مهندسی مکانیک مدرس

مهندسی مکانیک مدرس

تعیین تحلیلی توزیع مولفه‌های کرنش و خمیدگی در فرآیند اکستروژن مستقیم مقاطع متقارن بر مبنای نگاشت ریمان و روش حدبالا

نوع مقاله : پژوهشی اصیل

نویسندگان
دانشگاه صنعتی نوشیروانی بابل
چکیده
هدف از این مقاله تعیین تحلیلی مولفه‌های کرنش در فرآیند اکستروژن مستقیم برای پیش‌بینی خمیدگی محصول خروجی می‌باشد. برای این منظور از نظریه نگاشت همدیس ریمان جهت مدل‌سازی ناحیه تغییر شکل و ایجاد تناظری یک به یک بین نقاط مقطع ورودی و خروجی قالب استفاده می‌شود. به کمک منحنی بزیر، خطوط جریان بین این نقاط ایجاد شده و سپس یک حل حدبالا برای میدان سرعت به دست می‌آید. با استفاده از روابط به‌دست آمده، فشار فرآیند و توزیع مولفه‌های کرنش برای مقاطع متقارن مربعی، شش ضلعی منتظم و مستطیلی تعیین می‌گردد. همچنین یک روش نظری مبتنی بر خمش الاستیک-پلاستیک تیرها جهت محاسبه خمیدگی محصول خروجی برای قالب‌های خارج از مرکز ارائه می‌شود. در این روش نظری با استفاده از مولفه‌های کرنش تعیین شده، توزیع مولفه‌های تنش و گشتاور خمشی محاسبه می‌شود. در واقع مقدار گشتاور خمشی بیانگر میزان خمیدگی محصول خروجی است. مدل نظری ارائه شده از طریق مقایسه با نتایج شبیه‌سازی اجزای محدود و پژوهش‌های پیشین صحت سنجی می‌گردد. نتایج حاصل نشان می‌دهد که با بکارگیری نگاشت همدیس ریمان و روش حد بالا علاوه بر تخمین فشار فرآیند، می‌توان برای تعیین توزیع مولفه‌های کرنش و پیش بینی خمیدگی محصول خروجی استفاده نمود.
کلیدواژه‌ها

موضوعات


عنوان مقاله English

AAnalytical determination of strain components distribution and curvature in the direct extrusion process of symmetric sections based on Riemann mapping and Upper bound method

نویسندگان English

Majid Sheikhpour
Seyed Jamal Hosseinipour
M.J. Mirnia
Babol Noshirvani University of Technology
چکیده English

The aim of this paper is to analyze the strain components in the direct extrusion process to predict the curvature of the exit product. For this purpose, Riemann mapping theory is used to model the deformation zone and create a one-to-one correspondence between the input and output cross sections of the die. With the help of the Bezier curves, flow lines are created between these points and then an upper bound solution is obtained for the velocity field. The process pressure and the distribution of the strain components are determined for the square, hexagonal, and rectangular sections using the obtained velocity field. A theoretical method based on the elastic-plastic bending of beams is presented for calculating the curvature of the exit product for the eccentric dies. In this theoretical method, the distribution of stress components and the bending moments is calculated using the specified strain components. In fact, the amount of bending moments indicates the curvature of the exit product. Finally, the presented theoretical model is validated through comparison with the results of the finite element simulation and the previous studies. The results show that Riemann conformal mapping theory and upper bound method can be used to determine the distribution of strain components and predict the curvature of the output product, in addition to estimate the process pressure.

کلیدواژه‌ها English

Extrusion
upper bound
Riemann mapping
Strain distribution
Process pressure
Product curvature
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