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LICENSE.txt

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+Creative Commons Attribution 4.0 International (CC BY 4.0)
+===========================================================
+
+Copyright (c) 2026 Innovative Process Applications (IPA)
+
+This dataset is licensed under the Creative Commons Attribution 4.0
+International License. You are free to:
+
+  - Share: copy and redistribute the material in any medium or format
+  - Adapt: remix, transform, and build upon the material
+    for any purpose, even commercially.
+
+Under the following terms:
+
+  - Attribution: You must give appropriate credit, provide a link to
+    the license, and indicate if changes were made. You may do so in
+    any reasonable manner, but not in any way that suggests the
+    licensor endorses you or your use.
+
+Recommended attribution:
+
+  "Roller Compaction: Ribbon Density vs. Process Parameters (Synthetic),
+   v1.0, by Innovative Process Applications (IPA), CC BY 4.0,
+   https://www.innovativeprocess.com"
+
+Full license text: https://creativecommons.org/licenses/by/4.0/legalcode
+
+DISCLAIMER: This dataset is synthetic and intended for educational use
+only. It does not represent real equipment, customer, or production
+data. IPA makes no warranty as to its fitness for any particular
+purpose, including regulatory, commercial, or safety-critical use.

README.md

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----
-license: cc-by-4.0
----
+# Roller Compaction: Ribbon Density vs. Process Parameters (Synthetic)
+
+**Version:** 1.0
+**Publisher:** [Innovative Process Applications (IPA)](https://www.innovativeprocess.com)
+**License:** Creative Commons Attribution 4.0 International (CC BY 4.0)
+**Contact:** Crestwood, IL, USA
+
+> ⚠️ **This dataset is 100% synthetic and intended for educational use only.**
+> It was generated from a published physical model (Johanson rolling theory + Heckel densification) — not measured on any real equipment, customer, or production batch. Do not use it for regulatory submissions, equipment validation, or commercial process design.
+
+---
+
+## What's in this dataset
+
+600 simulated roller compaction runs on a representative pharmaceutical excipient blend (microcrystalline cellulose / lactose), spanning the operating envelope of a lab-to-pilot scale twin-feed-screw roller compactor.
+
+| Column | Units | Description |
+|---|---|---|
+| `run_id` | — | Unique run identifier |
+| `roll_force_kN_per_cm` | kN/cm | Specific roll force (normalized by roll width) |
+| `roll_speed_rpm` | rpm | Roll rotation speed |
+| `feed_screw_rpm` | rpm | Twin feed screw rotation speed |
+| `roll_gap_mm` | mm | Target ribbon thickness / roll gap |
+| `peak_pressure_MPa` | MPa | Computed peak nip pressure (Johanson) |
+| `ribbon_rel_density` | — | Relative density (fraction of true density) |
+| `ribbon_density_g_cc` | g/cc | Absolute ribbon density |
+| `ribbon_porosity` | — | 1 − relative density |
+| `density_CV_percent` | % | Across-width density coefficient of variation (uniformity) |
+| `throughput_kg_hr` | kg/hr | Mass throughput |
+
+## Realistic ranges (grounded in the literature)
+
+The generator uses ranges consistent with published roller compaction studies on MCC/lactose blends:
+
+- **Roll force:** 2–14 kN/cm (typical lab/pilot range)
+- **Roll speed:** 1–12 rpm
+- **Feed-to-roll speed ratio:** 3–30 (optimum ≈ 11 for twin feed screws on MCC)
+- **Peak nip pressure:** ~30–200 MPa
+- **Relative density:** 0.55–0.80 (ribbons below ~0.55 tend to crumble; above ~0.85 you over-compact and lose downstream granulation behavior)
+- **Material:** true density 1.55 g/cc, bulk density 0.45 g/cc, Heckel K ≈ 0.018 MPa⁻¹
+
+## Physical model
+
+The synthetic data is generated from:
+
+1. **Johanson rolling theory (1965)** — peak nip pressure as a function of roll force, gap, and roll geometry.
