Machine design Basics II - Screws, Fasteners, Springs, Belt

Explore lead screws, their design and specifications, and how rotation converts to translation, with square and Acme threads, backlash, and applications in lathe, 3D printer, and jack systems.

Explore lead screw specifications, including square and acme threads, pitch diameter, minor and major diameters, helix and thread angles, and pitch measurements for single and multi-start, right and left-handed designs.

Explore the screw principle as an inclined plane: applying torque to lift a nut, relate pitch and lead angle to movement, and analyze forces with the free body diagram.

Examine force analysis of a power screw by unfolding a thread into an inclined plane, applying static equilibrium with P_r, friction, and normal forces to lift the nut.

Derive the torque needed to raise and lower a load on a screw, using lead, pitch diameter, mean diameter, and the coefficient of friction.

Understand the self locking condition for power screws, where the friction coefficient exceeds the tangent of the lead angle, and how friction influences the efficiency of raising loads.

Derive acme thread equations from the square-thread model by substituting f with f/cos alpha; increasing friction lowers efficiency, yet acme threads are easier to manufacture and more widely used.

Analyze stresses in lead screws, including torque-induced shear and axial stresses at the root diameter, and bending stresses in the threads treated as a cantilever, using pitch and turns.

Analyze the 3D state of stress in the lead screw-nut interface, identify maximum stress at the first turn, and apply von Mises criteria using sigma and tau components.

Describes bearing stress at the screw-nut contact, how to compute the contact area and load distribution among engaged turns, and how friction coefficients of steel and bronze materials influence self-locking.

Explore metric threaded fasteners and power screws, highlighting thread angles, pitch, lead, and self-locking features, and learn how fasteners clamp components under shear, axial, and moment loading.

Torque converts to clamping via compressive plate contact and a tensile preload in the bolt. Preload maintains joint integrity within the bolt's elastic limit.

Explore how axial loads affect a bolted joint by analyzing load versus deflection, showing bolt elongation, plate compression, preload and the elastic limit margin for safe operation.

Learn how bolt stiffness arises from the shank and threaded portion in the grip, and determine the floating fastener stiffness kb from kd and kt.

Derive fixed fastener stiffness by evaluating grip length and the larger of ld or major diameter. Compute kb from kt and kd using the bolt’s cross sections and Young’s modulus.

Assess the stiffness of clamped plates in series and model nonuniform compression with Rodgers' pressure cone, deriving the pressures, cone angle, and disk-element deflections to form effective stiffness equations.

Derive the deflection of a frustum under Rotcher's cone pressure distribution, and express member stiffness as P divided by delta, then combine two in series to obtain joint stiffness.

Apply the Rodgers code to a floating fastener design problem with two members—steel and aluminum—computing three frustum segments and deriving the effective stiffness km from k1, k2, k3.

Understand bolt strength limits and preload, where torque induces tensile load that can reach the elastic limit, causing permanent deformation; learn about proof load, proof strength, and class 4.6–9.8 bolts.

Derive design equations for a bolt joint under external tensile load. Express the bolt load as P_B = C P with C = k_b/(k_b + k_m), and highlight preventing separation.

Relate applied torque to bolt preload to ensure joint integrity by measuring preload via torque or bolt deflection, using the torque coefficient K and friction and thread factors.

Organize the factor of safety and load factor to balance external tensile load with preload and internal tensile forces, preventing joint separation and exceeding the material's proof strength.

Explain how preload sustains voltage joint integrity and how loss mechanisms—improper preload calculation, vibrations, creep relaxation, and corrosion—lead to loosening, and outline design strategies to prevent it.

Explore how helical coil springs enable flexible motion, store and dissipate energy, damp vibrations, and provide restraint on motion across compression, extension, torsion, conical, and dual-rate variants, via stiffness.

explain the stresses in a compression coil spring under load, combining direct shear and torsional shear, highlighting the mean diameter D, wire diameter d, and the stress concentration factor Ks.

Explore the waals factor and curvature correction for compression coil springs, showing how curvature increases stress and how the walls factor adjusts ks to kw with spring index effects.

