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1
CHAPTER
1
Introduction:
1.1 Design
1.2 Mechanical Engineering Design
1.3 The Phases of Design (Design Process Elements)
1.4 Design Considerations
1.5 Design Tools and Resources
1.6 The Design Engineer’s Professional Responsibilities
1.7 Codes and Standards
1.8 Economics
1.9 Safety and Product Liability
1.10 Stress and Strength
1.11 Design Factor and Factor of Safety
1.12 Reliability
1.1 Design
 To design is either to formulate a plan for the satisfaction of a human need or to solve a
problem.
 If the plan results in the creation of something having a physical reality, the product must
be:
i. Functional: product must perform to fill its intended need and customer expectation.
ii. Safe: product is not hazardous to the user, bystanders, or surrounding property.
iii. Reliable: product will perform its intended function satisfactorily or without failure
at a given age.
iv. Competitive: product is a contender in its market.
v. Usable: Easy to use. Accommodating to human size, strength, posture, reach, force,
power, and control.
vi. Manufacturability: product has been reduced to a minimum number of parts, suited
to mass production, with dimensions, distortion, and strength under control.
vii. Marketable: product can be bought, and service.
 It is important that the designer begin by identifying exactly how he will recognize a
satisfactory alternative, and how to distinguish between two satisfactory alternatives in
order to identify the better.
 From this kernel (most important part), optimization strategies can be formed or selected.
 Then the following tasks unfold (open out):
1. Invent alternative solutions.
2. Establish key performance metrics.
3. Through analysis and test, simulate and predict the performance of each alternative,
retain satisfactory alternatives, and discard unsatisfactory ones.
4. Choose the best satisfactory alternative discovered as an approximation to
optimality.
2
5. Implement (put into operation) the design.
1.2 Mechanical Engineering Design:
 Mechanical Design: Transformation of concepts and ideas into useful machinery. Or the
design of components and systems of a mechanical nature-machines, structure, devices, and
instruments.
 Machine: Combination of mechanisms and other components that transforms, transmit or
uses energy, load or motion for a specific purpose.
 It utilizes: mathematics, materials sciences, and engineering mechanics sciences.
 It involves: all the disciplines (rules) of mechanical engineering
 Its ultimate goal: is to size and shape the element and choose appropriate materials and
manufacturing processes so that the resulting system can be expected to perform its intended
function without failure.
 Example: design of journal bearing involves: fluid flow, heat transfer, friction, energy
transport, material selection, and thermo-mechanical treatments.
1.3 The Phases of Design (Interaction between Design Process Elements)
The process of design is basically an
exercise in creativity.
It can be outlined by design flow
diagrams with feedback loops as shown
in next figure.
Note that the process is neither
exhaustive nor rigid and will probably
be modified to suit individual
problems.
Identification of Need:
 Design process begins with
recognition of the need, real or
imagined, and a decision to do something about it.
 Need is often not evident at all
 Sensitive person, one who is easily disturbed by things, is more likely to recognize a
need and more likely to do something about it.
 Example: The need for cleaner air or present equipment requires improving
durability.
3
Definition of the Problem:
It include all the specifications for the object that is to be design.
Specifications which include all forms of input and output quantities must be spelled
out.
Once the specifications have been prepared, relevant design information is collected
to make a feasibility study.
As a result of this study, changes are made in the Specifications and requirements.
When some idea as to the amount of space needed or available for a project has been
determined, to-scale layout drawings may be started.
Synthesis:
 Putting together of the solution represents maybe the most challenging and interesting
part of design.
 Ideation and invention phase (where the largest possible number of creative solutions
is originated).
 The designer combines separate parts to form a complex whole of various new and
old ideas and concepts to produce an overall new idea or concept.
Analysis and optimization:
 It has as its objective satisfactory performance, as well as durability with minimum
weight and competitive cost.
 Synthesis cannot take place without both analysis or resolution and optimization,
because the product under design must be analyzed to determine whether the
performance compiles with the specifications.
 If the design fails, the synthesis procedure must begin again.
 Designer must: specify the dimensions, select the components and materials, and
consider the manufacturing, cost, reliability, serviceability, and safety.