+2. **Heckel equation** — relative density as a function of applied pressure: `ln(1/(1−D)) = K·P + A`.
+3. **Twin feed screw effect** — a Gaussian optimality response centered on feed/roll ratio ≈ 11, penalizing both starved and over-fed nip conditions. This reflects IPA's twin-feed-screw design advantage for maintaining uniform nip feeding.
+4. **Realistic measurement noise** (~1.5% on density, proportional noise on uniformity and throughput).
+
+Full generator source is in `generate_dataset.py` — reproducible with seed 42.
+
+## What you can teach with it
+
+- **DOE / Response Surface Methodology:** fit a quadratic model to ribbon density as a function of roll force, roll speed, and feed screw speed.
+- **Process optimization:** find the operating window that maximizes density while keeping CV% under a target (e.g., < 3%).
+- **Regression & ML:** compare linear regression, random forests, and Gaussian processes on a small-but-physical dataset.
+- **Quality-by-Design (QbD):** illustrate design space, critical process parameters (CPPs), and critical quality attributes (CQAs).
+
+## Cross-links (other places to find this dataset)
+
+- **Kaggle:** [link after publication]
+- **Hugging Face Datasets:** [link after publication]
+- **Zenodo (DOI):** [link after publication]
+- **GitHub:** [link after publication]
+- **IPA website:** https://www.innovativeprocess.com
+
+## About IPA
+
+Innovative Process Applications designs and manufactures twin-feed-screw roller compactors, mills, and size-reduction equipment for the pharmaceutical, nutraceutical, chemical, and food industries. Based in Crestwood, Illinois, IPA is a direct OEM alternative to legacy Fitzpatrick Chilsonator and FitzMill systems, with American manufacturing and direct engineer access. Learn more at [innovativeprocess.com](https://www.innovativeprocess.com).
+
+## Citation
+
+If you use this dataset in teaching, a notebook, a paper, or a blog post, please cite:
+
+> Innovative Process Applications (2026). *Roller Compaction: Ribbon Density vs. Process Parameters (Synthetic), v1.0*. CC BY 4.0. https://www.innovativeprocess.com
+
+## Version history
+
+- **v1.0** (April 2026) — Initial release. 600 runs, 4 process parameters, 6 response variables.

generate_dataset.py

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+"""
+IPA Roller Compaction Synthetic Dataset Generator v1.0
+========================================================
+Generates a physically plausible synthetic dataset based on:
+  - Johanson rolling theory (Johanson, 1965) for nip angle & pressure
+  - Heckel equation for powder densification under pressure
+  - Empirical twin-feed-screw effect on ribbon uniformity
+
+THIS IS SYNTHETIC EDUCATIONAL DATA. NOT REAL CUSTOMER OR LAB DATA.
+Generated by Innovative Process Applications (IPA) for teaching DOE/RSM.
+"""
+
+import numpy as np
+import pandas as pd
+
+rng = np.random.default_rng(seed=42)  # reproducible
+
+# ---- Physical constants & realistic ranges ----
+# Grounded in published roller compaction literature for pharma excipients
+# (microcrystalline cellulose / lactose blends on lab-to-pilot scale rolls)
+
+N_RUNS = 600  # enough for DOE/RSM teaching, small enough to inspect by eye
+
+# Process parameter ranges (realistic for IPA CL-series lab/pilot compactors)
+ROLL_FORCE_KN_CM = (2.0, 14.0)     # kN/cm of roll width
+ROLL_SPEED_RPM   = (1.0, 12.0)     # roll rotation speed
+FEED_SCREW_RPM   = (10.0, 120.0)   # twin feed screw speed
+ROLL_GAP_MM      = (1.5, 4.5)      # ribbon thickness target
+
+# Material parameters (MCC-lactose blend, representative)
+RHO_TRUE = 1.55           # true density, g/cc
+RHO_BULK = 0.45           # tapped bulk density, g/cc
+HECKEL_K = 0.018          # 1/MPa, Heckel compressibility constant
+HECKEL_A = 0.62           # Heckel intercept (related to initial packing)
+
+# Machine geometry (representative of CL2x6 class roller compactor)
+ROLL_DIAMETER_MM = 150.0
+ROLL_WIDTH_MM    = 50.0
+
+def johanson_pressure_mpa(force_kn_per_cm, gap_mm):
+    """
+    Approximation of peak nip pressure from Johanson rolling theory.
