6. Advanced Variables: Geometric Dimensioning & Tolerancing (GD&T)
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Weaknesses / limitations
Identify which component contributes the highest percentage to the RSS variance (as demonstrated by Sensitivity_Pct in our calculator code). Tighten the tolerance only on that specific high-impact component to achieve maximum cost-efficiency.
The plot demonstrates that while the absolute Worst-Case boundaries extend out to tolerance stack up calculator exclusive
Standard spreadsheets rarely integrate seamlessly with Geometric Dimensioning and Tolerancing (GD&T) principles, such as bonus tolerances from Maximum Material Condition (MMC) modifiers.
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To better understand how TolStack processes these statistical distributions, we can visualize the difference between individual component variations and the cumulative assembly variation.
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Summary
import numpy as np import pandas as pd class ToleranceStackCalculator: def __init__(self): self.components = [] def add_dimension(self, name, nominal, tolerance, direction): """ Adds a component dimension to the loop. direction: +1 for positive vector, -1 for negative vector """ self.components.append( 'Name': name, 'Nominal': nominal, 'Tolerance': abs(tolerance), 'Direction': direction ) def analyze(self): if not self.components: return "No data to analyze." df = pd.DataFrame(self.components) # Calculate signed nominals df['Signed_Nominal'] = df['Nominal'] * df['Direction'] # Aggregations total_nominal = df['Signed_Nominal'].sum() worst_case_tolerance = df['Tolerance'].sum() rss_tolerance = np.sqrt((df['Tolerance'] ** 2).sum()) # Sensitivity Analysis (Contribution percentage to RSS variance) total_variance = (df['Tolerance'] ** 2).sum() df['Sensitivity_Pct'] = ((df['Tolerance'] ** 2) / total_variance) * 100 results = 'Nominal_Gap': total_nominal, 'Worst_Case': 'Tolerance': worst_case_tolerance, 'Min': total_nominal - worst_case_tolerance, 'Max': total_nominal + worst_case_tolerance , 'RSS': 'Tolerance': rss_tolerance, 'Min': total_nominal - rss_tolerance, 'Max': total_nominal + rss_tolerance , 'Component_Report': df[['Name', 'Nominal', 'Tolerance', 'Direction', 'Sensitivity_Pct']] return results # Example Deployment: Analysing a shaft and housing alignment calc = ToleranceStackCalculator() calc.add_dimension("Housing Bore Depth", 50.00, 0.15, 1) calc.add_dimension("Retaining Ring Groove", 3.00, 0.05, 1) calc.add_dimension("Shaft Shoulder Length", 48.00, 0.10, -1) calc.add_dimension("Bearing Width", 4.50, 0.08, -1) report = calc.analyze() print(f"Nominal Expected Gap: report['Nominal_Gap']:.3f mm\n") print(f"Worst-Case Boundaries: [report['Worst_Case']['Min']:.3f mm, report['Worst_Case']['Max']:.3f mm]") print(f"Worst-Case Total Variation: ±report['Worst_Case']['Tolerance']:.3f mm\n") print(f"RSS Boundaries (Statistical): [report['RSS']['Min']:.3f mm, report['RSS']['Max']:.3f mm]") print(f"RSS Total Variation: ±report['RSS']['Tolerance']:.3f mm\n") print("Component Contribution Report:") print(report['Component_Report'].to_string(index=False)) Use code with caution. 5. Visualizing the Dimensional Distribution