Design of Machine Elements; material selection to product functionality (CDS 1-2; LBYMF3F)

TARGET AUDIENCE: Students, Self

Note: Taglish; Personal notes that are scanned maybe blurry

About the thumbnail: My handwritten calculations for the machine design of a rudimentary ferris wheel axle considering cyclic loading

OVERVIEW: Machine element design basically covers the early stages hardware product design lifecycle. I like to think that this is the case since we cover from providing the proper functional requirements and the calculations to validate the design. This will be helpful in other courses in the future like that of product design and finite element modelling (both I have made posts, do check it out!).

These lecture serves as the foundation talaga for us engineers that will deal with products in the future and we can ensure that we are efficient in the material and component selections that we do. In relation to this, this was helpful in my passion projects like that of my anaerobic digester since there are mechanical components that I need to verify if it is capable to do its functionality over its RUL. Maybe in the future, directing how we can do predictive maintenance in these machines are equally important in the manufacturing field.

Below is the compilation of my outputs and calculations that I have made via the activities as well as the projects that I have led along with other batchmates (shoutout to you guys!, ykwya) to validate mechanical systems!

CDS1 LECTURE:

The lectures revolved around the single book, our holy grail, Machine Elements Design by Richard Mott where he details the different machine elements that makes up more complex systems IRL. Aside from the calculations to determine stress and deflections from moments, the class also focused on material selection and functionality requirements which I appreciate since this converts into a basic skill often asked to product engineers which is FMEA and BOM which we have to justify how we can minimize cost without compromising the safety and functionality of the product.

Examples of common machine elements include:

• Fasteners (bolts, nuts, screws)
• Shafts and Keys (for power transmission)
• Bearings (to reduce friction between moving parts)
• Gears, Springs, Couplings, and Clutches
• Joints and Welds

The goal is to ensure these elements can withstand applied loads, operate efficiently, and provide durability over the machine’s intended service life.

Core Principles in Machine Element Design

• Strength of Materials → Ensuring elements can handle stresses without failure.
• Kinematics and Dynamics → Understanding motion, forces, and torque transmission.
• Fatigue and Wear Analysis → Designing for long-term reliability under repeated use.
• Standardization → Following ISO/ANSI/DIN standards for interchangeability and safety.

Relevance to Manufacturing Engineers

For manufacturing engineers, machine element design is highly relevant because it directly impacts:

1. Product Reliability and Safety
   • Properly designed elements prevent breakdowns, accidents, and costly recalls.
2. Efficiency of Manufacturing Systems
   • Knowledge of gears, belts, and bearings helps engineers design efficient production machinery.
3. Cost-Effectiveness
   • Selecting the right materials and standard components reduces costs while maintaining performance.
4. Process Innovation
   • Manufacturing engineers often work on automation and robotics—both of which rely heavily on well-designed machine elements.
5. Sustainability
   • By designing durable and maintainable elements, manufacturing engineers contribute to longer product life cycles and reduced waste.

Of course, some of the technical calculations that I did here were already covered in ENGMEC (check that post haha) but application more on machine elements where highlighted that there are already specific formulas for it. We were provided a 6-page formula sheet in exams that still that was not enough if you dont know what you are doing!

Specific conditions on terms of determination of max stress in stress element, shear-bending diagrams, stress variation over time were more defined in this case. Below is the consolidated calculations and activity reports that I have done for this lecture class:

As an example for this, we presented the reason why the Challenger Space Shuttle crashed via a faulty O-ring. We have explored it in a case study that can be checked in the pdf below :>

Determination of Appropriate Axle and Speed Reducer for a Small Scale Ferris Wheel:

Lastly, here is a final practical where we covered an ideal diameter size of an axle for a specific size of Ferris wheel. The motivation is that ung mga nakikita sa perya, ano ung appropriate na axle diameter size and speed reducer so that we can ensure safety and longevity of the system. Here is a more detailed coverage of this with the report given below.

