John Vallance | Mechanical Engineering Portfolio

Featured Project

Modular Through-Spindle Coolant Nozzle Redesign

Mazak INTEGREX i-200S | Capto C6 Tooling | CNC Design, CFD, FEA & Physics-Constrained ML

★ Flagship Project

Modular Through-Spindle Coolant Nozzle Redesign

Mazak INTEGREX i-200S | Capto C6 Tooling Configuration

Redesigned a failure-prone through-spindle coolant interface into a serviceable dual-material assembly. The final design uses a permanently installed SS 316 threaded body and a replaceable 15-5 PH H1025 coolant tube, allowing the primary wear components to be serviced without repeatedly removing the M20×2 threaded interface from the tool holder.

Prototype Iterations

0.257 PSI

CFD Tube ΔP @ ~3 GPM

115×

Min FEA FOS @ 213 PSI

91.5%

Lower Direct Replacement-Event Cost

SCENARIO $58.3k five-year fleet savings projected under the documented 10-holder / 10-event-per-holder / 30% removal-damage-risk scenario.

Redesigned nozzle installed in Mazak tool holder — modular tube protrudes through the threaded body, sealed with O-rings and retained by internal spiral clip ring

Redesigned nozzle installed in the Mazak tool holder on the Capto C6-equipped INTEGREX i-200S configuration used in this project.

Installed Hardware Context

This is the final redesign installed in the tool holder. The permanently installed SS 316 threaded body stays in the holder; routine service swaps only the replaceable 15-5 PH H1025 tube and its seals.

Everything below maps to this hardware: the architecture, the analysis, the machining, and the measured results.

1. The Problem

Finished modular coolant nozzle prototype — SS 316 threaded body with replaceable 15-5 PH H1025 coolant tube

The nozzle part itself: finished prototype showing the modular architecture before installation into the Capto C6 tool holder.

The Problem — A Small Wear Component Put a High-Value Tool Holder at Risk

Three observed problems with the OEM monolithic design on this configuration:

1. High breakaway/removal torque at the threadlocked threaded interface created a risk of damaging the female tool-holder threads during service.
2. Corrosion / surface degradation was observed during water-based coolant service.
3. The monolithic service architecture required the threaded body to be removed when wear components needed replacement.

High breakaway torque during removal, combined with corrosion and galling risk, could damage the female tool-holder threads.

~$150

PROJECT / SHOP COSTS
OEM replacement nozzle

~$1,500

PROJECT / SHOP COSTS
Potential damaged tool-holder

"The redesign goal was therefore not simply to make the nozzle stronger — it was to separate the permanent interface from the replaceable wear components."

2. Redesign Architecture

Modular Architecture — Two Material Roles

Threaded Body

SS 316

Permanently installed interface

Primary design driver: corrosion resistance / serviceability

Thread: M20 × 2.0-6g external thread
Confirmed on final hardware

Coolant Tube

15-5 PH H1025

Replaceable coolant tube

Primary design drivers: strength, fatigue resistance, dimensional stability

OD: 7.874 mm | ID: 5.998 mm | Wall: 0.938 mm
Effective length: 20.32 mm

Nozzle components lineup — physical architecture

Physical components: modular assembly showing threaded body, coolant tube, O-rings, washer, and retaining ring.

Assembled modular nozzle components together — threaded body, coolant tube, O-rings, washer, and retaining ring

Sectioned CAD model of the modular assembly showing the replaceable coolant tube, dual O-ring sealing arrangement, retaining hardware, and permanently installed threaded body.

Retaining System

McMaster 92602A310 — two-turn spiral retaining ring

Housing/bore ID

0.5530 in = 14.0462 mm

Groove diameter

0.5795 in = 14.7193 mm | Catalog groove diameter: 14.72 mm

Groove width

0.029538 in = 0.75027 mm | Catalog groove width: 0.75 mm

Derived radial depth

(D_g − D_bore)/2 = (0.5795 − 0.5530)/2 = 0.01325 in = 0.3365 mm

Seating shoulder → nearest groove edge

0.0600 in = 1.524 mm

"The measured groove diameter and width essentially match the retaining-ring catalog geometry to the measurement resolution."

3. Material Selection

Material Selection — Different Components, Different Design Drivers

PREN was used as a comparative corrosion-screening metric alongside strength, machinability, cost, galvanic/interface considerations, and prototype service observations. Exact PREN depends on certified material chemistry and is not used here as a standalone service-life prediction.

Threaded Body Matrix

4130 + Black Oxide

5.25

SS 316

6.65SELECTED

15-5 PH H1025

5.95

Coolant Tube Matrix

4130 + Black Oxide

6.05

SS 316

5.25

15-5 PH H1025

7.80SELECTED

"Separate role-specific matrices were used because the threaded body is corrosion-critical while the replaceable tube is primarily strength/fatigue-critical."

