Machine Design and Shop Practice - Exhaustive Study Guide

Welding and Foundation Design

• Welded Joint Efficiency: Welded joints allow for the precise placement of added metal to create an integral structure. For mild metal materials, these joints can develop an efficiency of $100\%$ on any thickness section.

• Equipment Foundation Mass: A common academic and practical rule of thumb for calculating the mass of an equipment foundation is that it should be $3$ to $5$ times the weight of the machinery it is intended to support.

• Oxy-acetylene Gas Consumption (3/8 in. Plate): For welding a $3\,ft$ long seam in a $\frac{3}{8}\,in$ thick plate, where the consumption rate is $9\,ft^3/ft$ for oxygen and $7\,ft^3/ft$ for acetylene, the combined gas consumption is calculated as:

  • $\text{Total} = (9 + 7)\,ft^3/ft \times 3\,ft = 48\,ft^3$

• Oxy-acetylene Gas Consumption (1/2 in. Plate): For a $10\,ft$ long seam in a $\frac{1}{2}\,in$ thick plate with consumption rates of $10\,ft^3/ft$ for oxygen and $8\,ft^3/ft$ for acetylene, the total gas consumption is:

  • $\text{Total} = (10 + 8)\,ft^3/ft \times 10\,ft = 180\,ft^3$

• Cutting Rate and Time: Using an oxy-acetylene cutter with a rate of $10\,in/min$ to divide a $10\,ft \times 20\,ft$ plate into eight pieces of $5\,ft \times 5\,ft$ size requires a total time of $60\,min$.

Mechanics of Materials: Stress, Strain, and Elasticity

• Modulus of Elasticity ($E$): Defined as the ratio of stress ($\sigma$) to strain ($\epsilon$).

  • If $\sigma = 300\,MPa$ and $\epsilon = 0.00138$, the modulus is:

  • $E = \frac{300}{0.00138} = 217.39 \times 10^3\,MPa$

• Tensile Load and Diameter Calculation: For a steel wire $10\,m$ long supporting a tensile load of $2\,KN$, with a stress limit ($\sigma$) of $140\,MPa$, total elongation limit ($\delta$) of $5\,mm$, and $E = 200\,GPa$:

  • Based on stress: $140 = \frac{2000}{A}$, so $A = 14.28\,mm^2$.

  • Based on elongation: $\delta = \frac{PL}{AE} \rightarrow 5 = \frac{2000 \times 10000}{A \times 200000}$, so $A = 20\,mm^2$.

  • The required diameter $d$ based on the larger area ($20\,mm^2$) is approximately $5\,mm$.

• Steel Hanger Area: A member $2\,m$ long carrying an axial load of $18\,KN$ restricted to $104\,MPa$ stress and $1\,mm$ elongation ($E = 200,000\,MPa$) requires a minimum cross-sectional area of $180\,mm^2$.

• Steel Rod Allowable Load: A steel rod $30\,mm$ in diameter ($\phi$) and $800\,mm$ long with a maximum elongation of $1.5\,mm$ allows for a load of approximately $265\,KN$ (calculated value near $274\,KN$ based on available options).

• Definitions:

  • Deformation/Strain: The change in shape or geometry of a body due to the action of a force.

  • Poisson's Ratio: A property that relates lateral strain to longitudinal strain ($\nu = -\frac{\epsilon_{lateral}}{\epsilon_{longitudinal}}$). For a material with $E = 15,000,000\,psi$ in tension and $G = 8,000,000\,psi$ in shear, the ratio is calculated using $G = \frac{E}{2(1+\nu)}$. (Note: Standard calculation yields $\nu = -0.0625$, but specified options include values like $0.25$).

  • Modulus of Rigidity ($G$): The ratio of shear stress to shear strain.

  • Tensile Stress: Defined as the maximum load during a test divided by the original cross-sectional area ($\sigma = \frac{P_{max}}{A_o}$).

Flywheel Design and Kinematics

• Flywheel Rim Speed Limits:

  • Cast iron material: $6000\,fpm$.

  • Cast steel material: $7000\,meters/min$.

• Factor of Safety: Cast iron flywheels are commonly designed with a factor of safety ranging from $10$ to $13$.

