Interdisciplinary Integrated Problem-Solving Training for Pre-U CAIE Engineering

📚 Interdisciplinary Integrated Problem-Solving Training for Pre-U CAIE Engineering | 跨学科综合题型训练

Pre-U CAIE Engineering challenges students to connect principles from mechanics, electronics, materials, and control in a single design problem. This integrated approach mirrors real-world engineering, where a solar tracker, for instance, demands structural analysis, sensor circuit design, motor selection, and embedded programming. The following sections break down a comprehensive training session built around a sun-tracking photovoltaic system, providing worked examples, design decisions, and a final practice set to sharpen your interdisciplinary reasoning.

Pre-U CAIE 工程考核学生将力学、电子学、材料学和控制原理综合运用于一个设计问题的能力。这种综合方式反映了真实的工程实践，例如一个太阳能追踪器就需要结构分析、传感器电路设计、电机选型和嵌入式编程。下面的内容围绕一个太阳追踪光伏系统构建全面的训练，给出解题范例、设计决策和最后的练习集，以强化你的跨学科推理能力。

1. Problem Statement and System Overview | 问题陈述与系统概述

A small single-axis solar tracker is to be designed for a 50 W photovoltaic panel of dimensions 600 mm × 400 mm. The system must rotate the panel about a horizontal east–west axis to follow the sun’s elevation, increasing daily energy yield by at least 20% compared with a fixed-tilt installation. Power for tracking must be drawn from the panel itself via a rechargeable battery. The design must withstand a maximum wind speed of 15 m/s, operate in temperatures from -5 °C to 50 °C, and use a microcontroller for closed-loop control based on two light-dependent resistors (LDRs).

需要为一个尺寸为 600 mm × 400 mm 的 50 W 光伏板设计一个小型单轴太阳追踪器。系统必须围绕东西水平轴旋转面板以跟随太阳高度角，相较于固定倾角安装，日能量产出至少提高 20%。追踪所用的电能必须通过可充电电池取自光伏板自身。该设计需承受最大 15 m/s 的风速，在 -5 °C 至 50 °C 的温度范围内工作，并利用两个光敏电阻 (LDR) 通过微控制器实现闭环控制。

2. Mechanical Load Analysis | 机械载荷分析

The worst-case wind load occurs when the panel faces the wind directly. Wind pressure q is estimated by q = 0.5ρv², where ρ is air density (1.2 kg/m³) and v is wind speed (15 m/s). Thus q = 0.5 × 1.2 × 15² = 135 Pa. Panel area A = 0.6 × 0.4 = 0.24 m². The total wind force F = q × A = 135 × 0.24 = 32.4 N, assumed to act at the panel centre. If the support arm length is 0.5 m from the axis to the centre, the maximum bending moment M = F × d = 32.4 × 0.5 = 16.2 N m. A safety factor of 1.5 raises the design moment to 24.3 N m.

最不利的风荷载出现在面板正对来风时。风压 q 由 q = 0.5ρv² 估算，其中空气密度 ρ = 1.2 kg/m³，风速 v = 15 m/s，故 q = 0.5 × 1.2 × 15² = 135 Pa。面板面积 A = 0.6 × 0.4 = 0.24 m²。总风力 F = q × A = 135 × 0.24 = 32.4 N，假定作用在面板中心。若支撑臂从转轴到中心的长度为 0.5 m，则最大弯矩 M = F × d = 32.4 × 0.5 = 16.2 N m。取安全系数 1.5，设计弯矩提升至 24.3 N m。

q = 0.5ρv² M = Fd M_design = 24.3 N·m

q = 0.5ρv² M = Fd M_设计 = 24.3 N·m

3. Material Selection for Support Structure | 支撑结构材料选择

The support arm and bracket are to be made from a lightweight, corrosion-resistant material with sufficient yield strength to handle the bending moment. Two candidates are considered: aluminium alloy 6061-T6 (yield strength 240 MPa, density 2700 kg/m³) and structural steel S275 (yield strength 275 MPa, density 7850 kg/m³). For a tubular arm with outer diameter 25 mm and wall thickness 3 mm, the section modulus Z is calculated. The bending stress σ = M/Z must be well below the allowable stress (σ_allow = yield strength / factor of safety). Aluminium is preferred for outdoor corrosion resistance and lower mass, which reduces the load on the motor and bearings.