This project focuses on the design and analysis of a Ferris wheel center axle—also called the hub—by applying machine element design principles. The study emphasizes structural integrity, load distribution, and material selection under cost constraints. Using the Goodman criterion for fatigue analysis, the research identifies the optimal axle dimensions and material, ultimately recommending 2024-T361 Aluminum alloy as the most cost-effective and suitable choice.

• Design Goals
  The axle was optimized to ensure safety and reliability while keeping within a ₱200,000 budget. Initial design requirements were based on online sources but were later refined after detailed calculations and analysis.

• Material Selection
  After evaluating different options, the group recommended 2024-T361 Aluminum alloy.
  • Ultimate strength: ≥205 MPa
  • Elongation: 13%
  • Cost: ₱26,516.64, making it the most economical option considered
• Ferris Wheel Specifications
  • Diameter: 20 meters
  • Gondolas: 12 units
  • Max load per gondola: 135,906.64 N (≈ 3 riders at 100 kg each)
• Axle Dimensions
  • Length: 12.33 mm
  • Diameter: 600 mm
  • Designed to withstand static cyclic loading
  • External factors such as wind and seismic forces were excluded
• Cost-Reduction Strategies
  Design iterations included:
  • Testing smaller axle lengths
  • Exploring hollow axle configurations
  • Considering cheaper yet strong materials

With this we can see how this project validated typical shaft design of these type of ferris wheel via ensuring structural safety under cyclic loads; selected materials that balance strength, ductility, and cost; Optimized designs through iterations and trade-offs; Create cost-effective solutions without sacrificing durability!

CDS2 LECTURE:

This the continuation for the previous machine element design now more focused on specific elements like that of columns, fasteners and belt/chain drives. This is barely scratches the surface btw but we have also covered considerations of power requirements, forces, and material that play on the performance of the element. Below is a consolidation of the formulas that we have covered in class that I have transcribed from my personal notes that can also be checked below!

Personal Notes

Columns:

Geometry & inertia

• Area: (A)
• Second moment of area (minimum bending axis): (I)
• Radius of gyration:
  \(r = \sqrt{\dfrac{I}{A}}\)

Effective length and slenderness

• Column unsupported length: (L)
• End-condition effective length factor: (K) (e.g. pinned-pinned (K=1), fixed-fixed (K=0.5), fixed-pinned (K\approx0.7), fixed-free (K=2)).
• Effective length: (L_e = K L)
• Slenderness ratio (dimensionless):
  \(\lambda = \dfrac{L_e}{r}\)

Euler (elastic) critical load (long/slender columns)

• Euler critical load: \(P_{cr,E} = \dfrac{\pi^2 E I}{(L_e)^2} = \dfrac{\pi^2 E I}{(K L)^2}\)
• Expressed as critical stress: \(\sigma_{cr,E} = \dfrac{P_{cr,E}}{A} = \dfrac{\pi^2 E}{\lambda^2}\)

Johnson (parabolic) formula — short/intermediate columns

For columns with low slenderness (inelastic range), Johnson’s parabola interpolates between yield and Euler buckling: \(\sigma_{cr,J} = \sigma_y - \left(\dfrac{\sigma_y^2}{4\pi^2 E}\right) \left(\dfrac{L_e}{r}\right)^2\) where (\sigma_y) is the material compressive yield strength.

Transition (critical) slenderness ratio

The commonly used transition slenderness (where Johnson and Euler meet) is: \(\left(\dfrac{L_e}{r}\right)_{crit} = \sqrt{\dfrac{2\pi^2 E}{\sigma_y}}\)

Design factor / allowable load

• Select design factor (safety factor) (N).
• Allowable stress: \(\sigma_{allow} = \dfrac{\sigma_{cr}}{N}\)
• Allowable load: \(P_{allow} = A \,\sigma_{allow}\)

Fasteners — bolts, screws, grades, preload and torque

Tensile stress (thread) area (A_t)

Approximate (metric): \(A_t \approx \dfrac{\pi}{4}\Big(d - 0.9382\,p\Big)^2\)

Bolt tensile capacity

\(F_{ult} = A_t \cdot S_{ut}\)

