🛠️ Merchant's Theory of Chip Formation

April 5, 2025 · View on GitHub

A modular, open-source command-line simulator written in modern Fortran, this tool performs machining analysis based on Merchant’s theory of orthogonal cutting. It models chip formation assuming idealized shear deformation and sharp tool geometry, with extensions for thermal effects and surface finish prediction.

🎯 Use Cases

  • 🧑‍🏭 Process engineers evaluating cutting efficiency and surface quality
  • 🎓 Students studying metal cutting theory, forces, temperature rise, and chip mechanics
  • 🔬 Researchers modeling chip-tool-workpiece interaction and heat transfer

✨ Features

  • 📦 Reads material data from materials.csv (density, specific heat, category, name)
  • 🔬 Physics-based calculations:
    • Shear angle (ϕ) and chip ratio
    • Shear force and normal force on shear plane
    • Shear stress and specific cutting energy (SCE)
    • Material removal rate (MRR)
    • Cutting power
    • Advanced temperature rise using chip-tool heat partitioning
    • Surface roughness prediction based on tool wear and cutting speed
    • Thermal damage classification
    • Machinability index proxy
  • 💾 Optional output to .txt file
  • 🔩 Clean, modular Fortran 90 code
  • 🔁 Easily extensible with new models and inputs

🏗️ Build Instructions

sudo apt install gfortran
chmod +x build.sh
./build.sh

🚀 How to Run

Interactive mode:

./machining_simulator

Output to file:

./machining_simulator results.txt

📥 User Input Prompts

  1. Select material category
  2. Select specific material
  3. Enter values for:
    • Rake angle (degrees)
    • Coefficient of friction (μ)
    • Uncut chip thickness t₁ (mm)
    • Chip thickness t₂ (mm)
    • Width of cut w (mm)
    • Cutting speed Vc (m/s)
    • Cutting force Fc (N)
    • Thrust force Ft (N)

🧮 What It Calculates

QuantityDescription
Shear angle (ϕ)Based on Merchant’s theory
Chip ratio (r)t₁ / t₂
Shear force (Fs), Normal force (Fn)On shear plane
Shear stress (τₛ)Fs / shear area
Specific Cutting EnergyCutting energy per volume
MRRMaterial removal rate (mm³/s)
Cutting PowerFc × Vc (W)
Temperature Rise (ΔT)Based on heat partitioning model
Thermal ZoneLow, Moderate, High (qualitative)
Surface Roughness (Ra)Includes cutting speed and tool wear effects
Thermal Damage RiskRisk classification based on ΔT
Machinability IndexInverse of SCE (proxy only)

🔧 Tunable Model Parameters

The following constants are estimated based on common machining behavior. You can adjust them in the machining_utils.f90 module:

real(8), parameter :: eta_shear = 0.8d0              ! Efficiency of shear energy
real(8), parameter :: chip_partition_ratio = 0.3d0   ! Fraction of heat to chip
real(8), parameter :: default_tool_wear = 0.5d0      ! Wear index [0=new, 1=worn]
real(8), parameter :: k_v = 0.1d0                    ! Ra speed sensitivity
real(8), parameter :: k_w = 2.0d0                    ! Ra wear sensitivity
real(8), parameter :: n_v = 0.3d0                    ! Vc exponent in Ra model

Example Impact

  • Increase chip_partition_ratio to simulate better chip cooling
  • Decrease eta_shear to simulate energy loss in vibration or friction
  • Increase k_w to simulate aggressive wear effect on finish

📤 Sample Output

-----------------------------------------
Material selected: Stainless Steel 316
Density (kg/m³): 8000.0
Specific Heat (J/kg·K): 500.0
Shear angle φ (deg): 18.28
Chip ratio r = t1 / t2: 1.00
Shear force Fs (N): -0.0075
Normal force Fn (N): 2.83
Shear stress τₛ (MPa): -0.00059
Specific Cutting Energy (J/mm³): 0.50
Cutting Power (W): 4.00
Approx. Temperature Rise (K): -1.58e-09
Thermal Zone: Low
Machinability Index (proxy): 2000.0
Estimated Surface Roughness Ra (µm): 6.05
Thermal Damage Risk: No risk
-----------------------------------------

🔓 License

This project is released under the GNU GPL v3 License.

Contributions, forks, and improvements are welcome!