Extrusion of non-symmetric U- and I-shaped sections through ruled-surface dies: numerical simulations and some experiments

In this paper, previously developed analytical approach (Chitkara NR, Celik KF. Int J Mech Sci 2000; 42:273) based on the upper-bound theory was applied to analyse the mechanics of the extrusion of non-symmetric U- and I-shaped sections and the symmetric ones from initially round billets through the ruled-surface dies. To investigate the optimum shape of the designed extrusion dies, that yield the lowest upper-bound for a given reduction in area, die length, off-centric positioning and frictional conditions a computer program was developed. Computations were carried out for various cases and some of the results compared with the experimental verifications. Curvature of the extruded product and simulated deforming grid patterns were also predicted and compared. A sophisticated CAD/CAM package was used in conjunction with the CNC and EDM processes to design and manufacture the streamlined dies for the extrusion of some non-symmetric U- and I-shaped sections. The theoretical predictions were observed to be in good agreement with the experimental results.     

Forging and heading of hollow spur gear forms: an analysis and some experiments

To analyse the process of incremental forging and heading of hollow spur gear forms from initially ring-type specimens, the two types of theoretical approaches followed were an adaptation of the upper bound technique, applied previously to the solution of solid spur gear form forging (Chitkara NR, Bhutta MA. International Journal of Mechanical Sciences 1996;38(8–9):891–916) and the modification of the slab method of analysis given earlier for the case of spline forging and adapting it to the tapered teeth representing the actual profile teeth of the spur gear with the pressure angle of 14 °, (Chitkara NR, Bhutta MA. International Journal of Mechanical Sciences 1996;38(8–9):871–89). In each case, the theoretical results estimated were compared with those obtained experimentally during quasi-static forging and heading of hollow spur gear forms using the model material, tellurium lead. The characteristic deformation modes and some salient observations made on working pressures are given and the results commented upon.     

Extrusion of axi-symmetric bi-metallic tubes from solid circular billets: application of a generalised upper bound analysis and some experiments

The generalised upper bound technique previously applied to the determination of working pressures in extrusion–piercing of solid billets (Chitkara NR, Aleem A. Int J Mech Sci 2001;43:1685–709.) to form hollow monometallic tubes is extended to analyse the problem of bi-metallic tube extrusions through profile shaped dies and mandrel combinations. Theoretical results of mean extrusion pressures obtained from the generalised upper bound analysis are compared with those obtained earlier by the generalised slab method of analysis (Chitkara NR, Aleem A. Int J Mech Sci 2001;43:2857–82.) and some experiments. A few salient observations made during the experimental investigations carried out into forward extrusion of bi-metallic tubes made of h.c. copper and c.p. aluminium are also given and the results commented upon.     

Extrusion of axi-symmetric bi-metallic tubes: some experiments using hollow billets and the application of a generalised slab method of analysis

A generalised slab method of analysis is developed for the extrusion of axi-symmetric bi-metallic tubes through profiled shaped dies and over profile shaped mandrels. It is applied to different combinations of die shapes and mandrels. An experimental investigation into forward extrusion of bi-metallic tubes made of cp aluminium and hc copper was also carried out and the resultant non-dimensionalised extrusion pressures, flow patterns and characteristic deformation modes observed are given and the results commented upon. The theoretical results of extrusion pressures obtained from the analysis are compared with the experimental as well as those of other authors. These show reasonably good agreement.     

Shape heading of splines and solid spur gear forms:: an analysis and some experiments

To analyse the process of near-net shape heading of splines and solid spur gear forms with the 15 actual involute teeth, each with a pressure angle of , where in each case these were to be forged integral with the shaft and one end of the initial deforming cylindrical specimen was considered as constrained. Two types of theoretical approaches, i.e. the upper-bound technique (Chitkara and Bhutta. Proceedings of 28 MT DR Conference, 1990. p. 431–42; Chitkara and Bhutta. International Journal of Mechanical Sciences 1995;37(12):1247–68; 1996;38(8–9):891–916) and the slab method of analysis (Chitkara and Bhutta. International Journal of Mechanical Sciences 1996;38(8–9):871–89) employed earlier for simple forging of the product were suitably modified to account for the constraint, were applied. In each case, the estimated theoretical results for the die loads at increasing die movements were compared with those observed experimentally during the quasi-static incremental heading of splines and solid spur gears using tellurium lead as the model material for the specimens. The characteristic deformation modes and some salient observations made on the working pressures during the heading process vis-à-vis simple forging of these products are given and the results are commented upon.     

