UNIT 4: Computer Aided Engineering Applications in Turbomachinery and Product Design

I. TURBOMACHINERY ANALYSIS AND DESIGN

A. Fundamental Theoretical Principles

Euler's Turbomachinery Equation

• Definition: Fundamental equation relating energy transfer to change in angular momentum.

• Derivation: From moment of momentum principle (Stefan's theorem):

$$ \dot{W} = \dot{m} (U_2 V_{\theta 2} - U_1 V_{\theta 1}) $$

where $U$ = blade speed, $$\displaystyle V_\theta $$ = tangential velocity component.

• Euler's Energy Equation for Reaction Turbine:

$$ \dot{W} = \dot{m} \left[ (h_0)_1 - (h_0)_2 \right] $$

For ideal fluid, Euler equation equals stagnation enthalpy drop.

• Key Assumptions: Steady flow, one stage, no friction, uniform velocity.

First and Second Law Applications

• First Law (Energy Conservation):

$$ Q - W = \Delta H + \Delta KE + \Delta PE $$

For turbomachines, often $\Delta KE, \Delta PE \approx 0$.

• Second Law (Entropy):

$$ dS \ge \frac{\delta Q}{T} $$

Isentropic efficiency $$\displaystyle \eta_s = \frac{\text{Actual work}}{\text{Isentropic work}} $$.

• Role of Entropy: Measures irreversibility (losses). Higher entropy generation → lower efficiency.

Dimensional Analysis and Similarity

• ** Buckingham Pi Theorem**: For efficiency $$\displaystyle \eta = f(\rho, \mu, \omega, D, Q) $$.

• Dimensionless Groups:

  • Reynolds number $$\displaystyle Re = \frac{\rho \omega D^2}{\mu} $$ (viscous effects)

  • Flow coefficient $$\displaystyle \phi = \frac{Q}{\omega D^3} $$

  • Head coefficient $$\displaystyle \psi = \frac{gH}{\omega^2 D^2} $$

  • Power coefficient $$\displaystyle \lambda = \frac{P}{\rho \omega^3 D^5} $$

• Similarity Laws:

$$ \frac{Q_1}{Q_2} = \frac{N_1 D_1^3}{N_2 D_2^3}, \quad \frac{H_1}{H_2} = \frac{N_1^2 D_1^2}{N_2^2 D_2^2} $$

[!TIP]

Exam Focus: Deriving $\eta$ as $$\displaystyle \phi(\pi_1, \pi_2, ...) $$ is a 8-mark question. Practice forming pi-groups with $\rho, \mu, \omega, D, Q, H, P$.

B. Velocity Diagrams and Blade Geometry

Construction of Velocity Diagrams

• Impulse Turbine (Symmetrical blades, nozzle angle $\alpha$):

  • $$\displaystyle V_1 = V_2 $$ (no friction), $$\displaystyle \beta_1 = \beta_2 $$, $U$ constant.

  • Vector diagram: $$\displaystyle V_1 $$ at angle $\alpha$, $U$ horizontal, $$\displaystyle V_2 $$ reflected.

• Parsons Reaction Turbine (50% reaction):

  • Fixed & moving blades symmetric: $$\displaystyle \alpha_1 = \beta_2 $$, $$\displaystyle \beta_1 = \alpha_2 $$.

  • $$\displaystyle V_1 \neq V_2 $$ due to pressure drop in both stages.

• Axial Flow Compressor:

  • $U$ increases along axis (multi-stage).

  • $$\displaystyle V_{\theta} $$ decreases, $$\displaystyle V_a $$ ≈ constant.

• Centrifugal Compressor:

  • Inlet: axial ($$\displaystyle V_{a1} $$), outlet: radial ($$\displaystyle V_{r2} $$) with $$\displaystyle U_2 $$ high.

Blade Angle Determination

• Shockless Inflow: Steam enters blade without shock → relative velocity $$\displaystyle W_1 $$ aligns with blade inlet angle $$\displaystyle \beta_1 $$.

$$ \tan \beta_1 = \frac{V_{\theta 1} - U_1}{V_{a1}} $$

• For Parsons stage with $$\displaystyle \alpha_1 = \beta_2 $$, $$\displaystyle \beta_1 = \alpha_2 $$.

