Limits and Tolerences for Design

Design and Manufacturing

A machine element, after design, requires to be manufactured to give it a shape of a product. Therefore, in addition to standard design practices like, selection of proper material, ensuring proper strength and dimension to guard against failure, a designer should have knowledge of basic manufacturing aspects.

In this lesson, we will discuss briefly about some of the basic manufacturing requirements and processes.

First and foremost is assigning proper size to a machine element from manufacturing view point. As for example, a shaft may be designed to diameter of, say, 40 mm. This means, the nominal diameter of the shaft is 40 mm, but the actual size will be slightly different, because it is impossible to manufacture a shaft of exactly 40 mm diameter, no matter what machine is used. In case the machine element is a mating part with another one, then dimensions of both the parts become important, because they dictate the nature of assembly. The allowable variation in size for the mating parts is called limits and the nature of assembly due to such variation in size is known as fits.

Limits

Fig. 1 explains the terminologies used in defining tolerance and limit. The zero line, shown in the figure, is the basic size or the nominal size. The definition of the terminologies is given below. For the convenience, shaft and hole are chosen to be two mating components.

Fundamentals Of Machine Design

Introduction

Design is essentially a decision-making process. If we have a problem, we need to design a solution. In other words, to design is to formulate a plan to satisfy a particular need and to create something with a physical reality. Consider for an example, design of a chair. A number of factors need be considered first:

(a) The purpose for which the chair is to be designed such as whether it is to be used as an easy chair, an office chair or to accompany a dining table.

(b) Whether the chair is to be designed for a grown up person or a child. (c) Material for the chair, its strength and cost need to be determined.

(d) Finally, the aesthetics of the designed chair.

Almost everyone is involved in design, in one way or the other, in our daily lives because problems are posed and they need to be solved.

 concept of machine design

Decision making comes in every stage of design. Consider two cars of different makes. They may both be reasonable cars and serve the same purpose but the designs  are  different.  The  designers  consider  different  factors  and  come  to certain conclusions leading to an optimum design. Market survey gives an indication of what people want. Existing norms play an important role. Once a critical decision is made, the rest of the design features follow. For example,once we decide the engine capacity, the shape and size, then the subsequent course of the design would follow. A bad decision leads to a bad design and a bad product.

Design may be for different products and with the present specialization and knowledge bank, we have a long list of  design disciplines e.g. ship design, building design, process design, bridge design, clothing or fashion design and so on.

Types of design

There may be several types of design such as

Adaptive design

This is based on existing design, for example, standard products or systems adopted for a new application. Conveyor belts, control system of machines and mechanisms  or  haulage  systems  are  some  of  the  examples  where  existing design systems are adapted for a particular use.

Developmental design

Here we start with an existing design but finally a modified design is obtained. A

new model of a car is a typical example of a developmental design  .

Examples of Sections Views

Examples of Sections Views

SECTIONS OF SOLIDS

Full Section View
A full section view is made by passing the imaginary cutting plane completely through the object. As shown in figure 1, all the hidden features intersected by the cutting plane are represented by visible lines in the section view. Surfaces touched by the cutting plane have section lines drawn at a 45-degree angle to the horizontal.  Hidden lines are omitted in all section views unless they must be used to provide a clear understanding of the object. The top view of the section drawing shows the cutting plane line, with arrows pointing in the direction of line of sight to view the sectioned half of the object. In a multi-view drawing, a full-sectioned view is placed in the same position that an unsectioned view would normally occupy, I.e., a front section view would replace the traditional front view.

Figure 1 shows a full section view of an object.

Half Section view
Half sections are created by passing an imaginary cutting plane only halfway through an object. Hidden lines are omitted on both halves of the section view. Hidden lines may be added to the un-sectioned half, for dimensioning or for clarity. External features of the part are drawn on the un-sectioned half of the view. A center line, not an object line, is used to separate the sectioned half from the un-sectioned half of the view. The cutting plane line shown in the top view. The cutting plane line in the top view is bent at 90° and one arrow is drawn to represent the line of sight needed to create the front view in section. Half section views are used most often on parts that are symmetrical, such as cylinders. Also, half sections are commonly used in assembly drawings when external features are also to be shown. figure 2 shows a half section view of an object.