• Angular Acceleration ($\alpha$):

  • A wheel accelerating from rest to a speed in $4\,seconds$ with $\alpha = 5\,rad/s^2$ results in a total displacement of $6.36\,rev$.

  • Formula: $\theta = \frac{1}{2} \alpha t^2 = \frac{1}{2}(5)(4^2) = 40\,rad$.

  • $\text{Revolutions} = \frac{40}{2\pi} \approx 6.36\,rev$.

• Punching Operation Acceleration: A flywheel slowing from $120\,rpm$ ($12.57\,rad/sec$) to $102\,rpm$ ($10.68\,rad/sec$) over $4\,seconds$ has an angular acceleration of:

  • $\alpha = \frac{\omega_f - \omega_i}{t} = \frac{10.68 - 12.57}{4} = -0.4725\,rad/sec^2$ (Alternative context suggests $2.22\,rad/sec^2$ or similar calculations based on cycle portions).

• Flywheel Radius: A wheel turning at $360\,rpm$ with a tangential speed of $150.80\,ft/s$ has a radius of $4\,ft$.

  • $\omega = \frac{360 \times 2\pi}{60} = 37.7\,rad/s$

  • $v = r\omega \rightarrow 150.80 = r(37.7) \rightarrow r = 4\,ft$

• Pulley Peripheral Speed: A $5\,ft$ diameter pulley turning at $200\,rpm$ has a speed at its midpoint (at radius $1.25\,ft$) of $26.18\,ft/s$.

Beam Deflection and Bending Moments

• Cantilever Beam Stress: A $1000\,lb$ force at the end of a $10\,ft$ cantilever beam with a section modulus ($Z$) of $8.0\,in^3$ induces a stress of:

  • $M = 1000\,lb \times (10 \times 12)\,in = 120,000\,lb \cdot in$

  • $\sigma = \frac{M}{Z} = \frac{120,000}{8.0} = 15,000\,psi$

• Maximum Bending Moment Formulas:

  • Simply supported beam with total load $W$ uniformly distributed over length $L$: $M_{max} = \frac{WL}{8}$.

  • Bending moment at a section is derived from the sum of the moments of all external forces on one side of that section.

• Deflection Calculations:

  • Restrained beam ($15\,m$, both ends fixed) with a uniform load of $3\,kN/m$ and $EI = 9,000\,kN \cdot m^2$: Maximum deflection is $43.94\,mm$.

  • Cantilever beam ($10\,m$) with concentrated load of $10\,KN/m$ at the free end and $EI = 7,000\,kN/m^2$: Maximum deflection is $476.20\,mm$.

• Shear Equation Differential: The differential of the shear equation is the load on the beam.

Shaft Design and Torsional Analysis

• Linear Shaft Diameter (Torsional Deflection Limit): To transmit $12\,Hp$ at $180\,rpm$ with a torsional deflection of $0.08\,degrees$ per foot length, the required diameter is $2.35\,in$.

• Hollow Shaft Angular Deflection: A hollow shaft ($OD = 14\,cm$, $t = 0.8\,cm$) transmitting $200\,kW$ at $400\,rpm$ over a length of $5\,meters$ has an angular deflection of $1.14\,deg$.

• Countershaft Horsepower: A $1\frac{1}{2}\,inch$ diameter shaft with an allowable stress of $8500\,psi$ running at $15.7\,rad/s$ delivers approximately $13.31\,Hp$.

• Line Shaft Diameter: A shaft transmitting $150\,kW$ at $15\,rps$ ($900\,rpm$) requires a diameter of approximately $3.54\,in$.

• Short Shaft Pulley Speed: A $61\,mm$ diameter shaft transmitting $120\,Hp$ with a $55\,cm$ diameter pulley mounted on it has a linear pulley speed of $1870\,fpm$.

• Shear Stress Distribution: Shear stress induced in a shaft because of an applied couple changes from zero at the center to maximum at the circumference.

• Torsional Design Limit: As a significant consideration in shaft design, the limit for torsional deflection should be in the range of $0.08$ to $1\,degree$.

Metallurgy: Properties and Classification of Metals

• Cast Iron Tensile Strength: Common varieties of cast iron have a tensile strength range of $150$ to $180\,MPa$.

• Deoxidizers: Manganese is the common deoxidizer and cleanser of steel, forming oxides and sulfates that are carried off in the slag.

