# Influence of Lubrication Systems on the Fatigue Strength of Bolted Joints
## 1 Introduction
### Theoretical Background
\[\text{T}=\text{F}.\left[0.159\cdot\text{P}+0.577\cdot\text{d}_{2}\cdot\mu_{ \text{th}}+\frac{\text{D}_{\text{b}}}{2}\cdot\mu_{\text{b}}\right] \tag{2}\]  
T: tightening torque, F: preload, P: thread pitch, d\({}_{2}\): pitch diameter,  
\(\mu_{\text{th}}\): thread friction coefficient, D\({}_{\text{b}}\): head friction diameter, \(\mu_{\text{b}}\): head friction coefficient. The thread friction torque and the head friction torque represent loss torques, whereas the thread pitch torque generates the preload F.  
Depending on the test system configuration, the tightening torque and a partial torque, for example the thread friction torque, are measured directly. The partial friction coefficient is calculated via the partial torque measured at the defined test force. The missing third variable, in this example the head friction torque, is determined mathematically via the relationship with the total torque [27]. \[\mu_{\text{th}}=\frac{\frac{\text{T}_{\text{th}}}{\text{T}}-\frac{\text{P}}{ 2\cdot\pi}}{0.577\cdot\text{d}_{2}} \tag{3}\]  
F: force, T\({}_{\text{th}}\): thread friction torque, P: thread pitch, d\({}_{2}\): pitch diameter. In industrial practice, the friction coefficients are adjusted by precisely matching the basecoat and topcoat. The basecoat forms the first layer to protect the base material from corrosion. In the automotive industry in particular, non-electrolytically produced zinc flake protection systems are used as basecoat in addition to electroplated coating systems, due to hydrogen-free production. This provides heavy-duty corrosion protection for exterior applications. The salt spray resistance is greater than 720 h in laboratory tests according to DIN EN ISO 9227, depending on the coating thickness [28]. The zinc flake surface represents a cathodic corrosion protection in which the zinc is applied mechanically, rolled out in an inorganic binder matrix with the addition of aluminum in a dip spinning process. With the addition of temperature, the paint is baked into the base material to be coated. The heat input creates a metallic bond between the flakes themselves and between the flakes and the substrate. The coating process does not change the mechanical and physical properties of the base material [20]. Typical applications for components protected with zinc flake coatings include wheel bolts, chassis attachments and gearbox connections in the wind power sector. Exceptions, for which no corrosion protection is required due to an existing oil bath, include, for example, bolted connections in the engine and gear box applications. The topcoat forms the next optional top layer on the basecoat and can fulfill both the task of higher corrosion protection and take on a lubricating effect. For bolted joints, there are applications with a lubricant integrated into the topcoat or additional lubrication is applied before assembly. The screw and nut thread as contact partners form a tribological system with the lubricant. For initial assembly, the lubrication fulfills the function of defined and constant friction conditions, with the aim of ensuring a reproducible preload level under defined assembly parameters, even for a large number of joints. The following lubricant groups are typically used for the setting of the friction coefficient:  
* Oil
* Grease
* Bonded coating  
In operation, the lubrication additionally fulfills the function of minimizing wear in the thread contact, where corrosion and wear phenomena can occur due to load-induced relative movements or environmental influences. A further requirement is long-term resistance to ensure that the connection can be detached for component replacement or repair. Lubrication is selected specifically and depending on the requirements of the application. Ambient media, temperatures and static or cyclic operating loads represent a wide variety of boundary conditions. Lubricating oils are high-boiling temperature mixtures of hydrocarbons to which lubricant additives are added. On average, the mixture consists of 90% base oil and 10% chemical additives [29].