Slip Factor

• Definition: $$\displaystyle \sigma = \frac{\text{Actual } \Delta V_{\theta}}{\text{Ideal } \Delta V_{\theta}} $$ (Stodola's slip factor: $$\displaystyle \sigma = 1 - \frac{0.63 \pi}{n} $$ for radial turbines).

• Effect: Reduces work output → lowers diagram efficiency. More significant in radial-flow machines.

C. Performance Parameters and Efficiencies

Degree of Reaction (R)

• Definition: Ratio of static enthalpy drop in rotor to total stage enthalpy drop.

$$ R = \frac{\text{Enthalpy drop in rotor}}{\text{Total stage drop}} = \frac{h_2 - h_3}{h_1 - h_3} $$

• Parsons Turbine: $$\displaystyle R = 0.5 $$ (blades symmetric, pressure drop equally in fixed & moving blades).

• Calculation: From velocity diagram:

$$ R = \frac{1}{2} + \frac{V_{\theta 2} + V_{\theta 1}}{2U_2} \cdot \frac{V_a}{U_2} $$

Stage and Diagram Efficiencies

• Stage Efficiency $$\displaystyle \eta_{stage} = \frac{\text{Actual work output}}{\text{Isentropic enthalpy drop in stage}} $$

• Diagram (Blade) Efficiency $$\displaystyle \eta_b = \frac{2 U (V_{\theta 1} + V_{\theta 2})}{V_1^2} $$ (for impulse).

• Optimization: For symmetrical impulse blades, max $$\displaystyle \eta_b $$ when $$\displaystyle U = \frac{V_1}{2 \cos \alpha} $$.

Hydraulic Turbine Efficiencies

• Hydraulic Efficiency $$\displaystyle \eta_h = \frac{\text{Power at runner}}{\rho g Q H} $$

• Mechanical Efficiency $$\displaystyle \eta_m = \frac{\text{Shaft power}}{\text{Runner power}} $$

• Overall Efficiency $$\displaystyle \eta_o = \eta_h \times \eta_m $$

• Manometric Head: Net head available at turbine inlet (accounting for losses).

Compressor Efficiencies

• Polytropic Efficiency $$\displaystyle \eta_p = \frac{n-1}{n} \cdot \frac{\gamma-1}{\gamma} $$ (for small stage).

• Isentropic Efficiency $$\displaystyle \eta_s = \frac{\text{Isentropic work}}{\text{Actual work}} $$

• Surging: Flow reversal at low flow, high pressure rise → unstable.

• Choking: Sonic flow at narrowest section → mass flow limit.

Reheat Factor (RF)

• Definition: $$\displaystyle RF = \frac{\text{Total isentropic enthalpy drop (multi-stage)}}{\text{Sum of stage isentropic drops}} $$

• Cause: Moisture formation in later stages → entropy increase.

• Improves efficiency by allowing higher average stage loading.

D. Steam Turbines

Types and Configurations

• Impulse: Pressure drop only in nozzles; high blade speed ratio.

• Reaction: Pressure drop in both fixed & moving blades.

• Velocity Compounding (Curtis): Multiple blade rows in one stage, single nozzle.

• Pressure Compounding (Rateau): Multiple nozzles & blade rows, each with partial pressure drop.

Losses in Turbines

1. Nozzle losses (friction, sudden expansion)

2. Blade friction losses (surface roughness)

3. Leaving losses (kinetic energy of exit steam wasted)

4. Leakage losses (clearance losses)

5. Disk friction (bearing losses)

• Effect on Vane Efficiency: $$\displaystyle \eta_b \propto \frac{\text{Useful work}}{\text{Energy supplied}} $$; losses reduce numerator.

Governing of Steam Turbines

• Purpose: Maintain constant speed under varying load.

