Skip to main content
CalcPro

Hertzian Contact Stress: Sphere-on-Flat Calculator

Easily calculate and compute hertzian contact stress: sphere-on-flat calculator with accurate equations, live formulas, and expert guidance.

Calculated Result
2,395.1 MPa

Peak Hertzian Contact Pressure (p_0)

Peak Hertzian Contact Pressure (p_0)

2,395.1 MPa

Contact Radius Mm

0.489

Max Subsurface Shear Stress Mpa

742.5

Peak Shear Depth Below Surface Mm

0.235

Yield Status

ELASTIC CONTACT REGIME

2,395.1 — MPa

Calculation Breakdown

  1. Applied FormulaDetermines the elastic contact patch radius, peak central pressure, and maximum subsurface shear stress for a spherical indenter or ball bearing on a flat plane.p_0 = \frac{3 F_N}{2 \pi a^2} = \left( \frac{6 F_N E^{*2}}{\pi^3 R^2} \right)^{1/3}, \quad a = \left( \frac{3 F_N R}{4 E^*} \right)^{1/3}

Hertzian Sphere-Flat Stress Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.05991.2k1.8k2.4kPeak Hertzian Contact Pressure (p_0)

What Is the Hertzian Contact Stress: Sphere-on-Flat Calculator?

This tool computes hertzian contact stress: sphere-on-flat calculator with high precision arithmetic.

How Does the Hertzian Contact Stress: Sphere-on-Flat Calculator Work?

Determines the elastic contact patch radius, peak central pressure, and maximum subsurface shear stress for a spherical indenter or ball bearing on a flat plane.

Hertzian Contact Stress: Sphere-on-Flat Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

p0=3FN2πa2=(6FNE∗2π3R2)1/3,a=(3FNR4E∗)1/3p_0 = \frac{3 F_N}{2 \pi a^2} = \left( \frac{6 F_N E^{*2}}{\pi^3 R^2} \right)^{1/3}, \quad a = \left( \frac{3 F_N R}{4 E^*} \right)^{1/3}

Determines the elastic contact patch radius, peak central pressure, and maximum subsurface shear stress for a spherical indenter or ball bearing on a flat plane.

How to Use the Hertzian Contact Stress: Sphere-on-Flat Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Hertzian Contact Stress: Sphere-on-Flat Calculator Example

Input Values:

sphereRadiusMm:15
normalLoadNewtons:1200
sphereModulusGpa:210
flatModulusGpa:210
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required MPa.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

\n

Related Calculators

Explore more tools and calculators in Technology Calculators

Length Converter

Convert length and distance between metric and imperial units including meters, feet, inches, kilometers, miles, and yards with exact SI definitions.

Percentage Calculator

Calculate percentages: what % X is of Y, P% of X, % change, discount price, and percentage points.

Temperature Converter

Convert temperatures between Celsius (°C), Fahrenheit (°F), Kelvin (K), and Rankine (°R) with step-by-step thermodynamic formulas.

Wien Bridge Oscillator Frequency & Barkhausen Stability Calculator

Calculates the oscillation frequency f₀, non-inverting op-amp voltage gain A_v, and verifies Barkhausen stability criterion for Wien bridge circuits.

Schmitt Trigger Inverting Comparator Hysteresis Thresholds Calculator

Calculates the upper trip point (V_TP), lower trip point (V_TN), and hysteresis voltage band V_H for inverting op-amp Schmitt trigger circuits.

Active Sallen-Key 2nd-Order Low-Pass Filter Cutoff & Q Calculator

Calculates the corner cutoff frequency f_c, quality factor Q, damping factor ζ, and response shape (Butterworth, Bessel, Chebyshev) for Sallen-Key low-pass filters.