MEC223 Design of Machine Element - I: Design of Threaded Joints Notes

Introduction to Threaded Joints\n\n* Definition: A threaded joint is a type of separable joint used to connect two or more machine parts. These parts are held together using threaded fasteners such as bolts, nuts, screws, and studs.\n* Classifications of Threaded Joints:\n * Mechanical Engineering Bolted Joint.\n * Screw Joint.\n * Stud Joint.\n\n# Features of Threaded Joints\n\n* Detachable Nature: These joints are easily detachable, making them ideal for assembly, inspection, repair, or replacement of parts.\n* Reliability: They provide a large clamping force, ensuring the joint is reliable under load.\n* Ease of Operation: The force required to tighten the joint is relatively small regardless of the resulting clamping force.\n* Compactness: They have small overall dimensions, allowing for compact machine construction.\n* Versatility of Positioning: Threads are naturally self-locking. This allows the assembly to be placed in any orientation, including vertical, horizontal, or inclined positions.\n* Manufacturing: They are economical to manufacture and highly standardized across the industry.\n\n# Shortcomings of Threaded Joints\n\n* Stress Concentration: There is a significant stress concentration near the vicinity of the threaded portion of the fastener.\n* Loosening: The joints can become loose when subjected to constant vibrations.\n* Assembly Efficiency: They are considered a main obstacle for efficient automated assembly.\n* DFMA Recommendations: Design for Manufacturing and Assembly (DFMA) guidelines recommend minimizing the number of threaded fasteners used in a product design.\n\n# Elements of Threaded Fasteners\n\n* Primary Components:\n * A bolt.\n * A nut.\n * A washer.\n* Functions of a Washer:\n * Prevents damage to the clamped parts during the assembly process.\n * Distributes the clamping load over a larger surface area on the clamped parts.\n\n# Types of Screw Fastenings\n\n* Through Bolt:\n * Suitable for parts of medium thickness and weak materials.\n * Ideal for components requiring frequent dismantling and reassembly.\n * Commonly known as Machine bolts ($5\,mm$ to $75\,mm$), automobile bolts ($5\,mm$ to $40\,mm$), eye bolts, or carriage bolts.\n* Tap Bolt:\n * Used for thick parts where there is no space to accommodate a nut.\n * The threaded material in the part must be strong enough to hold the bolt.\n * Difference: A tap bolt is turned into a threaded hole, whereas a through bolt is turned into a nut.\n* Stud:\n * Commonly used when one of the parts is thick.\n * The threaded material of the main part must be strong, though the other part may be of a weaker material.\n * Suitable for frequent dismantling and reassembly.\n\n# Cap Screws and Set Screws\n\n* Cap Screws: These are categorized by how the head is engaged:\n * Group 1: Head is engaged externally by a spanner (e.g., Hexagonal head).\n * Group 2: Head is engaged internally or from the end face (e.g., Socket head).\n * Head Shapes: Hexagonal head, Filister head, Button head, Flat head, and Hexagonal Socket Head.\n* Set Screws: These are used specifically to prevent relative motion between two parts.\n\n# Bolt of Uniform Strength\n\n* Design Considerations: Resilience of the bolt is the primary consideration specifically for those subjected to shock and impact loads. The bolt acts like a spring during these conditions.\n* Mathematical Principle: The energy absorbed during elastic deformation ($U$) is proportional to the square of the stress ($\sigma$) induced in the material and the volume ($V$) of the material under stress.\n* Stress Regions in a Standard Bolt:\n * Threaded portion: Diameter is the core diameter ($d_c$). Since d_c < d (nominal diameter), the threaded portion is subject to stress concentration. Most energy is absorbed here.\n * Shank portion: Diameter is $d$. Since d > d_c, there is no stress concentration in the shank, but the strain energy absorbed is linearly proportional to its length.\n* Methods to Increase Shock Absorbing Capacity:\n 1. Reduce the shank diameter to match the core diameter ($d_c$) of the thread or even less.\n 2. Increase the overall length of the shank.\n\n# Locking Devices\n\n* Jam Nut:\n * Procedure: A lower nut is tightened with normal force. An upper nut is then tightened upon it. The upper nut is held with a spanner while the lower nut is slackened back against it. This creates additional friction at the interface.