آناليز تحليلي و عددي نيروهاي عكس العمل در قيد و بند قطعات با هندسه چندوجهي

Analytical and Numerical Investigation of Reaction Forces in Fixturing of Rigid Workpiece with Polyhedral Geometry

اﻧﺪازه ﻧﯿﺮوﻫﺎي ﻋﮑﺲاﻟﻌﻤﻞ در ﻧﻘﺎط ﺟﺎﺳﺎزي ﻗﯿﺪ و ﺑﻨﺪﻫﺎ ﺣﺎﺋﺰ اﻫﻤﯿﺖ ﺑﺎﻟﺎﯾﯽ ﺑﻮده و ﺑﻪ ﻋﻨﻮان ورودي در ﻣﺮاﺣﻠﯽ ﻫﻤﭽﻮن ﻃﺮحرﯾـﺰي ﻗﯿـﺪ و ﺑﻨﺪﻫﺎ، ﻃﺮاﺣﯽ اﻟﻤﺎنﻫﺎ و ﺻﺤﺖﺳﻨﺠﯽ اﺳﺘﻔﺎده ﻣﯽﺷﻮد. در اﯾﻦ ﻣﻘﺎﻟﻪ، روﺷﯽ ﭼﺎﺑﮏ و دﻗﯿـﻖ ﺑـﺮ ﻣﺒﻨـﺎي اﺻـﻞ ﮐﻤﯿﻨـﻪ اﻧـﺪازه ﻧﯿﺮوﻫـﺎ، ﺑـﺮاي ﻣﺤﺎﺳﺒﻪ ﻧﯿﺮوﻫﺎي ﻋﮑﺲاﻟﻌﻤﻞ در ﻗﯿﺪ و ﺑﻨﺪﻫﺎي ﻣﺎﺷﯿﻦﮐﺎري ﭘﯿﺸﻨﻬﺎد ﻣﯽﺷﻮد. ﺑﺮاي ﺻﺤﺖﺳﻨﺠﯽ ﻣﻘﺎدﯾﺮ ﭘﯿﺶﺑﯿﻨﯽ ﺷﺪه از ﺗﺌـﻮري، ﺷـﺒﯿﻪ-ﺳﺎزي ﻋﺪدي ﺑﻪﮐﻤﮏ ﻧﺮماﻓﺰار آﺑﺎﮐﻮس روي ﻗﻄﻌﺎت ﺑﺎ ﻫﻨﺪﺳﻪ ﭼﻨﺪوﺟﻬﯽ اﺟﺮا ﺷﺪه اﺳﺖ. ﺑـﺎ ﻣﻘﺎﯾﺴـﻪ ﻧﺘـﺎﯾﺞ، اﻧﻄﺒـﺎق ﻣﻨﺎﺳـﺒﯽ ﺑـﯿﻦ ﻣﻘـﺎدﯾﺮ ﭘﯿﺶﺑﯿﻨﯽ ﺷﺪه ﺑﺮاي ﻣﺆﻟﻔﻪ ﻋﻤﻮدي ﻧﯿﺮوﻫﺎي ﻋﮑﺲاﻟﻌﻤﻞ از ﺗﺌﻮري، ﻧﺘﺎﯾﺞ آﻧﺎﻟﯿﺰ ﻋﺪدي و ﻧﺘﺎﯾﺞ اراﺋﻪ ﺷﺪه در ﭘـﮋوﻫﺶﻫـﺎي ﭘﯿﺸـﯿﻦ ﻣﺸـﺎﻫﺪه ﺷﺪ. ﺑﯿﺸﯿﻨﻪ ﺧﻄﺎ در ﭘﯿﺶﺑﯿﻨﯽ ﻧﯿﺮوﻫﺎي ﻧﺮﻣﺎل ﺑﺮ ﺳﻄﺢ از ﺗﺤﻠﯿﻞ ﭘﯿﺸﻨﻬﺎدي ﻧﺴﺒﺖ ﺑﻪ ﻧﺘﺎﯾﺞ ﺷﺒﯿﻪﺳﺎزي 3/9% ﺑﺪﺳﺖ آﻣﺪ. ﻣﻘـﺎدﯾﺮ ﺑﺪﺳـﺖ آﻣﺪه از ﺗﺤﻠﯿﻞ اراﺋﻪﺷﺪه ﺑﺮاي ﻣﺆﻟﻔﻪ ﻣﻤﺎﺳﯽ ﻧﯿﺮوﻫﺎي ﻋﮑﺲاﻟﻌﻤﻞ دﻗﯿﻖ ﻧﺒﻮده و ﻗﺎﺑﻞ اﻋﺘﻨﺎ ﻧﯿﺴـﺖ. ﻫﺮﭼﻨـﺪ ﺑـﺎ ﺗﻮﺟـﻪ ﺑـﻪ اﻧـﺪازه اﻧـﺪك اﯾـﻦ ﻧﯿﺮوﻫﺎ، اﻣﮑﺎن ﭼﺸﻢﭘﻮﺷﯽ از آنﻫﺎ در ﻃﺮاﺣﯽ ﻗﯿﺪ و ﺑﻨﺪﻫﺎ وﺟﻮد دارد. ﺗﻄﺎﺑﻖ ﻣﻨﺎﺳﺐ ﺑﯿﻦ ﭘﯿﺶﺑﯿﻨﯽﻫﺎي ﺗﺌﻮري و ﻧﺘﺎﯾﺞ ﻋﺪدي، ﺑﯿﺎﻧﮕﺮ ﮐﺎراﺋﯽ ﻣﺪل اراﺋﻪﺷﺪه ﺑﺮاي ﻣﺤﺎﺳﺒﻪ ﺳﺮﯾﻊ ﻧﯿﺮوﻫﺎي ﻋﮑﺲاﻟﻌﻤﻞ در ﻗﯿﺪ و ﺑﻨﺪ ﻗﻄﻌﺎت ﺑﺎ ﻫﻨﺪﺳﻪ ﭼﻨﺪوﺟﻬﯽ اﺳﺖ

Reaction forces at the locating points of the machining fixture are considered as one of the important input parameters in different stages of fixture design procedure including fixture planning, unit design, and verification. In the present study, an agile tool is proposed for calculation of the reaction forces based on the minimum norm principle. For validation of the results, finite element analysis is performed in Abaqus® software on a rigid workpiece with polyhedral geometry. The reaction forces are calculated from the numerical analysis and compared to the theoretical predictions. In comparison to the numerical results, the worst-case error of 3.9% is obtained for the theoretical predictions of the normal-to-surface components of reaction forces. The theoretical predictions of the tangential components of reaction forces are not accurate. However, their effects are negligible by considering that the intensity of these forces is low in comparison to the normal components. It was concluded that the theoretical predictions of the normal components of reaction forces agreed well to the numerical data and results that were published in the previous studies. The agreement between the theoretical predictions, results of the previous studies, and the finite element analysis confirmed the accuracy of the suggested model.