Shafts, Fits and Torque Transmission

Worked Engineering Derivation:

**Question:** Calculate nominal torsional shaft stress using T=180 N m, diameter=0.032 m. Using the explicit relationship for this simplified case, the arithmetic is `16*180/(pi*0.032**3)/1e6`. The computed result is **27.98 MPa**. This is a synthetic, rounded result; it is not a measured or independently certified design capacity. Recalculate with an independent calculator before passing it into a later sizing step. A result outside a plausible physical range is evidence that units or assumptions may be wrong, not automatically a new discovery. **Interpretation:** The number answers only the posed arithmetic question. A design release would require a defined allowable, actual load spectrum, material condition, geometric tolerances and a standard-appropriate assessment. The main danger in this particular lesson is that calculating with diameter in millimetres while using N*m without conversion creates a billion-fold scale error. A responsible notebook records both the numerical output and the reason why the model is incomplete. For a learner, try replacing a primary load with 80% and 120% of its base value; check whether the response is linear, quadratic or more sensitive, and explain what happens to the corresponding margin.

Worked Engineering Derivation:

**Question:** Calculate shaft combined von Mises stress using M=110 N m, T=180 N m, d=0.04 m. Using the explicit relationship for this simplified case, the arithmetic is `sqrt((32*110/(pi*0.04**3))**2+3*(16*180/(pi*0.04**3))**2)/1e6`. The computed result is **30.36 MPa**. This is a synthetic, rounded result; it is not a measured or independently certified design capacity. Recalculate with an independent calculator before passing it into a later sizing step. A result outside a plausible physical range is evidence that units or assumptions may be wrong, not automatically a new discovery. **Interpretation:** The number answers only the posed arithmetic question. A design release would require a defined allowable, actual load spectrum, material condition, geometric tolerances and a standard-appropriate assessment. The main danger in this particular lesson is that applying pure-torsion sizing to a bent shaft underestimates equivalent stress. A responsible notebook records both the numerical output and the reason why the model is incomplete. For a learner, try replacing a primary load with 80% and 120% of its base value; check whether the response is linear, quadratic or more sensitive, and explain what happens to the corresponding margin.

Worked Engineering Derivation:

**Question:** Calculate beam deflection screen using F=500 N, L=0.4 m, E=210 GPa, d=0.025 m. Using the explicit relationship for this simplified case, the arithmetic is `500*0.4**3/(48*210e9*(pi*0.025**4/64))*1e3`. The computed result is **0.1656 mm**. This is a synthetic, rounded result; it is not a measured or independently certified design capacity. Recalculate with an independent calculator before passing it into a later sizing step. A result outside a plausible physical range is evidence that units or assumptions may be wrong, not automatically a new discovery. **Interpretation:** The number answers only the posed arithmetic question. A design release would require a defined allowable, actual load spectrum, material condition, geometric tolerances and a standard-appropriate assessment. The main danger in this particular lesson is that ignoring bearing compliance and concentrated loads gives falsely small predicted deflection. A responsible notebook records both the numerical output and the reason why the model is incomplete. For a learner, try replacing a primary load with 80% and 120% of its base value; check whether the response is linear, quadratic or more sensitive, and explain what happens to the corresponding margin.

Worked Engineering Derivation:

**Question:** Calculate parallel key nominal shear using T=120 N m, d=0.03 m, b=0.008 m, L=0.045 m. Using the explicit relationship for this simplified case, the arithmetic is `2*120/(0.03*0.008*0.045)/1e6`. The computed result is **22.22 MPa**. This is a synthetic, rounded result; it is not a measured or independently certified design capacity. Recalculate with an independent calculator before passing it into a later sizing step. A result outside a plausible physical range is evidence that units or assumptions may be wrong, not automatically a new discovery. **Interpretation:** The number answers only the posed arithmetic question. A design release would require a defined allowable, actual load spectrum, material condition, geometric tolerances and a standard-appropriate assessment. The main danger in this particular lesson is that using key length without accounting for the actual loaded contact length exaggerates capacity. A responsible notebook records both the numerical output and the reason why the model is incomplete. For a learner, try replacing a primary load with 80% and 120% of its base value; check whether the response is linear, quadratic or more sensitive, and explain what happens to the corresponding margin.

Worked Engineering Derivation:

**Question:** Calculate coupling transmitted power using torque=110 N m, speed=900 rpm. Using the explicit relationship for this simplified case, the arithmetic is `110*(900*2*pi/60)/1000`. The computed result is **10.37 kW**. This is a synthetic, rounded result; it is not a measured or independently certified design capacity. Recalculate with an independent calculator before passing it into a later sizing step. A result outside a plausible physical range is evidence that units or assumptions may be wrong, not automatically a new discovery. **Interpretation:** The number answers only the posed arithmetic question. A design release would require a defined allowable, actual load spectrum, material condition, geometric tolerances and a standard-appropriate assessment. The main danger in this particular lesson is that choosing a flexible coupling solely from torque rating overlooks shaft reactions and speed limits. A responsible notebook records both the numerical output and the reason why the model is incomplete. For a learner, try replacing a primary load with 80% and 120% of its base value; check whether the response is linear, quadratic or more sensitive, and explain what happens to the corresponding margin.