Figure 2 shows the cutting plane passing halfway through an object and one quarter of the object being removed

Projections on Auxiliary Planes

Projections on Auxiliary Planes 
Sometimes none of the three principal orthographic views of an object show the different edges and faces of an object in their true sizes, since these edges and faces, are not parallel to any one of the three principal planes of projection.  In order to show such edges and faces in their true sizes, it becomes necessary to set up additional planes of projection other than the three principal planes of projection in the positions which will show them in true sizes.  If an edge or a face is to be shown in true size, it should be parallel to the plane of projection.  Hence the additional planes are set up so as to be parallel to the edges and faces which should be shown in true sizes.  These additional planes of projection which are set up to obtain the true sizes are called Auxiliary Planes. The views projected on these auxiliary planes are called Auxiliary Views.

The auxiliary view method may be applied

·        To find the true length of a line.

·        To project a line which is inclined to both HP and VP as a point.

·        To project a plane surface or a lamina as a line.

Types of auxiliary planes 
Usually the auxiliary planes are set up such that they are parallel to the edge or face which is to be shown in true size and perpendicular to any one of the three principal planes of projection.  Therefore, the selection of the auxiliary plane as to which of the principal planes of projection it should be perpendicular, obviously depends on the shape of the object whose edge or face that is to be shown in true size.

·        If the auxiliary plane selected is perpendicular to HP and inclined to VP, the view of the object projected on the auxiliary plane is called auxiliary front view and the auxiliary plane is called auxiliary vertical plane and denoted as AVP.

·        If the auxiliary plane is perpendicular to VP and inclined to HP, the view of the object projected on the auxiliary plane is called auxiliary top view and the auxiliary plane is called auxiliary inclined plane and denoted as AIP.

·        Auxiliary Vertical Plane (AVP) 
An AVP is placed in the first quadrant with its surface perpendicular to HP and inclined at Φ to VP. The object is assumed to be placed in the space in between HP, VP and AVP. The AVP intersects HP along the X₁Y₁ line.  The direction of sight to project the auxiliary front view will be normal to AVP.  The position of the auxiliary vertical plane w.r.t  HP and VP is shown in figure 1.

·        After obtaining the top view, front view and auxiliary front view on HP, VP and AVP, the HP, with the AVP being held perpendicular to it, is rotated so as to be in-plane with that of VP, and then the AVP is rotated about the X₁Y₁ line so as to be in plane with that of already rotated HP.

 Figure 1. The position of the auxiliary vertical plane w.r.t  HP and VP

·  

Projections of Points in 2nd, 3rd and 4th Quadrant

Point in the Second quadrant

Point P is 30 mm above HP, 50 mm behind VP and 45 mm in front of left PP. Since point P is located behind VP, the VP is assumed transparent.  The position of the point w.r.t the three planes are shown in Figure 1.  The direction of viewing are shown by arrows. After projecting the point on to the three planes, the HP and PP are rotated such that they lie along the VP. The direction of rotation of the HP  and PP is shown in figure 2. As shown in figure 3, after rotation of the PP and HP, it is found that the VP and HP is overlapping. The multi-view drawing for the point P lying in the second quadrant is shown in figure 4. Though for the projection of a single point, this may not be a problem, the multi-view drawing of solids, where a number of lines are to be drawn, will be very complicated. Hence second angle projection Technic is not followed anywhere  for engineering drawing.

Figure 1. The projection of point P on to the three  projection planes

Figure  2. The direction of rotation of HP.

Figure 3. The projection of point P after complete rotation of the HP and PP.

Figure 4. The multiview drawing of the point P lying in the second quadrant.

Point in the Third quadrant

Projection of a point P in the third quadrant  where P is 40 mm behind VP, 50 mm below HP and 30 mm behind the right PP is shown in figure 5.

Since the three planes of projections lie in between the observer and the point P, they are assumed as transparent planes. After the  point P is projected on to the three planes, the HP and VP are rotated  along the direction shown in figure 6, such that the HP and PP is in plane with the VP. The orthographic projection of the point P lying in the third quadrant is shown in figure 7.

Figure 5. Projection of a point P placed in the third quadrant

In the third angle projection, the  Top view is always above the front view and the  Right side view will be towards the right of the Front view.

Figure 6. shows the sense of direction of rotation of PP and HP.