4. Engineering Analysis

Internal Flow — SolidWorks Flow Simulation CFD ASSUMED FLOW CONDITION

CFD Model

Software: SolidWorks 2026 Flow Simulation
Geometry: isolated coolant-tube internal-flow domain
Fluid approximation: ρ = 1000 kg/m³ | μ = 0.00120 Pa·s
Mass-flow inlet: m_dot = 0.189 kg/s
Equivalent flow: Q = m_dot / ρ = 1.89 × 10&sup-4; m³/s = 2.9957 GPM
Outlet: 101,325 Pa absolute (atmospheric)
Tube ID: D = 5.998 mm

Flow trajectories colored by velocity magnitude through the isolated coolant passage at 0.189 kg/s

Continuity & Regime

A = πD²/4 ≈ 2.826 × 10&sup-5; m² → V = Q/A ≈ 6.689 m/s

SolidWorks CFD mean outlet velocity: 6.7292 m/s

Re = ρVD/μ ≈ 33,500 — TURBULENT

f_D = 0.316 Re&sup-0.25 ≈ 0.02337 (smooth-pipe Blasius)

Static-pressure distribution through the isolated tube with atmospheric outlet

Darcy-Weisbach vs CFD

ΔP = f_D (L/D)(ρV²/2) L = 20.32 mm

Analytical: 1771.11 Pa = 0.25688 PSI | SolidWorks CFD: 1770.04 Pa = 0.25672 PSI | Difference: 0.061%

"At the same prescribed ~3 GPM condition, Darcy-Weisbach predicted a 0.2569 PSI pressure drop while SolidWorks Flow Simulation returned 0.2567 PSI. The agreement provides a strong analytical consistency check on the isolated-tube CFD result."

CFD outlet velocity distribution graph at the ~3 GPM prescribed flow condition

CFD Results — Solver-Converged

6.729 m/s

Mean outlet velocity

6.987 m/s

Max outlet velocity

0.2567 PSI

Pressure drop

78.84 Pa

Avg wall shear

671.83 Pa

Max wall shear

109

Iterations

Monitored solver goals converged — solver-converged CFD.

Wall shear stress along the wetted tube surface; average 78.84 Pa with a localized 671.83 Pa peak

Main Finding & System Context

"The isolated coolant tube itself introduces only ~0.257 PSI of pressure drop at the assumed ~3 GPM operating flow. An analytical system estimate placed entry/contraction/friction losses at approximately 2.60 PSI. A further ~3.26 PSI corresponds to exit kinetic head and should not be described as pressure dissipated inside the tube."

Monitored SolidWorks solver goals converging over 109 iterations

Pressure Containment — SolidWorks Simulation FEA

Material: 15-5 PH H1025 | E = 196 GPa | ν = 0.272 | σ_y = 1000 MPa | σ_u ≈ 1070 MPa

Analytical Benchmark — Lamé Thick-Wall Cylinder

The tube is sufficiently thick relative to its diameter that Lamé thick-wall-cylinder equations were used as a benchmark.

D_i = 5.998 mm | D_o = 7.874 mm | r_i = 2.999 mm | r_o = 3.937 mm

At 213 PSI: P = 1.469 MPa → Lamé von Mises reference: 6.062 MPa → Analytical yield FOS: ≈ 165

FOS = σ_y / σ_VM

Lamé thick-wall cylinder equations applied to the tube cross-section under internal pressure. The analytical result of 6.062 MPa at 213 PSI serves as a first-principles benchmark against which the FEA result is compared. The difference (FEA: 8.679 MPa vs Lamé: 6.062 MPa) arises from flange/end geometry and realistic support effects not captured by the ideal cylinder model.

FEA von Mises stress distribution at 213 PSI nominal; peak 8.679 MPa gives minimum yield FOS of 115.2

SolidWorks — 213 PSI

"213 PSI is treated as the machine/system nominal through-spindle coolant rating and a conservative structural pressure-containment load for the tube. It is not the CFD pressure drop across the isolated tube."

8.679 MPa

Max von Mises

0.163 μm

Max displacement

3.576×10&sup-5;

Max equiv strain

115.2

Min yield FOS

"The FEA maximum exceeded the ideal Lamé benchmark because the real CAD contains flange/end geometry and realistic support effects that the ideal cylinder does not."

Mesh sensitivity: 8.657 MPa → 8.679 MPa — a mesh-refinement sensitivity check changed peak stress by only 0.25%.

FEA von Mises stress at the 320 PSI static design-overpressure case; peak 13.04 MPa gives minimum yield FOS of 76.7

320 PSI Design Case 1.5× static design-overpressure case

NOT a measured pressure spike or water-hammer transient.

13.04 MPa

Max von Mises

0.2444 μm

Max displacement

5.453×10&sup-5;

Max equiv strain

76.7

Min yield FOS

320/213 pressure ratio ≈ 1.502 | 13.04/8.679 stress ratio ≈ 1.503

"The applied-pressure and stress ratios agree almost exactly, confirming the expected linear-elastic model response."

FEA equivalent strain at 320 PSI; maximum 5.453e-5

Displacement Check

Even at the 1.5× overpressure case, resultant displacement peaks at 0.2444 μm — negligible relative to the 0.938 mm wall and the runout budget. The tube is stiffness-dominated by a wide margin at both load cases.

FEA resultant displacement at 320 PSI; maximum 0.2444 micrometers

Pressure-Cycle Fatigue Screening FATIGUE

Loading event: 0 → 213 → 0 PSI — zero-based loading

σ_a ≈ 8.679 MPa / 2 ≈ 4.34 MPa

H1025 S-N reference data used (published unnotched longitudinal specimen data, not fatigue tests of the finished nozzle):

758 MPa at 10⁵ cycles | 621 MPa at 10⁶ cycles | 607 MPa at 10⁷ cycles | Mean-stress correction: Gerber

SolidWorks result: alternating stresses remained below the minimum stress represented by the entered S-N curve.

