Introduction to Pin Joints

Joints made by rivets or welding form a rigid joint, while a pin joint permits movement along the axis of the pin. These joints join two parts under tensile loads. Examples of a pin joint are, cross head, valve rod, and eccentric in a steam engine, a cycle chain, etc. The most commonly used pin joint is the knuckle joint, whose design is described in this chapter.

Knuckle Joint

Knuckle joint consists of an eye on one end and a forked end on other side (Figure 13.1). Each end has a hole in it. Both the ends are placed such that the holes are aligned in one line. A circular pin is inserted in the holes to form a pin joint. Then, a collar is placed over the protruding length of the pin. A thin tapered circular pin is inserted in the hole drilled in the collar and the main pin. This prevents the main pin from coming out of the hole. The ends of the knuckle joint are generally made octagonal and then square near the eye and forked ends, as shown in Figure 13.1 and Figure 13.2.

Design Procedure for a Knuckle Joint

Rather than the theoretical analysis, some empirical relations have been established after experience and are used to get the dimensions of the knuckle joint. These relations are marked in Figure 13.2. Thus, the design consists of calculating sizes for the given force P by these relations and then checking for different possible failures.

Introduction

Spring is an elastic machine element, which deflects when loaded, and stores energy and releases it when it comes to its original position. They are used for many applications as given below:

• a. In automobiles, to absorb the road shocks and vibrations.

• b. Used to measure the load, for example, a spring balance and load transducers.

• c. To keep any machine element pressed or stretched, like engine valve and clutches.

• d. Used to store energy and use when required, for example, clocks and toys.

Classification of Springs

a. According to deflection due to load

• • Compression spring Gets compressed with load [Figure 22.1(a)]

• • Tension spring Gets elongated with load [Figure 22.1(b)]

• • Torsional spring Gets twisted when turned at one end, while the other end is fixed [Figure 22.1(c)]

• • Spiral spring It is of spiral shape, and gets twisted with load [Figure 22.1(d)]

• • Torsion bar A long rod fixed at one end and twisted at the other end.

b. According to geometrical shape

• • Cylindrical helical spring The wire is wound in a helical fashion [Figure 22.1(a)]. The outside diameter remains constant.

• • Conical helical spring The wire is wound in a helical fashion, but the outside diameter reduces [Figure 22.2(a)] and Plate 22.1.

• • Double conical helical spring The wire is wound in a helical fashion, but the outside diameter first reduces and then again increases [Figure 22.2(b)].

• • Leaf spring Flat leaves of different lengths in an arc shape are stacked one over the other [Figure 22.2(c)]. The load is applied at the ends or at the center.

Torsional Shear Stresses

When a machine member is twisted, shear stress is developed. Because it is developed due to torsion, the stress is called torsional shear stress. Its value is zero at neutral axis and increases as its distance from its neutral axis increases. Thus, the stress is the maximum at the outer surface (Figure 7.1).

If a rod is fixed at one end to take the reaction torque, as shown in Figure 7.1, it gets twisted by an angle q due to torque at the other end. The torque and the shear stress are related as:

Design for Rigidity

A shaft is not only designed for strength to bear the torsional shear stresses, but it has to be rigid enough as well, such that it does not twist beyond a certain twist angle. Rigidity can be calculated using the following equation:

The term (G × J) is called the torsional rigidity of a shaft.

Design of a Hollow Shaft

For a hollow shaft having outside diameter D and inside diameter d, the design procedure is same as that for solid shaft, but the polar moment of inertia is calculated as under:

From the given allowable stress t and assuming a suitable ratio of inside to outside diameter k (about 0.5), outside shaft diameter D can be calculated for the required torque.

Torsion of Non-Circular Shafts

Some machine components are not circular, but are subjected to torsion.

Introduction

A leaf spring is made of many rectangular steel strips of different lengths (called leaves) stacked one over the other. The length, cross section, and number of strips depend on the load to be supported. The leaves are bent in elliptical shape and, hence, the leaf spring is also known as elliptical spring. Helical spring cannot take any lateral force, while a leaf spring can take lateral force also, hence, is widely used in the suspension of automobiles, railway carriages, etc.

The longest leaf, called the master leaf, is at the top and the other leaves of calculated length, called graduated leaves, are placed below the master leaf. The topmost leaf is provided with a circular eye at each end for fixing (Figure 23.1). The ends of the master leaf can also be straight for some applications. The smallest leaf is at the bottom. The leaves are clamped together with U-shaped clamps to keep them aligned. Sometimes, one or two extra full-length leaves are provided below the master leaf to take transverse shear force. Leaves are kept in their position by a center clamp or U bolts.

Each leaf of the spring is made circular with radius of curvature R. Vertical distance from the center of the upper-most leaf to the line joining the bottom of eye is called camber y. There is a difference between the terms spring arch and spring camber. Each is measured when the spring is without any external load.

Arch is measured from the center of the line joining center of eyes, to center of the upper surface of top leaf.