Figure 7. Multi-view drawing of the point lying in the third quadrant.

In the third angle projection, the  Top view is always above the front view and the  Right side view will be towards the right of the Front view.

Point in the Fourth quadrant

If A point is lying in the fourth quadrant, the point will be below the HP and infront of the VP. The point is projected on to the respective projection planes. After rotation of the HP and PP on to the VP, it will be observed that that the HP and VP are overlapping, similar to the second angle projection.  The multi-view drawing of objects in such case would be very confusing and hence fourth angle projection technique is not followed by engineers. 

Projection of Points

A  POINT 
The position of a point in engineering drawing is defined with respect to its distance from the three principle planes i.e., with respect to the VP, HP, & PP.
The point is assumed to be in the respective quadrant shown in figure.  The point at which the line of sight (line of sight is normal to the respective plane of projection)  intersects the three planes are obtained.  The horizontal plane and the side planes are rotated so such that they lie on the plane containing the vertical plane. The direction of rotation of the horizontal plane is shown in figure 

The relative positions of projection planes and the quadrants

The direction of rotation of the Horizontal plane.

Conventions used while drawing the projections of points

With respect to the 1^st angle projection of point “P’ shown in figure 2,

·        Top views are represented by only small letters eg. p .

·        Their front views are conventionally represented by small letters with dashes eg. p΄

·        Profile or side views are represented by small letters with double dashes eg. p΄΄

·        Projectors are shown as thin lines.

·        The line of intersection of HP and VP is denoted as X-Y.

·        The line of intersection of VP and PP is denoted as X1-Y1

Showing the three planes and the projectionof the point P after the planes have been rotated on to the vertical plane.

Point in the First quadrant

Projection of the point “P” on to the three projection planes after the planes are partially rotated.

Figure 3 shown the projections of a point P which is  40 mm in front of VP, 50 mm above HP, 30 mm in front of left profile plane (PP)

Projection of the point “P” on to the three projection planes before the planes are rotated.

The procedure of drawing the three views of the point “P” is shown in figure-4.

·        Draw a thin horizontal line, XY, to represent the line of intersection of HP and VP.

·        Draw X₁Y₁ line to represent the line of intersection of VP and PP.

·        Draw the Top View (p).

·        Draw the projector line

·        Draw the Front View (p΄) .

·        To project the right view on the left PP, draw a horizontal projector through p to intersect the 45 degree line at m. Through m draw a vertical projector to intersect the horizontal projector drawn through p΄ at p΄΄.

·        p΄΄ is the right view of point P

First angle multi-view drawing of the point “P”

Orthographic projections Conventions and projections of simple solids

Orthographic Projections

Lines are used to construct a drawing. Various type of lines are used to construct meaningful drawings. Each line in a drawing is used to convey some specific information.  The types of lines generally used in engineerign drawing is shown in Table

Types of lines generally used in drawings

All visible edges are to be represented by visible lines. This includes the boundary of the object and  intersection between two planes. All hidden edges and features should be represented by dashed lines.  Figure  shows the orthographic front view  (line of sight in the direction of arrow)of an object. The external boundary of the object is a rectangle and is shown by visible lines.  In Figure, the step part of the object is hidden and hence shown as dashed lines while for the position of the object shown in figure, the step part is directly visible and hence shown by the two solid lines.

shows the pictorial view and front view of the object when the middle stepped region is (a) hidden and (b) visible.

Projection Methods: 1st Angle and 3rd Angle Projections

Projection Methods

Universally either the 1^st angle projection or the third angle projection methods is followed for obtaining engineering drawings. The principal projection planes and quadrants used to create drawings are shown in figure 16. The object can be considered to be in any of the four quadrant.

First Angle Projection

In this the object in assumed to be positioned in the first quadrant and is shown in figure 17 The object is assumed to be positioned in between the projection planes and the observer. The views are obtained by projecting the images on the respective planes. Note that the right hand side view is projected  on the plane placed at the left of the object. After projecting on to the respective planes, the bottom plane  and left plane is unfolded on to the front view plane.  i.e. the left plane is unfolded towards the left side to obtain the Right hand side view on the left side of the Front view and aligned with the Front view. The bottom plane is unfolded towards the bottom to obtain the Top view below the Front view and aligned with the Front View.