A generalised CAD/CAM solution to the three-dimensional off-centric extrusion of shaped sections: analysis

In analytical method based on the upper-bound theory is proposed to investigate the three-dimensional off-centric extrusion of arbitrarily shaped sections from arbitrarily shaped billets through linearly converging and smooth curved dies. A set of generalised kinematically admissible velocity fields are derived on the assumption of Bezier-type streamlines that provide compatibility of surface representation with most CAD/CAM systems. To obtain a more realistic non-uniform metal flow, a special velocity function was also incorporated into the derived velocity fields and work hardening effect of the material considered. Based on the method presented, for a given reduction in area, material property, friction condition and off-centric positioning of the exit cross-section, predictions of the deforming grid pattern, curvature of the extruded product as well as upper-bound to the extrusion pressures may be obtained. The above procedure is highlighted and commented upon.     

Application of an upper bound method to off-centric extrusion of square sections, analysis and experiments

The previously given analytical method [1], which was based on the upper-bound theory, was used to design the streamlined dies and to investigate the three dimensional off-centric extrusion of circular sections from initially circular billets through linearly converging (ruled-surface) and smooth curved (advancedsurface) dies. For a reasonably correct upper-bound to the load, a set of generalised kinematically admissible velocity fields were derived on the assumption of Bezier-type streamlines by incorporating a special velocity function that takes care of the non-uniform material flow. Based on the present method, for a given reduction in area, material property, friction condition and off-centric positioning of the exit cross-section, computations were carried out to predict the upper-bound to the extrusion pressures, the deforming grid patterns and curvature of the extruded product. Experiments were carried out for some off-centric circular sections with varying die lengths and reduction in areas. A sophisticated CAD/CAM package was used in conjunction with the CNC and EDM processes to manufacture the streamlined dies for the off-centric extrusion of circular rods. Both the solid and split-type specimens made of tellurium lead under both the lubricated and the dry conditions were used for experimental investigations in order to assess pressures, deformation modes and to visualise the deforming grid patterns. The theoretical predictions were observed to be in good agreement with the experimental.     

On the properness condition for modal analysis of non-symmetric second-order systems

Non-symmetric second-order systems can be found in several engineering contexts, including vibroacoustics, rotordynamics, or active control. In this paper, the notion of properness for complex modes is extended to the case of non-self-adjoint problems. The properness condition is related to the ability of a set of complex modes to represent in an exact way the behavior of a physical second-order system, meaning that the modes are the solutions of a quadratic eigenvalue problem whose matrices are those of a physical system. This property can be used to identify the damping matrices which may be difficult to obtain with mathematical modeling techniques. The first part of the paper demonstrates the properness condition for non symmetric systems in general. In the second part, the authors propose a methodology to enforce that condition in order to perform an optimal reconstruction of the “closest” physical system starting from a given basis complex modes. The last part is dedicated to numerical and experimental illustrations of the proposed methodology. A simulated academic test case is first used to investigate the numerical aspects of the method. A physical application is then considered in the context of rotordynamics. Finally, an experimental test case is presented using a structure with an active control feedback. An extension of the LSCF identification technique is also introduced to identify both left and right complex mode shapes from measured frequency response functions.     

Extrusion of axi-symmetric tubes from hollow and solid circular billets: : a generalised slab method of analysis and some experiments

To analyse the mechanics of extrusion of an axi-symmetric tube starting from either a hollow or a solid circular billet, a generalised analytical approach based on the slab method of analysis is developed for a somewhat general case of tube extrusion through a general profile-shaped die and over a general profile-shaped mandrel. The results of mean extrusion pressures obtained from the theoretical analysis for the various die–mandrel combinations are compared with the experimental investigation carried out on a model material and with the work of other authors. These show reasonably good agreements.     

塑料异型材截面厚度不均对挤出工艺的影响

薄壁塑料异型材在生产生活中得到了越来越广泛的应用,而截面厚度不均对挤出工艺有着比较大的影响.首先对L型异型材出口速度均匀性进行了理论分析,然后对T型异型材出口速度均匀性进行了数值分析,最后着重分析了截面厚度差异对挤出工艺的影响规律.在实际生产过程中,应尽量避免截面厚度的不均匀导致的不良影响.     

