Physics Behind Motion

Disclaimer: The tools and calculators on this site are built on standard engineering textbook principles and are meant for baseline estimation and educational use only. Always seek independent professional validation before taking anything into production. Epiphany Drives doesn't assume any liability for discrepancies, mechanical issues, or accidents resulting from the use of these tools. 

Setting Global Parameters

• Select Calculation Basis: Choose whether you are evaluating your components/system      based on Stress (MPa) or Torque (Nm).
• Define Target Mode: Specify the failure mode you are analyzing. Choose Pitting for contact fatigue (gear flanks or bearings), Bending (gear root fillets), or Both to evaluate them simultaneously.
• Define Steel Quality: Select your material grade. Choosing "Air Melted" or "Vacuum Degassed" will automatically populate the industry-standard material exponents. If you are using specialized alloys or want to execute Bearing Specific Calculations, select      "Custom Values" to manually input exponents.
• Select Material Exponents: Select pitting and bending exponents as per your application. For bearings, you will typically use a custom exponent of 3 (for ball bearings) or 10/3 (for roller bearings).

Module 1: Gear Torque/Stress Scaler

Use this module to quickly scale loads or operational hours based on the Basquin equation.

• Choose your scaling goal: solve for a new target load, or solve for target hours.
• Input your current operating hours and the known stresses or torques.
• Input your target parameters. The calculator will instantly output the scaled      requirements. Pay attention to the warning box; aggressive scaling can inadvertently alter the primary failure mode of your component.

Module 2: Damage Calculator for Duty Cycle

Calculate cumulative fatigue damage across complex, multi-state operations.

• Input pitting and bending limits.
• Paste your duty cycle data directly into the text box or upload .csv file.
• Click calculate to generate a step-by-step breakdown of the fractional damage      contributed by each load case, alongside the total composite damage.

Module 3: Sequential Test Calculator

Determine the exact number of test hours required to prove out a design change or target a specific load level.

• Provide your sequential baseline data, outlining the original load and the new target load for each operational state.
• The output table will dictate exactly how many additional test hours are required at the new stress levels to achieve mathematical damage equivalence.

Module 4: Evaluate Comparative Duty Cycle Severity

Compare multiple duty cycles against a baseline.

• Select the number of duty cycles you wish to compare (up to 5).
• Upload or paste the CSV data for your baseline (Duty Cycle 1) and your subsequent      target cycles.
• The module will output both the Absolute Damage Ratio and the True Severity      normalized over time, telling you exactly how much faster (or slower) a component will accumulate damage under the new cycle.

Module 5: HALT Duty Cycle Generator

Condense multi-load case duty cycle into a single Equivalent Highly Accelerated Life Test (HALT).

• Paste your duty cycle data into the input field.
• Define your targeted test hours (e.g., compressing 3,000 hours multi-load case DC into a 600-hour single load case test) and your test bench RPM.
• The system calculates the exact constant loads required to replicate 1x, 2x, and 3x field damage, generating a redefined, clean CSV output ready for your rig controllers.

Cumulative Damage

Components always operate under multiple loads over the period of their life span. Drivetrain systems, are subjected to multi-load case duty cycles that vary in torque, speed, and duration. To accurately predict the lifespan of these components, and optimal designs, engineers cannot rely on peak load analysis alone. Instead, we must quantify how each distinct operational state slowly consumes the fatigue life of the material.

This calculator is built upon the fundamental principles of cumulative fatigue analysis, utilizing industry-standard scaling to bridge the gap between complex field data and controlled laboratory testing.

The Palmgren-Miner Rule

At the core of our Duty Cycle and Damage modules is the Palmgren-Miner rule. The theorem posits that total fatigue life is exhausted when the sum of the fractional damage from individual stress cycles reaches unity.

While Miner's rule is a highly practical tool, it is important to note its engineering limitations. It assumes that damage accumulates linearly and ignores sequence effects—meaning it does not account for whether a massive shock load occurs at the very beginning of a component's life or near the end. Despite this, when combined with right material exponents, it remains the most robust method for comparative duty cycle severity and durability planning.

Load Scaling and Material Exponents (Basquin's Equation)

To accurately translate stresses across different lifespans or to compress field testing into Highly Accelerated Life Testing (HALT), this suite utilizes the Basquin relation. This method helps to predict how a change in load will proportionally affect the hours to failure.

The relationship is defined as:

N1 * S1^p = N2 * S2^p

Where "N" represents the number of cycles (or hours), "S" represents the applied stress or torque, and "p" is the material-specific exponent.

The exponent "p" is depends on both the failure mode (pitting vs. bending) and the cleanliness of the steel. Contact fatigue (pitting) occurs on the surface of gear flanks or bearing races and is highly sensitive to non-metallic inclusions in the steel. Therefore, moving from standard air-melted steel to vacuum-degassed steel alters the pitting exponent. Root bending fatigue, utilizes a lower exponent range.

By applying these exponents, the HALT Generator module can calculate the equivalent constant test rig load required to reproduce the damage that a component would experience over thousands of hours of variable field use.