Conclusion

"No pressure-fatigue damage was predicted within the supplied H1025 S-N data range. Pressure-induced fatigue was not the governing structural design mode under the modeled loading."

5. Physics-Constrained ML Extension

Physics-Constrained ML Extension PINN / ML

Reduced-Order Data-Assisted PINN Surrogate

"To explore physics-constrained machine learning, I developed a reduced-order data-assisted PINN surrogate for the same isolated coolant tube. The network combines analytical turbulent-profile guidance with exact geometric boundary constraints, bulk-flow conservation, and reduced pressure-gradient physics."

Important clarification: "The PINN is an ML extension of the analytical model — not an independent turbulence solver."

PINN Physical Problem

Tube ID: 5.998 mm | Length: 20.32 mm | Mass flow: 0.189 kg/s (2.9957 GPM) | ρ = 1000 kg/m³ | μ = 0.00120 Pa·s

Analytical mean velocity: 6.6890 m/s | Re: 33,434 | Blasius f_D: 0.02337

Corrected pressure endpoints: Inlet: 0.25688 PSI(g) → Outlet: 0 PSI(g)

The machine's 213 PSI value is a system/supply structural-design basis, NOT the pressure drop across the isolated 20.32 mm tube.

Reduced-order PINN velocity surrogate for the isolated ~3 GPM tube-flow condition

PINN Architecture

                Inputs: r/R, z/L

                Output: normalized axial velocity + gauge pressure

                Hidden layers: 3 × 32 neurons | Activation: tanh

                Optimizer: Adam | LR schedule: StepLR

                Training: 1,200 epochs | Profile-guidance points: 600 | Physics collocation points: 500

PINN Physics / Constraints

Exact wall no-slip: u_z(R,z) = 0
Exact centerline symmetry: du_z/dr = 0 at r = 0
Exact pressure endpoints: P_in = 0.25688 PSI(g), P_out = 0 PSI(g)
Bulk-flow conservation: area-weighted mean velocity constrained to prescribed flow
Reduced Darcy pressure-gradient physics
Radial pressure-uniformity constraint
Reduced axial-development constraint
Analytical turbulent-profile guidance

"The analytical velocity guidance uses a regularized 1/7-power-law-like reference expressed in a symmetry-compatible radial coordinate. It is guidance data, not independent validation data."

Corrected PINN gauge-pressure field: 0.2569 PSI(g) at the isolated-tube inlet to atmospheric outlet

Corrected PINN Results

6.70057 m/s

PINN mean velocity

0.173%

vs analytical

0.425%

vs SolidWorks

8.06815 m/s

PINN centerline

0.024%

Reference diff

0.000 m/s

Wall velocity

0.01370 m/s

Profile RMS error

0.02123 m/s

Profile max error

0.25688→0

PSI(g) endpoints

0.01138 Pa

Pressure-linearity RMS

PINN surrogate compared with regularized and classical turbulent analytical reference profiles

PINN / CFD Pressure Cross-Check

Darcy-Weisbach: 1771.11 Pa = 0.25688 PSI | SolidWorks CFD: 1770.04 Pa = 0.25672 PSI | Difference: 0.061%

"At the same ~3 GPM condition as the SolidWorks CFD, the reduced-order Darcy pressure drop used by the PINN was 0.2569 PSI versus 0.2567 PSI in CFD. Because the PINN uses the same reduced Darcy physics, this close agreement demonstrates internal consistency rather than independent CFD validation."

Model Scope

"The PINN velocity field is guided toward an idealized turbulent analytical profile. The real tube has L/D ≈ 3.39, and the SolidWorks outlet remains more developing / plug-like. The PINN therefore demonstrates physics-constrained ML implementation rather than reproducing the complete CFD turbulence field."

Training Convergence

Training-loss history over 1,200 epochs: Adam optimizer with StepLR decay, 600 profile-guidance points and 500 physics collocation points.

PINN training-loss history over 1,200 epochs.

"A reduced-order data-assisted PINN surrogate was trained for the isolated coolant tube using exact wall/symmetry constraints, bulk-flow conservation, reduced Darcy pressure-gradient physics, and a regularized turbulent reference profile."

6. CNC Manufacturing

From Analysis to Hardware

This was not a simulation-only project.

Mazatrol conversational program for the threaded body, including turning and threading operations.

Manufacturing Details

Mazatrol conversational programming
CNC turning / boring
M20 × 2.0 external threading
O-ring gland machining
Retaining-ring groove machining
425 SFM finishing condition where applicable
0.002 IPR finishing feed where applicable
~20 min threaded-body machining cycle

Machined modular nozzle components during prototype development

CAD model vs real machined component side-by-side comparison

CAD vs Real

Machining process on the Mazak Quick Turn 250MY

7. As-Built Verification

ID measuring — verifying internal geometry of the machined coolant tube during prototype inspection.

As-Built Verification MEASURED

Prototype dimensional inspection was performed on five units using micrometers, depth measurement, pitch verification, runout inspection, and comparative surface-finish inspection. n = 5 is a prototype sample.