• Methods:

  • Throttle governing (control valve at nozzle inlet)

  • Nozzle governing (sequential nozzle control)

  • Bypass governing

  • Combination governing

Design Calculations (Parsons Stage)

Given: $D$, $N$, $$\displaystyle V_2 $$, $$\displaystyle \beta_2 $$, $\dot{m}$

• Blade speed: $$\displaystyle U = \frac{\pi D N}{60} $$

• For 50% reaction: $$\displaystyle \beta_1 = \alpha_2 $$, $$\displaystyle \alpha_1 = \beta_2 $$, $$\displaystyle V_1 = V_2 $$, $$\displaystyle V_{\theta 1} = V_{\theta 2} $$

• Blade inlet angle: $$\displaystyle \tan \beta_1 = \frac{V_{\theta 1}}{V_{a1}} = \frac{U}{V_1 \cos \beta_2} $$ (since $$\displaystyle V_{\theta 1} = U $$ for shockless)

• Tangential Force: $$\displaystyle F_t = \dot{m} (V_{\theta 1} + V_{\theta 2}) $$

• Power Developed: $$\displaystyle P = F_t \cdot U $$

• Axial Thrust: $$\displaystyle F_a = \dot{m} (V_{a1} - V_{a2}) \approx 0 $$ for Parsons.

E. Hydraulic Turbines

Pelton Wheel

• Design Parameters:

  • Speed ratio $$\displaystyle K_u = \frac{U}{V_j} \approx 0.45-0.5 $$ (optimal)

  • Jet ratio $$\displaystyle m = \frac{D}{d} \approx 6-10 $$

  • Bucket diameter $$\displaystyle D = \frac{60 U}{\pi N} $$

• Power available at nozzle:

$$ P_{avail} = \rho g Q H \quad \text{(theoretical)} $$

• Hydraulic Efficiency:

$$ \eta_h = \frac{2 U (V_j - U)}{V_j^2} \cdot \cos \phi $$

where $\phi$ = bucket deflection angle (usually $$\displaystyle 165^\circ $$).

• Side clearance angle ($$\displaystyle 15^\circ $$): Prevents water interference between buckets.

Francis Turbine

• Draft Tube:

  • Purpose: Convert kinetic energy to pressure, allow negative head at runner exit.

  • Types: Conical, cylindrical, Moody (elbow).

  • Efficiency gain: $$\displaystyle \eta_d = \frac{H_{actual}}{H_{draft}} $$

• Specific Speed $$\displaystyle N_s $$:

  • Definition: Speed of geometrically similar turbine developing 1 HP under 1 m head.

  • Derivation: From similarity laws:

$$ N_s = N \sqrt{\frac{P}{H^{5/4}}} \quad (\text{metric}) \quad \text{or} \quad N_s = \frac{N \sqrt{P}}{H^{5/4}} $$

• Significance: Selects turbine type (Pelton low $$\displaystyle N_s $$, Francis medium, Kaplan high).

Cavitation

• Phenomenon: Vapor bubbles form at low pressure (below vapor pressure) → collapse → erosion.

• Effects: Material damage, vibration, efficiency drop.

• Prevention: Maintain Net Positive Suction Head (NPSH):

$$ NPSH_{available} > NPSH_{required} $$

where $$\displaystyle NPSH_{req} $$ from manufacturer charts.

F. Pumps and Compressors

Centrifugal Pumps

• Main Parts: Impeller, casing (volute/diffuser), suction pipe, delivery pipe, shaft.

• Advantages over Reciprocating:

  • Continuous flow, less maintenance, higher flow rates, no valves.

• Specific Speed of Pump $$\displaystyle N_s $$:

$$ N_s = N \sqrt{\frac{Q}{H^{3/4}}} \quad (\text{metric}) $$

• Indicates impeller shape: radial $$\displaystyle N_s < 40 $$, mixed $40-100$, axial $$\displaystyle >100 $$.

Positive Displacement Machines

• Definition: Trap fixed volume, force into discharge (e.g., reciprocating pumps, gear pumps).

• Characteristics: High pressure, low flow, pulsating discharge.

Compressors

• Axial vs Centrifugal:

  | Axial Flow | Centrifugal | |---|---| | High flow, low pressure rise per stage | High pressure rise per stage | | Multistage common | Usually single stage | | Higher efficiency at high flow | Compact, robust | | Surging critical | Choking critical |

• Surging: System instability at low flow (compressor characteristic curve & system curve intersection).

• Choking: Sonic velocity at throat → max mass flow.

• Polytropic Process: $$\displaystyle P v^n = \text{const} $$; $n$ = polytropic index.

G. Power Transmission Devices

Fluid Coupling

• Working: Impeller (pump) → fluid kinetic energy → turbine (runner). Slip $$\displaystyle s = \frac{N_t}{N_p} $$.

• Efficiency: $$\displaystyle \eta = s $$ (torque transmitted $\propto s$).

