Mechanical Design: Shafts, Bearings, Gears, Springs, and Fasteners
Key Takeaways
- Mechanical Design and Analysis is one of the largest FE Mechanical domains, so component-level formulas deserve timed practice.
- Shaft design starts with torque, bending, speed, stress concentration, and fatigue context.
- Bearing life is highly sensitive to load, so equivalent load and life exponent must be handled carefully.
- Gears require speed ratio, pitch geometry, transmitted load, and awareness of bending and contact stress.
- Springs combine stiffness, deflection, shear stress, and stored energy; wire diameter has a strong effect.
- Fastener questions require load path, preload concept, shear versus tension, and stress area recognition.
Component design is applied mechanics
FE Mechanical design questions are not separate from statics, dynamics, and mechanics of materials. They use those topics inside components: shafts, bearings, gears, springs, fasteners, couplings, and welded or pressure-containing parts. Start every problem by naming the component and the likely failure mode. A shaft may fail in torsion, bending fatigue, keyway stress concentration, excessive deflection, or critical speed. A bolt may fail in tension, shear, bearing, thread stripping, or by joint separation.
| Component | First questions to ask |
|---|---|
| Shaft | What torque, bending moment, diameter, speed, and fatigue condition exist? |
| Bearing | What equivalent load, life target, speed, and bearing type are assumed? |
| Gear | What speed ratio, pitch diameter, tooth count, pressure angle, and transmitted load apply? |
| Spring | What deflection, rate, mean diameter, wire diameter, and active coils are given? |
| Fastener | Is the bolt loaded in tension, shear, bearing, or preload-controlled joint separation? |
Shafts and power transmission
Shaft problems often begin with power and speed. Convert speed to angular velocity, then use P = T omega to find torque. For a solid circular shaft in torsion, maximum shear stress scales with T/d^3. That cubic diameter relationship means a small diameter change can have a large stress effect. If a pulley or gear load is also present, include bending. For fatigue, watch for rotating bending, keyways, shoulders, surface finish, and stress concentration.
The handbook can help with torsion equations and section properties, but it will not decide whether bending must be combined with torque. Read the setup. If forces act transverse to the shaft, there is bending even when the question emphasizes transmitted power.
Bearings and gears
Bearing questions frequently use L10 life, the life exceeded by 90 percent of a population under specified conditions. For ball bearings, life varies approximately with (C/P)^3. For roller bearings, the exponent is commonly larger. The exam may give the equation; your job is to apply the load ratio correctly. Increasing load sharply reduces life.
Gears require kinematic and force thinking. For meshing gears, pitch-line velocity is common at the contact point. Tooth count and pitch diameter control speed ratio for a given module or diametral pitch. Transmitted tangential force comes from torque divided by pitch radius. Bending stress at the tooth root and contact stress on the tooth surface are different failure checks.
Springs and fasteners
Helical compression spring rate increases strongly with wire diameter and decreases with larger mean coil diameter and more active coils. If the formula includes d^4, a small wire-diameter error creates a large stiffness error. Also separate spring rate from maximum shear stress and from energy storage.
Bolted joints require load-path judgment. A simple direct-shear problem may divide load among bolts, but an eccentric bracket creates unequal bolt loads. A preloaded joint may keep external load from fully increasing bolt tension until members separate. For FE purposes, recognize tension stress area, shear area, bearing on connected plates, and the role of washers, thread engagement, and preload.
Fast exam workflow
- Name the component and failure mode.
- Convert power, speed, force, and length units early.
- Search the handbook for the component term if needed.
- Use geometry that matches the actual part, such as solid versus hollow shaft.
- Check whether the answer should be a stress, load, life, speed ratio, or size.
This sequence prevents the common design error: doing correct algebra for the wrong component model.
A shaft transmits 30 kW at 600 rpm. Which quantity should be found before using a torsional shear stress equation?
For a ball bearing using L proportional to (C/P)^3, what happens to predicted life if the equivalent load is increased by 25 percent with C unchanged?
A helical compression spring formula shows k proportional to d^4, where d is wire diameter. If all else stays constant, what is the main design implication?