新方法解决老问题-使用模拟软件计算冒口尺寸及位置

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新方法解决老问题

使用模拟软件计算冒口尺寸及位置

A New Approach to an OldProblemCalculating Feeder Sizeand Location with 3D Models

J. F.Meredith

CastingSolutions Pty Ltd

天津浩宇天仿科技有限公司

Introduction概述

One of the most fundamental problems facing the foundry engineeris developing an adequate design and position of risers for feeding acasting. Most alloys contract as theliquid metal cools and solidifies, and this contraction must be compensated forby providing risers (or “feeders”). Theriser is essentially a reservoir of molten metal which flows into the castingcavity as the casting alloy cools and contracts, thus preventing shrinkageporosity from forming within the casting and ensuring a sound part.

铸造工程师面对的最终的一个问题就是为铸件设计一套合理的补缩方案，大多数合金随着液态金属的冷却和凝固而收缩，同时这种收缩必须得到冒口的补偿。从本质上来讲，冒口就像一个熔融金属的水库，随着铸件的冷却收缩，水库中的液态金属流到铸件型腔中，从而阻止铸件内产生收缩类缺陷以获得零缺陷的铸件。

The approaches taken by foundries to design adequate risers varywidely. Some rely on experience andinstinct, which takes the design process essentially into the realm ofart. Others rely on calculations todetermine riser size and location. Theclassical approach to estimation of riser size is to calculate the volume andcooling surface area of various parts of the casting. The ratio of volume to surface area (V/SA) isknown as the modulus, and is generally expressed in centimetres. Regions of the casting which have the lowestmodulus values solidify first, while those parts of the casting which have thehighest modulus solidify last. Accordingto Chvorinov’s Rule, which has been in use for many years in the foundryindustry, solidification time is proportional to the square of the calculatedgeometric modulus value.

铸造企业设计方案的方法千差万别，有些企业依靠经验和知觉，整个设计过程基本上如艺术创作一样。其他企业使用公式计算得出冒口的尺寸及位置。经典的方式是根据冒口的尺寸及铸件不同部分的冷却面积来计算冒口尺寸。体积与表面积的比成为模数，以厘米为单位。模数低的铸件部分先凝固，模数高的部分后凝固。Chvorinov的理论，即凝固时间与几何模数的平方成正比，已经应用于铸造工业很多年了。

Using these facts, one can fairly easily derive a few simpledesign rules. Since the riser must beable to provide feed metal, it should remain liquid longer than the region ofthe casting to which it is attached. This means that the riser should have a higher modulus than this region,so that it freezes later. Also, toprovide progressive feeding from thinner sections to thicker sections, acasting should ideally be designed such that section thicknesses (and modulus)increase progressively from the thinner sections to the thickest sections wherethe risers are to be attached.

根据以上的一些理论，能够得出一些基本的设计规则。由于冒口必须能提供不错金属，那么它应该比其连接部分的铸件保持更长的液态时间。这意味着冒口要比其连接部分的区域有更高的模数，这样才能后凝固。要保持从薄截面到厚截面的渐进补缩，理想的设计方案是从薄截面到与冒口连接的厚截面的截面厚度铸件增加。

Another consideration in riser design has to do with the volume offeed metal required. The volume of metalwhich a casting requires is a function of the amount of total contraction thatit undergoes from pouring to solidification. The volume of metal which a riser can provide is a function of thevolume of the “pipe”, i.e., the void which represents the amount of liquiddrained from the riser.

冒口需要需要考虑的另外一个因素是补缩量。铸件需要的金属量是一个铸件从浇注到凝固总收缩量的函数。冒口能提供的液态金属量是一个“管”（即冒口）金属量的函数，即空的量代表从冒口中流出的用于补缩的金属量。

This pipe is deeper and more pronounced in open-top risers whichare not sleeved; in these risers, less of the total volume of the riser isavailable as feed metal. In risers whichare sleeved and/or hot-topped, more of the metal tends to remain liquid duringthe solidification process, so more of the total riser metal is available tofeed. The amount of metal required bythe casting must be equal to or exceeded by the amount that the riser candeliver, or shrinkage porosity will likely form.

没有冒口套的明冒口的缩管即深又明显，这种冒口中，只有少量的冒口中的金属用于补缩。有保温套和（或者）覆盖剂的冒口，在凝固过程中有较多的金属保持液态，因此有较多金属用于补缩即冒口的补缩效率高。冒口能提供的补缩金属量必须等于或者大于铸件需要的金属量，否则将形成缩孔、缩松等缺陷。

In general, in heavy-section castings, the modulus values governthe design of the riser; in “rangy” castings (those with large dimensions butthinner wall sections), the volume consideration often is the governing factor.

