【正文】 外文資料翻譯 Overview of adaptable die design for extrusions . . Van . Moon ABST RACT The term ―adaptable die design‖ is used for the methodology in w hich the tooli ng shape is determi ned or modified to produce so me opti mal property in either product or process. The adaptable die design me thod, used in conj unctio n w ith a n upper bound model, allow s the rapid evaluatio n of a large number of die shapes and the discovery of the one tha t produces the desired outco me. In order for the adaptable di e design me thod to be successful, it is necessary to have a realistic velocity field for the de for matio n process thro ugh extr usion dies of a ny s hape a nd the velocity field must allow flexibility in material move me nt to ac hieve the required material flow description. A variety o f criteria can be used in the adaptable die design me thod. For exa mple, dies w hich prod uce mini mal distortio n in the produc t. A double opti mi zatio n process is used to deter mine the values for the flexible variables in the velocity fie ld and seco ndly to de ter mine the die shape that bes t mee ts the give n criteria. The me thod has been exte nded to the design of dies for nonaxisymmetric product shapes. 169。 2021 Elsevier . All rights reserved. Keyw ords: E xtr usion。 Die design。 Upper bound approach。 Mini mum distortion criterion 1. Introduction New metal alloys and co mposi tes are being developed to mee t dema ndi ng applications. Ma ny of these new materials as well as traditional materials have li mi ted w orkability. E xtrusio n is a me talw orki ng process that ca n be used to defor m these diffi c ult ma terials into the shapes ne eded for specific applications. For a successful extrusio n proc ess, me talw orki ng e ngineers and designers need to know how the e xtr usion die s hape ca n affect the fi nal produc t. The present w ork foc uses on the design o f appropriate e xtr usion die shapes. A me thodology is presented to deter mi ne die s hapes tha t mee t specific criteria: either s hapes w hich pro duce prod uct w ith opti mal set of specified properties, suc h as mi ni mum distor tion i n the extr udate, or shapes w hic h produce prod uct b y a n opti mi zed pro cess, suc h as mi ni mum e xtr usion pressure. The term ―adaptable die design‖ is used for the method nology in w hic h the die s ha pe is deter mi ned or modified to prod uce so me opti mal proper ty i n either produc t or process. This adaptable die design method, used in co njunc tion w ith anupper bound model, allows the r apid evaluatio n of a large number of die s hapes and the discove ry of the o ne tha t ca n op ti mize the desired outco me. T here are several conditi ons tha t need to be me t for the adaptable die design method to be viable. First, a ge neralized but realistic velocity field is needed for use in an upper bo und model to ma the ma tically describe the flow of the material during e xtrusio n through dies of any shape. Second, a robust crite rion needs to be es tablished for the op ti miza tion o f the die shape. T he criterion must be useable within a n upper bound model. The full details of the me thod are presented elsew here [1–6]. In the present paper, follow ing a review of previous models for extr usion, the flexible velocity field for the d e for matio n re gion i n a direct extrusio n will be briefly pr esented. T his velocity field is able to characterize the flow thro ugh a die of al mos t a ny co nfi g uratio n. T he adap table equatio n, w hic h describes the die shape, is also presented. T he consta nts in this die shape equatio n are optimi zed with respect to a criterion. T he criterion, w hich can be used to mi ni mize distor tion, i s presented. Finally, the shape o f a n adaptable die, w hic h produces o f an e xtr uded produc t w ith mi ni mal distortio n, is presented. T he objective of the present paper is to provide a brief overview of the adaptable die design method. 2. Background . Axisymmetric extrusion Numero us studies have a nalyzed the a xisymme tric extr usion of a cylindrical prod uct fro m a c ylindrical billet. Avitzur[7–10] proposed upper bound models for axisymme tric extrusio n thro ugh conical dies. Zi mer ma n a nd Avitzur [11] modeled extrusio n using the upper bo und me thod, b ut w ith ge neralized s hear boundaries. Finite eleme nt me thods w ere used b y C he n et al. [12] and Liu a nd C hung [ 13] to model axis ymmetric extr usion thro ugh co nical dies. Che n and Li ng [14] and Na gpal [15] anal yzed other die shapes. T he y developed velocity fields for a xisymme tric extr usion thro ug h arbitrarily s haped dies. Richmo nd[16] w as the first to propose the concept of a streamlined die shape as a die profile optimi zed for mini mal distortio n. Ya ng et al. [17] as w ell as Yang a nd Han [18] developed upper bo und models for strea mli ned dies. Srinivasan e t al.[19] proposed a co ntrolled strain rate die as a s trea mlined s hape, w hic h improved the e xtr usion process for materials w ith li mited w orkability. Lu a nd Lo [20] proposed a die shape with a n i mproved strain rate control . . Distortion and die shape analysis Numero us analytical and experi me ntal a xisymmetric extrusio n investiga tions have e xa mi ned the die s hape a nd resulti ng distortio n. Avitzur [9] show ed that distortio n increases w ith increasing reduction a nd die angle for a xisymme tric extrusio n thro ugh co nical dies. Zi mer ma n a nd Avitzur [11] and Pa n e t al. [21] prop