📚 Year 12 WJEC Engineering: Core Knowledge Points Review | Year 12 WJEC 工程：核心知识点梳理
The Year 12 WJEC Engineering course introduces you to the foundational principles that underpin modern technology and design. From understanding material properties to analysing electrical circuits and mechanical systems, you will develop a toolkit for solving real-world engineering problems. This article consolidates the core knowledge points you need to master, structured into ten focused sections for effective revision.
Year 12 WJEC 工程课程为你介绍支撑现代技术与设计的基础原理。从理解材料特性到分析电路和机械系统，你将逐步掌握解决真实工程问题的工具包。本文将梳理你需要掌握的核心知识点，分为十个重点小节，方便你高效复习。
1. Engineering Materials: Classification and Properties | 工程材料：分类与特性
Materials are at the heart of every engineering product. Engineers classify materials into metals (ferrous and non-ferrous), alloys, polymers, ceramics and composites. Ferrous metals contain iron and are typically magnetic and prone to rust, while non-ferrous metals like aluminium and copper offer corrosion resistance and high conductivity. Key mechanical properties include tensile strength, hardness, ductility, toughness and elasticity.
材料是每个工程产品的核心。工程师将材料分为金属（黑色金属和有色金属）、合金、聚合物、陶瓷和复合材料。黑色金属含铁，通常有磁性且易生锈；而有色金属如铝和铜则具有耐腐蚀性和高导电性。重要的力学性能包括抗拉强度、硬度、延展性、韧性和弹性。
Ferrous metals, such as mild steel and cast iron, are widely used in structural applications because of their high strength and low cost. However, they often require protective coatings to prevent corrosion.
黑色金属如低碳钢和铸铁因强度高、成本低而广泛用于结构件，但通常需要保护涂层以防腐蚀。
Non-ferrous metals are chosen for lightweight and corrosion-resistant requirements. Aluminium alloys, for instance, are essential in aerospace and automotive industries due to their high strength-to-weight ratio.
有色金属则因轻量化和耐腐蚀需求而被选用。例如铝合金凭借其高强度重量比在航空航天和汽车工业中至关重要。
Polymers are divided into thermoplastics and thermosets. Thermoplastics can be reheated and reshaped, making them suitable for injection moulding, while thermosets undergo a permanent chemical change and are used for high-heat applications.
聚合物分为热塑性和热固性两类。热塑性塑料可反复加热重塑，适用于注塑成型；热固性塑料则发生永久化学变化，用于高温场合。
Composites combine two or more materials to achieve properties that are superior to the individual constituents. Carbon-fibre-reinforced polymer (CFRP) offers exceptional stiffness and strength with minimal weight.
复合材料将两种或以上材料结合，以获得优于单一组分的性能。碳纤维增强聚合物（CFRP）具有极高的刚度和强度，且重量极轻。
Ceramics are known for their hardness, high melting points and brittleness. They are used in cutting tools, engine components and electronic substrates.
陶瓷以高硬度、高熔点和脆性著称，常用于切削工具、发动机部件和电子基板。
2. Material Testing Methods | 材料测试方法
Understanding material properties requires reliable testing. Common destructive tests include tensile testing, hardness testing (Brinell, Rockwell, Vickers) and impact testing (Izod and Charpy). Non-destructive testing (NDT) methods like ultrasonic and dye penetrant inspection are used to detect flaws without damaging the component.
理解材料性能需要可靠的测试。常见的破坏性测试包括拉伸测试、硬度测试（布氏、洛氏、维氏）和冲击测试（Izod 和 Charpy）。无损检测（NDT）方法如超声波和着色渗透检测则用于在不损坏部件的前提下发现缺陷。
A tensile test stretches a standardised specimen at a constant rate until fracture. The resulting stress-strain curve reveals the material’s Young’s modulus, yield strength, ultimate tensile strength (UTS) and elongation at break.
拉伸测试以恒定速率拉伸标准试样直至断裂，得到的应力-应变曲线可揭示材料的杨氏模量、屈服强度、极限抗拉强度（UTS）和断裂延伸率。
σ = F / A₀ and ε = ΔL / L₀
Hardness tests measure a material’s resistance to indentation. The Brinell test uses a hardened steel or carbide ball, while Vickers uses a diamond pyramid. The hardness value helps predict wear resistance and can be correlated with tensile strength.
硬度测试衡量材料抵抗压入的能力。布氏硬度使用硬钢或碳化钨球，维氏硬度使用金刚石棱锥。硬度值有助于预测耐磨性，并可间接推算抗拉强度。
Impact testing assesses a material’s toughness, or its ability to absorb energy before fracturing. The Charpy test supports the specimen horizontally and strikes from behind the notch, whereas the Izod test holds the specimen vertically. Results are especially critical for materials used in low-temperature environments where brittleness can increase.
冲击测试评估材料的韧性，即断裂前吸收能量的能力。夏比冲击测试水平支撑试样并从缺口背面冲击，而艾氏冲击测试则垂直夹持试样。其结果对低温环境中脆性增强的材料尤为关键。
3. Forces and Equilibrium in Mechanical Systems | 机械系统中的力与平衡
Forces are vector quantities, meaning they have both magnitude and direction. Newton’s laws of motion govern how objects move or stay still. The first law states that an object remains at rest or in uniform motion unless acted upon by a resultant force.