Testing (Evaluation):
 It is the final proof of a successful design and usually involves the testing of a
prototype in the laboratory.
 Is it really satisfying the need?
 Is it reliable?
 Will it compete successfully with similar product?
 Can a profit be made from this product?
 Is it easy to maintained and adjusted?
Presentation:
 It is a selling job.
4
 The engineer, when presenting a new solution to administrative, management, or
supervisory persons, is attempting to sell or to prove to them that this solution is better one.
Unless this can be done successfully, the time and effort spent on obtaining the solution have
been largely wasted.
 When designers sell a new idea, they also sell themselves.
1.4 Design Considerations:
 It means the characteristic that influences the design of the element or the entire system.
 Many of the important ones (not necessarily in order of importance) are as follows:
 Some of these characteristics have to do directly with the dimensions, the material, the
processing, and the joining of the elements of the system. Several characteristics may be
interrelated, which affects the configuration of the total system.
1.5 Design Tools and Resources:
 Computational Tools:
o Computer-aided design (CAD): software allows the development of 3-D design from
which conventional 2-D orthographic views with automatic dimensioning can be
produced. Manufacturing tool paths can be generated from the 3-D models from a 3-
D database. This database can rapidly helps in calculation of mass properties.
Geometric properties are also easy to find. Examples of such software are: AutoCAD,
I-Deas, ProEngineer……etc.
o Computer-aided engineering (CAE): It is applied to all engineering application. With
this definition, CAD can be considered as a subset of CAE. Some example of
engineering based software for mechanical engineering application ( software that
might be integrated within a CAD system) include:
5
1) Finite Element Analysis: Algor, Ansys, Abaqus.
2) Program for Simulation: Adams, Working Model.
o Computer-aided applications: word processing (e.g. Excel, Lotus) and mathematical
solvers (e.g. Maple, Matlab, MathCad).
 Acquiring (obtaining) Technical Information:
Libraries: such as Engineering dictionaries, handbooks, journals
Government sources: such as ministries, Institutions
Professional societies: such as American Society of Mechanical Engineering
Commercial vendors: such as Catalogs, samples, cost information
Internet: The computer network gateway to websites associated with most of the
categories listed above.
Etc...
1.6 The Design Engineer’s Professional Responsibilities:
 When you are working on a design problem, it is important to develop a systematic approach.
The following steps will help you organize your solution processing technique:
 Understand the problem.
 Identify the known.
 Identify the unknown and formulate the solution strategy.
 State all assumptions and decisions.
 Analyze the problem.
 Evaluate your solution.
 Present your solution.
1.7 Codes and Standards:
 A Standard: is a set of specifications for parts, materials, or processes intended to achieve
uniformity, efficiency, and specified quality.
 A code: is a set of specifications for the analysis, design, manufacture, and construction of
something.
 Purpose of Code: to achieve a specified degree of safety, efficiency, and performance
or quality.
 Some organization and societies that have established specifications for standards and safety
or design code. Such as:
1. American Institute of Steel Construction (AISC).
2. American Society of Mechanical Engineers (ASME).
3. International Standards Organization (ISO).
6
1.8 Economics:
The cost plays an important role in the design decision process that we could easily spend as
much as time in studying the cost factor as in the study of the entire subject of design.
Few general approaches and simple rules that will help reduce the cost in design:
 Standard Sizes: Using the standard stock and size is the first principle of cost reduction.
In design something; there are many purchased parts, such as motors, pumps, bearings, and
fasteners. In this case, it is important for designers to make a special effort to specify parts
that are readily available. Parts that are made and sold in large quantities usually are least in
cost.
 Large Tolerances: close tolerances need additional steps in manufacturing which means
additional cost. In this case, parts with large tolerances can often be reduced by machines
with higher production rates and at the same time low cost.
 Cost Estimates: there are many ways of obtaining relative cost figures; cost so that two
or more designs can be roughly compared. For example, to compare the cost of one design
with another is simply to count the number of parts or the steps to make the design.
 Breakeven Points: when two or more
design approaches are compared for cost,
the choice between them depends upon a set
of conditions such as the quantity of
production, the speed of the assembly lines,
or some other condition.