• Slip: $$\displaystyle 0 < s < 1 $$; at $$\displaystyle s=1 $$, rigid coupling.

• Diagram:

  DiagramSEARCH: "fluid coupling diagram impeller turbine"

Torque Converter

• Construction: Impeller, turbine, stator (reaction member).

• Working:

  Fluid from impeller hits turbine → stator redirects flow → torque multiplication.

  Multiplication factor: $$\displaystyle M = \frac{T_{out}}{T_{in}} > 1 $$ at low turbine speed.

• Applications: Automatic transmissions, marine propulsion.

Hydraulic Intensifier

• Working: Large diameter piston (low pressure, high force) → small diameter piston (high pressure, low force).

$$ P_1 A_1 = P_2 A_2 \quad \Rightarrow \quad P_2 = P_1 \frac{A_1}{A_2} $$

• Applications: Hydraulic presses, testing machines.

Industrial Applications

• Fluid coupling: Conveyors, crushers, boiler fans.

• Torque converter: Cars, earthmovers.

• Hydraulic intensifier: Forging presses, jacking systems.

H. Applied Problem Solving

Nozzle Flow Calculations

• Mass discharge with friction:

$$ \dot{m} = C_d A \sqrt{2 \rho \Delta h} $$

$$\displaystyle C_d $$ = discharge coefficient (0.95-0.99).

• Critical pressure ratio (convergent nozzle):

$$ \left( \frac{p^*}{p_0} \right)_{critical} = \left( \frac{2}{\gamma+1} \right)^{\frac{\gamma}{\gamma-1}} $$

Stage Analysis (Parsons Turbine)

Given: $D$, $N$, $$\displaystyle V_2 $$, $$\displaystyle \beta_2 $$, $\dot{m}$

1. $$\displaystyle U = \frac{\pi D N}{60} $$

2. For 50% reaction & shockless: $$\displaystyle V_{\theta 1} = U $$, $$\displaystyle V_1 = V_2 $$, $$\displaystyle \beta_1 $$ from $$\displaystyle \tan \beta_1 = \frac{U}{V_2 \cos \beta_2} $$

3. $$\displaystyle F_t = \dot{m} (V_{\theta 1} + V_{\theta 2}) = 2 \dot{m} U $$ (since $$\displaystyle V_{\theta 2} = V_{\theta 1} $$)

4. $$\displaystyle P = F_t \cdot U = 2 \dot{m} U^2 $$

Impulse Turbine Optimization

• Blade speed for max efficiency: $$\displaystyle U = \frac{V_1 \cos \alpha}{2} $$ (for frictionless, symmetrical blades).

• Diagram efficiency with velocity coefficient $$\displaystyle K_v = \frac{V_2}{V_1} $$:

$$ \eta_b = \frac{2 U (V_{\theta 1} + V_{\theta 2})}{V_1^2} = \frac{2 \cos^2 \alpha}{1 + K_v^2 - 2 K_v \cos \alpha} \cdot \frac{U}{V_1 \cos \alpha} \left( 2 - \frac{U}{V_1 \cos \alpha} \right) $$

II. PRODUCT DESIGN AND MANUFACTURING WITH CAE

A. Product Development Process

Product Life Cycle (PLC)

Product Strategy and Policy

• Elements: Vision, objectives, market segmentation, positioning, portfolio.

• Resource Allocation: R&D budget, manufacturing capacity, marketing spend.

• Innovation's Role: Drives differentiation, extends PLC, creates new markets.

Customer-Centric Design

• Importance: Ensures market acceptance, reduces redesign.

• Methods: Surveys, focus groups, user testing, empathy mapping.

• Input Methods: Interviews, observation, feedback loops, social media analysis.

Competitive Analysis

• Assessing Rivals: Benchmarking (performance, cost, features), SWOT analysis.

• Role in Planning: Identifies gaps, sets targets, informs differentiation.

Challenges in NPD

• Time-to-market pressure, cost overruns, technical feasibility, market uncertainty.

• Mitigation: Stage-gate process, cross-functional teams, prototyping.

B. Design Methodologies and Creativity

Value Engineering (VE)

• Definition: Systematic method to improve value ($$\displaystyle Value = \frac{Function}{Cost} $$).

• Objectives: Reduce cost, improve function, increase profit.

