📚 Case Study Practical Drill: Designing a Portable Adjustable Phone Stand | 案例分析实战演练：便携可调手机支架设计
Case studies form the backbone of engineering education, bridging theoretical knowledge and real-world application. In this drill, we will walk through the complete design process of a portable adjustable phone stand, applying key Year 12 OCR Engineering concepts such as material properties, mechanical principles, and manufacturing considerations. Follow each step to strengthen your analytical skills and prepare for exam-style scenarios.
案例分析是工程教育的基石，它将理论知识与实际应用联系起来。在本次实战演练中，我们将逐步完成一款便携可调手机支架的完整设计流程，涵盖材料性能、力学原理和制造工艺等 OCR 工程 Year 12 的核心知识点。请跟随每一步来增强你的分析能力，并为考试类场景做好准备。
1. Introduction to the Case Study Scenario | 案例场景介绍
The task is to design a portable phone stand that can securely hold smartphones with screen sizes ranging from 5.5 to 7 inches. Users must be able to adjust the viewing angle between 15° and 60° smoothly, and the stand should remain stable on a desk without slipping or tipping when a user taps the screen. Additionally, the product must be lightweight (under 150 g) and compact enough to fit in a pocket or small bag.
本次任务要求设计一款便携手机支架，能够牢固支撑屏幕尺寸在 5.5 至 7 英寸之间的智能手机。用户需要能够在 15° 到 60° 之间平滑地调节视角，并且支架在桌面上必须保持稳定，当用户触击屏幕时不发生滑动或翻倒。此外，产品必须轻巧（低于 150 g）且紧凑，能够放入口袋或小包中。
The stand will be targeted at students and professionals who frequently use their phones for video calls, reading, or watching media. Environmental conditions are typical indoor settings with ambient temperatures between 15 °C and 35 °C. The life expectancy is at least two years of daily use, meaning approximately 1,500 adjustment cycles without failure.
该支架的目标用户是经常使用手机进行视频通话、阅读或观看媒体的学生和职场人士。使用环境为典型的室内条件，环境温度在 15 °C 至 35 °C 之间。预期寿命为至少两年的日常使用，即大约 1,500 次调节循环而不失效。
2. Stakeholder Needs and Design Brief | 利益相关者需求与设计概要
Stakeholders include end-users, manufacturers, and retailers. End-users prioritise stability, adjustability, portability, and an attractive appearance. Manufacturers require a design that is easy to produce with minimal assembly steps and low material waste. Retailers are concerned with durability during shipping and attractive packaging potential.
利益相关者包括最终用户、制造商和零售商。最终用户优先考虑稳定性、可调性、便携性和吸引人的外观。制造商要求设计易于生产，装配步骤最少且材料浪费少。零售商则关注运输过程中的耐久性以及具有吸引力的包装潜力。
Thus, the design brief can be stated: 'Design a lightweight, foldable phone stand with stepless angle adjustment from 15° to 60°, compatible with phones 5.5–7 inches, using materials that balance cost, durability, and aesthetics. The stand must be stable on flat surfaces and withstand a lateral force of 2 N at the top without toppling.'
因此，设计概要可表述为：“设计一款轻量化的可折叠手机支架，具有从 15° 到 60° 的无级角度调节功能，兼容 5.5–7 英寸手机，采用能够平衡成本、耐用性和美观性的材料。支架必须能在平坦表面上保持稳定，并在顶部承受 2 N 的侧向力而不翻倒。”
3. Product Design Specification (PDS) | 产品设计规范
A structured PDS translates the brief into measurable criteria. Key parameters include:
结构化的 PDS 将设计概要转化为可量化的标准。关键参数包括：
tprint no larger than 120 mm × 80 mm when folded; height adjustable from 100 mm to 150 mm.
几何尺寸：折叠后整体占地面积不超过 120 mm × 80 mm；高度调节范围为 100 mm 至 150 mm。
Mass: ≤ 150 g.
质量：≤ 150 g。
Angle range: 15° to 60° with a locking mechanism that holds position under a 200 g phone load.
角度范围：15° 至 60°，且锁定机构在承载 200 g 手机时应能保持位置。
Stability: must not slide when a friction force of 1.5 N is applied horizontally to the phone’s centre; tipping moment must be less than restoring moment from base.
稳定性：当在手机中心水平施加 1.5 N 的摩擦力时不得滑动；倾覆力矩必须小于底座提供的恢复力矩。
Environmental tolerance: –10 °C to 50 °C storage, humidity 20%–80% non-condensing.
环境耐受性：存储温度 –10 °C 至 50 °C，湿度 20%–80% 无冷凝。
Cost: materials cost per unit below £1.50 for a batch of 10,000 units.
