# Comparison of Crack Detection Performance of Low and High Contact Ratio Spur Gears
## 1 Introduction  
Gearboxes are largely preferred in power transmission systems compared to other elements because they are capable of transmitting high power values with high reliability and a constant gear ratio. The traditional spur gears cannot meet high load and high-speed needs in many applications. HCR spur gears are an alternative design, as both reduce dynamic loads, noise, and the high load-sharing ratio since they have a high contact ratio and transmit the power through two to three tooth pairs [1]. When the literature is examined, it is seen that many researchers emphasize the superior features of HCR gears. [PERSON] et al. [2] proposed a novel non-involute HCR spur gear model to reduce sliding contact and decrease root stress. The proposed method shows better root strength and surface durability. [PERSON] [3] compared the dynamic and strength performances of LCR and HCR gears. A 2-DOF dynamic model was proposed for the calculation of dynamic loads and static structural bending analysis were performed to calculate the bending stress on the tooth root. As a result of the study, the HCR gears showed approximately 40% lower dynamic loads and 50% lower bending stress when compared to the LCR ones. [PERSON] et al. [4] investigated the dynamic performances of LCR and HCR gears under four different speeds, which were 1, 2000, 5000, and 9000 rpm. A 2-DOF dynamic model was developed for the calculation of dynamic loads. As a result of the study, HCR gears provided a marked advantage compared to the LCR spur gears. [PERSON] et al. [5] proposed a method to define the efficiency of HCR gears with asymmetric teeth. The results showed that when the drive side pressure angle increased, the instantaneous sliding loss decreased. [PERSON] [6] used HCR gears and profile modifications to minimize the dynamic load. Time-varying mesh stiffness (TVMS) is a critical factor in determining the dynamic loads for both LCR and HCR gears. In the literature, different methods are available for calculating TVMS, such as numerical and experimental. The researchers generally prefer numerical methods to experimental methods due to their easy application. Moreover, the numerical methods can be applied easily to teeth with faults such as cracks, pitting, wear, etc. [PERSON] et al. [7] calculated the effect of tooth root cracks on the mesh stiffness of HCR gears with the FE method. It was observed that as the length of cracks increased, the mesh stiffness decreased. [PERSON] et al. [8] proposed an improved TVMS algorithm based on the energy method for both healthy and cracked spur gears. When the cracked tooth entered the contact, periodic impulses were seen because the TVMS sharply decreased. [PERSON] et al. [9] developed an analytical model for TVMS, load sharing, and transmission error for LCR and HCR spur gears. [PERSON] et al. [10] proposed approximate equations for calculating the TVMS of both LCR and HCR gears, including Hertzian effects. [PERSON] et al. [11] developed an empirical equation for calculating the TVMS of spur gears with asymmetric teeth. [PERSON] et al. [12] proposed a novel method for mesh stiffness calculation of LCR and HCR gears with tooth cracks and profile modification. Various types of damage may occur in gears due to high operating forces, heavy working conditions, fatigue, wear, etc. Failure types in gears are grouped into five categories: root fatigue, side surface fatigue, wear, crack propagation, and pitting on tooth surfaces. One of the most important types of these damages is tooth cracks that occur on gears and progress over time, causing fractures. The crack on the gears starts as a small notch and progresses on the tooth over time, causing the tooth or body to break. For this reason, this type of failure must be detected at the initial stage, and the system must be stopped and maintained in a safe zone without completely breaking the tooth or body [13]. Many experimental and numerical studies exist in the literature on gear failure detection and monitoring of LCR and HCR gears. [PERSON] et al.