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Original Research Paper 原始研究论文

Received 13 October 2017 收稿日期：2017 年 10 月 13 日
Received in revised form 以修订后的形式接收
6 February 2018 6 二月 2018
Accepted 9 February 2018 2018 年 2 月 9 日接受
Available online xxx 在线可用 xxx

Brake booster 制动助力器
Valve body 阀体
Material selection 材料选择
Weighting 加权
Ranking 排名

© 2018 Periodical Offices of Chang’an University. Publishing services by Elsevier B.V. on
© 2018 长安大学期刊社.Elsevier B.V. 的出版服务
behalf of Owner. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).
代表所有者。这是一篇在 CC BY-NC-ND 许可证 （http:// creativecommons.org/licenses/by-nc-nd/4.0/） 下的开放获取文章。

Safety is the most significant factor in automotive components. The safety of components needs to be considered in the design, material selection, and manufacturing process. One of the most critical components in a vehicle is the braking system because any failure in braking performance can lead to a fatal accident. Brake booster valve body is one of the main parts of the braking system that can be indubitably considered as the heart of the braking system. The valve body has direct interaction with many other components needs to operate faultlessly during the lifetime of the vehicle. Booster amplifies the force provided by the push of the driver’s foot on the brake, and it decreases the pressure on the driver’s foot. The performance of this component is based on vacuum and pressure difference. That is why booster valve body must be able to tolerate the pressure caused by vacuum and also operate faultlessly in its moving course. Therefore, the material selection and manufacturing process of this component is really important since the life of human beings relies on its safety. Formerly these components were made from thermoset materials, but research indicated that thermoplastic valve bodies offer much better properties and valve body boosters are usually produced by injection molding process recently (Alam and Kamal, 2005; Jahan et al., 2010; Kuo et al., 2009; Lam et al., 2004; Oktem et al., 2006; Seaman et al., 1994). A sample of brake booster valve body is shown in Fig. 1.
安全性是汽车零部件中最重要的因素。在设计、材料选择和制造过程中需要考虑组件的安全性。制动系统是车辆中最关键的部件之一，因为制动性能的任何故障都可能导致致命事故。制动助力器阀体是制动系统的主要部件之一，毫无疑问可以被认为是制动系统的心脏。阀体与许多其他部件直接相互作用，需要在车辆的使用寿命内无故障运行。Booster 放大了驾驶员的脚踩制动器所提供的力，并降低了驾驶员脚的压力。该组件的性能基于真空和压差。这就是为什么增压阀体必须能够承受真空引起的压力，并在其移动过程中无故障运行。因此，该组件的材料选择和制造过程非常重要，因为人类的生命取决于其安全性。以前，这些组件由热固性材料制成，但研究表明，热塑性阀体具有更好的性能，并且阀体增压器最近通常通过注塑成型工艺生产（Alam 和 Kamal，2005 年;Jahan et al.， 2010;Kuo et al.， 2009;Lam et al.， 2004;Oktem 等人，2006 年;Seaman et al.， 1994）。制动助力器阀体样品如图 1 所示。

Wang et al. (2014) investigated the plastic injection molding of brake booster valve body. They optimized the compressive strength of such components with respect to process parameters including molding temperature, number of gates and gate size. Their results showed that the compressive strength improved up to $12\mathrm{\%}$$12\mathrm{\%}$12%12 \%. The first step in the manufacturing process of a component is to select the most appropriate material. Different materials allocate different properties to the product and no material can meet all desired criteria. As a result, selecting the optimum material among multiple alternatives is really difficult especially when different parameters should be considered. In this situation, the best decision is the material with the highest degree of satisfaction for different properties. In order to solve the challenge of the material selection process, multi criteria decision making (MCDM) technique is used in many aspects. Thus different factors of a problem do
Wang et al. （2014） 研究了制动助力器阀体的塑料注射成型。他们根据工艺参数（包括成型温度、浇口数量和浇口尺寸）优化了此类组件的抗压强度。他们的结果表明，抗压强度提高到 $12\mathrm{\%}$$12\mathrm{\%}$12%12 \% 。组件制造过程的第一步是选择最合适的材料。不同的材料为产品分配不同的特性，没有一种材料可以满足所有所需的标准。因此，在多种选择中选择最佳材料确实很困难，尤其是在应考虑不同参数时。在这种情况下，最好的决定是对不同性能的满意程度最高的材料。为了解决材料选择过程的挑战，多标准决策 （MCDM） 技术被用于许多方面。因此，问题的不同因素确实