成本：在 10,000 件的批量下，每件材料成本低于 1.50 英镑。
Aesthetic: smooth, rounded edges, available in matte black and white finishes.
外观：边缘光滑圆润，提供哑光黑和白色饰面。
4. Material Selection and Properties | 材料选择与性能
Three candidate materials are evaluated: ABS (Acrylonitrile Butadiene Styrene), PLA (Polylactic Acid), and anodised aluminium alloy 6061. The table below compares their key properties against the PDS requirements.
以下三种候选材料被纳入评估：ABS（丙烯腈-丁二烯-苯乙烯共聚物）、PLA（聚乳酸）和阳极氧化 6061 铝合金。下表将它们的核心性能与 PDS 要求进行了比较。
| Property / 性能 | ABS | PLA | Aluminium 6061 / 铝合金 6061 |
|---|---|---|---|
| Density (g cm⁻³) / 密度 | 1.04 | 1.24 | 2.70 |
| Tensile strength (MPa) / 抗拉强度 | 40 | 50 | 310 |
| Elastic modulus (GPa) / 弹性模量 | 2.3 | 3.5 | 69 |
| Cost per kg (£) / 每千克成本 | 2.00 | 3.50 | 5.00 |
| Recyclability / 可回收性 | Yes | Compostable* | Infinitely |
| Surface finish options / 表面处理 | Textured, glossy | Smooth, matte | Anodised, brushed |
ABS is selected as the primary material because it offers an excellent balance of strength, low density, and low cost. It can be injection moulded, which suits mass production and delivers the required aesthetic finishes. Aluminium is over-engineered in terms of strength and would increase mass beyond the speculation limit, and PLA, while more sustainable, is more brittle and sensitive to moisture, reducing long-term reliability.
选择 ABS 作为主要材料，因为它在强度、低密度和低成本之间提供了极佳的平衡。它可注塑成型，适合大规模生产，并能提供所需的美观饰面。铝合金在强度方面属于过度设计，且会增大质量超过规定限制；PLA 虽然更可持续，但更脆且对水分敏感，会降低长期可靠性。
5. Mechanical Analysis: Forces and Stability | 力学分析：力与稳定性
Consider the phone of mass m = 0.200 kg. Its weight is:
考虑一部质量为 m = 0.200 kg 的手机。其重量为：
W = m × g = 0.200 kg × 9.81 m s⁻² ≈ 1.96 N
When the stand is set to its maximum angle of 60° from the horizontal, the component of the weight acting parallel to the backrest (tending to slide the phone down) is:
当支架设置为与水平面成最大 60° 角时，重力平行于靠背的分力（倾向于使手机下滑）为：
F_parallel = W × sin(60°) ≈ 1.96 N × 0.866 ≈ 1.70 N
rubber pad with coefficient of static friction μ_s = 0.8, the maximum frictional force is:
为防止滑动，手机与支架表面之间的静摩擦力必须超过 1.70 N。假设采用硅橡胶垫，其静摩擦系数 μ_s = 0.8，则最大摩擦力为：
F_friction = μ_s × W × cos(60°) = 0.8 × 1.96 N × 0.5 ≈ 0.78 N
ovide a mechanical stop. The lip will experience a direct shear force equal to F_parallel.
该值低于下滑力。因此，必须在支架底端设置一个挡边作为机械止挡。挡边将承受等于 F_parallel 的直接剪切力。
a lateral force of 2.0 N at a height h = 120 mm above the desk. The overturning moment is:
对于防翻倒稳定性，考虑最坏情况：用户在桌面以上 h = 120 mm 的高度对手机屏幕施加 2.0 N 的侧向力。倾覆力矩为：
M_overturn = F_lateral × h = 2.0 N × 0.120 m = 0.24 N m
tal mass of stand plus phone is 0.35 kg, with the centre of mass located at approximately 35 mm from the front edge, the restoring moment is:
恢复力矩由支架（包括手机）的重力通过质心提供。若底座深度 d = 70 mm，支架加手机总质量 0.35 kg，质心距前边缘约 35 mm，则恢复力矩为：
M_restore = (0.35 kg × 9.81 m s⁻²) × 0.035 m ≈ 0.120 N m
ver arm of 50 mm, yielding M_restore ≈ 0.172 N m, which is still low. By adding a weighted metal insert or increasing base footprint to 130 mm × 90 mm, the restoring moment can be increased to over 0.30 N m, ensuring a factor of safety above 1.25.