 Example: Consider a situation in which
a certain part can be manufactured at the
rate of 25 parts per hour on an automatic
screw machine or 10 parts per hour on a hand screw machine. Let us suppose, too, that the
setup time for the automatic is 3 h and that the labor cost for either machine is $20 per hour,
including overhead. Figure 1–3 is a graph of cost versus production by the two methods. The
breakeven point for this example corresponds to 50 parts. If the desired production is greater
than 50 parts, the automatic machine should be used.
1.9 Safety and Product Liability:
 A concept states that the manufacturer of an article is liable for any damage or harms that
result because of a defect. And it does not matter whether the manufacturer knew about the
defect, or even could have known about it.
7
 Example: a product was manufactured say 10 years ago, the manufacturer is still liable for
any damage or harm even if the product could not have been considered defective on the
basis of all technological knowledge that are available at that time.
1.10 Stress and Strength:
 Strength: is a property of a material or of a mechanical element. The strength of an element
depends upon the choice, the treatment, and the processing of the material.
 One of the basic problems in dealing with stress and strength is how to relate the two in order
to develop a safe, economic, and efficient design.
 The AISC: is developing the permissible-stress method that defined the allowable stress and
possible loads.
1.11 Design Factor and Factor of Safety:
 Engineers employ a safety factor to ensure against foregoing unknown uncertainties involving
strength and loading.
 Uncertainty: Uncertainties in machinery design abound. Examples of uncertainties concerning
stress and strength include:
o Composition of material and the effect of variation on properties.
o Variations in properties from place to place within a bar of stock.
o Effect of processing locally, or nearby, on properties.
o Effect of nearby assemblies such as weldments and shrink fits on stress conditions.
o Effect of thermomechanical treatment on properties.
o Intensity and distribution of loading.
o Validity of mathematical models used to represent reality.
o Intensity of stress concentrations.
o Influence of time on strength and geometry.
o Effect of corrosion.
o Effect of wear.
o Uncertainty as to the length of any list of uncertainties.
 This factor is used to provide assurance that the load applied to a member dose not exceed the
largest load it can carry
 The factor of safety can be defined as:
𝑛 𝑠 =
𝐹𝑎𝑖𝑙𝑢𝑟𝑒 𝑙𝑜𝑎𝑑
𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝑙𝑜𝑎𝑑
 If it is defined in terms of strength design:
8
𝑛 𝑠 =
𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ
𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝑠𝑡𝑟𝑒𝑠𝑠
In this case, the material strength represents either static or dynamic properties. If loading is static, the
material strength is either the yield strength or the ultimate strength.
For fatigue loading, the material strength is based on the endurance limit (will take it later on).
Allowable stress is also called Design Stress.
 After the design is completed, the actual design factor may change as a result of changes such
as rounding up to a standard size for a cross section or using off-the-shelf components with
higher ratings instead of employing what is calculated by using the design factor. The factor is
then referred to as the factor of safety, ns. The factor of safety has the same definition as the
design factor, but it generally differs numerically.
1.12 Reliability:
 The statistical measure of the probability that a mechanical element will not fail in use.
 It is expressed by a number having the range:
0 < 𝑅 < 1
 For example: 𝑅 = 0.9 , means that there is a 90 percent chance that the part will perform its
proper function without failure.
 Suppose we have 6 parts fail out of 1000 parts manufactured, then 𝑅 = 1 −
6
1000
= 0.994.
 In the reliability method of design, the designer’s task is to make a judicious selection of
materials, processes, and geometry so as to achieve a reliability goal.
9
1.13 Dimensions and Tolerances:
The following terms are used generally in dimensioning:
 Nominal size :
 The size we use in speaking of an element. For example, we may specify a 1.5 in pipe
or a 0.5 in bolt.
 Either the theoretical size or the actual measured size may be quite different.
 The theoretical size of a 1.5 in is 1.490 in for the outside diameter. And the diameter of the 1.5
in bolt, say, may actually measure 0.492 in.
 Limits:
 The stated maximum and minimum dimensions
 Tolerance:
 The difference between the two limits.
 Bilateral tolerance:
 The variation in both directions from the basic dimension.
 That is, the basic size is between the two limits, for example, 1.005 ± 0.002 in.
 The two parts of the tolerance need not be equal.