not have an equal importance, methods like entropy and analytical hierarchy process (AHP) are used to weight the factors and techniques such as multi objective optimization on the basis of ratio analysis (MOORA), Višekriterijumsko kompromisno rangiranje (VIKOR) and technique for order preferences by similarity (TOPSIS) are used to rank the alternatives regarding to qualitative and quantitative factors of the problem (Edwards and Deng, 2007; Farag, 1997, 2008; Parker, 2001; Sandström and Grahn, 1986; Yoon and Hwang, 1995).
没有同等的重要性，熵和分析层次过程 （AHP） 等方法用于对因素进行加权，并且使用基于比率分析的多目标优化 （MOORA）、Višekriterijumsko kompromisno rangiranje （VIKOR） 和相似性排序偏好技术 （TOPSIS） 等技术用于对问题的定性和定量因素的替代方案进行排名（Edwards 和 邓， 2007;Farag， 1997， 2008;Parker， 2001;Sandström 和 Grahn，1986 年;Yoon 和 Hwang，1995 年）。

In recent years, many researchers have worked on material selection with MCDM techniques. Çalișkan et al. (2013) used TOPSIS, VIKOR and extended PROMETHE II (EXPROM2) methods to compare the operation of nine different materials as a tool holder under hard milling condition. The results stated that $\mathrm{Fe}-5\mathrm{Cr}-\mathrm{Mo}-\mathrm{V}$$\mathrm{Fe}-5\mathrm{Cr}-\mathrm{Mo}-\mathrm{V}$Fe-5Cr-Mo-V\mathrm{Fe}-5 \mathrm{Cr}-\mathrm{Mo}-\mathrm{V} and Tungsten carbidecobalt are the best selections for the tool holder. TOPSIS technique was carried out by Shanian and Savadogo (2006) Q2 to choose the most suitable material for a metallic bipolar plate among twelve different materials versus eleven criteria. The solution indicated that 316L austenitic stainless steel has the best satisfaction value for all factors. Jahan et al. (2011) proposed a new edition of VIKOR method, and compared this proposed comprehensive VIKOR method with traditional VIKOR in different examples, choosing the best material for the hip joint prosthesis. It was obtained from results that the new method can reduce the errors of traditional VIKOR. Ashby’s approach was used by Rashedi et al. (2012) in order to select material for wind turbine blade and tower, among different materials, Epoxy/HS carbon fiber and cast iron BS 900/2 was chosen as the most appropriate materials due to the results. Mansor et al. (2013) studied the material selection for automotive brake lever among thirteen different materials. Performance, weight, and cost were chosen as main criteria. Kenaf bast fibers represented the best performance among alternatives. Karande and Chakraborty (2012) examined the performance of three different decision making methods in four different material selection examples. MOORA, MULTIMOORA and reference point approach methods were compared with other popular MCDM method using Spearman’s rank correlation. The results illustrated that these three methods provided an accurate ranking for a different number of alternatives. Modanloo et al. (2016) investigated the use of MOORA and
近年来，许多研究人员致力于使用 MCDM 技术进行材料选择。Çalișkan 等人（2013 年）使用 TOPSIS、VIKOR 和扩展的 PROMETHE II （EXPROM2） 方法比较了九种不同材料作为刀架在硬铣削条件下的操作。结果表明， $\mathrm{Fe}-5\mathrm{Cr}-\mathrm{Mo}-\mathrm{V}$$\mathrm{Fe}-5\mathrm{Cr}-\mathrm{Mo}-\mathrm{V}$Fe-5Cr-Mo-V\mathrm{Fe}-5 \mathrm{Cr}-\mathrm{Mo}-\mathrm{V} 碳化钨钴是刀架的最佳选择。Shanian 和 Savadogo （2006） Q2 进行了 TOPSIS 技术，从 12 种不同的材料与 11 个标准中选择最适合金属双极板的材料。解表明 316L 奥氏体不锈钢对所有因素的满意度最高。Jahan 等人（2011 年）提出了一种新版本的 VIKOR 方法，并在不同的示例中将这种提出的综合 VIKOR 方法与传统 VIKOR 进行了比较，为髋关节假体选择了最佳材料。从结果中得出，新方法可以减少传统 VIKOR 的误差。Rashedi 等人（2012 年）使用了 Ashby 的方法，以便为风力涡轮机叶片和塔架选择材料，在不同的材料中，环氧树脂/HS 碳纤维和铸铁 BS 900/2 被选为最合适的材料。Mansor 等人（2013 年）研究了 13 种不同材料中汽车制动杆的材料选择。选择性能、重量和成本作为主要标准。洋麻韧皮纤维代表了替代品中最好的性能。Karande 和 Chakraborty （2012） 在四个不同的材料选择示例中检查了三种不同决策方法的性能。使用 Spearman 秩相关将 MOORA 、 MULTIMOORA 和参考点方法与其他流行的 MCDM 方法进行了比较。 结果表明，这三种方法为不同数量的备选方案提供了准确的排名。Modanloo 等人。（2016） 调查了 MOORA 和