Core Nominal / As-Built Details

Tube OD: 7.874 mm nominal
Tube ID: 5.998 mm nominal
Wall thickness: 0.938 mm
Primary tube-to-thread-axis TIR target: < 0.002 in
Sealing surfaces: ≤ 32 Ra μin comparative inspection
Thread: M20 × 2.0-6g confirmed on final hardware
Retaining groove: measured 14.7193 mm diameter vs 14.72 mm reference | measured 0.75027 mm width vs 0.75 mm reference

Design / Reference

Tube OD: 7.874 mm
Tube ID: 5.998 mm
Wall: 0.938 mm
TIR: < 0.002 in
Thread: M20 × 2.0-6g
Groove: 14.72 mm / 0.75 mm

As-Built

Tube OD: 7.874 mm
Tube ID: 5.998 mm
Wall: 0.938 mm
TIR: < 0.002 in achieved
Thread: M20 × 2.0-6g confirmed
Groove: 14.7193 mm / 0.75027 mm

8. Prototype Iteration

20 Prototypes — Five Major Development Stages

V1–V3

Seal Leakage

Observed: seal leakage | Root cause: initial gland geometry / insufficient effective sealing compression | Change: revised gland geometry toward ~22% nominal squeeze

V4–V6

O-Ring Extrusion / Gland-Volume Issue

Observed: O-ring extrusion / gland-volume issue | Change: increased available gland volume | Calculated final gland fill: ≈ 71.9%

V7–V9

Thread/Burr-Related Sealing Issues

Observed: thread/burr-related sealing issues | Change: improved deburring and finishing procedure

V10–V12

Runout / Abnormal Vibration

Observed: runout / abnormal vibration | Change: improved boring rigidity and added runout inspection

V13–V20

Final Tested Configuration

Results: no visible leakage at documented 213 PSI operating condition | replaceable service concept demonstrated | tube swap approximately 77 seconds | physical rotational testing documented to 2,000 RPM | "All observed prototype failure modes were resolved in the final tested configuration." "Physical rotational testing was documented to 2,000 RPM; full-speed physical validation remains future work."

9. FMEA / Design Risk

1,832

OEM-model total RPN

255

Redesigned-model total RPN

86.1%

Aggregate RPN reduction

720 → 72

Max individual RPN

"Aggregate FMEA RPN decreased 86.1% within the project scoring model. RPN is an engineering prioritization metric, not a measured failure probability."

Final groove geometry was dimensionally verified against the McMaster 92602A310 catalog geometry.

10. Engineering Impact

Direct Replacement Cost

91.5%

Lower Direct Replacement-Event Cost

Approximate OEM purchased nozzle: ~$150 | Redesign replacement service event: ~$12.70 | ($150 − $12.70) / $150 = 91.5%

$12.70 is a replacement/service-event estimate including tube/wear-component cost assumptions.

Service Time

< 90 sec

Service Threshold Achieved

Final demonstrated tube replacement: ≈ 77 seconds

SCENARIO

Risk-Adjusted Business Scenario

Assumption: 30% modeled probability of removal-related $1,500 tool-holder damage in the OEM maintenance scenario

Expected modeled OEM event cost: $150 + 0.30($1,500) = $600

Scenario: 10 replacement events per holder | 10 holders | 5-year projected fleet savings: $58,257.50

$58.3k

Scenario-Projected 5-Year Fleet Savings

"Under the stated maintenance-frequency and risk assumptions."

Cost comparison chart: OEM replacement nozzle at about $150 versus redesign replacement service event at about $12.70 per event

Cost model breakdown of the risk-adjusted five-year fleet savings scenario across 10 holders and 10 events per holder

Removal-Related Risk

"The redesign removes the recurring need to extract the threaded body during routine tube/seal service, eliminating that specific removal-related damage mechanism."

Final Takeaway

"The project evolved from a shop-floor maintenance problem into a complete mechanical design study spanning failure analysis, material selection, fluid mechanics, structural simulation, fatigue screening, physics-constrained machine learning, CNC manufacturing, metrology, and iterative testing. The final architecture shifts routine maintenance away from the high-value threaded tool-holder interface and into an inexpensive replaceable tube/seal module."

DESIGNED

Serviceable dual-material architecture

VALIDATED

Analytical + CFD + FEA + physical testing

BUILT

20 prototype iterations on CNC hardware

CAD / SolidWorks CNC Machining FMEA Fluid Dynamics / CFD FEA / Structural PINN / Machine Learning Materials Science Metrology

Project Portfolio

Engineering Projects

Five additional projects spanning control systems, biomedical sensing, structural analysis, precision manufacturing, and mechanical reverse engineering.

Built an Arduino-based optical sensing system around the MAX30102 to acquire Red/IR reflectance signals and explore heart-rate extraction, filtering, numerical differentiation, and comparison with reference readings.

MAX30102

Optical Biosensor

Red + IR

Dual Channels

~25 Hz

Logged Cadence

Reference Comparisons

Hardware & Assembly

Arduino Uno with MAX30102 breakout used for optical acquisition.

Embedded Sensor Integration

The MAX30102 is an integrated heart-rate / pulse-oximetry biosensor with red and IR emitters. It was interfaced to an Arduino Uno over I2C, acquiring Red/IR reflectance channels for signal-processing experiments.

Dual-channel Red + IR acquisition over I2C
Moving-average filtering of the raw optical signal
Derivative-based peak-detection concept for heartbeat identification
MAX30102 configured for 100-Hz acquisition; the saved/displayed analysis data show approximately 25-Hz effective sample cadence

Soldering setup used during sensor-prototype assembly.

