# Soft Sensor Technology for the Determination of Mechanical
## 3 Evaluation of the Accuracy of the Soft Sensor Determination  
### Soft Sensor Validation Test Bench  
To validate the soft sensor algorithm (Algorithm 1), a test bench was developed. Mechanical seals of various sizes can be tested. Figure 1(a) shows the structure of the test bench. The mechanical seal is located in a pressure chamber. Linear bearings allow the pressure chamber to be moved. By pulling the pressure chamber against a carrier, the preload on the primary ring can be adjusted. The change in preload is measured by a distance sensor. Water is used as the medium in the pressure chamber. The temperature of the medium is measured by a PT1000 temperature sensor. The pressure in the pressure chamber can be varied. This is measured by a pressure sensor. The primary ring is mounted on a shaft with two bearing supports. A motor with variable speed allowed via a frequency converter drives the shaft. A torque transducer measures the power delivered by the motor to the shaft. This records the torque and speed. The power consumption of the bearing is measured in addition to the power consumption of the mechanical seal (\(P_{\rm S}\)). This determination of the power consumption of the bearing is based on experimentation and is expressed by a regression function. The power losses of the bearings are subtracted from the measurement signals of the power consumption. The power of the mechanical seal (\(P_{\rm S}\)) consists of the friction power (\(P_{\rm R}\)) and the ventilation power (\(P_{\rm V}\)) resulting from the power transfer between the mechanical seal and the medium [24]:  
\[P_{\rm S}:=P_{\rm R}+P_{\rm V}. \tag{19}\]  
Due to speeds \(n\leq 3000\) rpm and low-viscosity media such as water, it holds \(P_{\rm R}\gg P_{\rm V}\)[24], and, as a good approximation, it is \(P_{\rm S}\dot{=}P_{\rm R}\). Figure 1(b) shows the coupling of the PT1000 temperature sensor to the mating ring. A coupling paste facilitates heat transfer between the temperature sensor and the mating ring with a surface temperature, \(\theta_{2}\). The coupling paste has a thermal conductivity of \(\lambda=74\frac{\dot{W}}{\rm mK}\). The temperature sensor is attached to the mating ring using superglue. The thermal conductivity of the superglue can be assumed to be \(\lambda=15\frac{\dot{W}}{\rm mK}\). Placing a temperature sensor on the surface of the mechanical seal causes a localised temperature change due to variations in the thermal conductivity against the base material [25]. In order to assess the impact of the sensor on the surface temperature in its vicinity, the coupling factor (\(B_{\text{S}}\)) was calculated using Equation (20) [25]. To calculate \(B_{\text{S}}\), the temperature measured by PT1000 (\(\theta_{\text{S}}\)), the ambient temperature (\(\theta_{\text{amb}}\)) and the actual surface temperature at the measuring point (\(\theta_{2}\)) are required. The coupling factor for the sensor coupling is assumed to be \(B_{\text{S}}=5\text{e}^{-3}\). \[B_{\text{S}}:=\frac{\vartheta_{\text{S}}-\vartheta_{2}}{\vartheta_{\text{amb }}-\vartheta_{2}} \tag{20}\]  
A PT1000 sensor was also used to record the ambient temperature (\(\vartheta_{\text{amb}}\)). The sampling frequency for all measured quantities was \(f_{\text{S}}=500\) Hz. The Gaussian law of error propagation was used to calculate the maximum relative errors for the variables \(P_{\text{R}}\) and \(\Delta\vartheta\). \(\Delta\vartheta\) is the temperature difference between the temperature of the mating ring (\(\vartheta_{2}\)) and the temperature of the medium in the pressure chamber (\(\vartheta_{\text{M}}\)). The maximum relative errors of all variables are summarised in Appendix C. To validate the soft sensor approach, three mechanical seals were measured. Table 1 shows the parameters of the three mechanical seals. These are labelled as test objects (POs). The table contains ring material information in addition to the geometric parameters. It can be seen that the mechanical seals have different dimensions. They also have different material combinations.