\n* Lock Nut: A nut specialized to resist loosening under torque and vibrations.\n* Castle Nut: Features a cylindrical portion with six slots and a split pin for visual and mechanical security.\n* Split Nut: The nut is tightened, then a slot is opened using a cap screw. This deformation introduces additional friction into the threads.\n* Set Screw Locking: Uses a set screw and an elastic piece (often copper or lead) to lock the nut in place.\n* Spring Washer: Consists of a hardened steel ring with a cut at a $15^{\circ}$ angle to maintain tension.\n\n# Terminology of Screw Threads\n\n* Major Diameter ($D$ or $d$): The largest diameter of the thread.\n* Minor Diameter ($D_c$ or $d_c$): The smallest diameter of the thread (core diameter).\n* Pitch Diameter ($D_p$ or $d_p$): An imaginary diameter where thread width equals space width.\n* Pitch ($p$): The distance between corresponding points on adjacent threads.\n* Other terms: Thread angle, Root, Crest.\n\n# Standard Dimensions of ISO Metric Threads\n\n* Coarse Series (Designated as "M" + Nominal Diameter):\n * M4: Pitch $0.70$, Tensile stress area $8.78\,mm^2$.\n * M6: Pitch $1.00$, Tensile stress area $20.10\,mm^2$.\n * M20: Pitch $2.50$, Tensile stress area $245\,mm^2$.\n * M36: Pitch $4.00$, Tensile stress area $817\,mm^2$.\n * M100: Pitch $6.00$, Tensile stress area $7000\,mm^2$.\n* Fine Series (Designated as "M" + Diameter x Pitch):\n * M6 x 0.75: Pitch $0.75$, Tensile stress area $22.0\,mm^2$.\n * M16 x 1.5: Pitch $1.50$, Tensile stress area $167\,mm^2$.\n * M24 x 2: Pitch $2.00$, Tensile stress area $384\,mm^2$.\n\n# Analysis of Bolted Joint\n\n* Assumptions for Analysis:\n 1. Each thread turn in contact with the nut supports an equal amount of load.\n 2. There is no stress concentration (idealized).\n 3. Yield strength in shear ($S_{sy}$) is half of yield strength in tension ($S_{yt}$) per Maximum Shear Stress Theory ($S_{sy} = 0.5 \times S_{yt}$).\n 4. Failure occurs in the bolt threads, not the nut threads.\n* Maximum Tensile Stress Calculation:\n $\sigma_t = \frac{P}{\frac{\pi}{4} \times d_c^2}$\n Permissible stress based on Factor of Safety ($f_s$):\n $\sigma_t = \frac{S_{yt}}{f_s}$\n* Nut Height ($h$): Determined by equating the tension strength of the bolt to the shear strength of the threads. Standard hex nut height is approximately $0.8 \times d$.\n\n# Numerical Problems and Solutions\n\n* Eye Bolt Design Problem 1:\n * Given: Load $P = 8\,kN$ (later used as $10\,kN$ in solution), $S_{yt} = 400\,N/mm^2$, $f_s = 6$.\n * Permissible Stress: $\sigma_t = \frac{400}{6} = 66.67\,N/mm^2$.\n * Core Diameter Calculation: $66.67 = \frac{10000}{\frac{\pi}{4} \times d_c^2} \Rightarrow d_c = 13.82\,mm$.\n * Nominal Diameter: $d = \frac{d_c}{0.8} = \frac{13.82}{0.8} = 17.27\,mm$.\n * Standard Selection: M20 bolt.\n\n* Plate Fastening Problem:\n * Given: $P = 5\,kN$, 2 bolts, $S_{yt} = 400\,MPa$, $f_s = 5$.\n * Permissible Shear Stress: $\tau = \frac{0.5 \times 400}{5} = 40\,N/mm^2$.\n * Diameter calculation: $5000 = 2 \times (\frac{\pi}{4} \times d^2) \times 40 \Rightarrow d = 8.92\,mm$.\n * Standard Selection: M10 bolt.\n\n# Eccentrically Loaded Bolted Joints in Shear\n\n* Core Logic: An eccentric force is equivalent to a primary force ($P$) acting at the Center of Gravity (C.G.) and a moment ($P \times e$) about the C.G.\n* Primary Shear Force ($P'$):\n $P' = \frac{P}{n}$ (where $n$ is the number of bolts).\n* Secondary Shear Force ($P''$):\n * Assumed proportional to the distance from the C.G.\n * $P'' = \frac{(P \times e) \times r}{\sum r^2}$.\n* Resultant Shear Force: Calculated via vector addition:\n $P_{res} = \sqrt{(P')^2 + (P'')^2 + 2 \times P' \times P'' \times \cos(\theta)}$\n\n# Torque Requirements for Tightening\n\n* Total Torque ($M_t$): Sum of torque to overcome thread friction ($M_{t1}$) and torque to overcome collar friction between nut and washer ($M_{t2}$).\n* Assumptions for ISO Metric Threads: Friction coefficient $\mu = 0.15$. Calculations often involve uniform wear theory for the nut-washer interface.\n\n# Questions & Discussion\n\n* Q1: The designation M20 means?\n * Answer: (a) metric coarse threads of 20 mm outside diameter.\n* Q2: The largest diameter of external or internal screw thread is called?\n * Answer: (a) major diameter.\n* Q3: The designation M36 x 2 means?\n * Answer: (a) metric fine threads of 36 mm outside diameter and 2 mm pitch.", "title": "MEC223 Design of Machine Element - I: Design of Threaded Joints Notes"}