 Unilateral tolerance:
 The basic dimension is taken as one of the limits, and variation is permitted in only one
direction, for example, 1.005 (+0.004/−0.000) in.
 Clearance:
 A general term that refers to the mating of cylindrical parts such as a bolt and a hole.
 The word clearance is used only when the internal member is smaller than the external
member.
 The diametral clearance is the measured difference in the two diameters. The radial
clearance is the difference in the two radii.
 Interference:
 The opposite of clearance, for mating cylindrical parts in which the internal member is
larger than the external member.
 Allowance:
 The minimum stated clearance or the maximum stated interference for mating parts.
 When several parts are assembled, the gap (or interference) depends on the dimensions and
tolerances of the individual parts.

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Chapter 1 intr m dfina

  • 1. 1 CHAPTER 1 Introduction: 1.1 Design 1.2 Mechanical Engineering Design 1.3 The Phases of Design (Design Process Elements) 1.4 Design Considerations 1.5 Design Tools and Resources 1.6 The Design Engineer’s Professional Responsibilities 1.7 Codes and Standards 1.8 Economics 1.9 Safety and Product Liability 1.10 Stress and Strength 1.11 Design Factor and Factor of Safety 1.12 Reliability 1.1 Design  To design is either to formulate a plan for the satisfaction of a human need or to solve a problem.  If the plan results in the creation of something having a physical reality, the product must be: i. Functional: product must perform to fill its intended need and customer expectation. ii. Safe: product is not hazardous to the user, bystanders, or surrounding property. iii. Reliable: product will perform its intended function satisfactorily or without failure at a given age. iv. Competitive: product is a contender in its market. v. Usable: Easy to use. Accommodating to human size, strength, posture, reach, force, power, and control. vi. Manufacturability: product has been reduced to a minimum number of parts, suited to mass production, with dimensions, distortion, and strength under control. vii. Marketable: product can be bought, and service.  It is important that the designer begin by identifying exactly how he will recognize a satisfactory alternative, and how to distinguish between two satisfactory alternatives in order to identify the better.  From this kernel (most important part), optimization strategies can be formed or selected.  Then the following tasks unfold (open out): 1. Invent alternative solutions. 2. Establish key performance metrics. 3. Through analysis and test, simulate and predict the performance of each alternative, retain satisfactory alternatives, and discard unsatisfactory ones. 4. Choose the best satisfactory alternative discovered as an approximation to optimality.
  • 2. 2 5. Implement (put into operation) the design. 1.2 Mechanical Engineering Design:  Mechanical Design: Transformation of concepts and ideas into useful machinery. Or the design of components and systems of a mechanical nature-machines, structure, devices, and instruments.  Machine: Combination of mechanisms and other components that transforms, transmit or uses energy, load or motion for a specific purpose.  It utilizes: mathematics, materials sciences, and engineering mechanics sciences.  It involves: all the disciplines (rules) of mechanical engineering  Its ultimate goal: is to size and shape the element and choose appropriate materials and manufacturing processes so that the resulting system can be expected to perform its intended function without failure.  Example: design of journal bearing involves: fluid flow, heat transfer, friction, energy transport, material selection, and thermo-mechanical treatments. 1.3 The Phases of Design (Interaction between Design Process Elements) The process of design is basically an exercise in creativity. It can be outlined by design flow diagrams with feedback loops as shown in next figure. Note that the process is neither exhaustive nor rigid and will probably be modified to suit individual problems. Identification of Need:  Design process begins with recognition of the need, real or imagined, and a decision to do something about it.  Need is often not evident at all  Sensitive person, one who is easily disturbed by things, is more likely to recognize a need and more likely to do something about it.  Example: The need for cleaner air or present equipment requires improving durability.