力是矢量，既有大小又有方向。牛顿运动定律支配着物体的运动或静止。第一定律指出，除非受到合外力作用，物体将保持静止或匀速直线运动状态。
For static equilibrium, the sum of all forces in any direction must be zero (ΣF = 0) and the sum of moments about any point must be zero (ΣM = 0). A moment is the turning effect of a force, calculated as moment = force × perpendicular distance from the pivot.
对于静力平衡，任何方向上的合力必须为零（ΣF = 0），且对任一点的合力矩必须为零（ΣM = 0）。力矩是力的转动效应，计算公式为 力矩 = 力 × 垂直距离。
M = F × d
Free-body diagrams are used to isolate a body and display all forces acting on it, including weight, normal reaction, friction and applied loads. This visual tool is essential for applying the conditions of equilibrium correctly.
受力分析图用于隔离物体并显示所有作用力，包括重力、法向反力、摩擦力和外加载荷。这一可视化工具对于正确应用平衡条件至关重要。
Simple machines such as levers and pulleys provide mechanical advantage. The mechanical advantage (MA) is the ratio of load to effort, while velocity ratio (VR) relates distances moved by effort and load. Efficiency = (MA / VR) × 100%.
杠杆和滑轮等简单机械可提供机械效益。机械效益（MA）是载荷与施力之比，而速比（VR）关系着施力点与载荷移动的距离。效率 = (MA / VR) × 100%。
4. Stress, Strain and Elasticity | 应力、应变与弹性
When a material is loaded, it experiences stress (internal resistive force per unit area) and strain (deformation relative to original dimensions). For direct tension or compression, engineering stress σ = F / A and engineering strain ε = ΔL / L₀.
材料受载时内部产生应力（单位面积上的抵抗力）和应变（相对于原始尺寸的变形）。对于简单拉伸或压缩，工程应力 σ = F / A，工程应变 ε = ΔL / L₀。
Young’s modulus E is a measure of stiffness, defined as the ratio of stress to strain within the elastic limit, where Hooke’s law applies and deformation is reversible. E = σ / ε, with units of pascals (Pa) or gigapascals (GPa).
杨氏模量 E 是刚度的量度，定义为弹性限度内应力与应变之比，在此范围内胡克定律适用且变形可恢复。E = σ / ε，单位为帕斯卡（Pa）或吉帕（GPa）。
E = σ / ε (valid within the linear elastic region)
The factor of safety (FoS) is used to account for uncertainties in loading, material defects and consequences of failure. FoS = ultimate tensile strength / allowable working stress. A typical FoS might range from 1.5 to 10, depending on the criticality of the component.
安全系数（FoS）用于涵盖载荷不确定性、材料缺陷和失效后果的影响。FoS = 极限抗拉强度 / 许用工作应力。典型的安全系数范围从1.5到10，取决于部件的重要性。
Materials can fail by yielding, fracture or fatigue. The stress-strain curve for ductile materials shows a clear yield point, plastic deformation and necking before fracture, while brittle materials fail suddenly with little plastic strain.
材料可能因屈服、断裂或疲劳而失效。韧性材料的应力-应变曲线显示明显的屈服点、塑性变形和断裂前的颈缩，而脆性材料在很小的塑性应变后便突然失效。
5. Fundamentals of Electrical Circuits | 电路基础
An electrical circuit requires a complete loop for current to flow. Ohm’s law relates voltage (V), current (I) and resistance (R): V = I R. This linear relationship holds for ohmic conductors at constant temperature.
电路需要闭合回路才能让电流流动。欧姆定律给出了电压（V）、电流（I）和电阻（R）之间的关系：V = I R。对于恒定温度下的欧姆导体，这一线性关系成立。
Resistors can be connected in series or parallel. The total resistance in series is the sum of individual resistances: Rtotal = R₁ + R₂ + R₃ + … In parallel, the reciprocal of total resistance equals the sum of reciprocals: 1/Rtotal = 1/R₁ + 1/R₂ + …
电阻可以串联或并联。串联总电阻为各电阻之和：Rₜₒₜₐₗ = R₁ + R₂ + R₃ + …。并联时，总电阻的倒数等于各电阻倒数之和：1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + …
Kirchhoff’s laws are fundamental for analysing complex circuits. Kirchhoff’s current law (KCL) states that the sum of currents entering a node equals the sum of currents leaving it. Kirchhoff’s voltage law (KVL) states that the algebraic sum of voltages around any closed loop is zero.
基尔霍夫定律是分析复杂电路的根本依据。基尔霍夫电流定律（KCL）指出，流入节点的电流之和等于流出节点的电流之和。基尔霍夫电压定律（KVL）指出，沿任意闭合回路的电压代数和为零。
The potential divider circuit is a simple and widely used arrangement where the input voltage is divided across two resistors. The output voltage Vout = Vin × (R₂ / (R₁ + R₂)). This circuit is the basis for many sensor and control applications.
