PSI - Issue 10

K.G. Raptis et al. / Procedia Structural Integrity 10 (2018) 33–40 K.G. Raptis and A.A. Savaidis / Structural Integrity Procedia 00 (2018) 000 – 000

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The analytical determination of the crucial section has been first proposed by Lewis (1882), who initially assumed that it is located in the isosceles parabola which is tangential to the gear toe. Later, after comparing with photoelasticity measurements (Dnyaneshwar and Mangrulkar (2016); Niemann (1965); Naik and Dhananjay (2016); Abdullah et al. (2017); Patil et al. (2017); Surajit and Sachin (2015); Vivek et al. (2013); Vishwakama (2017); Wable and Mate (2013)), the assumed location has been moved lower along the toe. Photoelasticity has been widely used since the beginning of the previous century for illustrating the stress field during coupling of gears, as it provides high accuracy and minimum external disturbance of the system (Prajapati et al. (2014); Seok-Chul et al. (2013); Spitas et al. (2005a; 2005b; 2007)). According to the method of the tangent of 30  (Niemannn (1965)) the crucial section does not depend on the loading position and is always located in an invariable position at the tooth toe. Other methodologies which are used for the determination of the maximum stress at the crucial toe section are time-consuming and require availability of more data (DIN (1987); Kawalec et al. (2006)). Those methods lack accuracy and are not appropriate to tooth configur ations subjected to high loads. The proposed method rests on the assumption that maximum loading during the cooperation of the spur gears is acting at HPSTC (Colbnourne (1987); Costopoulos and Spitas (1994; 2009); Spitas et al. (2005a; 2005b; 2007)). In order to experimentally study the strains in the vicinity of the loaded gear region a batch of specimens have been fabricated. The dimensions of the specimens have been chosen as to simulate realistic gears in terms of gear teeth number and module and to be compatible with the polariscope utilized. The sheet had been doubly coated and annealed in order to extinguish any residual stress. The actual sheet thick ness has been measured at various positions and found to be approximately 9.25 mm. In addition, four prismatic specimens with dimensions 120 x 20 x 9.25 mm 3 have been fabricated in order to be utilized for determining the elasticity modulus and the stress-optical constant of the material, as well as their variance within the material. In order to experimentally determine the maximum stress developed at HPSTC for every tooth combination the dark field polariscope of the National Technical University of Athens (SHARPLES Stress Engineers Ltd) has been used (Raptis et al. (2010)). The specimens have been fabricated using a special photosensitive material PSM-1 and their geometrical char acteristics are provided in Table 1. They are illustrated in Figs. 1 and 2. 2. Experimental methodology

Table 1. Specimen geometrical characteristics

m (mm)

Specimen Number

Serial

Description

z

1 2 3

18N 22N 28N

Normal Gear with 18 teeth Normal Gear with 22 teeth Normal Gear with 28 teeth

18 22 28

20 20 20

3. Gear subjected to point load

The most unfavourable stress situation for a gear tooth is not occurring when loading acts on the head, since in that case the load is distributed between two tooth pairs. In the contrary, when the load acts at a gear contact trajectory point, the stress situation is mostly unfavourable, since only a single pair of tooth is coupled. Thus, when a spur gear is subjected to a point load maximum bending stress occurs when the load is applied on a special spot, which is called Highest Point of Single Tooth Contact - HPSTC. The position of this spot depends on the basic geometrical characteristics of the teeth (Figs.3 & 4) and may be determined on the basis of analytical calcula tions. Contact initiates at point A (LPSTC), where the foot of the pinion gear touches the head of the coupled gear, and it ends at point B (HPSTC) (Prajapati et al. (2014); Seok-Chul (2013); Vaghela and dayal (2014); Vivek et al. (2013)). The data of the tests conducted on the specimens of the gears described above are synoptically summarized in next Table 2.