# Influence of Lubrication Systems on the Fatigue Strength of Bolted Joints
## 2 Materials and Methods
### Experimental and Numerical Methods  
In order to evaluate the coefficients of friction for the comparison of the selected lubricants, tightening tests were carried out on a tightening test system from the manufacturer Schatz at Dorken Coating GmbH & Co. KG, Herdecke, Germany. The test bench was designed for torque/preload testing according to DIN EN ISO 16047 [27]. With regard to  
Figure 2: Screw M8x55-8.8 and ISO-4032 nut M8-10. the fatigue tests to be performed, in which the preload was controlled as a constant mean load by the test system, the partial friction coefficient in the thread was of particular interest, since this influenced the local stresses in the bolt. The installation speed n was 10 rpm, and the head-bearing clamping part was a through-hardened steel washer of type HH (hardness high) [27]. The bolt was tightened with a steel nut DIN EN ISO 4032 M8-10 [30]. Numerical simulation was used to validate hypotheses derived from the experimental results. The influence of thread friction on the local stress in the bolt was investigated. The software ABAQUS 6.14 was used for the numerical calculations. Based on the findings from [3] for the determination of local stresses, an axially symmetrical model of the bolt-nut connection was created. For the simulation of stress under fatigue loading, an ISO metric M8 bolt (tolerance 6 g) was paired with a standard M8 ISO 4032 nut (tolerance 6 H). The load was applied to the reference point which was coupled to the head bearing area. The nut was fixed in the axial direction and was able to move laterally. The normal contact behavior was set as hard contact using the augmented lagrange method. The tangential behavior was chosen as the penalty method, whereas the coefficient of friction was \(\mu=0.12\). The connection was stressed to a preload of 23 kN load, and a fatigue operating load of 5 kN was superimposed. Three load cycles were calculated until a cyclically stabilized behavior was established. Plastic behavior was approximated bilinearly in ABAQUS using yield curves from [3] and implemented with kinematic hardening. Exemplary stress simulation was carried out for three thread friction coefficients. The damage evaluation was performed using the parameter \(P_{\text{SWT}}\) according to [PERSON], [PERSON] and [PERSON] [31]. According to the local concept, the calculated local stress was compared with the stressability of unnotched material specimens (Kt = 1) determined at a stress ratio of R = \(-\)1. Bolted joints have a mean stress due to the preload required for operational safety. Therefore, the Bergmann mean stress correction was applied here, taking into account the location of the local hysteresis and thus reducing the strong mean stress dependence of \(P_{\text{SWT}}\)[32]. The numbers of cycles to crack initiation were calculated by comparing the calculated local damage with the material strain curve. The fatigue tests were performed on a high-frequency resonance test system as a bolt-nut connection. The joint was axially pre-stressed to a defined mean load F\({}_{\text{m}}\) (F\({}_{\text{m}}\) = 0.4\(\cdot\)F\({}_{\text{02}}\), with F\({}_{\text{02}}\) as the force at the yield point), which was kept constant by the controlling of test system. A sinusoidal force with constant amplitude F\({}_{\text{A}}\) was superimposed as the fatigue operating force (Figure 3). The test was carried out in accordance with the specification DIN 969 [25]. The resonance test system represents, in a simplified form, a single-mass oscillator as an analogous model. By setting up the equation of motion for this oscillatory system, the solution of a harmonic sinusoidal oscillation from the differential equation resulted in the relationship that the frequency being equal to the root of the stiffness divided by the mass of the system. Fatigue loading led to cracking in the bolt material, which resulted from dislocation movements and surface roughening due to the formation of intrusions and extrusions.