Fig. 1 - Brake booster valve body. (a) Position in the braking system. (b) Front view.
图 1 - 制动助力器阀体。（a） 在制动系统中的位置。（b） 前视图。

TOPSIS approaches to choose the optimum parameters in hydroforming process. Alternatives were nine different experiment conditions and the criteria were radial stress, final sheet thickness and forming force. The results demonstrated that MCDM method can also be used for optimization of processes.
TOPSIS 方法在液压成型过程中选择最佳参数。备选方案是九种不同的实验条件，标准是径向应力、最终板材厚度和成型力。结果表明，MCDM 方法也可用于工艺优化。

However, a research based on the material selection for brake booster valve body using MCDM methods was not found in the literature with respect to the best knowledge of the authors. Due to the critical performance of brake booster valve body in vehicles, it is necessary to choose the best possible material to manufacture of this part. In addition, since the safety standards of the vehicles is in direct connection with human life and health, present study somehow helps to prevent injury of many people around the world. In the current work, several synthesis and compromised approaches are proposed using combination of two weighting methods and three ranking methods for material selection to help the automobile industry engineers. At first, all criteria were weighted using compromised weighting method, composed of the entropy and AHP methods. Afterwards, the alternatives (materials) were ranked via MOORA, TOPSIS and VIKOR methods in order to determine the best material regarding to different criteria. Finally, the performance of these methods is compared with each other using Spearman’s ranking correlation.
然而，就作者的最佳知识而言，文献中没有发现基于使用 MCDM 方法选择制动助力器阀体材料的研究。由于车辆制动助力器阀体的关键性能，有必要选择最好的材料来制造该部件。此外，由于车辆的安全标准与人类的生命和健康直接相关，本研究以某种方式有助于防止世界各地许多人受伤。在目前的工作中，提出了几种综合和折衷方法，结合使用两种加权方法和三种排序方法进行材料选择，以帮助汽车行业工程师。首先，所有标准都使用由熵和 AHP 方法组成的妥协加权方法进行加权。之后，通过 MOORA、TOPSIS 和 VIKOR 方法对替代品（材料）进行排序，以确定符合不同标准的最佳材料。最后，使用 Spearman 的排名相关性将这些方法的性能相互比较。

Since the brake booster valve body is used in all vehicles, this component has a special importance in automotive industry. On the other hand, material selection plays a significant role in the competition between manufacturers to decrease the cost and increase the quality of the final product simultaneously. The art of material selection is to select the best option among different alternatives based on specific criteria. The first step of MCDM technique is to identify the main required properties of the product and then to recognize available materials that can be used to manufacture the product.
由于制动助力器阀体用于所有车辆，因此该部件在汽车行业中具有特殊的重要性。另一方面，材料选择在制造商之间的竞争中起着重要作用，以同时降低成本并提高最终产品的质量。材料选择的艺术是根据特定标准在不同的备选方案中选择最佳选项。MCDM 技术的第一步是确定产品的主要所需特性，然后识别可用于制造产品的可用材料。