Tightening torque — practical/approximate rule

\(T \approx K \, F_{preload} \, d\)

• Rearranged: \(F_{preload} \approx \dfrac{T}{K d}\)

Belt and Chain Drives — kinematics, tensions, V-belt specifics

Kinematic relations

Speed ratio: \(i = \dfrac{N_1}{N_2} = \dfrac{D_2}{D_1}\)

Belt speed: \(v = \pi D_1 \dfrac{N_1}{60} = \omega_1 R_1\)

Power & tensions

\(P = (T_1 - T_2)\, v\) \(T_1 - T_2 = \dfrac{P}{v}\)

Belt friction (capstan / flat belt)

\(\dfrac{T_1}{T_2} = e^{\mu \theta}\)

V-belt generalization

\(\dfrac{T_1}{T_2} = e^{\dfrac{\mu\,\theta}{\sin(\alpha/2)}}\)

Angle of wrap

\(\alpha = \arcsin\!\left(\dfrac{d_l - d_s}{2C}\right)\) \(\theta_s = \pi - 2\alpha, \quad \theta_l = \pi + 2\alpha\)

Centrifugal tension

\(T_c = m_b v^2\)

An sample of the calculations that I did for this class in practical is seen below!

LBYMF3F LAB:

Of course, the counterpart to the dizzy formulas that we juggle in class is the lab where we got to experiment on actual machine element designs. All the calculations above where covered and tackled in demonstration. I have my notes on this class below along with the reference lab works :>

Design of a spur gear system in a toy car!

Lastly, I have to share here my final project here where I calculated the appropriate design of a spur gear for a model car driveshaft, applying machine element design principles to a scaled-down version of real automotive components. The gear is responsible for transmitting power from the differential to the wheels, a critical part of ensuring smooth and efficient motion.

Components in Focus

• Spur Gear (Driven) → the main gear in the driveshaft system
• Pinion Gear (Driver) → transmits input torque from the differential

Material Properties (ABS Plastic)

• Tensile Strength: 41 MPa
• Tensile Modulus: 2480 MPa
• Bendable Stress: 20.6 MPa
• Safety Factor: 1.5

Assumed Variables for Design

• Torque: 2.0 N·m
• Input Speed: 2830 rpm
• Output Speed: 300 rpm
• Driveshaft Length: 39 mm
• Gear Ratio: 5:1
• Horsepower: 0.25 hp
• Material: ABS Plastic

Final Gear Specifications

Pinion Gear (Driver)

• Diametral Pitch: 16 teeth/inch
• Number of Teeth: 18
• Pitch Diameter: 1.125 in
• Face Width: 0.156 in
• Bore: 0.625 in
• Keyway: 3/16 × 3/16 in
• Material: ABS Plastic

Spur Gear (Driven)

• Diametral Pitch: 16 teeth/inch
• Number of Teeth: 70
• Pitch Diameter: 4.375 in
• Face Width: 0.156 in
• Material: ABS Plastic

Performance Check

• Stress on Gear Tooth: 1626.59 psi
• Result: Within acceptable range for ABS plastic

The study successfully designed a spur gear for a miniature differential system, demonstrating how machine element design principles can be applied even at model scale. Particularly, the use of ABS plastic for smooth torque transmission and scaling to automotive concepts were discussed. Future improvements of the design can further explore bevel gear connections for improved efficiency and conducting a more detailed shaft strength analysis.

REFLECTIONS: One of the few things that I believe can be applied for the course is product design and validating product functionality based off pure calculation. Of course we can rely on more advanced techniques like that of finite element modelling pero we have to embrace tradition since we can never believe the simulation until we have an initial assumption at hand. Maganda ung application nito if career path is focused on product development which I can target lalo na ung new product introduction (NPI) which is a trending job for specific companies!!

PS. Shoutout to Doc Mayol and sir Homer for the learnings

PPS. Solid na kasama sina Nic, Gabby, and Adam for these classes! Thank you guys for being co-devs in the projects and learnings :>