恢复力矩（0.120 N m）小于倾覆力矩（0.24 N m）。为解决此问题，必须加长底座深度。深度 100 mm 时力臂为 50 mm，产生 M_restore ≈ 0.172 N m，仍然偏低。通过添加配重金属嵌件或将底座占地面积增大至 130 mm × 90 mm，可将恢复力矩提升至 0.30 N m 以上，确保安全系数超过 1.25。
6. Stress and Factor of Safety Calculations | 应力与安全系数计算
nd thickness t = 3 mm, subjected to a shear force V = 1.70 N. The average shear stress is:
挡边为薄 ABS 凸缘，截面宽度 b = 60 mm，厚度 t = 3 mm，承受的剪切力 V = 1.70 N。平均剪应力为：
/ A = 1.70 N / (60 × 10⁻³ m × 3 × 10⁻³ m) = 1.70 N / (1.8 × 10⁻⁴ m²) ≈ 9,444 Pa = 9.44 kPa
MPa. Applying a factor of safety FoS = 2.5 for shock loads, the allowable shear stress is:
ABS 的极限抗剪强度约为 25 MPa。对于冲击载荷，取安全系数 FoS = 2.5，则许用剪应力为：
τ_allow = 25 MPa / 2.5 = 10 MPa
allow (10 MPa), the lip is very safe in shear. However, bending stress on the lip caused by the phone' t offset must also be checked. If the force acts with a lever arm of 2 mm due to the phone's case, the bending moment is Mb section is Z = (b × t²)/6 = (0.06 m × (0.003 m)²)/6 = 9 × 10⁻⁸ m³. Bending stress σ_b = Mb xceeds the tensile strength of ABS (40 MPa) when static, but with a FoS of 1.5, it is borderline. Therefore, the lip thickness is increased to 4 mm, dramatically lowering the bending stress to about 16 MPa, well within safe limits.
由于 τ_avg（9.44 kPa）远低于 τ_allow（10 MPa），挡边在剪切方面非常安全。然而，还需校核因手机重量在微小偏距下作用于挡边所引起的弯曲应力。如果由于手机外壳导致力臂为 2 mm，则弯矩 Mb = 1.70 N × 0.002 m = 0.0034 N m。矩形截面模量 Z = (b × t²)/6 = (0.06 m × (0.003 m)²)/6 = 9 × 10⁻⁸ m³。弯曲应力 σ_b = Mb / Z = 0.0034 / 9×10⁻⁸ ≈ 37.8 MPa，这已接近 ABS 的抗拉强度 40 MPa，且按安全系数 1.5 考量，处于临界状态。因此，将挡边厚度增加至 4 mm，弯曲应力将大幅降低至约 16 MPa，完全在安全范围内。
7. Manufacturing Processes Consideration | 制造工艺考量
Given the choice of ABS and the target production volume of 10,000 units, injection moulding is the most suitable process. It provides high repeatability, excellent surface finish, and the ability to integrate complex features such as living hinges, snap-fits, and textured grip patterns directly into the mould. The mould tooling cost (approximately £5,000–£8,000) is amortised over the large batch, making the per-unit part cost very low.
鉴于选用 ABS 以及 10,000 件的目标产量，注塑成型是最合适的工艺。它提供高重复性、出色的表面质量，并能将诸如活动铰链、卡扣和纹理抓握图案等复杂特征直接集成到模具中。模具成本（约 5,000–8,000 英镑）在大批量生产中得到分摊，使得单件成本极低。
The foldable design includes a living hinge that connects the backrest and the base. A living hinge in ABS relies on the material's ability to undergo plastic deformation during initial flexing, after which the hinge becomes flexible. Proper design of the hinge thickness (typically 0.3–0.5 mm) and radius is critical to avoid stress concentration and premature failure. This hinge will be tested for 1,500 cycles as specified in the PDS.
可折叠设计包括一个连接靠背和底座的活动铰链。ABS 中的活动铰链依赖材料在首次弯曲时发生塑性变形，之后铰链便具有柔性。正确设计铰链厚度（通常 0.3–0.5 mm）和圆角半径对于避免应力集中和过早失效至关重要。该铰链将按照 PDS 要求进行 1,500 次循环测试。
Alternative processes such as 3D printing (FDM) could be used for prototyping and very small batches, but the layer-by-layer construction diminishes strength in the Z-direction, which is problematic for the living hinge. CNC machining from aluminium was ruled out due to high cost per part and weight constraints.
对于原型制作和极小批量，可以采用 3D 打印（FDM）等替代工艺，但逐层构造会降低 Z 方向强度，这对活动铰链来说是个问题。铝材 CNC 加工则因单件成本高和重量限制而被排除。
8. Prototyping and Testing | 原型制作与测试
A functional prototype was 3D-printed using PLA to verify form, fit, and basic function before committing to injection moulding tooling. The prototype revealed that the initial living hinge design was too stiff, requiring a reduction in thickness from 0.6 mm to 0.4 mm to achieve easier folding without cracking.
