# Multiphase Conjugate Heat Transfer Analyses on the Assembly Situation of Rotary Shaft Seals
## 1 Introduction  
In many technical applications, seals are required to keep lubricants and operating fluids within a system as well as to keep contaminants out of this system. Rotary shaft seals (RSS) are mainly used to seal pressureless shaft passages that are splashed or flooded, e.g., in automotive and mechanical engineering [1, 2]. The rotary shaft seal is a complex tribological system that includes not only the sealing ring, but also its counterface, i.e., the shaft surface, and the fluid to be sealed [1]. The sectional view of a rotary shaft seal made of elastomer according to DIN 3760 [3] or ISO 6194 [2] is shown in Figure 1.  
In the assembled state, the sealing lip is pressed against the shaft surface with the aid of a garter spring. This results in a narrow contact area between the sealing edge and the shaft surface, with a contact width of about 0.1 mm [1]. The static sealing mechanism, i.e.,  
Figure 1: Sectional view of a rotary shaft sealing ring made of elastomer. when the shaft is not rotating, is additionally ensured by the interference of the shaft outer diameter and the sealing ring inner diameter [1]. When the shaft rotates, the lubricant to be sealed is dragged into the contact area between the sealing edge and the shaft. Due to the active sealing mechanism, this fluid entering the sealing gap is pumped back from the air side to the oil side. Various models have been suggested to explain this dynamic sealing mechanism of rotary shaft seals [4; 5; 6]. During operation, the contact area is subjected to friction. The more frictional heat is generated in the contact area and the less of this heat can be dissipated from the contact area, the greater the temperature in the contact area. The generation and dissipation of heat and, thus, the contact temperature is affected by numerous interacting factors, some of which are illustrated in Figure 2.  
Failures of rotary shaft seals and, thus, of the entire system are often caused by the overheating of the contact area. An increase in temperature in the sealing contact of about 10 K can already lead to a significantly reduced service life of a rotary shaft seal [8]. Therefore, in order to better assess the risk of a temperature-induced failure and to achieve a long service life, the temperatures in the contact area must be below the operating temperature limit of the sealing ring and the fluid. The contact temperature to be expected during operation must, thus, be known as accurately as possible. In general, it can be distinguished between three different ways of determining the contact temperature. The first option is to measure directly on a real component [9]. This is usually the most accurate method for determining the contact temperature, but these measurements can be extremely difficult or even impossible due to the very small gap heights between the sealing edge and the shaft. Furthermore, a prototype must already have been manufactured. For an initial design, before a prototype is manufactured, these measurements, therefore, cannot be performed. The second option is the possibility of estimating the temperature in the contact area without a prototype by using an approximation equation [7; 10; 11]. This can be conducted, for example, with the InsECT beta-18.10.08 [12; 13] calculation tool developed at the Institute of Machine Components of the University of Stuttgart. In the current state of development, this tool is not applicable to sealing systems with certain configurations, such as rotary shaft seals with a protective lip or coated shafts, hollow shafts or shafts with sleeves. The third option is to simulate the entire system. Through simulations, the expected contact temperature can already be developed for the first design without the need to build a prototype. This offers the possibility to simulate different variants and compare them with each other. Moreover, the results are more accurate than when using approximation equations.