  • 3. 3 Definition of the Problem: It include all the specifications for the object that is to be design. Specifications which include all forms of input and output quantities must be spelled out. Once the specifications have been prepared, relevant design information is collected to make a feasibility study. As a result of this study, changes are made in the Specifications and requirements. When some idea as to the amount of space needed or available for a project has been determined, to-scale layout drawings may be started. Synthesis:  Putting together of the solution represents maybe the most challenging and interesting part of design.  Ideation and invention phase (where the largest possible number of creative solutions is originated).  The designer combines separate parts to form a complex whole of various new and old ideas and concepts to produce an overall new idea or concept. Analysis and optimization:  It has as its objective satisfactory performance, as well as durability with minimum weight and competitive cost.  Synthesis cannot take place without both analysis or resolution and optimization, because the product under design must be analyzed to determine whether the performance compiles with the specifications.  If the design fails, the synthesis procedure must begin again.  Designer must: specify the dimensions, select the components and materials, and consider the manufacturing, cost, reliability, serviceability, and safety. Testing (Evaluation):  It is the final proof of a successful design and usually involves the testing of a prototype in the laboratory.  Is it really satisfying the need?  Is it reliable?  Will it compete successfully with similar product?  Can a profit be made from this product?  Is it easy to maintained and adjusted? Presentation:  It is a selling job.
  • 4. 4  The engineer, when presenting a new solution to administrative, management, or supervisory persons, is attempting to sell or to prove to them that this solution is better one. Unless this can be done successfully, the time and effort spent on obtaining the solution have been largely wasted.  When designers sell a new idea, they also sell themselves. 1.4 Design Considerations:  It means the characteristic that influences the design of the element or the entire system.  Many of the important ones (not necessarily in order of importance) are as follows:  Some of these characteristics have to do directly with the dimensions, the material, the processing, and the joining of the elements of the system. Several characteristics may be interrelated, which affects the configuration of the total system. 1.5 Design Tools and Resources:  Computational Tools: o Computer-aided design (CAD): software allows the development of 3-D design from which conventional 2-D orthographic views with automatic dimensioning can be produced. Manufacturing tool paths can be generated from the 3-D models from a 3- D database. This database can rapidly helps in calculation of mass properties. Geometric properties are also easy to find. Examples of such software are: AutoCAD, I-Deas, ProEngineer……etc. o Computer-aided engineering (CAE): It is applied to all engineering application. With this definition, CAD can be considered as a subset of CAE. Some example of engineering based software for mechanical engineering application ( software that might be integrated within a CAD system) include:
  • 5. 5 1) Finite Element Analysis: Algor, Ansys, Abaqus. 2) Program for Simulation: Adams, Working Model. o Computer-aided applications: word processing (e.g. Excel, Lotus) and mathematical solvers (e.g. Maple, Matlab, MathCad).  Acquiring (obtaining) Technical Information: Libraries: such as Engineering dictionaries, handbooks, journals Government sources: such as ministries, Institutions Professional societies: such as American Society of Mechanical Engineering Commercial vendors: such as Catalogs, samples, cost information Internet: The computer network gateway to websites associated with most of the categories listed above. Etc... 1.6 The Design Engineer’s Professional Responsibilities:  When you are working on a design problem, it is important to develop a systematic approach. The following steps will help you organize your solution processing technique:  Understand the problem.  Identify the known.  Identify the unknown and formulate the solution strategy.  State all assumptions and decisions.  Analyze the problem.  Evaluate your solution.  Present your solution. 1.7 Codes and Standards:  A Standard: is a set of specifications for parts, materials, or processes intended to achieve uniformity, efficiency, and specified quality.  A code: is a set of specifications for the analysis, design, manufacture, and construction of something.  Purpose of Code: to achieve a specified degree of safety, efficiency, and performance or quality.  Some organization and societies that have established specifications for standards and safety or design code. Such as: 1. American Institute of Steel Construction (AISC). 2. American Society of Mechanical Engineers (ASME). 3. International Standards Organization (ISO).