Prototype Assembly

Header connections were soldered and continuity checked before powering. The breadboard platform allowed rapid iteration on sensor positioning and finger placement during testing.

Raw Signal Acquisition

Raw Red/IR optical signal during the resting acquisition. Large DC baseline and drift are visible; this is not presented as a detrended pulse morphology plot.

Resting Acquisition

The resting trace shows the raw Red/IR reflectance with a large DC baseline and visible drift. Heart-rate estimates were extracted from the moving-average-filtered signal using the derivative-based peak detector.

Project-recorded estimate: 72.4 BPM at rest.

Raw Red/IR optical signal after exercise; displayed as raw optical sensor data rather than a clinical PPG morphology trace.

Post-Exercise Acquisition

After exercise the oscillation visibly speeds up while the raw trace retains the same DC-baseline and drift characteristics. Project-recorded estimate: 124.6 BPM post-exercise.

Formal HRV/PRV analysis was outside the scope of this short acquisition; robust HRV typically requires beat-to-beat interval analysis over a substantially longer record.

Reference Comparison

Single-Session Reference Comparison

Condition	Sensor Estimate	Reference	Abs. Difference
Resting	72.4 BPM	74 BPM	1.6 BPM
Post-exercise	124.6 BPM	126 BPM	1.4 BPM

Single-session comparison; not a population-level accuracy validation.

Numerical Signal Processing

The processing chain — acquire → filter → differentiate → threshold → count peaks — was implemented as a numerical exercise on the logged data.

Trapezoidal integration was applied as a numerical signal-area exercise. Because raw PPG amplitude depends strongly on sensor contact, optical geometry and tissue, the integral is not interpreted as cardiac work or cardiac output.

Circuit Diagram & Data

Basic Arduino-to-MAX30102 I2C wiring diagram

MAX30102 breakout-board close-up

Excerpt from saved resting optical dataset

Excerpt from saved optical dataset; visible timestamps correspond to approximately 25-Hz effective logged cadence

Excerpt from saved post-exercise optical dataset

Post-exercise dataset excerpt — same ~25-Hz logged cadence with elevated estimated rate

The project demonstrated embedded optical sensing, I2C acquisition, basic digital filtering, numerical signal processing, and the importance of validating analysis against the actual recorded dataset.

Signal Processing PPG / Biosensing I2C / Embedded Data Analysis Filtering / Peak Detection Biomedical

Analyzed the classical stress-concentration problem — a circular hole in a tensile plate — using the Kirsch analytical solution, a Python numerical evaluation of that solution over a computational grid, and a separate Arduino strain-sensor acquisition experiment.

K_t = 3

Kirsch SCF (Infinite Plate)

500×500

Python Numerical Grid

d/W = 0.25

Finite-Width Specimen

Arduino

Sensor Acquisition

The actual stress opticon — physical experimental setup for the stress concentration project.

Project Overview

1. Analytical Kirsch Solution

Kirsch stress distribution around a circular hole

Kirsch analytical stress distribution around a circular hole under uniaxial tension.

Kirsch Analytical Solution

For an infinite plate with a circular hole under uniaxial remote tension, the Kirsch solution predicts a maximum hoop stress of 3σ_∞ at the hole boundary at θ = ±90°:

K_t = σ_max / σ_∞ = 3 ANALYTICAL

Important limitation: the physical specimen had d/W = 12.5/50 = 0.25, so finite-width effects are not negligible. K_t = 3 is used as the classical infinite-plate reference, not asserted as the exact finite-specimen factor.

Polar representation of the Kirsch stress field — angular dependence of hoop stress at the hole boundary.

Stress Orientation

The maximum tensile hoop stress occurs at the hole boundary at points perpendicular to the applied loading axis (θ = ±90°) — the hole interrupts the load path and the material around it must redistribute that stress.

Stress concentration factor decay from hole edge

Normalized hoop stress decay in the infinite-plate Kirsch field as a function of r/a.

Decay with Distance

In the infinite-plate Kirsch field, the normalized stress falls below approximately 1.1 by r/a ≈ 2.7 — the concentration decays quickly away from the hole edge, though the exact decay on the finite specimen differs from the infinite-plate curve.

2. Python Numerical Visualization

Python Numerical Evaluation — Kirsch-derived von Mises stress field over the 500×500 computational grid.

Numerical Evaluation of the Kirsch Field

The analytical Kirsch equations were evaluated directly in Python (NumPy) over a 500×500 computational grid to visualize the full stress field — σ_r, σ_θ, τ_rθ — and derived quantities such as von Mises and principal stresses, all transformed from the same analytical solution.

This is a numerical evaluation of a closed-form solution, not a finite-element analysis. No mesh, no solver, no discretization error study — the grid simply samples the exact equations for plotting.

Output from the Python code — numerical evaluation of Kirsch stress field

Output from the Python code — numerical evaluation showing computed stress values across the grid.

Code Output

The Python script evaluates the Kirsch equations across the grid and outputs the computed stress field values. The von Mises stress is derived from the analytical stress components using the standard transformation:

σ_vm = √[ ½((σ_r − σ_θ)² + σ_r² + σ_θ² + 6τ_rθ²) ]

Derived formula for force integration across the net section

Derived formula — integrating the Kirsch hoop stress over the finite-width ligament to check force equilibrium.