Derive the relation between spring deflection and force using strain energy and Castigliano's theorem, and obtain the compression coil stiffness formula involving D, d, n, G, and C.

Explore compression coil springs, defining free length, pitch, and solid length; identify end types—open, squared, grounded, and squared plus ground—and distinguish active and inactive coils with their design equations.

Examine presetting that lengthens the spring beyond its free length, compresses to solid height to induce permanent set, and creates residual stresses that boost torsional strength, with fatigue considerations.

Analyze buckling stability of long, slender compression coil springs, identifying the critical lateral deflection y_cr and how the effective slenderness lambda effective governs stability through end conditions and material properties.

Designers limit spring torsion by percent of ultimate tensile strength, with presetting raising allowable torsion from 45% to 60–70% for music wire, while stainless and nonferrous alloys remain lower.

Explore helical coil torsion springs in machine design basics, where ends attach to rotating members, bending stress dominates, and total turns equal body turns plus beta/360 partial end turn.

Explore bending stresses in torsion springs, where inner elements bear the highest stress, and apply Ki factor for spring index to compute sigma = Ki 32 F L /(pi d^3).

Compute the rate of a torsion spring as torque per radian by combining end and body deflections, using the coil's mean diameter, active turns, and Young's modulus.

Explain how torsion springs reduce mean diameter under deflection, ensure clearance with the arbor, and apply material-specific allowable bending stresses and fatigue limits.

Analyze belt drives as flexible power transmission systems, including flat, V, and timing belts. Understand how friction and belt tension produce traction while slip and normal force govern power transfer.

Describe the design equations and notations for a belt drive, including driving rpm N1, driven N2, diameters d and D, tensions F1 and F2, and angle of wrap.

Belting theory derives equations to design belt drives, showing power transfer from driving to driven pulleys via a differential belt tension F1 and F2 and friction.

Perform a radial and tangential force analysis for belting theory, using a small-arc approximation to split F and F+df into tangential and radial components, and derive equilibrium with friction mu.

Derives the belting model equations, solving df/dtheta - mu f = - mu m r^2 omega^2, yielding F1, F2 with hoop tension FC via boundary conditions at the wrap angle.

Derives the relation between belt tension difference and torque to compute the initial tension required for torque transmission, accounting for centrifugal hoop tension and friction through F1 and F2 expressions.

Explain the operating tension versus initial tension graph for belts, showing f1 and f2 lines with different slopes, and identify maximum allowable tension f1a and initial tension fia.

Explore common belt materials such as nylon, rubber, polyurethane, polyester, and Kevlar-reinforced belts, and how coefficient of friction, tension, and center-to-center distance flexibility influence performance in belt drives.

Identify factors shaping belt drive design, including transmitted power, center distance, shaft speeds, layout, service conditions, and speed reduction; apply transmission power equations and safety factors to select belts.

Describe the belt drive design procedure from Shigley's design book, including center distance, pulley sizes, power and speed, belt material selection, tension calculations, and friction checks to prevent slip.

Explore a polyamide a2 belt design problem, calculating wrap angle, velocity, mass per unit length, centrifugal force, design torque, and allowable belt tension to determine the initial tension.

Compute the friction development, showing mu dash 0.198 versus polyamide 0.7 to confirm no slip. Then determine allowable power, factor of safety, and the transmission ratio.

Maintaining the belt's initial tension is essential for sustainable torque transmission; wear and elongation cause slip and sag, which idler pulleys or spring-loaded tensioners and adjusting center-to-center distance help prevent.

Explore v-belt drives with trapezoidal cross-sections, groove contact, higher power transmission, stability, and standard A–E sections, mu_e friction, and pulley geometry like pitch line and sheave diameter.

Explore the design procedure for v-belt drives, calculating pitch length and center distance, selecting cross sections A–E and pulley sizes from standard tables, and applying power and tension factors.

Select belt class and compute pitch length, inner length, center distance, belt velocity, and allowable power using k1 and k2 for a 5 kW drive from 1000 to 800 rpm.

Calculate the design power using H norm, K_s, and D for a soft-start, light-duty belt drive, then size belts and analyze centrifugal tension and belt tensions.