COREN Mechanical flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Normal stress formula

Normal stress equals axial force divided by cross-sectional area, σ = F/A. It acts perpendicular to the cut surface and is tensile when the force pulls away from the section.

Section modulus

Section modulus S equals I divided by the distance c from the neutral axis to the extreme fiber. Bending stress is then σ = M/S, useful for comparing beam shapes quickly.

Polar moment of inertia

For a solid round shaft, J = πd⁴/32. It measures resistance to torsion, and torsional shear stress is τ = Tc/J with twist θ = TL/(GJ).

Thermal stress, fully restrained

When a member is fully constrained against expansion, the induced stress is σ = EαΔT. The sign is compressive on heating and tensile on cooling.

Bearing L10 life

The rating life L10 is the number of revolutions that 90 percent of a group of identical bearings reach or exceed. L10 = (C/P)^p million revolutions.

Allowance versus tolerance

Allowance is the intentional difference between the sizes of mating parts, set by design. Tolerance is the permitted manufacturing variation around a nominal dimension.

Carnot efficiency limit

No heat engine operating between a hot reservoir at T_H and a cold reservoir at T_L can exceed η = 1 − T_L/T_H. Temperatures must be absolute.

Otto cycle efficiency

For the ideal air-standard Otto cycle, efficiency is 1 − r^(1−k), where r is compression ratio and k is specific heat ratio. Higher compression ratio raises efficiency.

Composite wall resistance

Conduction through layers in series adds thermal resistances R = L/(kA). Heat flow equals the overall temperature difference divided by the sum of resistances.

Nusselt number meaning

The Nusselt number Nu = hL/k is the dimensionless convection heat transfer coefficient. It represents the ratio of convective to conductive heat transfer across a fluid layer.

Reynolds number regimes

Re = ρVD/μ classifies internal flow. Values below about 2300 are laminar, 2300 to 4000 transitional, and above 4000 turbulent in a circular pipe.

Darcy-Weisbach equation

Major head loss in a pipe is h_f = f(L/D)(V²/2g). The friction factor f depends on Reynolds number and relative roughness, read from the Moody chart.

NPSH and cavitation

Cavitation occurs when local pressure falls below vapor pressure. Available net positive suction head must exceed the pump's required NPSH to prevent vapor bubbles and damage.

Parallel-axis theorem

The moment of inertia about any axis equals that about a parallel centroidal axis plus mass times the square of the distance: I = I_cm + md².

Coefficient of restitution

The coefficient e is the ratio of relative separation velocity to relative approach velocity after impact. e equals one for elastic and zero for perfectly plastic collisions.

Damping ratio definition

The damping ratio ζ = c/(2√(km)) compares actual damping to critical damping. Systems are underdamped below one, critically damped at one, and overdamped above.

Resonance condition

Resonance occurs when the excitation frequency approaches a system natural frequency. Amplitude peaks sharply for low damping and can cause rapid fatigue or structural failure.

Grashof linkage condition

A four-bar linkage has at least one fully rotating link when the shortest plus longest link lengths do not exceed the sum of the other two.

Static versus dynamic balance

Static balance requires the center of mass to lie on the rotation axis. Dynamic balance also requires zero products of inertia, so no couple arises at speed.

GD&T maximum material condition

MMC is the condition where a feature contains the maximum amount of material, such as the smallest hole. A modifier at MMC grants bonus tolerance as size departs from MMC.

Bend allowance formula

Bend allowance is θ(R + K·T) with θ in radians, R the inside radius, T thickness, and K the neutral-axis factor. It gives the flat-pattern length of the bend arc.

Surface roughness Ra

Ra is the arithmetic average of profile deviations from the mean line over a sampling length. Lower Ra means a smoother surface and generally higher finishing cost.

Hole-basis fits

In the hole-basis system the hole is the basic size with tolerance letter H. Shaft letters set the fit: a through c gives clearance, h transition, and p through z interference.

Casting draft angle

Draft is a slight taper on vertical pattern faces, typically one to three degrees, allowing the pattern to be withdrawn without tearing the mold.

Von Mises criterion

The distortion-energy theory predicts yielding when the von Mises stress equals yield strength. For plane stress it equals the square root of σ² plus three times τ².

Goodman fatigue line

The Goodman criterion linearly connects alternating stress over endurance limit plus mean stress over ultimate strength, equaling one. It is common for conservative fatigue design.

Fillet weld throat

The throat of an equal-leg fillet weld is 0.707 times the leg size. Shear stress on the throat area governs the design strength of the weld.

Helical spring rate

Spring rate k = Gd⁴/(8D³N_a), where G is shear modulus, d wire diameter, D mean coil diameter, and N_a the number of active coils.

Thread tensile stress area

The tensile stress area of a unified thread is approximately 0.7854(d − 0.9743/n)², where d is nominal diameter and n is threads per inch.

Process capability Cpk

Cpk measures centering relative to specification limits: the lesser of (USL − μ)/(3σ) and (μ − LSL)/(3σ). Values below 1.33 indicate inadequate capability.

Gauge repeatability and reproducibility

Repeatability is variation when one operator measures one part repeatedly. Reproducibility is variation between operators. Both are compared with tolerance in a gauge R&R study.

Reliability exponential model

For a constant failure rate λ, reliability is R(t) = e^(−λt) and MTBF equals 1/λ. This model fits the useful-life region of the bathtub curve.