Two further parameters defined by the inset feedstock are its heat of fusion and median grain size as the heat is transferred from its surface into its volume. The spraying distance is parameter controlling the time of flight of the particles in the plasma and therefore the time of exposure to heat, but there is a strong interdependency with the applied amperage. The higher the amperage, the higher is the temperature and heat capacity of the plasma, but also its velocity and therefore the time of flight for the particles decreases with raising the amperage. All together the functional dependency of the DE can be stated as follows:

$$\text{DE} = \text{f}\_{\text{(amperaçe, plasına şasıes, spırayirçı distance, particle size, ...)}}$$

or in other terms:

$$\mathbf{y} \text{ DE} = \mathbf{f} \begin{pmatrix} \mathbf{x}1, \mathbf{x}2, \dots, \mathbf{x}n \end{pmatrix} \tag{4}$$

One approach to derive information about the correlation of the coating´s criteria DE with the parameters is to vary the process parameters one by one in every single spraying experiment holding two complications: The number of experiments is large and the interdependency between distinct parameters cannot be estimated. Therefore the use of statistically designed experiments is a good alternative, as both goals can be realized utilizing this tools (for an example see Heimann, 2008). The experiments are arranged in matrices with a deterministic alteration of the factors (i.e. parameters to be investigated) on distinct levels. Afterwards the coatings criteria are measured and the results are analysed regarding the factorial effects (i.e. the correlation with the parameters). The ways to obtain the correlation can be divided into factorial analysis by means of multiple regressions on the one hand and by analysing the variance of the measured results according to the variation of process parameters (ANOVA) methods. The usability of the second approach in the field of thermal spraying is shown in the following using the examples of the experimental series described in chapter 2. For a comprehensive overview of the methods including model testing etc. see (Dean & Voss, 1999; Mason, 2003; National Institute of Standards and Technology [NIST], 2011).

### **3.2 Robust quality control basing on ANOVA techniques**

The variability of thermal spray processes regarding coatings characterics and quality is a well-known problem in application. In the field of the designing and development of feedstock and coating systems designed experiments are sophisticated tools to achieve

The goal of conducting experiments is to get information about the functional relation between the process conditions and the resulting coatings properties determining both the economical effectiveness of the coating process as well as the coatings behaviour under operational conditions. For example the deposition efficiency (DE) of the feedstock material in case of plasma spraying of oxide ceramics, i.e. the percentage of the inset feedstock contributing to the coating buildup, is dependent of the chosen federate as well as the achievable heat transfer from the plasma to the feedstock particles. Therefore it can be assumed, that there is a functional correlation between the powder feedrate, the applied amperage to the plasma and the chosen plasma and secondary gas mixture (species, total flow and ratio) controlling the specific heat and therefore the capacity of heat transfer of the plasma. Two further parameters defined by the inset feedstock are its heat of fusion and median grain size as the heat is transferred from its surface into its volume. The spraying distance is parameter controlling the time of flight of the particles in the plasma and therefore the time of exposure to heat, but there is a strong interdependency with the applied amperage. The higher the amperage, the higher is the temperature and heat capacity of the plasma, but also its velocity and therefore the time of flight for the particles decreases with raising the amperage. All together the functional dependency of the DE can be stated

DE = f (amperage, plasma gases, spraying distance, particle size, …)

One approach to derive information about the correlation of the coating´s criteria DE with the parameters is to vary the process parameters one by one in every single spraying experiment holding two complications: The number of experiments is large and the interdependency between distinct parameters cannot be estimated. Therefore the use of statistically designed experiments is a good alternative, as both goals can be realized utilizing this tools (for an example see Heimann, 2008). The experiments are arranged in matrices with a deterministic alteration of the factors (i.e. parameters to be investigated) on distinct levels. Afterwards the coatings criteria are measured and the results are analysed regarding the factorial effects (i.e. the correlation with the parameters). The ways to obtain the correlation can be divided into factorial analysis by means of multiple regressions on the one hand and by analysing the variance of the measured results according to the variation of process parameters (ANOVA) methods. The usability of the second approach in the field of thermal spraying is shown in the following using the examples of the experimental series described in chapter 2. For a comprehensive overview of the methods including model testing etc. see (Dean & Voss, 1999; Mason, 2003; National Institute of Standards and

The variability of thermal spray processes regarding coatings characterics and quality is a well-known problem in application. In the field of the designing and development of feedstock and coating systems designed experiments are sophisticated tools to achieve

y DE = f (x1, x2, …, xn) (4)

**3.1 Basic considerations** 

as follows:

or in other terms:

Technology [NIST], 2011).

