TPT May 2009

A study into rollforming of parabolical section By Dr Jiying Liu, Mr Yuanguang Li and Mr Zhengqing Ai, North China University of Technology, Beijing, China Supported by Beijing Municipal Natural Science Foundation (3082008)

Abstract In order to meet precision requirements, the parabola fitting is achieved by using the smallest arc. Based on the Biswas formula, the springback model of rollforming parabolic section is a viable option. It is possible to design the roll flower pattern of parabolic section. The correctness of the springback model is verified by experiments and finite element analysis. The rollforming method can be used for the manufacture of parabolic section in engineering applications. Key words: Parabolic section, rollforming, FEA simulation, Biswas springback 1. Introduction Directional light, which is normally present in sectional surface, can be focused on the focal line by use of a parabolic section. It can then achieve a highly efficient gathering that puts heat pipe on the focal line. Based on this feature, parabolic section can be used as a reflector of solar energy water heater. The principle drawing is shown in figure 1. Some research shows that heat energy efficiency of multiple parabolic reflector (composed of parabolic section), is higher than that of a plane and circle arc reflector by 60 to 70 per cent [1] [2] .

The difficulty of using roll forming technology lies in manufacturing the section of variable curvature, what with the complexity of spring back during forming which can not be resolved by existing technology. Aimed at reflector of solar energy water heater and combining finite element simulation and experiment analysis, we have investigated a roll forming method to form parabolic section. 2. Forming of a parabolic section In this study, an inside contour of parabolic section is used as the research object. The mathematical expression of the contour is The section material is 1060H18 aluminium sheet. The unfolding width of the section is 120mm, and the thickness is 0.5mm. Using a circle arc subsection fitting parabolic line, the variable curvature problem is simplified as a multi-arc problem. When experiencing a normal error with a maximum limit of less than 0.1mm, the parabolic section can be substituted with 4 arcs. Two outside arcs are formed first, and then two inside arcs. Due to this fact, forming with a large radius of thin wall, the springback must be considered. For fitting a circle arc, the over- bend forming method should be applied, and the over-bend radius is calculated by the following formula [3] : springback (mm), r f = yield curvature (mm), E = Young’s modulus (MPa), t = thickness of sheet materials (mm), S = yield stress of materials (MPa)) The roll flower pattern is shown in figure 2. It is possible to see that the third pass is an over-bending forming of the outside arc, and the ninth pass is over-bending forming in the side arc. 3. Experiments and result analysis According to the forming of the flower pattern, the rolls were designed and manufactured, and the experiment carried out by a rollforming machine at the North China University of Technology Roll-forming Laboratory (figure 3). The precut length of the aluminium strip was 1,000mm, width 120mm and thickness 0.48mm. The formed parabolic section samples are shown in figure 4. 1 72 y = x 2 , (–48 ≤ x ≤ 48) = 1–1.5 • + 0.5 • 3 ( ) r i 1 r i 2 r i 1 r f r i 1 r E × t 2 × S (where, r f = , r i 1 = bend radius (mm), r i 2 = radius after

At present, because of high cost and difficult forming, to some extent, application of parabolic section is limited in engineering. Roll forming is a high production and low cost of forming process of sheet metal. So, using roll forming technology to manufacture parabolic section has positive signification to industrial application.

 Figure 1 : Principle drawing of solar energy reflector with parabolic section

 Figure 2 : Roll flower pattern

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M ay 2009

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