Derived Formula & Force Check

As a consistency check, the truncated Kirsch hoop stress at θ = 90° was integrated over the two ligaments of the finite-width section CALCULATED:

σ_θ(r) = σ_∞ [ 1 + a²/(2r²) + 3a⁴/(2r⁴) ]
F_K = 2 t σ_∞ [ R − a²/(2R) − a⁴/(2R³) ]

Values plugged into the derived force equation

Values plugged into the derived equation — with W=50 mm, t=3 mm, a=6.25 mm, R=25 mm, and σ_∞=0.029 N/mm².

Notes on the Force Calculation

With W = 50 mm, t = 3 mm, a = 6.25 mm, R = W/2 = 25 mm, and σ_∞ = 0.029 N/mm²:

F_K ≈ 4.21 N versus the gross far-field resultant F_∞ = σ_∞ W t = 4.35 N — about a 3.3% difference, illustrating the limitation of applying the infinite-plate solution at a nearby finite boundary. This is an analytical consistency check, not experimental validation.

3. Arduino Strain-Sensor Experiment

Sensor Acquisition & Strain Gauge Data

An Arduino / Wheatstone-bridge experiment was built to acquire strain-sensor output near the hole. The strain gauge was bonded near the hole boundary at θ = ±90° where the Kirsch solution predicts maximum hoop stress.

The archived calibration implementation was not sufficient for a defensible absolute microstrain measurement, so the experiment is presented as a sensor-acquisition exercise rather than quantitative validation of the Kirsch SCF.

Raw ADC readings were logged during load application and compared against the expected strain signal direction. The gauge responded in the correct direction (tension at the predicted location), confirming sensor functionality and signal chain integrity PROJECT RECORD.

The lesson: instrumentation results must be verified against a sound calibration chain before they can be treated as measurement evidence.

The project demonstrates elasticity theory, coordinate stress transformation, numerical visualization, and experimental instrumentation — while also showing why computational and sensor methods must be independently validated before being treated as quantitative evidence.

Elasticity Kirsch Solution Python / NumPy Stress Analysis Arduino Instrumentation

Built and tuned a two-wheeled self-balancing robot using an Arduino Uno, MPU-6050 IMU, A4988 stepper drivers, and discrete PID control. The project focused on how proportional, integral, derivative, and sampling behavior affect stability in an inverted-pendulum system.

The system is conceptually related to other unstable attitude-control problems, although the actuator, dynamics, sensing, and control architecture are very different.

Arduino Uno

Controller

MPU-6050

6-DOF IMU

PID

Closed-Loop Control

Kp 4 / Ki .08 / Kd 3

Final Recorded Gains

Robot & Circuit Design

Mechanical design drawing of the self-balancing robot chassis

Mechanical design drawing for the self-balancing robot chassis.

System Architecture

The control challenge is the classical inverted pendulum: an inherently unstable system that tips over without continuous corrective actuation.

Controller: Arduino Uno running discrete PID with anti-windup / integral limiting
Sensing: MPU-6050 6-DOF IMU, gyro+accelerometer combined with a complementary-filter approach
Actuation: Two NEMA 17 stepper motors driven by A4988 drivers
Tuning: Serial gain adjustment without reflashing firmware

Concept design visualization of the two-wheeled balancing platform

CONCEPT / RENDER Design visualization of the two-wheeled balancing platform and component layout.

Mechanical Design

Laser-cut plywood chassis with the component layout organized around the axle line. A CAD-based mass-distribution calculation placed the center of mass approximately 29.7 mm above the axle CALCULATED.

Battery placement and component stacking were chosen to shape the pendulum's response — a higher center of mass gives the controller more time to react before the robot falls.

Control Law

Discrete PID Control

u[k] = K_p e[k] + K_i Σ( e Δt ) + K_d ( e[k] − e[k−1] ) / Δt

Complementary-filter attitude estimate:

θ = α ( θ_prev + ω Δt ) + (1 − α) θ_accel

Final tuning settled near Kp = 4, Ki = 0.08, Kd = 3 after qualitative iterative testing PROJECT RECORD. These gains are specific to this build and are not universal tuning values.

Implementation Notes

Archived firmware was used for iterative control testing; the portfolio focuses on the control architecture rather than claiming precise hard-real-time execution.

Tuning was performed through a serial command interface, allowing proportional, integral, and derivative gains to be adjusted during live balance testing without reflashing.

Project wiring diagram showing Arduino, MPU-6050, A4988 drivers, and dual stepper motors.

Electrical Architecture

Arduino/logic power was separated from the higher-current stepper-motor power path to reduce coupling of motor noise into the sensor/control electronics.

Firmware

Main control loop — PID computation and stepper actuation

MPU-6050 sensor reading and complementary filter

Firmware source code — serial tuning interface

Serial gain-adjustment interface

Firmware source code — stepper driver control

A4988 stepper driver control and timing

PID Tuning

PID tuning chart — system response across different gain combinations during iterative testing.

Iterative Tuning Process

Tuning was performed through a serial command interface, allowing proportional, integral, and derivative gains to be adjusted during live balance testing without reflashing firmware.

