Slab Method and FEM Simulation on Porous Cylinder in Rotating Compression under Constant Shear Friction

• Main Authors: Sai-Chih Pan, 潘賽智
• Other Authors: Gow-Yi Tzou
• Format: Others
• Language: zh-TW
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/handle/7qm9xg

博士 === 國立中山大學 === 機械與機電工程學系研究所 === 107 === Porous materials are getting more widely used in the industries and have become important engineering materials. In the process of material manufacturing by compression forming, die rotation can reduce compression force and improve product quality (such as improving density and dimensional accuracy, as well as increasing uniform forming). Therefore, assuming that the slab method (SLM) and the finite element method (FEM) are used under constant shear friction, this paper performs plasticity mechanics analysis on rotating compression and non-rotating compression forming of porous cylinders, makes comparison between both models and compression characteristics, and systematically investigates changes in vertical stress (p), radial stress (q), effective stress, effective strain, velocity field, density and radius of cylinderafter forming, compression force (P), and rotating torque (T). Since compression forming of porous materials can only enable conservation of mass but not conservation of volume, the mathematical derivation process with SLM is more complicated. However, the comparison of results between the plasticity analysis model and finite element analysis software DEFORM-2D and 3D, as well as the cross-comparison with experiment results using a 30-ton rotating compression forming machine, not only enable mutual verification, but can also establish an understanding of the differences between slab analysis and finite element simulation, and provide a reference for compression forming of porous materials in the industries. Based on the results of this study, the data obtained using SLM are always lower than those obtained using FEM. At three different rotational speeds, i.e. 0.1, 0.5, and 1.0 rad/s, the percentage errors of compression force (P) determined using both methods are 12.04%, 14.51%, and 13.73%, respectively; whereas the percentage errors of rotating torque (T) determined using both methods are 10.85%, 8.42%, and 8.72%, respectively. At three different aspect ratios (Height Diameter Ratio), i.e. 0.75, 1, and 1.25, the percentage errors of compression force (P) determined using both methods are 11.76%, 11.63%, and 12%, respectively; whereas the percentage errors of rotating torque (T) determined using both methods are 10.59%, 10.05%, and 9.02%, respectively. At three different frictional factors, i.e. 0.1, 0.3, and 0.7, the percentage errors of compression force (P) determined using both methods are 11.76%, 14.51%, and 23.9%, respectively; whereas the percentage errors of rotating torque (T) determined using both methods are 10.59%, 8.42%, and 18.9%, respectively. In addition to the fact that the data obtained using SLM are lower based on the charts and data shown in each chapter, the results of this study also indicate that interfacial friction is the most critical factor. The rotation of cylinder driven by friction can not only reduce compression force and bulging, but also increase relative density after forming (the advantage of increasing friction). However, friction can also increase compression force and bulging (the disadvantage of increasing friction). In other words, friction has its pros and cons in regard to rotating compression of porous cylinders, and the optimal lubrication level is determined according to the site or case requirements. Lastly, an experiment is conducted in this study, where compression tests are performed on nine porous metals (sintered iron-copper alloy) of the same material at three different aspect ratios, i.e. 0.75, 1, and 1.25, along with three different rotational speeds, i.e. 0, 0.26, and 0.52rad/s. Based on the comparison of values between the finite element simulation and the experiment, the minimum error of compression force (P) is 0.13% (at an aspect ratio of 0.75 and a rotational speed of 0.52 rad/s), whereas the maximum error of compression force (P) is 4.09% (at an aspect ratio of 1.25 and a rotational speed of 0.26 rad/s). On the other hand, the minimum error of cylinder dimensions (diameter) after compression is 0.15% (at an aspect ratio of 0.75 and a rotational speed of 0.26 rad/s), whereas the maximum error of cylinder dimensions (diameter) after compression is 4.96% (at an aspect ratio of 1 and a rotational speed of 0.52 rad/s). In addition, data obtained from the experiment, slab analysis and finite element simulation exhibit the exact same trend, in which the finite element simulation results are very identical to the experimental results. Although slab analysis is limited by the assumptions of the method itself, which causes the data and results obtained using this method to be lower than those obtained using finite element simulation, it is still an excellent quick-solving method due to its simple and quick-solving ability. In summary, based on the comparisons between SLM and the finite element simulation model proposed in this study, the error at a compression rate of 50% and below still lies within an acceptable range; therefore, the applicability of SLM can be known. Furthermore, the feasibility of FEM can also be known based on the comparisons between the experiment and FEM. Therefore, the results of this study provide a relatively useful reference to the powder forging industry.