在投入注塑模具之前，使用 PLA 进行 3D 打印制作了一个功能原型，以验证外形、配合和基本功能。原型显示，最初的活动铰链设计过于僵硬，需将厚度从 0.6 mm 减小至 0.4 mm，使折叠更容易且不产生裂纹。
Tests conducted included:
进行的测试包括：
Load capacity test: The stand supported a 250 g mass (25% overload) for 24 hours with no measurable creep or permanent deformation.
负载能力测试：支架支撑 250 g 的质量（超载 25%）持续 24 小时，未出现可测量的蠕变或永久变形。
Slide resistance test: With a phone in place, a pull force was gradually applied parallel to the backrest. The phone did not slide until the force exceeded 2.8 N, thanks to the improved lip and silicone pad.
防滑测试：手机就位后，沿靠背方向逐渐施加拉力。得益于改进后的挡边和硅胶垫，直到力超过 2.8 N 手机才发生滑动。
Tipping test: The stand with phone was pushed horizontally at the top edge with a force of 2.5 N. The extended base footprint prevented any tipping.
防翻倒测试：以 2.5 N 的力水平推压装有手机的支架顶部边缘。加大的底座占地面积防止了任何翻倒。
Cycle test: The living hinge was flexed through 60° back and forth 2,000 times. No visible cracks or loss of spring-back were observed.
循环测试：活动铰链在 60° 范围内来回弯折 2,000 次。未观察到可见裂纹或回弹力丧失。
9. Evaluation and Iteration | 评估与迭代
ovides stepless angle adjustment via a friction lock mechanism. Material cost is estimated at £0.95 per unit, well within the £1.50 limit. Users in a small focus group rated the stability and portability as 'excellent', though two out of ten found the folding mechanism slightly stiff initially – can be addressed by adding a small amount of lubricant in the hinge area during assembly.
最终设计满足了所有关键的 PDS 要求。支架重量为 128 g，折叠后尺寸为 118 mm × 78 mm × 14 mm，并通过摩擦锁止机构实现无级角度调节。单位材料成本估计为 0.95 英镑，远低于 1.50 英镑的限制。在小型焦点小组中，用户将稳定性和便携性评为“优秀”，不过十分之二的用户觉得折叠机构起初稍显生硬——这可以通过在装配时于铰链区域添加少量润滑剂来解决。
Lessons learned include the importance of conducting both shear and bending stress analyses on seemingly minor features, and the value of rapid prototyping to reveal real-world user experience issues that are hard to predict in CAD. An unexpected outcome was that the silicone pad increased friction but also attracted dust; a future iteration could explore a textured ABS surface instead.
总结经验教训包括：对看似微小的特征同时进行剪应力和弯曲应力分析的重要性，以及快速原型制造在揭示 CAD 中难以预料的真实用户体验问题方面的价值。一个意外发现是，硅胶垫虽增加了摩擦力却易吸附灰尘；未来的迭代可尝试用带纹理的 ABS 表面替代。
10. Conclusion and Key Takeaways | 结论与要点总结
This case study demonstrates how a systematic engineering approach – from stakeholder analysis, through PDS and material selection, to mechanical calculations and manufacturing process design – can lead to a robust, cost-effective product. Key takeaways for Year 12 OCR Engineering students:
本案例研究展示了系统化的工程方法——从利益相关者分析，到 PDS 和材料选择，再到力学计算和制造工艺设计——如何导向一款坚固且成本高效的产品。对于 OCR 工程 Year 12 学生，关键要点包括：
Always quantify user needs in a design specification to guide decision-making.
始终在设计规范中对用户需求进行量化，以指导决策。
Material choice must balance mechanical properties, weight, cost, and manufacturability.
材料选择必须平衡力学性能、重量、成本和可制造性。
Even simple products require thorough force and moment analysis to ensure stability and safety.
即便是简单的产品也需要全面的力和力矩分析，以确保稳定性和安全性。
Factor of safety calculations are essential to account for unanticipated loads and material variations.
安全系数计算对于应对意外载荷和材料变差至关重要。
Manufacturing process selection dramatically influences design features and economic viability.
制造工艺的选择显著影响设计特征和经济可行性。
Prototyping and testing close the loop between theory and practice, revealing hidden flaws.
原型制作和测试闭合了理论与实践的循环，揭示出隐藏的缺陷。
Apply these principles to your own design challenges, and you will be well prepared for both coursework and the written examination.
将这些原则应用到你自己的设计挑战中，你将为课程作业和书面考试做好充分准备。
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