The Shaft Keyway Shear Stress & Key Length Sizer provides an interactive three-variable algebraic modeling interface for exploring torsional load transmission, shaft keyway shear proportions, and mechanical coupling geometry.

### Algebraic Ratio Formulation The component evaluates mechanical parameters using three generalized algebraic relationships: - Primary Metric: $(val_1 \times val_2) / \max(0.01, val_3)$. In shaft coupling modeling, this represents transmitted torsional shear load scaled relative to allowable shear stress or safety margin. - Geometric Mean (Secondary Index): $\sqrt{\max(0, val_1 \times val_2)}$, modeling geometric mean cross-sectional keyway dimensions. - Efficiency Ratio (%): $\min(100, \max(0, (val_1 / (val_1 + val_2)) \times 100))$, modeling proportional shear capacity utilization.

### Note on Mechanical Engineering & ASME B17.1 Keyway Sizing This calculator computes a generalized three-parameter algebraic proxy. In certified mechanical drive design, square and rectangular parallel keyways (governed by standards like ASME B17.1 or DIN 6885) require precise torsional mechanics: - Transmitted Torque: $T = \frac{63{,}025 \times \text{HP}}{\text{RPM}}$ (in-lb) or $T = \frac{9550 \times \text{kW}}{\text{RPM}}$ (N-m) - Tangential Force on Key: $F = \frac{2 T}{d}$, where $d$ is shaft diameter - Key Shear Stress: $\tau = \frac{F}{w \times L}$, where $w$ is key width and $L$ is key length - Key Compressive (Crushing) Stress: $\sigma_c = \frac{2 F}{t \times L}$, where $t$ is key height - Required Key Length: $L = \frac{2 T}{d \times w \times \tau_{\text{allow}}}$

### Worked Numeric Example Using default component parameter values: - Primary Dimension / Load ($val_1$): 100 - Operating Coefficient ($val_2$): 20 - Safety Factor / Loss Ratio ($val_3$): 5 - Evaluated Outputs: - Primary Metric: $(100 \times 20) / 5 = 400.00$ - Geometric Mean: $\sqrt{100 \times 20} = \sqrt{2000} \approx 44.72$ - Efficiency Ratio: $(100 / (100 + 20)) \times 100 = 83.33\%$

### In-Browser Calculation Note All mechanical parameters and algebraic ratios evaluate locally within your web browser with zero server data transit.