liminfoShaft Design Calculator
Free web tool: Shaft Design Calculator
Parameters
Formula
d = (16n/π · √[4(KfMa/Se)² + 3(KfsTm/Sut)²])^(1/3)
About Shaft Design Calculator
The Shaft Design Calculator determines the minimum required shaft diameter for rotating shafts subjected to combined bending and torsion loading. It implements three widely used fatigue failure criteria: DE-Goodman (most conservative, commonly used in industry), DE-Gerber (less conservative, parabolic failure line), and ASME B106.1M (static yield-based criterion). Inputs include applied torque (T, N·m), bending moment (M, N·m), material yield strength (Sy), ultimate tensile strength (Sut), endurance limit (Se), safety factor (n), and stress concentration factors for bending (Kf) and torsion (Kfs).
The tool is used by mechanical engineers designing power transmission shafts in machines such as gearboxes, pumps, motors, turbines, and conveyor drives. Shaft design requires balancing fatigue resistance with practical standard sizes. After computing the theoretical minimum diameter, the tool automatically rounds up to the nearest standard shaft size from the ISO/ANSI preferred series (10, 12, 15, 17, 20, 25, 30, 35, 40, 45, 50 mm and beyond), so engineers can directly specify a stock dimension.
For the DE-Goodman criterion, the formula is: d = (16n/π × √[4(KfMa/Se)² + 3(KfsTm/Sut)²])^(1/3). Bending moment is treated as fully reversed (alternating) and torque as steady (mean), which is standard for solid rotating shafts. The endurance limit Se should already account for surface finish, size, reliability, and load modification factors before being entered into this tool.
Key Features
- Supports three design criteria: DE-Goodman, DE-Gerber, and ASME B106.1M
- Inputs bending moment (M) and torque (T) in N·m for combined loading
- Accepts separate stress concentration factors for bending (Kf) and torsion (Kfs)
- Uses material properties: yield strength (Sy), ultimate strength (Sut), endurance limit (Se)
- User-defined safety factor n for design margin control
- Displays computed minimum diameter in mm with 0.1 mm precision
- Automatically recommends the nearest standard shaft size from ISO preferred series
- Shows modified alternating moment (Kf×M) and modified mean torque (Kfs×T) used in calculation
Frequently Asked Questions
What is the DE-Goodman criterion for shaft design?
DE-Goodman (Distortion Energy - Goodman) combines the von Mises distortion energy theory with the Goodman fatigue line. It assumes fully reversed bending (alternating stress) and steady torque (mean stress). The formula produces a conservative diameter estimate suitable for most industrial shaft applications.
When should I use DE-Gerber instead of DE-Goodman?
DE-Gerber uses a parabolic (Gerber) fatigue line instead of the linear Goodman line, which is less conservative and may allow a smaller shaft diameter. It is used when test data supports a parabolic failure curve, often in aerospace and precision machinery where weight is critical. For general machinery, DE-Goodman is preferred due to its conservatism.
What does ASME B106.1M criterion calculate?
The ASME B106.1M criterion uses a static yielding approach: d = (32n/π × √[M² + ¾T²] / Sy)^(1/3). It checks for initial yielding rather than fatigue failure. It is appropriate for shafts with low cycle loading or when static overload governs the design rather than infinite-life fatigue.
What is the endurance limit (Se) and how do I determine it?
The endurance limit Se is the maximum stress amplitude below which a material can endure infinite fatigue cycles without failure. For steel, the baseline Se is approximately 0.5 × Sut (up to a limit of 700 MPa). In practice, Se is modified by factors for surface finish, size, reliability, load type, and temperature. Enter the fully corrected Se value into this tool.
What stress concentration factors (Kf and Kfs) should I use?
Kf (fatigue stress concentration factor for bending) and Kfs (for torsion) account for geometric features like shoulders, keyways, grooves, and holes that create local stress amplifications. They are derived from theoretical factors Kt and Kts using notch sensitivity q: Kf = 1 + q(Kt - 1). Values typically range from 1.0 (no stress concentration) to 3.0 or higher for sharp keyways.
Why does the tool round up to standard sizes?
Standard shaft sizes from ISO or ANSI preferred number series are available as stock material, reducing cost and lead time. The tool finds the smallest standard size that meets or exceeds the calculated minimum diameter. Standard sizes used include 10, 12, 15, 17, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 90, 100, 110, 120 mm.
Is bending moment treated as alternating or mean stress?
For a solid rotating shaft, bending creates fully reversed (alternating) stress because each fiber on the shaft surface cycles from tension to compression every revolution. Torque on a steady-load shaft is treated as mean (static) stress. This is the standard assumption in DE-Goodman and DE-Gerber shaft design.
What units does this calculator use?
Torque and bending moment are in N·m. Material strengths (Sy, Sut, Se) are in MPa. The resulting shaft diameter is in millimeters. The calculator internally converts N·m to N·mm (multiplies by 1000) for the diameter formula to output results in mm.