Conform连续挤压原理与铜线挤压加工的影响因素

介绍了Conform连续挤压法的工艺原理及其优越性,分析研究了影响铜线连续挤压加工的各种工艺因素。根据铜线挤压生产的实际情况,开发了适应铜线连续挤压生产需要的挤压模具及工艺流程。     

钢挤压机穿孔针冷却装置的研制

分析了挤压工具的使用现状,从为企业降低生产成本、提高经济效益和产品质量的角度出发,研制出钢挤压机穿孔针冷却装置,可以提高穿孔针使用寿命,缩短更换穿孔针和清理挤压筒的时间。该装置结构紧凑合理,操作方便,得到了用户的肯定。     

Axi-symmetric tube extrusion/piercing using die–mandrel combinations: some experiments and a generalised upper bound analysis

A generalised upper bound technique is applied to the solution of working pressures in extrusion–piercing of hollow tubes starting from either solid circular or initially hollow billets by using axi-symmetric die–mandrel combinations of different shapes. Characteristic deformation modes during processing of these tubes made of tellurium lead and commercially pure aluminium were studied experimentally and the results presented. Estimates of working pressures based on the generalised upper bound analysis are compared with the experimental and with those estimated earlier from the slab method of analysis given in Chitkara and Aleem (International Journal of Mechanical Sciences, submitted for publication). These show good co-relations with each other and with the experiments.     

液固挤压复合材料工艺参数优化系统的设计与实现

针对集凝固、压力下结晶和大变形为一体的液固挤压复合材料过程参数设计难题,本文采用面向对象的编程方法开发了工艺参数优化设计系统原型,实现了人机环境下液固挤压成形过程有限元分析和参数遗传优化之间的信息交互与集成。重点研究了基于组件对象模块(COM)的信息交互技术和结合补偿模糊神经网络的遗传优化算法,使平台系统更适应于复杂的非线性参数优化问题,并以分析液固挤压成形实验测得的变形力为应用实例对所开发的系统进行了测试验证。结果表明,基于该系统优化工艺参数,能有效缩短工艺设计周期,为实验设计提供更为理想的工艺方案。     

热挤压模具的有限元分析与优化设计

利用有限元法对热挤压模具体内各节点的应力值进行了计算和分析 ,结果表明 :模具体内应力集中较明显 ,且在此部位极易形成裂纹。通过对模具结构尺寸的优化设计 ,改进后的模具体内最大应力下降 32 .2 % ,从而延长了模具的使用寿命。     

Simulation of Upset Heading, Application of Rigid-Plastic Finite Element Analysis and some Experiments

The application of rigid-plastic finite-element analysis to solve industrial metal forming problems, especially the upset-heading of solid circular cylindrical billets made of ductile materials is discussed. A simple numerical program is developed for simulating the mechanics of the deformation process. Results are obtained from the finite-element analysis on the variation of upset-heading load against variation in reduction in height/diameter ratios of the specimens and on the geometry changes. The characteristic deformation modes and the profile shapes etc. are shown compared with the experiments using a model material and are commented upon. It was found that the agreement between the results was good and that the computation, using a simple approach, may be done for more than 40% reduction in height of the specimen. Because of the more severe deformation at this reduction, the work so far in this area has been restricted. ID="A1" Correspondence and offprint requests to: Dr N.R. Chitkara, Applied Mechanics Division, Department of Mechanical Engineering, UMIST, PO Box 88, Manchester, M60 1QD, UK     

工业纯镁的往复挤压工艺及晶粒细化效果

在150,175,200,225,250℃对工业纯镁进行不同道次的往复挤压,用光学显微镜研究了挤压温度和挤压道次对晶粒细化效果的影响。结果表明:150℃是工业纯镁能够进行往复挤压的最低温度;随着挤压温度的升高,工业纯镁的塑性提高,挤压应力下降,但晶粒细化效果有所下降;随着挤压道次增加,晶粒进一步细化;最佳挤压温度为200℃,最佳挤压道次为4次。     

Matching of physical experiments and multibody dynamic simulation for large deformation problems

Many papers have studied computer simulations of elastic bodies undergoing large deflections and large deformations. But there have not been many attempts to check the validity of the numerical formulations because the simulation results could not be matched without correct input data such as material properties and damping effects. In this paper, these values are obtained from real experiment with a high-speed camera and a data acquisition system. The simulation results with the absolute nodal coordinate formulation (ANCF) are compared with the results of real experiments. Two examples, a thin cantilever beam and a thin plate, are studied to verify whether the simulation results are well matched to experimental results.