The tuning process involved:

Starting with conservative gains and increasing Kp until the robot could maintain approximate balance
Adding Kd to damp oscillations and improve recovery from disturbances
Applying small Ki to correct steady-state lean from center-of-mass offset
Testing disturbance recovery by gently pushing the robot

Final tuning settled near Kp = 4, Ki = 0.08, Kd = 3 after qualitative iterative testing PROJECT RECORD. These gains are specific to this build and are not universal tuning values.

Step response — robot recovery from an applied disturbance during tuning.

Step Response & Stability

The step response shows how the robot recovers from an applied lateral disturbance. A well-tuned PID controller returns to equilibrium with minimal overshoot and no sustained oscillation.

Anti-windup / integral limiting was implemented to prevent integral accumulation from driving the steppers beyond their useful range during large tilt excursions.

PID Control Sensor Fusion Embedded C++ Arduino Control Theory Real-Time Systems

Production machining experience at American Precision Machining producing tight-tolerance components for industrial and instrumentation applications. Original customer drawings and programs are omitted for confidentiality; the project focuses on manufactured hardware, process knowledge, and documented inspection examples.

99%

QC Pass Rate

±0.0005"

Tightest Documented Tolerance

Ra 6.2

Best Documented Surface Finish (μin)

Multi-Axis

INTEGREX / CNC Experience

Machined Parts

Machined production components — photographed physical hardware from the project documentation.

Four-Part Manufacturing Portfolio

Part A: Multi-threaded brass fitting with turned/threaded features, live-tool geometry, and cross drilling.

Part B: Stainless flanged hub with bolt-circle features, internal threading, and milled geometry.

Part C (most complex): Stainless manifold-style component with multi-face features, ports/passages, and O-ring-related geometry.

Part D: Thin-wall stainless cage/retainer with open windows requiring attention to deflection and concentricity.

Additional machined components showing surface finish quality and geometric complexity.

Machines & Programming

Mazak INTEGREX i-200: multi-tasking / 5-axis-capable machine
Mazak turning/milling lathe: turning plus live-tool secondary operations
Hurco VMC: 3-axis vertical machining

Programming exposure: MAZATROL conversational, G-code, and GibbsCAM multi-axis CAM.

Detail view — thread form quality and surface finish on a machined component.

Metrology & Inspection

Project documentation records dimensional inspection using CMM and bench metrology including micrometers, calipers, thread gages, pin gages, optical comparison, and surface profilometry.

The project record contains 40 documented inspection characteristics reported within their stated limits with a 99% pass rate PROJECT RECORD.

Closeup of machined surface showing finish quality

Surface finish closeup — face-milled stainless steel; the best documented surface finish reached Ra 6.2 μin (0.16 μm).

Surface Finish

Surface-finish acceptance is drawing- and function-specific; the documented measurements demonstrate experience with profilometry and machining-process effects — Ra 6.2–36.4 μin across measured features.

For ideal turning geometry, Ra ≈ f²/(32r) and the approximate peak-to-valley theoretical height Rt ≈ f²/(8r) CALCULATED. For the documented brass example (f = 0.003 in/rev, r = 1/32 in): Ra_theory ≈ 9 μin versus project-recorded Ra ≈ 16.2 μin — real finish also depends on material, tool condition, vibration, built-up edge, cutting speed, and machine dynamics.

Tolerance & Surface Analysis

Tolerance-analysis method — worst-case (T_WC = Σ|T_i|) and RSS (T_RSS = √ΣT_i²) approaches applied to assembly dimension chains.

Tolerance Stack Analysis

Worst-case and RSS (root-sum-square) tolerance-stack analysis was applied to assembly-critical dimension chains to understand how feature tolerances accumulate — a core manufacturing-design skill, since unnecessarily tight tolerances add cost without functional benefit.

Studied Cp/Cpk and SPC concepts as part of manufacturing-quality analysis; the available portfolio inspection set is not used to claim statistical process capability.

CNC Machining Multi-Axis Metrology / CMM GD&T / ASME Y14.5 Tolerance Analysis MAZATROL G-Code GibbsCAM

Complete reverse engineering of a commercial mortise lock — from systematic disassembly and precision measurement through parametric SolidWorks reconstruction and a functional FDM 3D-printed prototype.

Components

SLDPRT Files

Phase Workflow

Functional

Prototype

Assembly & Mechanism

SolidWorks reconstruction of the mortise-lock assembly

CONCEPT / RENDER SolidWorks reconstruction of the 10-component mortise-lock assembly.

Six-Phase Reverse-Engineering Workflow

Disassembly with component cataloging
Measurement with digital calipers
CAD Modeling — 10 parametric SolidWorks component models
STL / print preparation with FDM tolerance compensation
FDM fabrication
Functional validation of the reassembled mechanism

Assembly mates preserved the real kinematics (concentric, coincident, limit mates); design intent was inferred from measurement clusters rather than simply copying geometry.

Engineering Analysis

The actual mortise lock — physical hardware that was disassembled, measured, and reverse-engineered for this project.

Physical Hardware

The commercial mortise lock shown here was systematically disassembled, measured with digital calipers, and reconstructed as parametric SolidWorks models. Each component was cataloged and individually modeled to preserve the full assembly kinematics.

Latch return spring analysis — helical compression-spring rate derived from measured geometry.