一般来讲，厚壁件由模数决定设计方案，对于尺寸比较大但是壁薄的件，由补缩量决定设计方案。

While these concepts are relatively simple and straightforward,their implementation in casting design is not. This is primarily due to the difficulty in calculating volumes andsurface areas for complex, real-world castings. The approach which has been taken by most foundry engineers is similarto that of weight calculation; the casting is arbitrarily broken into a numberof pieces, and each of these pieces is approximated by a simple geometric shapefor which surface area and volume can be calculated.

虽然上述的概念非常简单直接，但是却很难在铸造方案设计中应用，主要是由于对于复杂的铸件来讲计算体积和表面积非常困难。大多数铸造工程师采用计算重量的方法。将铸件随意的分割成很多个有简单几何形状的截面

Several software programs and worksheets for performing thesecalculations are currently in use. Inpractice, however, this process is cumbersome and inexact; the arbitrariness ofapproximating a casting shape with a series of simple shapes reduces bothrepeatability and accuracy. Anotherintrinsic problem with this method is that it is based only on geometry, anddoes not directly take into account thermal effects such as specific propertiesof chilling or insulating materials and heat saturation of cores or variousareas of the mould. Some factors havebeen proposed for correcting for these effects, but the introduction of suchfactors only increases the uncertainty surrounding the accuracy of results.

A New Approach新的方法

In recent years, computer simulation of the casting process usingaccurate three-dimensional models has become increasingly widespread. Such simulations can, in many cases, veryaccurately predict the progressive solidification of the casting and itsrigging system, along with the potential for formation of various castingdefects. However, one of the significantdrawbacks of casting simulation is that it requires an initial design tosimulate. It is ironic that mostfoundries, even those using the most advanced simulation tools, still use atraditional approach to developing the initial design to submit for simulation;in general, this means calculation of approximate surface areas, volumes andmodulus values through manual or software-based methods to break the castinginto arbitrary simple shapes.

近年来，使用精确的三维模型软件模拟铸造过程已逐渐普及。在多数情况下，这种模拟可以非常准确预测铸件及浇冒口系统的顺序凝固，以及可能形成的各种铸造缺陷。但是铸造模拟软件的一个非常大的弊端是模拟需要一个初始设计方案为前提。具有讽刺意味的是，大多数工厂即使使用最先进的铸造模拟软件，仍然使用传统的方法设计铸造工艺方案然后再模拟。总的来说，这就意味着，是将铸件任意分解成若干简单形状，通过手工或者软件计算近似表面积、体积和模数值来设计方案。

Since most new casting designs are available today in 3D CADformat from the casting buyer, it seemed that it should be possible to developa methodology for riser calculations that is both more accurate and moreautomated than those used by the industry today.

由于如今大多数情况下可以从铸件采购者处获得新的铸件三维模型，因此应该可以开发出一种比当前使用的更加准确、更加自动化的冒口计算方法。

Thestarting point for this development was the idea that the modulus approach isessentially an attempt to estimate the solidification times of various parts ofthe casting prior to attaching the rigging. However, using modern casting simulation software, the solidificationtime of every point within a casting can be calculated very quickly, and doesnot need to be estimated. It is oftenthe case that, having downloaded a 3D CAD model by email, it is possible to runa simulation of the casting within just a few minutes, using the FiniteDifference Method, to obtain solidification time information throughout thecasting.

开发的最初的构想是，在添加浇冒口系统前，模数法可以用于判断铸件不同部位的凝固时间。不过，利用现代铸造模拟软件，可以不用估算就能很快计算出铸件中每个点的凝固时间。通常是通过电子邮件下载三维模型，使用有限差分法（FDM），花几分钟时间对铸件进行一次模拟，得到整个铸件的凝固时间信息。

The next question was how to relate this information to potentialrisers of various sizes which might be attached to the casting. At this point, having simulated only thecasting with no risers, we cannot directly compare the solidification time ofany arbitrary riser with the casting. The answer to this question was the development of a calculation whichcould convert the solidification times in the casting to equivalent modulusvalues.

接下来的问题是，如何将这些信息与可能设置在铸件上的大小不同的冒口联系起来。在这点上，仅对不带方案的铸件进行了模拟，不能直接将铸件的凝固时间与铸件上的任何冒口的凝固时间做比较。问题的答案是进行一项计算，可将铸件内凝固时间转化成等效的模数值。

Thiswould allow the user to directly compare a riser with the casting, since amodulus value for a riser can generally be calculated easily. In order to develop such a procedure, it wasnecessary to devise a formula which would take into account the wide range ofproperties of the diverse array of casting alloys which are poured today, sothat the resulting modulus values would be accurate no matter what alloy wasbeing poured.

