The maximum torque the hollow shaft can transmit is:
0
Understanding Hollow Shaft Torque Calculation
In mechanical engineering, shafts are critical components used to transmit power and torque from one part of a machine to another. While solid shafts are common, hollow shafts are often preferred in high-performance applications like automotive driveshafts and aerospace engineering due to their superior strength-to-weight ratio.
The Physics of Torsion
When a shaft is subjected to a twisting force, it experiences shear stress. Interestingly, the stress is not uniform across the cross-section; it is zero at the center (neutral axis) and reaches its maximum value at the outer surface. Because the material near the center of a solid shaft carries very little stress, removing it to create a hollow shaft significantly reduces weight with a minimal loss in torque capacity.
The Formula
The torque capacity of a hollow shaft is calculated using the Torsion Equation. The specific formula used in this calculator is:
T = (π × τ × (D⁴ – d⁴)) / (16 × D)
T: Torque (N·m)
τ (tau): Maximum allowable shear stress (MPa)
D: Outer diameter of the shaft
d: Inner diameter of the shaft
Practical Example
Imagine you are designing a transmission shaft with an outer diameter of 100mm and an inner diameter of 80mm. If the steel has an allowable shear stress of 60 MPa, the calculation would look like this:
Calculate D⁴: 100,000,000
Calculate d⁴: 40,960,000
Calculate the difference: 59,040,000
Multiply by π and stress (60): 11,128,494,628
Divide by (16 * 100): 6,955,309 N·mm
Final Result: Approximately 6,955 N·m
Why Choose a Hollow Shaft?
Hollow shafts are more efficient for power transmission because they concentrate the material where the stress is highest—the outer diameter. This makes them ideal for:
Weight Reduction: Critical for aircraft and racing vehicles.
Internal Routing: The hollow center can be used to pass cooling fluids, electrical wires, or smaller internal shafts.
Higher Resonant Frequency: Hollow shafts are often stiffer for their weight, which helps avoid vibration issues at high RPMs.
function calculateTorque() {
var D = parseFloat(document.getElementById("outerDia").value);
var d = parseFloat(document.getElementById("innerDia").value);
var tau = parseFloat(document.getElementById("shearStress").value);
var resultBox = document.getElementById("resultBox");
var torqueDisplay = document.getElementById("torqueResult");
var polarDisplay = document.getElementById("polarMoment");
if (isNaN(D) || isNaN(d) || isNaN(tau)) {
alert("Please enter valid numerical values for all fields.");
return;
}
if (d >= D) {
alert("Inner diameter must be smaller than the outer diameter.");
return;
}
if (D <= 0 || tau <= 0) {
alert("Dimensions and stress must be greater than zero.");
return;
}
// Calculation in N-mm
// Formula: T = (PI * tau * (D^4 – d^4)) / (16 * D)
var dPow4 = Math.pow(d, 4);
var DPow4 = Math.pow(D, 4);
var torqueNmm = (Math.PI * tau * (DPow4 – dPow4)) / (16 * D);
// Convert N-mm to N-m for standard display
var torqueNm = torqueNmm / 1000;
// Polar Moment of Inertia J = PI/32 * (D^4 – d^4)
var polarJ = (Math.PI / 32) * (DPow4 – dPow4);
torqueDisplay.innerHTML = torqueNm.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}) + " N·m";
polarDisplay.innerHTML = "Polar Moment of Inertia (J): " + polarJ.toLocaleString(undefined, {maximumFractionDigits: 0}) + " mm⁴";
resultBox.style.display = "block";
}