+    Pressure scales with force/(contact area), and contact area grows
+    with sqrt(R * (gap_entry - gap)).
+    """
+    # Effective contact length proxy (mm): sqrt(R * delta_gap)
+    # Assume entry gap ~ 3x exit gap for MCC-like materials
+    contact_len_mm = np.sqrt(ROLL_DIAMETER_MM/2 * 2.0 * gap_mm)
+    # Force per unit area: (kN/cm * 10 N/mm) / (contact_len_mm) -> MPa-ish
+    pressure = (force_kn_per_cm * 100.0) / contact_len_mm
+    return pressure  # MPa
+
+def heckel_relative_density(pressure_mpa):
+    """Heckel equation: ln(1/(1-D)) = K*P + A  =>  D = 1 - exp(-(K*P + A))"""
+    return 1.0 - np.exp(-(HECKEL_K * pressure_mpa + HECKEL_A))
+
+def feed_ratio_effect(feed_rpm, roll_rpm):
+    """
+    Twin feed screw effect: under-feeding starves the nip (low density,
+    high variability); over-feeding causes slip and pre-compaction.
+    Optimal ratio roughly 8-15 for twin screws on MCC.
+    """
+    ratio = feed_rpm / roll_rpm
+    # Gaussian-like response centered at ratio=11
+    optimality = np.exp(-((ratio - 11.0) ** 2) / (2 * 6.0**2))
+    return optimality  # 0..1
+
+# ---- Generate runs ----
+roll_force = rng.uniform(*ROLL_FORCE_KN_CM, N_RUNS)
+roll_speed = rng.uniform(*ROLL_SPEED_RPM, N_RUNS)
+feed_speed = rng.uniform(*FEED_SCREW_RPM, N_RUNS)
+roll_gap   = rng.uniform(*ROLL_GAP_MM, N_RUNS)
+
+# Physics
+peak_pressure = johanson_pressure_mpa(roll_force, roll_gap)
+base_rel_density = heckel_relative_density(peak_pressure)
+feed_opt = feed_ratio_effect(feed_speed, roll_speed)
+
+# Combine: good feed ratio lets you reach base density; poor ratio penalizes
+relative_density = base_rel_density * (0.85 + 0.15 * feed_opt)
+# Add realistic measurement noise (~1.5% relative)
+relative_density += rng.normal(0, 0.015, N_RUNS)
+relative_density = np.clip(relative_density, 0.40, 0.95)
+
+ribbon_density = relative_density * RHO_TRUE               # g/cc
+porosity = 1.0 - relative_density                          # fraction
+
+# Ribbon uniformity: twin feed screws give lower CV across roll width
+# when feed ratio is in the sweet spot; degrades otherwise
+density_cv_pct = (2.0 + 4.5 * (1 - feed_opt)) + rng.normal(0, 0.4, N_RUNS)
+density_cv_pct = np.clip(density_cv_pct, 1.0, 10.0)
+
+throughput_kg_hr = (
+    roll_speed * roll_gap * ROLL_WIDTH_MM * ribbon_density * 60 / 1000 * 0.85
+) + rng.normal(0, 1.5, N_RUNS)
+throughput_kg_hr = np.clip(throughput_kg_hr, 0, None)
+
+df = pd.DataFrame({
+    "run_id": np.arange(1, N_RUNS + 1),
+    "roll_force_kN_per_cm": np.round(roll_force, 2),
+    "roll_speed_rpm": np.round(roll_speed, 2),
+    "feed_screw_rpm": np.round(feed_speed, 1),
+    "roll_gap_mm": np.round(roll_gap, 2),
+    "peak_pressure_MPa": np.round(peak_pressure, 1),
+    "ribbon_rel_density": np.round(relative_density, 4),
+    "ribbon_density_g_cc": np.round(ribbon_density, 4),
+    "ribbon_porosity": np.round(porosity, 4),
+    "density_CV_percent": np.round(density_cv_pct, 2),
+    "throughput_kg_hr": np.round(throughput_kg_hr, 2),
+})
+
+df.to_csv("ribbon_density_v1.0.csv", index=False)
+print(f"Wrote {len(df)} rows")
+print(df.describe().round(3))

ribbon_density_v1.0.csv

