Design of 3D-Printed Titanium Compliant Mechanisms
设计三维打印钛合金兼容机构

A compliant mechanism derives its motion from the deflection of its constituent members. Compliant mechanisms offer decreased part count, decreased complexity, lower weight, longer life, and lower cost. Since compliant mechanisms can be designed with no surface contact, wear and all its associated issues are eliminated. In many cases, bearings may be eliminated, along with their weight, complexity, and failure modes [1]. Preliminary work has shown the applicability of compliant mechanism technology to space applications [2]. Additionally, compliant mechanisms lend themselves to monolithic construction through additive manufacturing processes.
顺从式机构的运动来自于其组成部件的挠度。顺从式机构可减少零件数量、降低复杂性、减轻重量、延长寿命和降低成本。由于顺从式机构在设计时没有表面接触，因此消除了磨损和所有相关问题。在许多情况下，轴承可以连同其重量、复杂性和故障模式一起被淘汰[1]。初步研究表明，顺从机构技术适用于太空应用[2]。此外，顺从式机构可通过快速成型制造工艺进行整体构造。

Advances in Electron Beam Melting (EBM) enable additive manufacturing (also referred to as rapid manufacturing) in a variety of metals, including alloys of Titanium. The EBM process is well documented [3] [4]. Case studies have shown that rapid manufacturing offers reduced costs when production volumes are low, many design iterations are to be explored, high geometric complexity is needed, or when new materials are to be explored [5] [6]. Additionally, material scrap rate can be significantly reduced by printing a near-net-shape part rather than machining it from solid billet [7]. Combining compliant mechanisms with rapid manufacturing techniques opens up interesting possibilities for creating compliant space mechanisms that have unprecedented performance.
电子束熔化（EBM）技术的进步使包括钛合金在内的各种金属的快速制造成为可能。电子束熔化工艺有据可查 [3] [4]。案例研究表明，当产量较低、需要进行多次设计迭代、需要较高的几何复杂性或需要探索新材料时，快速制造可降低成本[5] [6]。此外，通过打印近净成形零件而不是从实心坯料上加工，可显著降低材料废品率 [7]。将顺应式机构与快速制造技术相结合，为创造具有前所未有性能的顺应式空间机构提供了有趣的可能性。

Figure 1. A compliant titanium hinge produced with EBM. This hinge is capable of $\pm {90}^{\circ }$$\pm {90}^{\circ }$+-90^(@)\pm 90^{\circ} of motion. Images provided courtesy of Robert Fowler. [8]
图 1.使用 EBM 生产的顺应性钛铰链。该铰链能够 $\pm {90}^{\circ }$$\pm {90}^{\circ }$+-90^(@)\pm 90^{\circ} 运动。图片由 Robert Fowler 提供。[8]

Rapid manufacturing processes have been used in multiple aerospace applications, including ductwork [5] [6] and a capacitor housing on the International Space Station [9]. These applications used selective laser sintered nylon parts, which established a basis for rapid manufacturing as a viable method for producing parts. Structural brackets [3], a shrouded cryogenic impeller [3] [10], and brackets for the Juno spacecraft [7] have also been manufactured in titanium using rapid manufacturing processes. While most parts built thus far have been structural members (brackets, etc.) or non-structural assemblies (ductwork and housings), in our work we use additive manufacturing to create monolithic mechanisms for aerospace applications. As part of that effort, it is desirable to know what to expect when printing slender geometries, and maximum allowable stresses in EBM-produced titanium parts.
快速制造工艺已应用于多种航空航天领域，包括管道系统 [5] [6] 和国际空间站的电容器外壳 [9]。这些应用使用了选择性激光烧结尼龙零件，为快速制造作为一种可行的零件生产方法奠定了基础。结构托架[3]、遮罩式低温叶轮[3][10]和朱诺号航天器的托架[7]也是使用快速制造工艺用钛制造的。虽然迄今为止制造的大多数部件都是结构件（支架等）或非结构性组件（管道系统和外壳），但在我们的工作中，我们使用快速成型制造技术为航空航天应用制造整体机构。作为这项工作的一部分，我们希望了解打印细长几何形状时需要注意的事项，以及 EBM 生产的钛零件的最大容许应力。