• Job Plan (7-step):

  1. Information → 2. Function Analysis → 3. Creative → 4. Evaluation → 5. Development → 6. Presentation → 7. Follow-up.

• Function Analysis: Identify primary, secondary, tertiary functions.

Function Analysis System Techniques (FAST)

• Diagram:

  
  How? → [Function] → Why?
  
  

  • Scope line: Separates customer needs from solutions.

  • Basic function: Essential purpose (verb + noun).

  • Secondary functions: Support basic.

  • Tertiary functions: Over-design or superfluous.

• Application in Automotive:

  Example: "Transport people" (basic) → "Provide comfort" (secondary) → "Have cup holders" (tertiary).

• Handling Tertiary: Eliminate or reduce cost if not value-adding.

Creative Problem-Solving

• Brainstorming: Free idea generation, no criticism.

• Synectics: Metaphorical thinking, "make the strange familiar."

• Morphological Analysis: Matrix of parameters → combinations.

• Integration: Use in VE's "Creative phase" for alternatives.

C. Computer-Aided Design and Manufacturing (CAD/CAM)

Role of CAD in Manufacturing

• Optimization: Design for tool access, minimize setups, simulate machining.

• DFM Tools in CAD:

  • Design rule checking (draft angles, wall thickness).

  • Manufacturability analysis (moldability, machinability).

  • Cost estimation modules.

Design for X (DFX)

• DFM (Design for Manufacture):

  • Principles: Minimize parts, use standard components, modular design.

  • Implementation: Tolerance analysis, material selection, process selection.

• DFA (Design for Assembly):

  • Guidelines: Reduce part count, symmetrical design, self-locating, easy grasp/insert.

  • Difference from DFM: DFM focuses on making parts; DFA on assembling them.

• DFMA: Integrated approach (DFM + DFA) → simultaneous cost reduction.

CAD Modeling

• 2D vs 3D:

  | 2D | 3D | |---|---| | Flat views (front, top) | Solid or surface model | | No volume/ mass data | Full geometric data | | Hard to visualize | Easy visualization, rendering | | Limited analysis | FEA/CFD possible |

• Impact on Validation: 3D enables interference check, stress analysis, kinematics.

Simulation and Analysis Tools

• FEA: Stress, deformation, vibration.

• CFD: Fluid flow, heat transfer.

• Thermal: Temperature distribution.

• Validation: Compare simulation results with physical testing → reduce prototypes.

D. Rapid Prototyping (RP) Technologies

Classification of RP Methods

Stereolithography (SLA)

• Process: UV laser cures liquid photopolymer layer-by-layer.

• Surface Finish: Excellent (smooth, ~0.1-0.5 µm).

• Applications: Master patterns, molds, dental/medical models.

• Limitations: Brittle, UV degradation, support structures needed.

Selective Laser Sintering (SLS)

• Powder Handling:

  1. Roller spreads thin powder layer.

  2. Laser sinters powder (no melting).

  3. Un-sintered powder supports part → easy removal.

• Process Parameters: Laser power, scan speed, powder size (50-100 µm).

• Materials: Nylon, TPU, metal (with binder).

• Surface Finish: Rough (powder grain), ~100 µm; worse than SLA.

Laminated Object Manufacturing (LOM)

• Process: Cut paper/foam sheets with laser/knife → glue layers.

• Surface Finish: Very rough (stair-stepping), requires finishing.

RP Process Workflow

1. CAD model (solid/surface).

2. Slicing (STL → layers).

3. RP process (machine builds).

4. Post-processing (support removal, curing, finishing).

5. Evaluation (dimensional check, testing).

Data Formats

• STL (Stereolithography):

  • Significance: De facto standard; represents surface as triangular mesh.

  • Limitations: No color, no tolerance info, faceted approximation.

• Others: OBJ (color/texture), STEP/IGES (CAD-native, exact geometry).

Applications and Advantages

• Concept modeling: Visualize, communicate.

• Functional testing: Fit/assembly, limited mechanical.

• Tooling: Direct molds, patterns.

• Benefits: Fast (days vs weeks), cost-effective for complex geometries, no tooling.

E. Manufacturing Process Design Guidelines

Casting Processes

• Sand Casting:

  • Draft angle: $$\displaystyle 1^\circ-3^\circ $$ (external/internal).

  • Radii: Fillets > sharp corners.