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+run_id,roll_force_kN_per_cm,roll_speed_rpm,feed_screw_rpm,roll_gap_mm,peak_pressure_MPa,ribbon_rel_density,ribbon_density_g_cc,ribbon_porosity,density_CV_percent,throughput_kg_hr
+1,11.29,6.25,72.3,3.33,50.5,0.7925,1.2284,0.2075,1.55,64.12
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+3,12.3,10.94,101.1,1.91,72.8,0.8489,1.3159,0.1511,2.07,71.47
+4,10.37,8.93,88.2,3.58,44.7,0.7605,1.1788,0.2395,1.07,93.54
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+87,10.67,5.62,53.1,1.88,63.5,0.8096,1.2548,0.1904,2.21,33.47
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+89,3.94,9.27,59.6,4.05,16.0,0.5888,0.9127,0.4112,2.8,87.78
+90,8.01,6.95,72.5,2.84,38.8,0.7301,1.1317,0.2699,1.99,54.91
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sample_analysis.ipynb

@@ -0,0 +1,101 @@
+{
+ "cells": [
+  {"cell_type": "markdown", "metadata": {}, "source": [
+    "# Roller Compaction DOE/RSM — Sample Analysis\n",
+    "\n",
+    "**Dataset:** Roller Compaction: Ribbon Density vs. Process Parameters (Synthetic) v1.0\n",
+    "**Publisher:** [Innovative Process Applications (IPA)](https://www.innovativeprocess.com)\n",
+    "**License:** CC BY 4.0\n",
+    "\n",
+    "> This is **synthetic educational data**. See `README.md` for the physical model (Johanson + Heckel) used to generate it.\n",
+    "\n",
+    "This notebook walks through a typical Quality-by-Design workflow:\n",
+    "1. Load and explore the data\n",
+    "2. Fit a response surface (quadratic) model for ribbon density\n",
+    "3. Identify the operating window that maximizes density while keeping uniformity (CV%) under 3%"
+  ]},
+  {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [
+    "import pandas as pd\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from sklearn.linear_model import LinearRegression\n",
+    "from sklearn.preprocessing import PolynomialFeatures\n",
+    "from sklearn.metrics import r2_score\n",
+    "\n",
+    "df = pd.read_csv('ribbon_density_v1.0.csv')\n",
+    "print(df.shape)\n",
+    "df.head()"
+  ]},
+  {"cell_type": "markdown", "metadata": {}, "source": ["## 1. Explore the process parameters"]},
+  {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [
+    "fig, axes = plt.subplots(1, 3, figsize=(14, 4))\n",
+    "axes[0].scatter(df['roll_force_kN_per_cm'], df['ribbon_rel_density'], alpha=0.4)\n",
+    "axes[0].set_xlabel('Roll force (kN/cm)'); axes[0].set_ylabel('Relative density')\n",
+    "axes[0].set_title('Force → density (Heckel)')\n",
+    "\n",
+    "axes[1].scatter(df['feed_screw_rpm']/df['roll_speed_rpm'], df['density_CV_percent'], alpha=0.4, color='C1')\n",
+    "axes[1].set_xlabel('Feed/roll speed ratio'); axes[1].set_ylabel('Density CV %')\n",
+    "axes[1].set_title('Feed ratio → uniformity')\n",
+    "\n",
+    "axes[2].scatter(df['peak_pressure_MPa'], df['ribbon_rel_density'], alpha=0.4, color='C2')\n",
+    "axes[2].set_xlabel('Peak nip pressure (MPa)'); axes[2].set_ylabel('Relative density')\n",
+    "axes[2].set_title('Pressure → density')\n",
+    "plt.tight_layout(); plt.show()"
+  ]},
+  {"cell_type": "markdown", "metadata": {}, "source": [
+    "## 2. Fit a quadratic response surface\n",
+    "\n",
+    "Classic RSM model: ribbon density as a quadratic function of the three main process parameters."