Cotter Joint

For applications where the machine elements are to be detached whenever desired, temporary joints are used. Riveted and welded joints are permanent joints. Threaded fasteners are one type of temporary joints and are discussed in Chapter 16. Cotter joints are used to join two rods having tensile or compressive loads. They cannot be used, if the members rotate. A typical application of a cotter joint can be seen in a piston rod joined with a cross head of a steam engine and pedal crank of a bicycle (shown by arrow in Plate 12.1).

Types of Cotter Joints

• Sleeve and cotter joint

• Socket and spigot joint

• Gib and cotter joint Cotter

A cotter is a tapered machine element with a rectangular cross section of approximate width 1.3d (d is the rod diameter), thickness 0.3d, and length 4d. One edge is straight, while the other edge has a taper on the width of the order of 1:30 to 1:100. Sometimes, the edges of the ends are rounded. The thickness remains constant. Top and bottom edges are curved, with radius equal to d and this curved portion is tapered for thickness at 60° as shown in middle view of Figure 12.1.

Sleeve and Cotter Joint

This is the simplest method of joining two rods. Each end is enlarged in diameter and rectangular slots of about 1.4d × 0.3d are cut diametrically at a distance of 1.3d from the end. Both the rods butt each other and a sleeve of length 8d having similar slots at required positions is aligned (Figure 12.2).

Bending Stresses

There is no single bending stress as such, but bending stress means stresses (both tensile at bottom and compressive at top) developed due to bending. When a load is applied to a beam at right angles to its axis, it gets deflected. The beam can be simply supported at its ends or as a cantilever, fixed only at one end.

Neutral axis of a beam is, where the stress is zero. For a beam of rectangular cross-section it is at the middle as shown in Figure 6.1(a). The load can be a single point load [Figure 6.1(b)], or point loads at many places along its axis, or a Uniformly Distributed Load (UDL)

[Figure 6.1(c)] The area above the Neutral Axis (NA) undergoes compression, while the area below the NA is under tension. Stress pattern is shown in Figure 6.2. The stress is proportional to the distance Y from the NA. In addition to compressive and tensile stress, the load also tries to shear the beam at the ends.

Flexural Strength

Flexural strength is same as the tensile strength for homogeneous materials. Due to various defects in materials, some local weakness is caused. When bending occurs, a material may fail at a stress lesser than its tensile strength, if there is a large flaw at the extreme fibre. Stress caused by bending is known as flexural or bending stress. The formula to calculate this strength is given in the following section by Equation (6.1).

Bending Moment

In simple terms, a bending force is a force that causes bending to any part. Bending moments occur when a bending force is applied at a given distance away from a fixed reference point.

Designing for Fluctuating Loads

Problems for completely reversible loads are described in Chapter 10. The present chapter describes the fatigue strength due to fluctuating loads. For fluctuating loads, there exists a mean value of load Fm and variable value Fa. Dividing these loads by area of cross-section A, mean stress σm and variable stresses σa are calculated with the following relations:

When both the components of these stresses exist, these are handled by any one of the following theories, described in the following sections.

• • Soderberg line (Section 11.2.1)

• • Goodman lines line (Section 11.2.2 and 11.2.3)

• • Gerber Parabola (Section 11.2.4)

• • ASME elliptical curve (Section 11.2.5)

Safe and Unsafe Zones

Fatigue or endurance strength depends on both mean stress σm and variable stress amplitude σa. Fatigue diagram for fluctuating loads is shown in Figure 11.1 with mean stress on the X-axis and variable stress amplitude on the Y-axis.

A straight line joining tensile yield strength Syt on both the axes called yield line. It is shown dashed in Figure 11.1. If there is stress indicated by a point above the yield line, it will surely fail.

Load line OP is an inclined line starting from the origin on the fatigue diagram and slope as where Sm is the strength for mean stress and Sa is for variable stress. P is any general point indicating mean and variable stresses on this diagram.

Introduction

A welded joint is a permanent joint. Instead of casting or forging, welding is used to fabricate parts which are light, strong, and economical. The parts to be joined are heated, either by electric arc or gas, up to the fusion temperature of the material and then a filler material is used to fuse with the base parts. On cooling, a strong joint is formed. Welding is also used in repair work to join broken parts. It can also be used to reform a worn surface and then do machining.

Welded versus Riveted Joint

While deciding on the type of a joint, the following points are to be considered:

The advantages of welded joints over riveted joints are:

• • These are lighter than riveted joints, as no gusset plate or cover plates, etc., are used.

• • Manufacturing cost is less as there is no hole drilling or rivet head forming required.

• • Unlike riveted joints, there is no weakening of member due to the stress concentration caused due to a rivet hole and hence their efficiency may be 100 per cent.

• • These can be used at places where even a riveted joint is not possible, for example, joining a pipe.

• • Welding process is faster than riveting.

• • These joints are leak proof as compared to riveting.

• • Appearance is better than riveted joints due to absence of rivet heads.

In spite of all the advantages mentioned above, these joints do have some disadvantages also, as given below:

• • The joint can distort the members due to additional stresses that are developed due to heat; hence, stress relieving is done by heat treatment.