支撑臂和支架需由轻质、耐腐蚀且具有足够屈服强度的材料制成，以承受弯矩。两种材料作为备选：铝合金 6061-T6（屈服强度 240 MPa，密度 2700 kg/m³）和结构钢 S275（屈服强度 275 MPa，密度 7850 kg/m³）。对于一个外径 25 mm、壁厚 3 mm 的管状支撑臂，需要计算其截面模量 Z。弯曲应力 σ = M/Z 必须远低于许用应力（σ_许 = 屈服强度 / 安全系数）。出于户外耐腐蚀性和较低质量的考虑，铝更受青睐，从而减轻电机和轴承的负载。

Property	Al 6061-T6	Steel S275
Yield strength (MPa)	240	275
Density (kg/m³)	2700	7850
Corrosion resistance	Good	Requires coating

属性	铝 6061-T6	钢 S275
屈服强度 (MPa)	240	275
密度 (kg/m³)	2700	7850
耐腐蚀性	良好	需涂层

4. Gear Train Design and Motor Selection | 齿轮系设计与电机选型

The torque required at the axis to overcome wind and inertia is estimated to be 3.0 N m under worst conditions. A small stepper motor provides a holding torque of 0.4 N m. A two-stage spur gear train is designed with a total reduction ratio i = 10:1 (e.g., stage 1: 3:1, stage 2: 3.33:1), giving an output torque τ_out = τ_motor × i × η, where efficiency η is assumed 0.85 per stage. Overall τ_out ≈ 0.4 × 10 × (0.85)² = 2.89 N m, which is slightly below the worst-case requirement. Adding a third stage or selecting a motor with higher torque resolves this. A worm gear alternative could provide self-locking to hold position when unpowered, reducing energy consumption.

在最恶劣条件下，克服风力和惯性所需的轴扭矩估计为 3.0 N m。一个小型步进电机提供 0.4 N m 的保持扭矩。设计一个两级直齿圆柱齿轮系，总减速比 i = 10:1（例如第一级 3:1，第二级 3.33:1），输出扭矩 τ_out = τ_motor × i × η，每级效率 η 取 0.85。总 τ_out ≈ 0.4 × 10 × (0.85)² = 2.89 N m，略低于最差工况要求。可增加第三级或选用更高扭矩的电机解决。蜗轮蜗杆方案可提供自锁性，在断电时保持位置，减少能耗。

τ_out = τ_motor × i × η₁ × η₂

τ_输出 = τ_电机 × i × η₁ × η₂

5. Sensor Circuit Design (Light Detection) | 传感器电路设计（光检测）

Two LDRs are mounted on either side of a small opaque divider so that their resistance differs according to the sun’s direction. Each LDR forms a voltage divider with a fixed 10 kΩ resistor connected to a 5 V supply. The output voltage V_out = 5 V × R_fixed / (R_LDR + R_fixed). When light intensity is high, R_LDR drops to about 1 kΩ, giving V_out ≈ 4.55 V; in shadow, R_LDR rises to ~100 kΩ, giving V_out ≈ 0.45 V. The two voltages are fed into analogue inputs of the microcontroller. The difference indicates the tracking error; the tracker activates the motor to equalise the readings.

两个 LDR 分别安装在一块小隔板的两侧，使其电阻根据太阳方向产生差异。每个 LDR 与一个固定在 10 kΩ 的电阻接至 5 V 供电构成分压器。输出电压 V_out = 5 V × R_固定 / (R_LDR + R_固定)。光照强时，R_LDR 降至约 1 kΩ，V_out ≈ 4.55 V；阴影下，R_LDR 升至约 100 kΩ，V_out ≈ 0.45 V。两个电压送入微控制器的模拟输入端。差值指示追踪误差；追踪器启动电机使读数相等。

V_out = 5 × 10kΩ / (R_LDR + 10kΩ)

V_输出 = 5 × 10kΩ / (R_LDR + 10kΩ)

6. Control Logic and Microcontroller Programming | 控制逻辑与微控制器编程

The microcontroller reads V_east and V_west every 2 seconds. If |V_east – V_west| < 0.2 V, the panel is aligned and the motor is idle. If V_east > V_west + 0.2 V, the west LDR receives more light, so the panel must rotate eastward; the microcontroller sends a sequence to the H-bridge to run the stepper motor clockwise for a fixed number of steps. Conversely, if V_west > V_east + 0.2 V, the motor turns anticlockwise. Limit switches at extreme angles prevent mechanical damage. The code is written in C with functions for ADC reading, motor stepping, and a main loop that only activates tracking while the panel is producing enough power (> 5 W).

微控制器每 2 秒读取一次 V_东和 V_西。若 |V_东 – V_西| < 0.2 V，面板已对准，电机闲置。若 V_东 > V_西 + 0.2 V，西侧 LDR 受光更多，面板须向东旋转；微控制器向 H 桥发送序列，使步进电机顺时针转过固定步数。反之，若 V_西 > V_东 + 0.2 V，电机逆时针转动。极端角度处的限位开关防止机械损坏。程序用 C 编写，包含 ADC 读取函数、电机步进函数和一个主循环，该循环仅在面板产生足够功率（> 5 W）时激活追踪。

State 1: Idle – no significant difference, no movement.
状态 1：空闲 – 无明显差异，无移动。
State 2: Track East – motor clockwise.
状态 2：向东追踪 – 电机顺时针。
State 3: Track West – motor anticlockwise.
状态 3：向西追踪 – 电机逆时针。