EBM produced parts can achieve full density [11]. Wooten and Dennies claim that the fully dense region occurs in bulk parts about 1.25 mm ( 0.05 in ) below the surface [3], but give no explanation of how this figure was arrived at. This depth is more than the thickness of many printed flexures. While the region near the surface may not be fully dense, Murr et al, mention that such micropores have no effect on shortterm tensile properties [12]. However, surface roughness and micro-cracks contribute to reduced fatigue life. Because of the slender geometry, machining of flexures is often impractical, so surface porosity is difficult to eliminate and must be accounted for in the design. This surface porosity constitutes a major obstacle to high cycle fatigue life. Hot isostatic pressing (HIP) improves the fatigue life of EBM produced parts [13]. If HIP treatment is impractical, property data obtained from raw (not treated with HIP or finish machined) tensile samples are available [14].
EBM 生产的零件可以达到全密度 [11]。Wooten 和 Dennies 声称，完全致密区域出现在表面以下约 1.25 毫米（0.05 英寸）的块状部件中[3]，但没有解释这一数字是如何得出的。这个深度超过了许多印刷挠性片的厚度。虽然表面附近的区域可能不是完全致密的，但 Murr 等人提到，这种微孔对短期拉伸性能没有影响 [12]。然而，表面粗糙度和微裂纹会导致疲劳寿命缩短。由于挠性结构的几何形状细长，对其进行机械加工往往是不切实际的，因此表面气孔很难消除，必须在设计中加以考虑。这种表面气孔是高循环疲劳寿命的主要障碍。热等静压（HIP）可提高 EBM 制件的疲劳寿命[13]。如果 HIP 处理不可行，则可使用原始拉伸样品（未经 HIP 处理或精加工）获得的属性数据 [14]。

Early design work for a two-degree-of-freedom (2 DOF) pointing mechanism [15] required testing the fabrication and performance of cross-axis flexural pivots. These flexures have a number of good characteristics, including good stability and load carrying capacity [16]. The flexure was modeled in ANSYS to predict its torsional stiffness, which was compared to analytical solutions. Finally, the flexures were produced using EBM, and an example is shown in Figure 2, along with the pointing mechanism.
两自由度（2 DOF）指向机构的早期设计工作[15]需要测试横轴挠性枢轴的制造和性能。这些挠性枢轴具有许多优良特性，包括良好的稳定性和承载能力 [16]。在 ANSYS 中对挠性枢轴进行建模，以预测其扭转刚度，并将其与分析解决方案进行比较。最后，使用 EBM 制作了挠性结构，图 2 显示了一个例子以及指向机构。

The torque and deflection characteristics of three printed flexures were found. The FE model significantly over-predicted ( $\sim 30\mathrm{\%}$$\sim 30\mathrm{\%}$∼30%\sim 30 \% ) the stiffness of the printed. Because of high surface roughness, it was thought that perhaps not all of the thickness of the flexure contributes to its bending stiffness. Applying a correction factor of 0.83 to the thickness resulted in good agreement between the FEA and measured stiffness of the flexures. Later this correction factor was used to predict the overall stiffness of the pointing mechanism, again resulting in good agreement. Therefore, when using thin flexures, a thickness correction factor of 0.83 is recommended to accurately predict the torsional stiffness of printed flexures.
研究发现了三种印刷挠性体的扭矩和挠度特性。FE 模型对印刷刚度的预测明显偏高（ $\sim 30\mathrm{\%}$$\sim 30\mathrm{\%}$∼30%\sim 30 \% ）。由于表面粗糙度较高，我们认为挠性体的厚度可能并没有完全影响其弯曲刚度。对厚度应用 0.83 的校正系数后，挠曲的有限元分析和测量刚度之间的一致性很好。之后，我们使用该修正系数来预测指向机构的整体刚度，结果也是一致的。因此，在使用薄挠性片时，建议使用 0.83 的厚度修正系数来准确预测印刷挠性片的扭转刚度。

Figure 2. Cross-axis flexural pivot and 2 DOF pointing mechanism used to compare FEA and analytical models to measured stiffness.
图 2.用于比较有限元分析和分析模型与测量刚度的横轴挠性枢轴和 2 DOF 指向机构。

Two grades of titanium powder are currently produced for use in EBM machines: Ti6AI4V and Ti6AI4V ELI (ELI is “extra low interstitials,” which improves ductility and fracture toughness of the alloy). These two alloys have slightly different strength characteristics, but Ti6AI4V has slightly higher strength [13]. Table 1 presents strength data from several sources. These data were gathered from samples prepared in different ways; some used highly polished samples while other samples are tested in the as-built condition, with no post-processing or heat treatment. Rafi et al, found a strong correlation between build orientation and strength [14], while the manufacturer data make no distinction between build orientations [13].
目前有两种等级的钛粉可用于 EBM 设备：Ti6AI4V 和 Ti6AI4V ELI（ELI 是 "超低间隙"，可提高合金的延展性和断裂韧性）。这两种合金的强度特性略有不同，但 Ti6AI4V 的强度略高[13]。表 1 列出了多个来源的强度数据。这些数据是从以不同方式制备的样品中收集的；其中一些使用了高度抛光的样品，而其他样品则是在未进行后处理或热处理的原样状态下进行测试的。Rafi 等人发现建造方向与强度之间有很强的相关性[14]，而制造商的数据则没有区分建造方向[13]。