• Alloying Elements:

  • Stainless Steel: Obtained principally by the use of Chromium.

  • Machining Additives: Machining properties of steel are improved by adding sulfur, lead, and phosphorous.

  • Molybdenum Alloys: Found in SAE43XX and SAE41XX; SAE6XXX and SAE5XXX generally do not contain it.

• Specific Alloys:

  • AISI 2330: Alloy steel used for bolts, studs, and tubing subjected to torsional stresses.

  • SAE 1030: Cheapest and most commonly utilized shaft material with a carbon content of $0.28$ to $0.34\%$.

  • Bronze: Usually a copper-tin alloy.

• Heat Treatments:

  • Stress Relieving: Heating to a subcritical temperature ($1000^{\circ}F$ to $1300^{\circ}F$) and holding to reduce internal residual stresses.

  • Annealing: Heating above the transformation range ($1300^{\circ}F$ to $1350^{\circ}F$) and cooling slowly to soften metal and increase machinability.

Machine Elements and Shop Practice

• Bearings:

  • Journal Bearing Pressure: A $2.5\,in$ diameter by $2\,in$ long journal bearing carrying a $5500\,lb$ load has a bearing pressure of $1100\,psi$.

  • Rated Life ($L_{10}$): The rated life of a bearing changes inversely as the cube of the load.

  • Manufacturing: Steel balls for ball bearings are manufactured by cold heading.

• Keys and Fasteners:

  • Flat Key Length: A $75\,mm$ shaft transmitting $150\,kW$ at $400\,rpm$ with $200\,MPa$ allowable shear stress and $55\,mm$ width requires a key length of $31.83\,mm$.

  • Key Force: A $25\,mm$ square key, $150\,mm$ long on a $100\,mm$ shaft, shears at $200\,MPa$ with a force of $75\,KN$ tangent to a $1\,meter$ pulley rim.

  • Stud Bolts: Ten $19\,mm$ stud bolts on a $250\,mm$ cylinder head with a $50\,MPa$ stress limit allow for an internal pressure of $2888\,KPa$.

• Gears and Sprockets:

  • Addendum: The height of the tooth above the pitch circle.

  • Involute: The curve used as the gear tooth profile, formed by a path of a point on a straight line rolling along a convex base curve.

  • Sprocket Teeth: For high-speed applications, the minimum number of teeth in a sprocket should be $18$ to $24$.

  • Sprocket Distance: The recommended center-to-center distance between sprockets should be no less than $1\frac{1}{2}$ times the diameter of the bigger sprocket.

• Shop Tools:

  • Oilstone: A fine-grained, salty silica rock used for sharpening edge tools.

  • Vickers Hardness: The pyramid indenter apex angle is $136^{\circ}$.

  • Reamer: Tool used in precision work to smooth or enlarge holes.

  • Trammel: A tool with hardened steel points used for scribing or laying off distances.

Thermodynamics and Miscellaneous Theory

• Entropy and Energy Snippets:

  • Water with entropy of $3\,KJ/kg \cdot K$; enthalpy check based on $h_f = 814.93, h_{fg} = 1972.7$.

  • Perfect crystalline solids have zero entropy at absolute zero (Third Law of Thermodynamics).

  • Carnot engine operates between two temperature reservoirs.

  • Thermal cracking is the process of changing heavy oils into gasoline via high temperature and time.

• Standard Values:

  • $1\,radian = 57.29^{\circ}$.

  • Module: Expressed in $mm$ or $mm/\text{number of teeth}$.

  • Tolerance: The total permissible variation in size of a dimension.

  • Kinematic Pairs: Parts that have point or line contact when in motion.

  • Slenderness Ratio: Defined as the ratio of unsupported length to the least radius of gyration ($L/r$).

  • Rankine Formula: Valid up to a slenderness ratio of $120$.

• Miscellaneous:

  • Impact Velocity: For a $1\text{-ton}$ drop hammer with $100\,psi$ air pressure and $12\,in$ diameter cylinder over a $28\,inch$ stroke, the impact velocity is $31.6\,fps$.

  • Steel Plate Weight: The total weight of steel plates measuring \frac{3}{4}\" \times 3' \times 20' is $1838\,lbs$.