## 1 Introduction  
Gears are machine elements that, as a result of the meshing of their profiles, allow the transmission of power between two rotary axes while maintaining a (nominal) constant ratio between the rotational velocity of the two axes [1; 2; 3]. Their working principle implies the presence of a loaded sliding/rolling contact condition that is located far from the base of the tooth (i.e., the tooth root). The contact implies the co-presence of several failure modes, such as tribological damages (i.e., scuffing and wear) and fatigue damages (e.g., (macro)pitting, micropitting, tooth flank fracture, and tooth root fatigue fracture). The latter (also called tooth root bending fatigue or tooth root breakage) is related to the pulsating normal force that acts on the tooth flanks, which causes a bending stress history in the tooth root that starts from a small negative value (when the previous tooth pair is in mesh) up to a maximum (ideally when the contact is at the outer point of the single tooth contact) [4; 5]. Furthermore, the root radius works as a notch, further increasing the maximum stress [5]. Amongst all the failures that can affect a gear, tooth root fatigue fracture is considered to be the most critical one. Indeed, the failure of a single tooth implies the stoppage of the power flow within the gearbox and typically leads to a total failure of the gear system. Fortunately, standards such as ISO 6336-3 [6] and ANSI AGMA 2001-D04 [7] provide gear designers with standardized analytical tools that can be used to assess a gear pair with respect to this failure mode. The assessment is based on the comparison of the occurring tooth root stress with the permissible tooth root stress. The first is primarily based on the maximum tensile stress at the surface in the tooth root fillet, typically for external gears at the 30\({}^{\circ}\) tangent, and depends on the gear pair meshing characteristics and the tooth root shape. The latter is based on typical gear material (together with the treatments) strength data and is defined at 1% gear failure probability. Typical resistance data are also part of these standards (i.e., [7,8]). However, due to their intrinsic limitations, the standards cannot cover all possible varieties of materials and (heat or surface) treatments. Moreover, as Figure 1 shows, even the standards do not provide a comprehensive gear SN curve but rather a scattering range (see the shaded area) for \(>\)\(3*10^{6}\) load cycles, leaving the designer to assume strength in the long-life region. Indeed, the standards themself strongly recommend performing experimental campaigns to properly estimate the gear load-carrying capacity. Three main testing methodologies for tooth root fatigue fracture are present in the literature: The Meshing Gear (MG) test (e.g., [9]), the pulsator test (e.g., [10, 11, 12, 13, 14, 15]), also known as the Single Tooth/Teeth Bending Fatigue (STBF) test, and the test of notched specimens (e.g., [16, 17, 18, 19, 20]). The most common testing methodology is the pulsator test [21]; indeed, the tests are performed on a gear, rather than a notched specimen, while using a generic uniaxial testing machine, rather than a full gearbox. Therefore, pulsator testing is a cost-effective method that considers a representative test specimen. A description of the typical testing rig is presented in Section 2. ISO 6336-5 [8] strength number data have been obtained based on both industrial experience and experimental investigations applying this kind of testing methodology. In this context, it is important to mention that although pulsator tests are part of the ISO 6336 series, the standard does not provide any indications about how to perform pulsator experimental campaigns and how to elaborate their outcome. The fact that in pulsator tests, the teeth are loaded by anvils (clamping jaws) rather than by gear meshing, implies that there are some differences between the pulsator test and the real-world application scenario. Those differences are related to two main aspects:  
1.