+  ]},
+  {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [
+    "X = df[['roll_force_kN_per_cm', 'roll_speed_rpm', 'feed_screw_rpm']].values\n",
+    "y = df['ribbon_rel_density'].values\n",
+    "\n",
+    "poly = PolynomialFeatures(degree=2, include_bias=False)\n",
+    "Xp = poly.fit_transform(X)\n",
+    "model = LinearRegression().fit(Xp, y)\n",
+    "y_pred = model.predict(Xp)\n",
+    "print(f'R² = {r2_score(y, y_pred):.3f}')\n",
+    "\n",
+    "plt.figure(figsize=(5,5))\n",
+    "plt.scatter(y, y_pred, alpha=0.4)\n",
+    "plt.plot([y.min(), y.max()], [y.min(), y.max()], 'k--')\n",
+    "plt.xlabel('Observed rel. density'); plt.ylabel('Predicted')\n",
+    "plt.title('RSM fit'); plt.show()"
+  ]},
+  {"cell_type": "markdown", "metadata": {}, "source": [
+    "## 3. Find the design space\n",
+    "\n",
+    "QbD asks: which combinations of process parameters give us a target density **AND** acceptable uniformity?\n",
+    "\n",
+    "Let's define an acceptable region as: relative density ≥ 0.70 AND density CV% ≤ 3.0%."
+  ]},
+  {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [
+    "in_spec = (df['ribbon_rel_density'] >= 0.70) & (df['density_CV_percent'] <= 3.0)\n",
+    "print(f'{in_spec.sum()} of {len(df)} runs meet spec ({100*in_spec.mean():.1f}%)')\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize=(7, 5))\n",
+    "ax.scatter(df.loc[~in_spec, 'roll_force_kN_per_cm'], df.loc[~in_spec, 'feed_screw_rpm']/df.loc[~in_spec, 'roll_speed_rpm'], alpha=0.3, label='Out of spec', color='lightgray')\n",
+    "ax.scatter(df.loc[in_spec, 'roll_force_kN_per_cm'], df.loc[in_spec, 'feed_screw_rpm']/df.loc[in_spec, 'roll_speed_rpm'], alpha=0.6, label='In spec', color='teal')\n",
+    "ax.set_xlabel('Roll force (kN/cm)'); ax.set_ylabel('Feed/roll ratio')\n",
+    "ax.set_title('Design space: density ≥ 0.70 AND CV ≤ 3%')\n",
+    "ax.legend(); plt.show()"
+  ]},
+  {"cell_type": "markdown", "metadata": {}, "source": [
+    "## Takeaway\n",
+    "\n",
+    "The design space clusters around **roll force ≥ 6 kN/cm** and **feed/roll ratio ≈ 8–15** — consistent with the physics of a well-fed nip on a twin-feed-screw roller compactor.\n",
+    "\n",
+    "For production-scale equipment that achieves this operating window consistently, see IPA's CL-series twin-feed-screw compactors: https://www.innovativeprocess.com\n",
+    "\n",
+    "---\n",
+    "*Dataset © 2026 Innovative Process Applications, CC BY 4.0. Synthetic educational data — not real measurements.*"
+  ]}
+ ],
+ "metadata": {
+  "kernelspec": {"display_name": "Python 3", "language": "python", "name": "python3"},
+  "language_info": {"name": "python", "version": "3.11"}
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}