Table 1. Summary of strength data gathered from other sources. (*) indicates that sample underwent HIP process.
表 1.从其他来源收集的强度数据汇总。(*) 表示样本经过 HIP 处理。

Geometry Constraints  几何限制

Minimum wall or flexure thickness depends on feature orientation. A minimum thickness of 0.75 mm is recommended for flexures that have the thickness orthogonal or parallel to the build direction. If the flexure is built at other angles, 1.00 mm is recommended as the minimum thickness. If the flexure is built at some angle from the vertical, the larger dimension is recommended. Figure 3a illustrates this orientation dependence. The authors have had good success building flexures that rise at ${45}^{\circ }$${45}^{\circ }$45^(@)45^{\circ} from the horizontal when the flexures are $1.00-\mathrm{mm}$$1.00-\mathrm{mm}$1.00-mm1.00-\mathrm{mm} thick.
最小壁厚或挠曲厚度取决于特征方向。厚度与构建方向正交或平行的挠曲，建议最小厚度为 0.75 毫米。如果挠曲以其他角度制作，建议最小厚度为 1.00 毫米。如果挠曲与垂直方向成一定角度，则建议使用较大的尺寸。图 3a 展示了这种方向依赖性。当挠性体厚度为 $1.00-\mathrm{mm}$$1.00-\mathrm{mm}$1.00-mm1.00-\mathrm{mm} 时，作者在制造从水平方向 ${45}^{\circ }$${45}^{\circ }$45^(@)45^{\circ} 上升的挠性体时取得了很好的效果。

Figure 2. (a) - Flexures built at angles not orthogonal or parallel to build plate should be slightly thicker. (b) - Horizontal flexures build more successfully when supported by build plate as shown on the right.
图 2. (a) - 与构建板成非正交或平行角度的挠曲应稍厚一些。(b) - 如右图所示，水平挠曲在构建板的支撑下更容易成功构建。

Because the build chamber is maintained at between ${500}^{\circ }\mathrm{C}$${500}^{\circ }\mathrm{C}$500^(@)C500^{\circ} \mathrm{C} and ${700}^{\circ }\mathrm{C}$${700}^{\circ }\mathrm{C}$700^(@)C700^{\circ} \mathrm{C}, most stresses are relieved during the part’s build cycle [11, 3], but some warping due to thermal stresses has been observed. Figure 4 shows a part where enough warping occurred that the part failed to build correctly. Although not fully understood, it is thought that this warping is due to stresses that occur when the molten metal solidifies but are subsequently relieved as the part is held at high temperature. Usually the part is bulky enough
由于成型室的温度保持在 ${500}^{\circ }\mathrm{C}$${500}^{\circ }\mathrm{C}$500^(@)C500^{\circ} \mathrm{C} 和 ${700}^{\circ }\mathrm{C}$${700}^{\circ }\mathrm{C}$700^(@)C700^{\circ} \mathrm{C} 之间，因此大部分应力都会在零件的成型周期内释放 [11, 3]，但也观察到一些因热应力而产生的翘曲。图 4 显示了一个发生了足够多翘曲的零件，导致零件无法正确成型。尽管还不完全清楚，但人们认为这种翘曲是由于熔融金属凝固时产生的应力造成的，但随后在高温下保持部件时应力得到释放。通常情况下，零件足够大
that these low stresses do not cause warping. For the geometry shown in Figure 4, the part was redesigned to have the flexures rest on the build plate (illustrated in Figure 3b). Supporting the flexures in this way eliminated the warping and allowed a successful build. It is postulated that other ways to avoid warping include better support of the cantilevered flexure from underneath (by having it connect to another portion of the part) or making it wider. In general, narrow, unsupported flexures are to be avoided.
这些低应力不会导致翘曲。对于图 4 所示的几何形状，对零件进行了重新设计，使挠性条靠在构建板上（如图 3b 所示）。以这种方式支撑挠曲件消除了翘曲，并成功完成了构建。据推测，避免翘曲的其他方法包括从下面更好地支撑悬臂挠性片（使其连接到零件的另一部分）或使其更宽。一般来说，应避免使用狭窄、无支撑的挠性结构。

Figure 3. Build failure due to warping of slender flexures.
图 3.由于细长挠曲翘曲而导致的建造故障。