这样就可以将铸件和冒口直接比较。因为冒口的模数值通常可以很容易计算出来。为了开发这种程序，有必要设计一个考虑了用于浇注的各种铸造合金的各种性能的公式，这样无论浇注何种合金，其结果模数值都是正确的。

Another question to be answered was whether, given an array ofmodulus values within the casting, a system could be devised which wouldrecognise separate feeding areas within the casting and thus give advice as tohow many risers would be required, and where they should be located.

This has been accomplished by development of pattern-recognitionsoftware which is able to locate isolated areas of high modulus values, whichare essentially “hot spots” in the casting which need to be fed. In some more rangy castings, there may bemany such areas; therefore the system must be able to discriminate between verysmall areas which don’t need feeding, and larger areas which do. The level of discrimination can be set by theuser, by adjusting a “slider bar” from a “Less Sensitive” position to a “More Sensitive”position.

Once the individual feed areas are identified, an appropriateriser can be sized for each of these. Since the maximum modulus value and the volume of each feeding area isknown, it is relatively simple to apply known rules (as discussed above) tocalculate the correct size riser for each area. Also, by plotting the location of the maximum modulus values within eachfeeding area, we can pinpoint the required attachment point for eachriser. Of course, the actual attachmentpoint is subject to considerations such as parting line location, ease ofremoval, machine locating points and other practical issues.

Using this methodology, what amounts to an almost automaticcalculation of required risering for a casting is achieved. The starting point is a 3D model of thecasting, which can be transmitted from a CAD system. Then, the alloy and mould material areselected and a simulation with no risers is run. With a few clicks of the mouse, the systemthen analyses the simulation results, calculates modulus values, and suggeststhe number and location of required risers. The details of each riser are then provided by calculations which embodyriser design rules based on modulus and volume requirements.

使用该方法，几乎相当于实现了自动计算铸件所需冒口。起点是从CAD系统输出的铸件3D模型。然后选择合金和模型材料，实施无冒口模拟。点几下鼠标，系统就会分析模拟结果，计算模数值，提供所需冒口的数量和位置。通过基于模数和所需体积的冒口设计规则计算，提供每个冒口的详细情况。

There are many reasons that such an approach provides moreaccuracy than traditional design calculations. One is the accuracy of the 3D model, which provides more exact geometrythan is usually considered. Another isthat, by running a simulation, thermal effects such as heat saturation of coresare accounted for explicitly. It wouldalso be possible to place chills on the casting model, and even gating for amould-filling simulation which would accommodate the effects of heat lossduring filling. All of these effects aredifficult to account for explicitly when performing traditional designcalculations.

有很多理由说明该方法比传统计算更加精确。其一，精确的三维模型，提供了比通常使用的更精确的几何体。其二，通过模拟，也明确了像砂芯的热效应等。也可以在铸件模型上设置冷铁，以及用于充型模拟的浇道，该充型模拟可以提供充型过程中的热损失结果。所有这些结果在使用传统设计方法时是难以精确计算的。

It is generally recommend that, after a rigging design iscompleted using this procedure, a verification simulation be run with theactual geometry of the calculated risers. However, it is expected that the percentage of “first-time” simulationsuccesses would be considerably higher using this approach.

一般情况下，建议使用该程序进行浇冒口系统设计后，加上计算所得浇冒口进行一次验证模拟。无论如何，使用该方法“首次”模拟成功的比率是相当高的。

As an example of how this approach might be applied, consider thecasting model shown in Figure 1, which has a number of relatively isolatedheavy sections.

举例说明该方法的操作过程，使用的铸件模型如图1所示，图中有一些相对孤立的厚截面。

Figure 1图1

Designing the risering for this casting begins with selecting thecasting alloy and mould material, which in this case are AISI 1030 carbon steeland green sand. A Finite Difference meshis generated, and a simulation is run with no risers attached. The result ofthis simulation is shown in Figure 2 as a plot of critical fraction solid timethroughout the casting.

铸件的冒口设计首先选择铸造合金和模型材料，这里选AISI1030碳钢和粘土砂。进行FDM 格划分，实施无冒口模拟。模拟结果如图2所示，为整个铸件的临界凝固时间图。

Figure 2图2

The next step is to apply the formula which converts thesimulation data to modulus values. Thisis done simply by clicking a button, as shown in Figure 3. This operation calculates a modulus value foreach point within the casting.

下一步是使用公式将模拟数据转化为模数值。操作很简单，点一下按钮，如图3所示。该操作计算出铸件每个点的模数值。

Figure 3

After this calculation is performed, the pattern-recognitionalgorithm is then applied to the modulus values, so that individual feedingareas within the casting can be identified. The user may slide the “sensitivity” bar to a low, intermediate or highposition, depending on the ranginess of the casting under analysis. This operation generally takes about aminute, and the result is a display which indicates the number of suggestedrisers to produce this casting. In thiscase, the system has suggested two risers as shown in Figure 4.