Spring Analysis

Spring rate from the helical compression formula k = Gd⁴/(8D³N_a) with d = 0.80 mm, D = 5.55 mm, N_a = 6, and G = 79.3 GPa CALCULATED ASSUMPTION (material):

k ≈ 3.96 N/mm
Preload ≈ 10.10 N
Max modeled spring load ≈ 60.39 N

Shear modulus and material properties come from handbook values, not a material certificate for this specific spring.

Cam Kinematics — Deadbolt Actuation

A simplified eccentric-cam model reproduces the measured approximately 15.88-mm deadbolt throw over approximately 90° of key rotation CALCULATED:

s(θ) = e ( 1 − cos θ ), e = 15.88 mm
s(90°) = 15.88 mm

The model captures the displacement relationship as documented; no force-amplification claim is made without a defined input torque and lever geometry.

ANALYTICAL ASSUMED Illustrative material-substitution comparison using representative material-property assumptions and estimated component weights.

Material Substitution

Under representative material-strength assumptions, the printed PLA deadbolt has approximately 21% of the modeled steel deadbolt shear capacity (6.2 kN vs 30.0 kN). This is an analytical material-substitution estimate, not a security rating or a destructive test ASSUMPTION.

Estimated assembly masses: steel ≈450 g, printed PLA ≈72 g — both estimates, not measured weights.

The PLA latch bevel was increased from 15° to 25° for self-retraction margin: the screening criterion tan(α) > μ was applied with representative PLA-on-steel friction used as a screening assumption, not measured on the printed surface. The final prototype was documented as functioning after post-processing.

Handle Force — Simplified Lever Statics

With lever-arm ratio r₂/r₁ = 22.0/8.5 ≈ 2.59 and the maximum modeled spring force of 60.39 N CALCULATED:

F_handle = F_spring × ( r₁ / r₂ ) ≈ 23.3 N

Simplified lever statics predicts approximately 23.3 N maximum handle force under the modeled spring load (and ≈1.28 N·m torque at the documented handle radius). This is a statics exercise, not ergonomic validation.

Project-recorded CAD-to-print dimensional comparison.

FDM Dimensional Accuracy

Observed dimensions in the documented sample fell within the project's ±0.30-mm prototype fit target, with documented deviations on the order of approximately ±0.25 mm PROJECT RECORD. This describes the documented sample only, not universal FDM process capability.

Holes and shaft fits were compensated (+0.2–0.4 mm) during print preparation to accommodate FDM shrinkage and layer artifacts.

This project demonstrates teardown-driven reverse engineering, parametric CAD reconstruction, mechanism analysis, material/process substitution, FDM tolerance compensation, and functional reassembly.

Reverse Engineering SolidWorks CAD Mechanism Design FDM 3D Printing Cam Kinematics Material Substitution

Precision engineering from theory to reality.

Modular Through-Spindle Coolant Nozzle Redesign

Modular Through-Spindle Coolant Nozzle Redesign

Installed Hardware Context

The Problem — A Small Wear Component Put a High-Value Tool Holder at Risk

Modular Architecture — Two Material Roles

Retaining System

Material Selection — Different Components, Different Design Drivers

Threaded Body Matrix

Coolant Tube Matrix

Internal Flow — SolidWorks Flow Simulation CFD ASSUMED FLOW CONDITION

CFD Model

Continuity & Regime

Darcy-Weisbach vs CFD

CFD Results — Solver-Converged

Pressure Containment — SolidWorks Simulation FEA

Analytical Benchmark — Lamé Thick-Wall Cylinder

SolidWorks — 213 PSI

320 PSI Design Case 1.5× static design-overpressure case

Displacement Check

Pressure-Cycle Fatigue Screening FATIGUE

Physics-Constrained ML Extension PINN / ML

Reduced-Order Data-Assisted PINN Surrogate

PINN Physical Problem

PINN Architecture

PINN Physics / Constraints

Corrected PINN Results

PINN / CFD Pressure Cross-Check

Training Convergence

From Analysis to Hardware

Manufacturing Details

As-Built Verification MEASURED

Core Nominal / As-Built Details

Design / Reference

As-Built

20 Prototypes — Five Major Development Stages

Direct Replacement Cost

Service Time

Risk-Adjusted Business Scenario

Removal-Related Risk

Engineering Projects

PPG Heart Rate Monitor

Embedded Sensor Integration

Prototype Assembly

Resting Acquisition

Post-Exercise Acquisition

Single-Session Reference Comparison

Numerical Signal Processing

Stress Concentration Around a Circular Hole

Project Overview

Kirsch Analytical Solution

Stress Orientation

Decay with Distance

Numerical Evaluation of the Kirsch Field

Code Output

Derived Formula & Force Check

Notes on the Force Calculation

Sensor Acquisition & Strain Gauge Data

PID Self-Balancing Robot

System Architecture

Mechanical Design

Discrete PID Control

Implementation Notes

Electrical Architecture

Iterative Tuning Process

Step Response & Stability

CNC Precision Machining — Production Experience

Four-Part Manufacturing Portfolio

Machines & Programming

Metrology & Inspection

Surface Finish

Tolerance Stack Analysis

Mortise Lock Reverse Engineering

Six-Phase Reverse-Engineering Workflow

Physical Hardware

Spring Analysis

Cam Kinematics — Deadbolt Actuation

Material Substitution

Handle Force — Simplified Lever Statics

FDM Dimensional Accuracy

Precision engineering
from theory to reality.