PSI - Issue 42

2

Author name / Structural Integrity Procedia 00 (2019) 000 – 000

1608 © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Omar D. Mohammed et al. / Procedia Structural Integrity 42 (2022) 1607–1618

Peer-review under responsibility of 23 European Conference on Fracture - ECF23 Keywords: Gear design; design requirements; microgeometry; PPTE; dependency in gear design

1. Introduction Gear design has been under development to meet the design requirements in terms of gear durability, functionality, speed ratio, assembly, weight, cost, manufacturing specifications and acceptable Noise, Vibration, and Harshness (NVH) levels. Therefore, the selected design must be compromised by obtaining the most optimal design that fulfils all the various design requirements (Kapelevich 2003, Radzevich 2016). Basically, gear geometry is over defined by many related design parameters that must be adjusted in order to obtain a valid design. However, gear macrogeometry, which defines the gear dimensions, is mainly restricted by the pre-selected generating cutter and also by the other connected elements. Therefore, the continuous demands to fulfil the design requirements pressured gear designers to pay higher attention to the microgeometry design area. Microgeometry defines all modifications in the micro-scale measured from the nominal involute tooth profile. The microgeometry modifications help in compensating for the misalignment and have a significant effect on reducing the generated stresses and transmission error (TE) (Kapelevich 2003). Therefore, a lot of research work has been conducted to investigate the design development and to study various design aspects, such as efficiency, TE, durability, weight, and cost. Furthermore, different design considerations have been studied, such as backup ratio, tooth flank modifications, and misalignment. The backup ratio which is defined as the ratio of the rim thickness to the whole tooth depth was studied in (Hiremagalur & Ravani 2004). The effect of the backup ratio on spur gear design was studied using the theory of elasticity, and several analytical expressions were developed for the critical gear tooth dimensions. The combined effects of the rim thickness and the pitch diameter on the generated gear tooth root stresses were studied in (Drago & Lutthans 1983). A linear elastic fracture mechanics approach for evaluating the crack propagation path at the root area as a function of the rim thickness was presented in (Bibel, Reddy & Savage 1991, Lewicki & Ballarini 1997). Fatigue test data were also presented to supporting the analysis. The effect of design parameters and tooth modifications on gear efficiency, TE, and durability was studied in (Li, Vaidyanathan, Harianto & Kahraman 2009). The authors tried to obtain a balanced design that meets the requirements of various design aspects. The tooth microgeometry modifications were studied to investigate the effects of those modification parameters on gear TE and durability (Beghini, Presicce & Santus 2004, Tavakoli & Houser 1986, Artoni et.al. 2014, Tesfahunegn, Rosa & Gorla 2010) A gear dynamic model was developed in (Wang 2018) to study the effect of tooth shape deviations and errors on the system dynamic behaviour. The effects of machining errors, assembly errors and tooth modifications on spur gear loading capacity, load-sharing ratio and TE were studied by (Li 2007) using a developed FEMmodel. Later, (Li 2015) studied the effects of tooth profile modifications, lead relieving, and misalignment errors on teeth engagement and tooth mesh stiffness. The effect of misalignment on gear teeth was studied (Li 2015, Saxena, Parey, & Chouksey 2015, Zhang & Liu 2015, Shehata, Adnan & Mohammed 2019, Mohammed 2005, Palazzolo et.al. 1992). The misalignment errors, the friction forces, and the time-varying mesh stiffness were studied in (Saxena, Parey, & Chouksey 2015) for a spur gear model. The effects of misalignment and tooth microgeometry modifications on spur gear surface wear were studied in (Zhang & Liu 2015). Moreover, the effects of misalignments and tooth microgeometry modifications on the generated stresses and the peak-peak transmission error (PPTE) were studied in (Shehata, Adnan & Mohammed 2019). With helical gears, the effects of changing the helix angle on the tooth load distribution, the transmission error, and the generated stresses were studied in (Luo et.al. 2015, Kang & Choi 2008, Bozca 2018). Nomenclature

fhb (µm): Lead slope cb (µm): Lead crown A & B: refers to designs A and B G1, G2 & RG: refers to Gear 1, Gear 2 and Ring Gear respectively D & C: refers to the drive and the coast flanks respectively

fHa (µm): Profile slope ca (µm): Profile crown caa (µm): Tip relief Dca (mm): Tip relief start diameter Roll angle (deg.): Roll angle of tip relief start