Clearances are important to ensure that the completed mechanism can move freely, without fusing sections that should move relative to one another. On a number of mechanisms with small ( $<2\mathrm{mm}$$<2\mathrm{mm}$< 2mm<2 \mathrm{~mm} ) gaps, the final gap dimension was significantly less than was specified in the part file. Additionally, gaps must be wide enough that un-melted powder can be easily removed to allow motion in the mechanism. Experience with successful mechanisms suggests a minimum gap of 1.0 mm . The final gaps are less than the specified gap. In one instance, a gap as small as 0.66 mm was specified and the part successfully printed without fusing the two sections together; the measured clearance was 0.23 mm . These clearances were measured in the horizontal direction (parallel to the build plate). Vertical clearances should be specified larger, especially in areas where powder removal is difficult.
间隙对于确保完成的机械装置能够自由移动，而不会使本应相对移动的部分相互融合非常重要。在一些间隙较小（ $<2\mathrm{mm}$$<2\mathrm{mm}$< 2mm<2 \mathrm{~mm} ）的机械装置上，最终间隙尺寸远远小于零件文件中指定的尺寸。此外，间隙必须足够宽，以便未熔化的粉末可以很容易地移除，从而允许机构运动。成功机构的经验表明，最小间隙为 1.0 毫米。最终间隙小于规定间隙。在一个例子中，指定的间隙小到 0.66 毫米，但零件在没有将两个部分熔合在一起的情况下成功打印出来；测量的间隙为 0.23 毫米。这些间隙是在水平方向（与构建板平行）测量的。垂直方向的间隙应指定大一些，尤其是在难以清除粉末的区域。

Another design consideration is that the geometry must allow for removal of un-melted powder and any support structure. Closed geometries should be avoided, or openings should be provided to allow access to loosen packed powder with hand tools or media blasting. In some cases this may not be possible, and post machining using special fixtures or tooling must be used. Figure 5 shows the tooling required to allow machining the inside of a particular feature. In another case example, a linear spring was printed that consisted of Belleville washers stacked end-to-end. The internal areas of the spring were inaccessible, but by using a press to compress the spring, enough powder was removed from between each washer segment to allow the spring to function as intended.
另一个设计考虑因素是，几何形状必须允许清除未熔化的粉末和任何支撑结构。应避免使用封闭的几何形状，或提供开口，以便使用手工工具或介质喷射松动包装粉末。在某些情况下，可能无法做到这一点，因此必须使用特殊夹具或工具进行后加工。图 5 显示了加工特定特征内部所需的工具。在另一个案例中，打印的线性弹簧由端对端堆叠的贝勒维尔垫圈组成。虽然无法进入弹簧的内部区域，但通过使用压力机压缩弹簧，可以从每个垫圈段之间去除足够的粉末，从而使弹簧发挥预期的功能。

Figure 4. The 2 DOF pointer mechanism in fixture for removal of powder and supports from inside a split-tube flexure.
图 4.夹具中的 2 DOF 指针机构，用于从挠性劈裂管内部取出粉末和支撑物。

The following checklist can be used for designing compliant mechanisms for EBM manufacturing:
以下清单可用于设计符合 EBM 生产要求的机制：
$◻$$◻$◻\square Select minimum thickness for desired flexure orientation ( 0.75 mm for horizontal or vertical flexures and 1.0 mm for other angles)
$◻$$◻$◻\square 为所需的挠曲方向选择最小厚度（水平或垂直挠曲为 0.75 毫米，其他角度为 1.0 毫米）。
$◻$$◻$◻\square Find flexure length sufficient to bring stress into allowable range, subject to deflection and thickness
$◻$$◻$◻\square 根据挠度和厚度，找出足以使应力达到允许范围的挠曲长度
$◻$$◻$◻\square Select flexure width to support applied loads without requiring excessive actuation torque
$◻$$◻$◻\square 选择挠曲宽度，以支持所施加的负载，而不需要过大的致动扭矩
$◻$$◻$◻quad\square \quad Ensure minimum gap width is observed ( 1.0 mm )
$◻$$◻$◻quad\square \quad 确保遵守最小间隙宽度（1.0 毫米）
$◻$$◻$◻\square Ensure horizontal flexures are supported at both ends
$◻$$◻$◻\square 确保水平挠曲两端都有支撑
$◻$$◻$◻\square Ensure that geometry allows powder removal
$◻$$◻$◻\square 确保几何形状允许清除粉末
$◻$$◻$◻quad\square \quad If post-machining is necessary, provide geometry for fixturing
$◻$$◻$◻quad\square \quad 如果需要后加工，提供夹具的几何形状
$◻$$◻$◻quad\square \quad Orient part so that every feature is built up from build plate or supported in some way
$◻$$◻$◻quad\square \quad 确定部件的方向，使每个特征都由构建板构建或以某种方式支撑

This work was supported by a NASA Office of the Chief Technologist’s Space Technology Research Fellowship. The support of NASA Marshall Space Flight Center in the fabrication of titanium parts is gratefully acknowledged.
这项工作得到了美国宇航局首席技术官办公室空间技术研究奖学金的支持。美国国家航空航天局马歇尔太空飞行中心在钛部件制造过程中给予了大力支持，在此一并表示感谢。

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