Effect of Shaft Misalignment on The Stresses Distribution of Spur Gears

Abstract

Shaft misalignment is considered as one of the common repeated problems in most rotating machineries , which leads to generate vibrations and extra dynamic loads on transmitting gears teeth, also leads to non-uniformity in distribution of applied load along the meshing tooth face by being concentrated on one side of tooth face. The present work concentrated on the analysis of stresses generated on transmitting gear tooth, also studied the effect of misalignment angle on stress distribution and its concentration. This is important for the gear design and those who works in gear maintenance , because fracture is expected to initiate and propagate at locations of stress concentration. ANSYS program using finite element technique had been used, as this program is efficient and accurate tool in stress analysis, especially for complicated shapes. Gear tooth model had been analyzed using finite element method in three dimensions. After calculating transmitted load and dynamic load, misalignment angle had been changed from (0°,0.2°,0.3°,0.4°,0.5°) then its effect on distribution of applied load had been calculated. The finite element program (ANSYS) had been executed for cases of misalignment angle (0°,0.2°,0.3°,0.4°,0.5°). The results showed clearly, that the stresses distribution and its concentration on tooth changed with misalignment angle and the equivalent stress is direct proportional with the misalignment angle. According to the values of generated stresses, the tooth fracture can be predicted. ‫ﺍﻟﻤﺤﺎﺫﺍﺓ‬ ‫ﻋﺩﻡ‬ ‫ﺘﺄﺜﻴﺭ‬ ‫ﺍﻟﺩﻭﺭﺍﻥ‬ ‫ﻋﻤﻭﺩ‬ ‫ﻓﻲ‬ ‫ﺍﻻﺠﻬﺎﺩﺍﺕ‬ ‫ﺘﻭﺯﻴﻊ‬ ‫ﻋﻠﻰ‬ ‫ﻟ‬ ‫ﺍﻟﻤﺴﺘﻘﻴﻤﺔ‬ ‫ﻠﺘﺭﻭﺱ‬ ‫ﺍﻟﺨﻼﺼﺔ‬ ‫ﺍﻟﻤﺤﺎﺫﺍﺓ‬ ‫ﻋﺩﻡ‬ ‫ﻤﺴﺄﻟﺔ‬ ‫ﺘﻌﺩ‬ ‫ﻓﻲ‬ ‫ﻭﺍﻟﻤﺘﻜﺭﺭﺓ‬ ‫ﺍﻟﺸﺎﺌﻌﺔ‬ ‫ﺍﻟﺘﺸﻐﻴﻠﻴﺔ‬ ‫ﺍﻟﻤﺸﺎﻜل‬ ‫ﻤﻥ‬ ‫ﺍﻟﺩﻭﺭﺍﻥ‬ ‫ﻋﻤﻭﺩ‬ ‫ﻓﻲ‬ ‫ﺍﻟﺘﺭﻭﺱ‬ ‫ﺍﺴﻨﺎﻥ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻀﺎﻓﻴﺔ‬ ‫ﺩﻴﻨﺎﻤﻴﻜﻴﺔ‬ ‫ﻭﺍﺤﻤﺎل‬ ‫ﺍﻫﺘﺯﺍﺯﺍﺕ‬ ‫ﺘﻭﻟﻴﺩ‬ ‫ﺍﻟﻰ‬ ‫ﺘﺅﺩﻱ‬ ‫ﺍﺫ‬ ،‫ﺍﻟﻤﻜﺎﺌﻥ‬ ‫ﻤﻌﻅﻡ‬ ‫ﻟ‬ ‫ﺍﻟﻨﺎﻗﻠﺔ‬ ‫ﻠﺤﺭﻜﺔ‬. ‫ﺒﺘﺭﻜﺯﻩ‬ ‫ﺍﻟﻤﻌﺸﻕ‬ ‫ﺍﻟﺴﻥ‬ ‫ﺴﻁﺢ‬ ‫ﺍﻤﺘﺩﺍﺩ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﻤﺴﻠﻁ‬ ‫ﺍﻟﺤﻤل‬ ‫ﺘﻭﺯﻉ‬ ‫ﺍﻨﺘﻅﺎﻡ‬ ‫ﻋﺩﻡ‬ ‫ﻭﺍﻟﻰ‬ ‫ﺍﻟﺴﻥ‬ ‫ﺴﻁﺢ‬ ‫ﻤﻥ‬ ‫ﺠﺎﻨﺏ‬ ‫ﻋﻠﻰ‬. ‫ﺘﺭﺱ‬ ‫ﺴﻥ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﻤﺘﻭﻟﺩﺓ‬ ‫ﺍﻻﺠﻬﺎﺩﺍﺕ‬ ‫ﺘﺤﻠﻴل‬ ‫ﺤﻭل‬ ‫ﺍﻟﺤﺎﻟﻲ‬ ‫ﺍﻟﺒﺤﺙ‬ ‫ﻴﺭﻜﺯ‬ ‫ﻭﺘﺭﻜﺯﻫﺎ‬ ‫ﺍﻻﺠﻬﺎﺩﺍﺕ‬ ‫ﻫﺫﻩ‬ ‫ﺘﻭﺯﻉ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﻤﺤﺎﺫﺍﺓ‬ ‫ﻋﺩﻡ‬ ‫ﺯﺍﻭﻴﺔ‬ ‫ﻓﻲ‬ ‫ﺍﻟﺘﻐﻴﺭ‬ ‫ﺘﺎﺜﻴﺭ‬ ‫ﻭﺩﺭﺍﺴﺔ‬ ، ‫ﻟﻠﺤﺭﻜﺔ‬ ‫ﻨﺎﻗل‬ ‫ﻟﻤﺎ‬ ‫ﻨﻅﺭﺍ‬ ‫ﻟﺩﺭﺍﺴ‬ ‫ﺍﻟﺘﺭﻭﺱ‬ ‫ﺘﺼﻤﻴﻡ‬ ‫ﻤﺠﺎﻻﺕ‬ ‫ﻓﻲ‬ ‫ﻟﻌﺎﻤﻠﻴﻥ‬ ‫ﺒﺎﻟﻨﺴﺒﺔ‬ ‫ﺍﻫﻤﻴﺔ‬ ‫ﻤﻥ‬ ‫ﺍﻻﺠﻬﺎﺩﺍﺕ‬ ‫ﺘﺭﻜﺯ‬ ‫ﺔ‬ ‫ﻭﺼﻴﺎﻨﺘﻬﺎ‬ ‫ﻭﺘﺸﻐﻴﻠﻬﺎ‬. ‫ﺍﻻﺠﻬﺎﺩﺍﺕ‬ ‫ﺘﺭﻜﺯ‬ ‫ﻤﻨﺎﻁﻕ‬ ‫ﻋﻨﺩ‬ ‫ﻭﻴﺘﻨﺎﻤﻰ‬ ‫ﺍﻟﻜﺴﺭ‬ ‫ﻴﺒﺩﺃ‬ ‫ﺍﻥ‬ ‫ﻴﺘﻭﻗﻊ‬ ‫ﺍﺫ‬. ‫ﻫﺫﺍ‬ ‫ﻓﻲ‬ ‫ﺘﻡ‬ ‫ﺒﺭﻨﺎﻤﺞ‬ ‫ﺨﻼل‬ ‫ﻤﻥ‬ ‫ﺍﻟﻤﺤﺩﺩﺓ‬ ‫ﺍﻟﻌﻨﺎﻁﺭ‬ ‫ﻁﺭﻴﻘﺔ‬ ‫ﺍﺴﺘﺨﺩﺍﻡ‬ ‫ﺍﻟﺒﺤﺙ‬ ANSYS ‫ﻭﺩﻗﻴﻘﺔ‬ ‫ﻓﺎﻋﻠﺔ‬ ‫ﺍﺩﺍﺓ‬ ‫ﺒﻭﺼﻔﻬﺎ‬ ‫ﻭﻻﺴ‬ ‫ﺍﻻﺠﻬﺎﺩﺍﺕ‬ ‫ﺘﺤﻠﻴل‬ ‫ﻓﻲ‬ ‫ﺍﻟﻤﻌﻘﺩﺓ‬ ‫ﻟﻼﺸﻜﺎل‬ ‫ﻴﻤﺎ‬. ‫ﺍﻟﻌﻨﺎﺼﺭ‬ ‫ﺒﺘﻘﻨﻴﺔ‬ ‫ﺍﻟﺘﺭﺱ‬ ‫ﺴﻥ‬ ‫ﻨﻤﻭﺫﺝ‬ ‫ﺘﺤﻠﻴل‬ ‫ﺍﺠﺭﻱ‬ ‫ﺯﺍﻭﻴﺔ‬ ‫ﺘﻐﻴﻴﺭ‬ ‫ﺘﻡ‬ ‫ﺍﻻﻀﺎﻓﻲ‬ ‫ﺍﻟﺩﻴﻨﺎﻤﻴﻜﻲ‬ ‫ﻭﺍﻟﺤﻤل‬ ‫ﺍﻟﻤﻨﻘﻭل‬ ‫ﺍﻟﺤﻤل‬ ‫ﺤﺴﺎﺏ‬ ‫ﻭﺒﻌﺩ‬ ، ‫ﺍﺒﻌﺎﺩ‬ ‫ﺒﺜﻼﺜﺔ‬ ‫ﺍﻟﻤﺤﺩﺩﺓ‬ PDF created with pdfFactory Pro trial version www.pdffactory.com 1322 ‫ﺍﻟﻤﺤﺎﺫﺍﺓ‬ ‫ﻋﺩﻡ‬) 0 ° ، 0.2 ° ، 0.3 ° ، 0.4 ° ، 0.5 ° (‫ﺍﻟﻤﺴﻠﻁ‬ ‫ﺍﻟﺤﻤل‬ ‫ﺘﻭﺯﻉ‬ ‫ﻋﻠﻰ‬ ‫ﺘﺎﺜﻴﺭﻫﺎ‬ ‫ﻭﺤﺴﺎﺏ‬ ، ‫ﻟﻠﺤﺭﻜ‬ ‫ﺍﻟﻨﺎﻗل‬ ‫ﺍﻟﺴﻥ‬ ‫ﻋﻠﻰ‬ ‫ﺔ‬. ‫ﺍﻟـ‬ ‫ﺒﺭﻨﺎﻤﺞ‬ ‫ﺘﻨﻔﻴﺫ‬ ‫ﺘﻡ‬ ANSYS ‫ﺍﻟﻤﺤﺎﺫﺍﺓ‬ ‫ﻋﺩﻡ‬ ‫ﺯﻭﺍﻴﺎ‬ ‫ﻤﻥ‬ ‫ﺤﺎﻻﺕ‬ ‫ﻟﻌﺩﺓ‬) 0 ° ، 0.2 ° ، 0.3 ° ، 0.4 ° ، 0.5 ° (‫ﺍﻟﺘﻐﻴﺭ‬ ‫ﻤﻼﺤﻅﺔ‬ ‫ﻴﻤﻜﻥ‬ ، ‫ﺍﻟﻤﺴﺘﺤﺼﻠﺔ‬ ‫ﺍﻟﻨﺘﺎﺌﺞ‬ ‫ﻋﺭﺽ‬ ‫ﻭﺒﻌﺩ‬ ، ‫ﻋﺩﻡ‬ ‫ﺯﺍﻭﻴﺔ‬ ‫ﺘﻐﻴﺭ‬ ‫ﻋﻨﺩ‬ ‫ﺍﻟﺘﺭﺱ‬ ‫ﺴﻥ‬ ‫ﻋﻠﻰ‬ ‫ﺒﻭﻀﻭﺡ‬ ‫ﻭﺘﺭﻜﺯﻫﺎ‬ ‫ﺍﻻﺠﻬﺎﺩﺍﺕ‬ ‫ﺘﻭﺯﻉ‬ ‫ﻋﻠﻰ‬ ‫ﻴﻁﺭﺃ‬ ‫ﺍﻟﺫﻱ‬ ، ‫ﺍﻟﻤﺤﺎﺫﺍﺓ‬ ‫ﺍﻟﻤﻜﺎﻓﺌﺔ‬ ‫ﺍﻻﺠﻬﺎﺩﺍﺕ‬ ‫ﻭﺍﻥ‬ ‫اﻟﻤﺤﺎذاة‬ ‫ﻋﺪم‬ ‫زاوﯾﺔ‬ ‫ﻣﻊ‬ ‫ﻃﺮدﯾﺎ‬ ‫ﺗﺘﻐﯿﺮ‬ ‫ھﺬه‬ ‫ﻗﯿﻢ‬ ‫وﺑﻤﻮﺟﺐ‬ ، ‫اﻟﺴﻦ‬ ‫ﻓﻲ‬ ‫ﻛﺴﺮ‬ ‫ﺣﺪوث‬ ‫اﻣﻜﺎﻧﯿﺔ‬ ‫ﺗﺤﺪﯾﺪ‬ ‫ﯾﺘﻢ‬ ‫اﻟﻤﺘﻮﻟﺪة‬ ‫اﻻﺟﮭﺎدات‬ .