**3.2 Robust quality control basing on ANOVA techniques** 

sufficient coating qualities in specified tolerance regions. Besides the gathering of the relevant know-how regarding the spraying of certain feedstock etc., the processes must be insensitive against deviations over longer periods of time to reach this goal. For example, in **Figure 7** a quadratic functional correlation between the deposition efficiency of feedstock and the applied amperage in the APS process is assumed.

Fig. 7. Assumed correlation between applied amperage and relative deposition efficiency

The sketch shows, that the same magnitude of deviation of the applied amperage from the chosen control value results in two different deviation spans of the resulting DE (Ry1 and Ry2). Another point is the influence of noise factors, which also can disturb the known relation between process parameters and the expected result. Following the approach after G. Taguchi, the effects of the control factors (i.e. process parameters) are extended by the effects of noise and signal factors (see **Figure 8**).

Fig. 8. Scheme of the effects of control, noise and signal factors on the coating process (after Phadke, 1989)

The basic tools of the method are the so called orthogonal arrays. Like the conventional matrices of designing experiments for factorial designs, the levels of the parameters to be investigated are arranged by given plans. But unlike the methods of DoE, the functional correlation between factors and the measured results are expressed in terms of a signal-to-

Thermal Spraying of Oxide Ceramic and Ceramic Metallic Coatings 179

surface roughness. Especially the carbide based coatings showed low Ra values (about 2.7 µm) compared to the Ra values of the standard samples (near 7 µm). The hardness of the

**Current, A (APS)** 

**Cr2O3** +25-5 (3) 650 (3) 100 (2) 12 (2) **Cr3C2-NiCr** +15-5 (1) 1.4 (1) 270 (1) 10 (1) **WC-CoCr** +15-5 (1) 1.4 (2) 310 (2) 11 (2)

**µm per pass** 

Measured 18.7 2.5 89 Standard 16.9 4.5 87

Measured 3.3 2.7 77 Standard 23.9 6.7 76

Measured 11.3 2.7 87 Standard 26.9 6.8 88

**Cr2O3** Predicted 18.4 3.2 87

**Cr3C2-NiCr** Predicted 3.6 2.8 73

**WC-CoCr** Predicted 11.8 3.1 89

Table 5. Predicted and measured results obtained from validation and standard samples

It can be summarized, that by applying the method of signal-to-noise ratios derived from the evaluation of orthogonal arrays, the workings could be reduced to nine experiments while investigating the effects of four quantitative parameters on three levels. The results show, that by applying this technique, reproducible forecasts regarding the optimisation of

As stated at the beginning there is the goal to make use of finer grain sizes of feedstock powders to reach denser coatings showing higher cohesion and adherence to the substrate. The lower limit of feeding powders into the process is in the one-digit micrometer range. By dispersing of the feedstock in a liquid outer phase or the formulation of feedstock direct in a suspension by chemical methods, use can be made of nanometer sized feedstock. In the following the efforts are shown in new results regarding the achievement of coatings, which

**or lambda (HVOF) Spray distance, mm**

**Surface roughness Ra, µm** 

**Powder carrier gas, slpm** 

**Hardness HR 15 N** 

coatings did not vary much regardless of which powder fraction was processed.

Table 4. Predicted optimum spray parameters (the numbers in brackets show the

**Feedstock Particle size** 

corresponding parameter level)

thermal spray coatings can be derived.

**4. Developments of new applications** 

could not be realized by means of thermal spraying before.

**µm** 

**Feedstock Sample Deposition rate,** 

noise ratio. The goal of the method is not to optimize one response regardless of other coatings criteria, but to achieve results being robust against the effect of noise factors like e.g. the wear of parts like the electrodes of the plasma gun etc. The signal factors also show effects on the results, but are kept normally constant, like e.g. the traverse speed of the gun relative to the substrate. In the following the results of applying the method are discussed.