分压电路是一种简单且广泛使用的电路，输入电压被分配在两个电阻之上。输出电压 Vₒᵤₜ = Vᵢₙ × (R₂ / (R₁ + R₂))。该电路是许多传感器和控制应用的基础。
Power in an electrical circuit is given by P = V I = I² R = V² / R. Selecting components with adequate power ratings prevents overheating and failure.
电功率由 P = V I = I² R = V² / R 给出。选择具有足够额定功率的元器件可防止过热和失效。
6. Semiconductor Devices and Logic Gates | 半导体器件与逻辑门
Semiconductors such as silicon and germanium have conductivity between that of conductors and insulators. Doping with impurities creates n-type (extra electrons) and p-type (extra holes) materials. A p-n junction forms a diode that allows current to flow in one direction only, enabling rectification.
硅和锗等半导体材料的导电性介于导体与绝缘体之间。掺杂杂质可制成 n 型（多余电子）和 p 型（多余空穴）材料。PN 结形成二极管，只允许电流单向流动，从而实现整流。
Transistors, particularly bipolar junction transistors (BJTs) and field-effect transistors (FETs), act as amplifiers or switches. In a digital switching application, a small base current or gate voltage controls a much larger collector-drain current, forming the basis of logic circuits.
晶体管，特别是双极型晶体管（BJT）和场效应晶体管（FET），可用作放大器或开关。在数字开关应用中，较小的基极电流或栅极电压控制着大得多的集电极-漏极电流，构成逻辑电路的基础。
Logic gates process binary signals (0 and 1). The basic gates include NOT (output opposite to input), AND (output 1 only if all inputs are 1), and OR (output 1 if at least one input is 1). NAND and NOR gates are universal gates, as any logic function can be built using only one type.
逻辑门处理二进制信号（0 和 1）。基本门包括非门（输出与输入相反）、与门（所有输入为1时输出才为1）、或门（至少一个输入为1则输出1）。与非门和或非门是通用门，因为只用其中一种就能实现任何逻辑功能。
Truth tables systematically list all possible input combinations and the corresponding output for a logic gate or circuit. Boolean algebra allows the simplification of logic expressions, reducing the number of gates needed in a circuit design.
真值表系统列出逻辑门或电路的所有可能输入组合及对应输出。布尔代数可用于简化逻辑表达式，减少电路设计中所需门电路的数量。
Common integrated circuits such as the 555 timer and operational amplifiers (op-amps) are built from semiconductor devices and can be configured for timing, amplification and comparator functions.
常见的集成电路，如 555 定时器和运算放大器（运放），由半导体器件构成，可配置用于定时、放大和比较等功能。
7. Manufacturing Processes Overview | 制造工艺概览
Engineering components can be produced through a variety of manufacturing processes, broadly categorised into casting, forming, machining, joining and additive manufacturing. The choice depends on material, shape complexity, production volume and cost.
工程部件可通过多种制造工艺生产，大致分为铸造、成形、机加工、连接和增材制造。选择取决于材料、形状复杂度、生产批量和成本。
Casting involves pouring molten metal into a mould cavity. Sand casting is economical for large parts with low volume, while die casting uses reusable metal moulds for high-volume production of non-ferrous metals with excellent surface finish and accuracy.
铸造是将熔融金属浇入模腔。砂型铸造对于大型单件生产经济实惠，而压铸使用可重复使用的金属模具，适用于有色金属的大批量生产，具有出色的表面光洁度和精度。
Forming processes reshape solid materials without adding or removing material. Examples include forging (compressive forces to shape metal), rolling (reducing thickness), extrusion (pushing material through a die) and sheet-metal bending.
成形工艺在不增减材料的情况下重塑固体材料。例如锻造（用压力使金属成形）、轧制（减薄厚度）、挤压（将材料推过模孔）以及钣金折弯。
Machining removes material from a workpiece using cutting tools. Common operations include turning (lathe), milling, drilling and grinding. CNC (Computer Numerical Control) machines allow high precision and repeatability for complex geometries.
机加工用刀具从工件上去除材料。常见操作包括车削（车床）、铣削、钻孔和磨削。数控（CNC）机床可实现复杂几何形状的高精度和重复性。
Joining techniques include welding (fusion of parent metals, often with filler), brazing and soldering (using a filler metal with a lower melting point) and adhesive bonding. Mechanical fasteners like bolts and rivets also join components.
连接技术包括焊接（母材熔化接合，通常使用填充金属）、钎焊和软钎焊（使用熔点较低的填充金属）以及粘接。螺栓和铆钉等机械紧固件也可连接部件。
Additive manufacturing (3D printing) builds parts layer by layer from digital models. Fused deposition modelling (FDM) is common for thermoplastics, while selective laser sintering (SLS) and stereolithography (SLA) are used for more precise or functional prototypes and end-use parts.
增材制造（3D 打印）根据数字模型逐层构建零件。熔融沉积成形（FDM）常用于热塑性塑料，而选择性激光烧结（SLS）和光固化立体造型术（SLA）则用于更高精度或功能原型及最终用途零件。
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