7. Power Supply and Energy Efficiency | 电源与能量效率

Tracking motors and electronics consume energy that must be offset by the increase in panel output. The tracker’s daily energy consumption is estimated: motor (5 W for 10% duty cycle over 10 hours of daylight = 5 Wh), microcontroller and sensors (0.5 W continuous = 5 Wh per day), giving a total of about 10 Wh. The fixed panel would generate about 200 Wh/day under average conditions. A 20% boost yields an extra 40 Wh, leaving a net gain of 30 Wh. A 12 V, 7 Ah lead-acid battery (84 Wh capacity) provides sufficient buffer for night operation and cloudy days. The panel’s own power is regulated by a charge controller to maintain battery health.

追踪电机和电子设备消耗的能量必须由面板输出增加的部分弥补。追踪器日能耗估算：电机（5 W，在 10 小时日照内占空比 10%，合 5 Wh），微控制器及传感器（连续 0.5 W，每天 5 Wh），合计约 10 Wh。固定面板在平均条件下每天约产生 200 Wh。20% 的提升额外带来 40 Wh，净增益 30 Wh。一个 12 V、7 Ah 的铅酸电池（容量 84 Wh）提供足够的缓冲用于夜间和阴天运行。面板自身的电能通过充电控制器调节，以保持电池健康。

Net gain = ΔE_panel – E_tracker = 40 Wh – 10 Wh = 30 Wh

净增益 = ΔE_面板 – E_追踪器 = 40 Wh – 10 Wh = 30 Wh

8. Thermal Management | 热管理

The stepper motor may reach 60 °C internally during continuous stall conditions; its winding resistance increases, reducing torque. A small aluminium heat sink attached to the motor casing and passive ventilation help keep temperatures within limits. The voltage regulators (5 V and 3.3 V) dissipate power (P_diss = (V_in – V_out) × I), approximately 0.5 W. This can be managed with a copper pad on the PCB. All components must be rated for the upper ambient limit of 50 °C, and the enclosure should include rainproof louvres.

步进电机在连续堵转条件下内部可能达到 60 °C；其绕组电阻升高，导致扭矩下降。电机外壳上加装小型铝散热片并利用被动通风有助于将温度控制在限值内。稳压器（5 V 和 3.3 V）耗散功率 P_diss = (V_in – V_out) × I，约为 0.5 W，可通过 PCB 上的铜敷层处理。所有元器件必须满足 50 °C 的上限环境温度，外壳应包含防雨百叶窗。

9. System Integration and Testing | 系统集成与测试

The mechanical assembly, wiring, and microcontroller code are integrated on a bench. Testing begins with sensor characterisation: a lamp is moved from left to right to verify the LDR voltage disparity disappears at alignment. Motor current is monitored during stall to ensure it does not exceed the driver’s rating. The full system is then placed outdoors on a sunny day. Data logging records panel voltage, battery state-of-charge, and tracking angles every minute. The energy yield is compared against a fixed reference panel over several days. Corrections to the tracking algorithm and gear backlash compensation are made based on these logs.

将机械总成、接线和微控制器代码在实验台上集成。测试从传感器标定开始：将灯从左向右移动，验证对准时 LDR 电压差异消失。测试电机堵转电流以确保不超过驱动器额定值。之后将完整系统置于户外晴天。数据记录每分钟记录面板电压、电池荷电状态和追踪角度。将多日内的能量产出与固定参考面板进行比较。根据这些记录修正追踪算法和齿轮间隙补偿。

10. Practice Problem Set | 综合练习题

Apply the same interdisciplinary approach to the following scenario: A wind turbine blade pitch mechanism is to be controlled by an electric linear actuator. The blades experience centrifugal and aerodynamic twisting moments. Design a system that measures wind speed via an anemometer, adjusts blade pitch for maximum power before furling, and contains emergency feathering using a battery-backed actuator. Determine: (a) maximum aerodynamic torque on a blade root; (b) actuator stroke and gear specifications; (c) sensor and control circuit to interface with a microcontroller; (d) energy budget for the pitch system; and (e) a test plan for the actuator response time.

将同样的跨学科方法应用于以下场景：风力涡轮机的叶片变桨机构需由一个电动直线执行器控制。叶片承受离心和气动扭转力矩。设计一个系统，通过风速计测量风速，在收桨前调整叶片桨距以获得最大功率，并包含使用电池后备执行器的紧急顺桨。请确定：(a) 叶片根部最大气动扭矩；(b) 执行器行程与齿轮规格；(c) 与微控制器接口的传感器及控制电路；(d) 变桨系统的能量预算；(e) 执行器响应时间的测试计划。

Published by TutorHao | Engineering Revision Series | aleveler.com

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Interdisciplinary Integrated Problem-Solving Training for Pre-U CAIE Engineering | 跨学科综合题型训练