Appendix 3

Subject of Machine Design is a combination of engineering and art. The engineering part is important for the functional working of a machine, so that all the machine elements when assembled as a machine, work properly e.g. as an automobile, sewing machine, a lathe etc. The engineering may also include ergonomics, to cause minimum fatigue, if the machine has to be handled by human beings for a long time. The art part is adding aesthetic for appealing shapes, selecting suitable colors etc. which attract the customers.

Fundamentals of machine design considers the concepts of design for each element separately like for a shaft, bearing, pulley etc. Loads on a part/component are assessed, checked for the stresses, whether it is within the safe strength of the selected material. Deflection also should not be beyond a certain limit. The subject should not be confused with strength of materials as the designer has to selecting a suitable material and consider the production aspects also.

Course content is limited to topics, included in the syllabi of the universities and colleges. The subject is so wide that it is covered in two semesters, for mechanical engineering students in most of the universities. Hence the book is also divided in two volumes.

English language used in this book is direct and simple, so that an average student can understand easily. The sequence of the chapters is arranged in such a way that the concepts described in earlier chapters become useful for subsequent chapters.

Symbols used for mathematical derivations have been so assigned, that they are easy to remember. There is no list of symbols in the beginning of the book, they are defined wherever they have been used in the text.

Volume - I is for the first course on Machine Design, covering first semester topics offered by most colleges. The main objective of this volume is to provide rules for the design of generalpurpose machine elements. This volume has four units.

Unit 1 of the book is on fundamentals and has four chapters. The first chapter introduces basic fundamentals and types of machine design.

Introduction

Bridges, boilers, tanks, etc., are made by using riveted joints (Plate 14.1). These are permanent joints and cannot be separated unless and until the rivet is destroyed. Welding is replacing riveted joints slowly, but where welding cannot be done, riveting is still being done.

Rivets

A rivet has a cylindrical part (called shank) and an integral head at one end. Figure 14.1 shows the shape of a rivet. The length of a rivet is about 3 to 4 times the shank diameter and is measured from the bottom of the head. The tail may slightly taper for easy insertion in the hole.

Rivets are available in many diameters. The shank diameter d of the rivet to be used for the joint depends on the thickness t of two plates, which are generally of equal thickness. Small rivets are used for sheet metal and light structural work. These are available from 3 to 10 mm shank diameter sizes. Large size rivets, from 15 to 48 mm shank diameter, are used in heavy steel structures. Type of joint and thickness of the plates decide the length of the rivet needed.

Small rivets are made by cold heading and then heat-treated to remove the work stresses due to cold heading process. Large sized rivets are made by hot forging and then cooled slowly to keep them soft.

For boiler construction or applications, where a leak proof joint is required, the edges are made from 90° to 80° by hammering with a fullering tool and the process is called fullering. Rivet heads can also be caulked [Figure 14.2 (e)] to make leak proof joint.

Introduction

It is not possible to make a part of exact dimensions due to inaccuracy of machines. Therefore, some error is to be tolerated within the acceptable limits. The variation in acceptable size is called limit. The allowable deviations in size are called tolerances. These limits have to be narrow to allow interchangeability of parts. Narrow limits increase the cost of production; hence, experience is needed to put tolerances on the drawing.

Terminology

Standard size Any handbook on machine design gives sizes of standard items. Some parts, like bolts, nuts, etc., are standardized for interchangeability of parts from one machine to the other. Some components are standardized for the purposes of the specifications, for example, wire sizes in Standard Wire Gauge (SWG), sheet metals in gauge number, structural sections, etc.

Limits Maximum and minimum allowable sizes to a basic size of a component are called limits.

Basic size This size is calculated by the designer to withstand the stresses in a component. Limits of tolerances are assigned to the basic size. For example, shaft diameter 50 mm is the basic size. This is represented by zero line in Figure 3.1. An instrument like a vernier caliper or a micrometre (shown on right side) is used to measure the size accurately.

Actual size It is the size that is obtained after manufacturing the product. It may not be as per the standard/basic required dimensions.

Introduction

A shaft is a cylindrical rotating machine member and is used to transmit power by torsion. Power is given to the shaft by a flange, or rotor mounted on it in the form of a pulley, a sprocket driven by a chain or gear, etc. The rotor is mounted on the shaft, fixing a key between the keyways cut or splines on the shaft and the rotor. The power may be transmitted to the same shaft from one side to another using a coupling, or from one shaft to another shaft by using belts and pulleys or chain and sprockets or a pair of gears. Shafts of small diameter are solid, but to make them light, shafts of large diameter are made hollow also. A rod is also circular, but it does not transmit torque and generally takes tensile loads.

Types of Shafts

Shafts are used for many applications like slow speed or high speed, some are of short length and some may be of big length. Following are the types of shafts according to length, speed and load.

• (a) Machine shafts use the rotor integral with it, for example, lay shaft in a gear box. All gears are forged integrally with the shaft itself. These are generally of small length.

• (b) Line shafts are generally long and transmit power to many machines, for example, overhead shafts. These shafts also have to bear bending along with torsion due to their length.