Regarding the conditions and forces that are applied on the valve body, this component should have a set of appropriate characteristics including mechanical stability in the wide range of temperatures and high strength to weight ratio. The valve body requires operating faultlessly during the lifetime of the vehicle, thus a material with high mechanical strength should be selected. In this regard, one of the main criteria that represent the mechanical strength of a material is tensile strength (TS). Moreover, the component is under a challenging temperature range near the vehicle engine. Therefore, the material should maintain its strength at elevated temperatures. To investigate the effect of temperature on strength drop, deflection temperature of the material at 1.8 MPa stress $(T)$$(T)$(T)(T) is considered. Using materials with lower density leads to components with lower weights, and lighter components help to reduce the fuel consumption of a vehicle. So density $(D)$$(D)$(D)(D) is
关于施加在阀体上的条件和力，该组件应具有一系列适当的特性，包括在较宽温度范围内的机械稳定性和高强度重量比。阀体要求在车辆的使用寿命内无故障运行，因此应选择具有高机械强度的材料。在这方面，代表材料机械强度的主要标准之一是拉伸强度 （TS）。此外，该组件在靠近车辆发动机的位置具有挑战性。因此，材料应在高温下保持其强度。为了研究温度对强度下降的影响，考虑了材料在 1.8 MPa 应力 $(T)$$(T)$(T)(T) 下的挠曲温度。使用密度较低的材料可以使部件重量更轻，而更轻的部件有助于降低车辆的燃料消耗。所以密度 $(D)$$(D)$(D)(D) 是
selected as one of the criteria in this study. On the other hand, to provide a competitive advantage among producers, there is a necessity to decrease the cost $(C)$$(C)$(C)(C) of the product.
被选为本研究的标准之一。另一方面，为了在生产商之间提供竞争优势，有必要降低产品成本 $(C)$$(C)$(C)(C) 。

A number of applicable polymers in the automotive industry are chosen as base materials in this study. Polyethylene terephthalate (PET), polypropylene (PP), polycarbonate (PC), polyamide6 (PA6), acrylonitrile butadiene styrene (ABS), polyethylene (PE), polyvinyl chloride (PVC) and polystyrene (PS) are taken into consideration. Based on aforementioned advanced properties needed for the materials, in addition to base materials, eight other materials are selected which are reinforced composites of base materials with glass fibers and the weight percentage of the glass fiber is given. The properties required in the valve body and selected alternatives with corresponding information are given in Table 1.
本研究选择了许多汽车行业的适用聚合物作为基础材料。聚对苯二甲酸乙二醇酯 （PET）、聚丙烯 （PP）、聚碳酸酯 （PC）、聚酰胺 6 （PA6）、丙烯腈丁二烯苯乙烯 （ABS）、聚乙烯 （PE）、聚氯乙烯 （PVC） 和聚苯乙烯 （PS） 也被考虑在内。基于材料所需的上述先进性能，除了基材外，还选择了其他八种材料，这些材料是基材与玻璃纤维的增强复合材料，并给出了玻璃纤维的重量百分比。表 1 给出了阀体所需的属性和选定的替代方案以及相应的信息。

In an MCDM problem, due to the different importance of each criterion, weighting process of the criteria should be carried out according to the performance of the target component. There are two important approaches to obtain weights, either by means of alternative’s data or designer’s experience. Entropy and AHP are two of common weighting methods which are used in this study.
在 MCDM 问题中，由于每个标准的重要性不同，应根据目标组件的性能对标准进行加权处理。有两种重要的方法可以获得权重，要么通过 alternative 的数据，要么通过 designer 的经验。熵和 AHP 是本研究中使用的两种常用加权方法。

Entropy weighting method uses uncertainty conception in the calculation of the weights of criteria. It implies that a sharp distribution is less uncertain than broad distribution (Hainmueller, 2012). The decision matrix of MCDM problem with $m$$m$mm alternatives and $n$$n$nn criteria is presented in Table 2 in which $X_{ij}(i=1,2,\dots ,m;j=1,2,\dots ,n)$$X_{ij}(i=1,2,\dots ,m;j=1,2,\dots ,n)$X_(ij)(i=1,2,dots,m;j=1,2,dots,n)X_{i j}(i=1,2, \ldots, m ; j=1,2, \ldots, n) demonstrates the performance value of the ith alternative to the $j$$j$jj th criteria (Rao, 2007).
熵加权法在计算标准权重时使用不确定性概念。这意味着尖锐分布比广泛分布的不确定性更小（Hainmueller，2012）。表 2 显示了 MCDM 问题的决策矩阵以及 $m$$m$mm 替代方案和 $n$$n$nn 标准， $X_{ij}(i=1,2,\dots ,m;j=1,2,\dots ,n)$$X_{ij}(i=1,2,\dots ,m;j=1,2,\dots ,n)$X_(ij)(i=1,2,dots,m;j=1,2,dots,n)X_{i j}(i=1,2, \ldots, m ; j=1,2, \ldots, n) 其中展示了 $j$$j$jj 第 i 个替代方案对第 2 个标准的性能价值（Rao，2007）。