Figure 4图4

The maximum modulus and the volume of each of the feeding areascan be displayed, based on the results of the modulus and patterncalculations. This allows the dimensionsof a riser for each area to be determined.

基于模数和模型计算结果，可以显示每个补缩区域的最大模数和补缩量，确定每个区域的冒口尺寸。

Severalalternative methods of calculating riser size are offered; for example, theuser can enter the height-to-diameter ratio, and an appropriate riser size willbe calculated.

提供了好几种可供选择的计算冒口的方法；例如，用户可以输入高度和直径的比例，计算适合的冒口尺寸。

Theriser size calculations take into account the ratio of the riser modulus to themaximum casting modulus, to ensure that the riser will solidify later than thecasting; they also account for the effect of insulated or exothermic sleeves,which effectively increase the modulus of a riser by blocking heat flow fromthe riser surface into the mould.

冒口尺寸的计算考虑了冒口和铸件最大模数的比例，确保冒口后于铸件凝固；也考虑了保温冒口套和发热冒口套的效果，其通过阻止从冒口面到模型的热量传递，有效增加冒口模数。

Required volume of the riser is estimated from curves published inthe AFS handbook on risering, which relate the volume ratio of the casting andriser to the modulus ratio. An examplecalculation of this type is shown in Figure 5, where the user has entered aheight-to-diameter ratio, and the software has calculated the height, diameterand actual-vs.-required volume for the riser.

需要的冒口体积通过出版的AFS手册中关于冒口的曲线来判断，该曲线涉及铸件与冒口的体积比和模数比。图5所示为此类计算的一个例子。其中用户输入了高度和直径的比例，软件计算高度、直径以及实际VS、冒口需要的体积。

Figure 5

Using the visualisation tools of the simulation software, thevarious feed areas of the casting can be examined and seen clearly. The system has indicated that the twodistinct feeding areas of the casting are as shown in Figure 6.

使用模拟软件的查看工具，可以检查并清楚的看到铸件的不同补缩区域。系统显示铸件的两个不同的补缩区域，如图6所示。

Figure 6

Further, the areas of highest modulus value can be viewed, so thatthe correct attachment points of the risers to the casting can be located. This information is shown in Figure 7:

更进一步，观察最大模数区域，可以确定铸件设置冒口的正确位置。信息如图7所示。

Figure 7

Using this information, the suggested risers were added to thecasting model and a verification simulation was run. This is an important step, as it must berealised that the riser size calculations are approximations and cannot takeinto account all of the complex thermal interactions which occur in afully-rigged casting. The riseredcasting, and the simulation results, appear as shown in Figure 8. The macroporosity prediction (the dark area inthe image on the right) shows clearly that the volume provided by the riserswas sufficient to feed the casting without formation of internal shrinkageporosity in the casting.

利用此信息，将推荐的冒口添加到铸件模型上，运行验证模拟。这是重要的一步。必须认识到冒口计算为近似值，并没有综合考虑带有工艺方案的铸件中发生的所有的热交互作用。带冒口的铸件与模拟结果如图8所示。宏观缩孔预测（右图中暗黑区域）清晰的显示出冒口提供的体积足够补缩铸件，铸件内没有内部缩孔。

Figure 8

Conclusion结论

Thus, within a time span of just a few minutes it was possible inthis case to fully design adequate risering for this casting, given a CAD filetransmitted from the customer. Theuser’s effort to perform these calculations is minimal, primarily just clickingon a few menu items and buttons on the screen.

因此，从客户处得到CAD文件后，用这种方法，只要在几分钟的时间段内就完全能够为铸件设计出恰当的冒口。用户实施这些计算的工作量是最小的，主要是点几下屏幕上的菜单项目和按钮。

There are a number of issues in confluence today which make suchan approach critical for a foundry to consider. First is the requirement by customers for shorter lead times as well aspressure to reduce cost and casting prices, meaning that getting the castingprocess designed correctly and quickly is imperative. Second is the wide availability today of 3DCAD models for most new castings. Third,and not the least in importance, is the fact that many experienced foundryengineers are nearing retirement age, and they are being replaced by youngerpeople without the years of experience needed to develop a “feel” for thecasting design process. Providing anautomation tool to these younger engineers can dramatically increase theirproductivity in designing casting processes.

现在汇总一些为铸造厂考虑使用这种方法的重要性的原因。首先是客户要求缩短交货期，以及降低成本和铸件价格的压力，意味着急需迅速而正确的获得铸件的工艺设计。其二，如今大部分新铸件广泛使用三维模型。其三，不是最重要的，实际上许多有经验的铸造工程师接近退休年龄，由没有多年经验的年轻工程师替代，因此，需要为这些年轻工程师在开发一项方案前提供一个思路，为年轻工程师提供一个可以大大提高铸造工艺设计能力的自动工具