Soft Sensor Technology for the Determination of Mechanical Seal Friction Power Performance
Abstract
:1. Introduction
2. Development of Soft Sensor Technology for Determination of Frictional Power Performance of Mechanical Seals
2.1. Derivation of Mechanical Seal Heat Flow Model
2.2. Development of the Soft Sensor for Friction Power Performance Determination
Algorithm 1: Soft sensor for determining the frictional power of a mechanical seal. |
define , define |
Calculation of |
3. Evaluation of the Accuracy of the Soft Sensor Determination
3.1. Soft Sensor Validation Test Bench
3.2. Comparison of Equivalent Dimensionless form Coefficient between Numerical and Experimental Results
3.3. Quality of Soft Sensor Calculation for Stationary Operation of Mechanical Seals
3.4. Soft Sensor Behaviour with Variation in the Mechanical Seal Stationary Operating Conditions
4. Conclusions
- -
- The calculation of the equivalent dimensionless form coefficient is highly dependent on the model used to determine the averaged Nusselt number. A variety of modelling approaches exist. The heat transfer coefficients determined by the models exhibit considerable variability, which results in discrepancies in the calculation of the dimensionless equivalent mould coefficient.
- -
- By varying the differential pressure across the mechanical seal and the preload on the mechanical seal primary ring, a small deviation between the algorithm and the measurement could be demonstrated.
- -
- Varying the geometry around the mechanical seal affects the heat transfer between the mechanical seal and the fluid. The arrangement of fins around the mechanical seal improves heat transfer and therefore increases the equivalent dimensionless form coefficient.
- -
- The soft sensor heat flow model is based on stationary assumptions. The algorithm reacts slowly to changes in the stationary operating conditions. Rapid changes, e.g., sudden increases in pressure, will not be considered by the algorithm. This significantly increases the errors. The algorithm is not suitable for the representation of dynamic changes in the operating conditions.
- -
- The described algorithm is easy to implement compared with data-based or machine-learning concepts of soft sensors. For this, only the equivalent dimensionless form coefficient characteristics need to be known. It is not necessary to have large amounts of data in order to train a model. There is no need for mechanical machining of the mating ring, as is required when integrating a torque sensor.
5. Patents
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
column matrix of form coefficients | |
heat transfer area | |
heat transfer area of the surface | |
equivalent dimensionless form coefficient | |
form coefficient of the sliding surface | |
form coefficient from surface to surface | |
equivalent form coefficient | |
exponent Prandl number ratio Nusselt approach | |
coupling factor temperature sensor | |
factor Reynolds number Nusselt approach | |
specific heat capacity of the medium | |
damping factor low pass filter | |
inner diameter mechanical seals | |
outer diameter primary ring | |
outer diameter mating ring | |
transmission efficiency | |
transmission efficiency from surface to surface | |
frequency | |
sampling rate | |
exponent Prandl number Nusselt approach | |
conventional form factor | |
characteristic length of the primary ring | |
characteristic length of the mating ring | |
exponent Reynolds number Nusselt approach | |
column matrix of the medium parameter | |
speed of the primary ring | |
experimental measured speed of the primary ring | |
local Nusselt number | |
averaged Nusselt number | |
differential pressure above the mechanical seal | |
friction power | |
experimental measured friction power | |
power of the mechanical seal | |
ventilation power of the mechanical seal | |
Prandl number of the medium at characteristic temperature of the medium | |
Prandl number of the medium at temperature of the solid surface | |
heat flow | |
convective heat flow | |
heat flow from surface to surface | |
characteristic width of the primary ring | |
characteristic width of the mating ring | |
radius | |
Reynolds number | |
Root Mean Squared Error | |
preload of the primary ring | |
axial coordinate of the mechanical seals | |
heat transfer coefficient | |
thermal conductivity | |
thermal conductivity of the primary ring | |
thermal conductivity of the mating ring | |
temperature | |
temperature of the surface | |
experimental measured temperature at the surface 2 | |
temperature of the ambient | |
temperature of the medium | |
experimental measured temperature of the medium | |
temperature of the temperature sensor at the mechanical seal | |
reference temperature | |
column matrix of the temperatures | |
Density of the medium | |
kinematic viscosity of the medium | |
dynamic viscosity of the medium |
Appendix A
Appendix B
Appendix C
Measured Quantity | Maximum Relative Error |
M | 0.054% |
n | 0.224% |
Δp | 0.524% |
s | 1.024% |
ϑamb | 0.084% |
ϑM | 0.124% |
ϑ2 | 0.084% |
PR | 0.325% |
Δϑ | 0.149% |
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Parameter | PO001 | PO002 | PO003 |
---|---|---|---|
inner diameter () | 38 mm | 38 mm | 50 mm |
outer diameter mating ring () | 54 mm | 54 mm | 69 mm |
outer diameter primary ring () | 46 mm | 46 mm | 58 mm |
characteristic length mating ring () | 11.3 mm | 11.3 mm | 10.5 mm |
characteristic length primary ring () | 5 mm | 5 mm | 5.4 mm |
characteristic width mating ring () | 5 mm | 5 mm | 4.5 mm |
characteristic width primary ring () | 3.5 mm | 3.5 mm | 3.9 mm |
material mating ring | SiC1 | SiC2 | SiC1 |
material primary ring | SiC1 | SiC1 | SiC1 |
heat conductivity mating ring () | |||
heat conductivity primary ring () |
Approach Function | PO001 | PO002 | PO003 | |||
---|---|---|---|---|---|---|
Ayadi [27] | 0.155 | 0.498 | 0.154 | 0.495 | 0.187 | 0.445 |
Becker [28] | 0.051 | 0.607 | 0.052 | 0.600 | 0.111 | 0.505 |
Tachibana [29] | 0.049 | 0.601 | 0.050 | 0.595 | 0.084 | 0.518 |
Doane [30] | 0.009 | 0.729 | 0.009 | 0.722 | 0.021 | 0.622 |
Luan [31] | 0.008 | 0.701 | 0.007 | 0.706 | 0.009 | 0.652 |
Brunetière [18] | 0.027 | 0.576 | 0.026 | 0.574 | 0.035 | 0.519 |
Approach | 0.810 | 0.773 | 1.376 |
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Reeh, N.; Manthei, G.; Klar, P.J. Soft Sensor Technology for the Determination of Mechanical Seal Friction Power Performance. Appl. Syst. Innov. 2024, 7, 39. https://doi.org/10.3390/asi7030039
Reeh N, Manthei G, Klar PJ. Soft Sensor Technology for the Determination of Mechanical Seal Friction Power Performance. Applied System Innovation. 2024; 7(3):39. https://doi.org/10.3390/asi7030039
Chicago/Turabian StyleReeh, Nils, Gerd Manthei, and Peter J. Klar. 2024. "Soft Sensor Technology for the Determination of Mechanical Seal Friction Power Performance" Applied System Innovation 7, no. 3: 39. https://doi.org/10.3390/asi7030039
APA StyleReeh, N., Manthei, G., & Klar, P. J. (2024). Soft Sensor Technology for the Determination of Mechanical Seal Friction Power Performance. Applied System Innovation, 7(3), 39. https://doi.org/10.3390/asi7030039