  • Wall thickness: Uniform, min 5-10 mm.

  • Avoid heavy sections (core prints for support).

• Die Casting vs Sand Casting:

  | Die Casting | Sand Casting | |---|---| | Thin walls (1-2 mm) | Thicker walls (5+ mm) | | Smaller draft ($$\displaystyle 0.5^\circ-2^\circ $$) | Larger draft ($$\displaystyle 1^\circ-3^\circ $$) | | Tighter tolerances | Looser tolerances | | Higher cost, high volume | Lower cost, low volume |

Injection Molding

• Factors Affecting Quality:

  • Material uniformity, mold temperature, injection pressure, cooling time.

• Design Guidelines:

  • Draft angles: $$\displaystyle 1^\circ-2^\circ $$ per side.

  • Uniform wall thickness: Avoid sinks, warpage.

  • Radii: Corners > 0.5 mm.

  • Fillets: Reduce stress.

  • Bosses: Thick walls → core pins.

Non-Metallic Product Design

• Considerations:

  • Mechanical loads: Creep, fatigue (lower than metals).

  • Thermal loading: CTE mismatch, glass transition.

  • UV/Chemical: Degradation, swelling → material selection (UV stabilizers, chemical resistance).

• Material Selection: Thermoplastics (PP, ABS), composites, elastomers.

Manual Assembly Design

• Guidelines for Easy Assembly:

  • Minimize parts → integrate functions.

  • Symmetrical parts → no orientation issues.

  • Self-aligning features (tapers, guides).

  • Reduce fasteners → snap fits.

  • Top-down assembly → gravity-assisted.

• Design for Disassembly:

  • Standard fasteners, accessible joints, material separation (different plastics).

F. Sustainability and Ergonomics

Design for Environment (DFE)

• Principles:

  • Waste reduction: Design out scrap, recyclable materials.

  • Recyclability: Mono-materials, mark plastics, avoid coatings.

  • Energy efficiency: Low-power operation, efficient use.

  • Eco-packaging: Minimal, biodegradable, reusable.

• Impact: Material selection, process choice (low-energy), end-of-life planning.

• Examples: Dell's recycled packaging, Tesla's battery recycling.

Ergonomics in Product Design

• Human Factors: Anthropometry (size ranges), biomechanics (force, posture), cognition (intuitive controls).

• Visual Design: Color contrast, typography, iconography, layout.

• User-Centered Design: Involve users early, iterative testing, accessibility (ADA compliance).

Robust Design

• Concept: Design insensitive to noise factors (variation in materials, environment, usage).

• Implementation:

  • Taguchi methods: Orthogonal arrays, signal-to-noise ratio.

  • Tolerance analysis: Stack-up analysis, Monte Carlo simulation.

• Challenges:

  • Complex interactions, cost of experimentation, supplier variability.

G. Organizational and Integration Aspects

Cross-Functional Integration

• Need:

  • Customer → needs/feedback

  • Designer → feasibility

  • Material supplier → availability/cost

  • Process planner → manufacturability

  → Concurrent engineering reduces cycles, avoids redesign.

Organizational Policies

• Product Planning: Stage-gate reviews, portfolio management.

• Process Management: Lean manufacturing, Six Sigma.

• Continuous Improvement: Kaizen, PDCA cycle.

Problem Identification

• Manufacturing-Related Issues:

  • Poor tolerances → assembly failure.

  • Complex geometry → high tooling cost.

  • Material choice → warpage/shrinkage.

• Feedback Loops: Design → prototype → test → production → field data → design update.

Final Summary for Exam:

1. Turbomachinery: Master Euler's equation, velocity diagrams (Parsons), degree of reaction, efficiencies, specific speed, cavitation (NPSH).

2. Product Design: PLC, VE/FAST, DFM/DFA, RP workflow (STL), DFE, ergonomics.

3. Problem-Solving: Practice Parsons stage calculations, Pelton design, nozzle flow.

4. Diagrams: Sketch velocity diagrams (impulse/reaction), torque converter, FAST diagram.

[!TIP]

Common Pitfalls:

• Confusing degree of reaction with blade efficiency.

• Misapplying specific speed (turbine vs pump formulas differ).

• Forgetting slip factor in radial turbines.

• Overlooking NPSH in cavitation problems.

• In product design, mixing DFM (manufacturing parts) with DFA (assembling).