  • 6. 6 1.8 Economics: The cost plays an important role in the design decision process that we could easily spend as much as time in studying the cost factor as in the study of the entire subject of design. Few general approaches and simple rules that will help reduce the cost in design:  Standard Sizes: Using the standard stock and size is the first principle of cost reduction. In design something; there are many purchased parts, such as motors, pumps, bearings, and fasteners. In this case, it is important for designers to make a special effort to specify parts that are readily available. Parts that are made and sold in large quantities usually are least in cost.  Large Tolerances: close tolerances need additional steps in manufacturing which means additional cost. In this case, parts with large tolerances can often be reduced by machines with higher production rates and at the same time low cost.  Cost Estimates: there are many ways of obtaining relative cost figures; cost so that two or more designs can be roughly compared. For example, to compare the cost of one design with another is simply to count the number of parts or the steps to make the design.  Breakeven Points: when two or more design approaches are compared for cost, the choice between them depends upon a set of conditions such as the quantity of production, the speed of the assembly lines, or some other condition.  Example: Consider a situation in which a certain part can be manufactured at the rate of 25 parts per hour on an automatic screw machine or 10 parts per hour on a hand screw machine. Let us suppose, too, that the setup time for the automatic is 3 h and that the labor cost for either machine is $20 per hour, including overhead. Figure 1–3 is a graph of cost versus production by the two methods. The breakeven point for this example corresponds to 50 parts. If the desired production is greater than 50 parts, the automatic machine should be used. 1.9 Safety and Product Liability:  A concept states that the manufacturer of an article is liable for any damage or harms that result because of a defect. And it does not matter whether the manufacturer knew about the defect, or even could have known about it.
  • 7. 7  Example: a product was manufactured say 10 years ago, the manufacturer is still liable for any damage or harm even if the product could not have been considered defective on the basis of all technological knowledge that are available at that time. 1.10 Stress and Strength:  Strength: is a property of a material or of a mechanical element. The strength of an element depends upon the choice, the treatment, and the processing of the material.  One of the basic problems in dealing with stress and strength is how to relate the two in order to develop a safe, economic, and efficient design.  The AISC: is developing the permissible-stress method that defined the allowable stress and possible loads. 1.11 Design Factor and Factor of Safety:  Engineers employ a safety factor to ensure against foregoing unknown uncertainties involving strength and loading.  Uncertainty: Uncertainties in machinery design abound. Examples of uncertainties concerning stress and strength include: o Composition of material and the effect of variation on properties. o Variations in properties from place to place within a bar of stock. o Effect of processing locally, or nearby, on properties. o Effect of nearby assemblies such as weldments and shrink fits on stress conditions. o Effect of thermomechanical treatment on properties. o Intensity and distribution of loading. o Validity of mathematical models used to represent reality. o Intensity of stress concentrations. o Influence of time on strength and geometry. o Effect of corrosion. o Effect of wear. o Uncertainty as to the length of any list of uncertainties.  This factor is used to provide assurance that the load applied to a member dose not exceed the largest load it can carry  The factor of safety can be defined as: 𝑛 𝑠 = 𝐹𝑎𝑖𝑙𝑢𝑟𝑒 𝑙𝑜𝑎𝑑 𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝑙𝑜𝑎𝑑  If it is defined in terms of strength design:
  • 8. 8 𝑛 𝑠 = 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝑠𝑡𝑟𝑒𝑠𝑠 In this case, the material strength represents either static or dynamic properties. If loading is static, the material strength is either the yield strength or the ultimate strength. For fatigue loading, the material strength is based on the endurance limit (will take it later on). Allowable stress is also called Design Stress.  After the design is completed, the actual design factor may change as a result of changes such as rounding up to a standard size for a cross section or using off-the-shelf components with higher ratings instead of employing what is calculated by using the design factor. The factor is then referred to as the factor of safety, ns. The factor of safety has the same definition as the design factor, but it generally differs numerically. 1.12 Reliability:  The statistical measure of the probability that a mechanical element will not fail in use.  It is expressed by a number having the range: 0 < 𝑅 < 1  For example: 𝑅 = 0.9 , means that there is a 90 percent chance that the part will perform its proper function without failure.  Suppose we have 6 parts fail out of 1000 parts manufactured, then 𝑅 = 1 − 6 1000 = 0.994.  In the reliability method of design, the designer’s task is to make a judicious selection of materials, processes, and geometry so as to achieve a reliability goal.
  • 9. 9 1.13 Dimensions and Tolerances: The following terms are used generally in dimensioning:  Nominal size :  The size we use in speaking of an element. For example, we may specify a 1.5 in pipe or a 0.5 in bolt.  Either the theoretical size or the actual measured size may be quite different.  The theoretical size of a 1.5 in is 1.490 in for the outside diameter. And the diameter of the 1.5 in bolt, say, may actually measure 0.492 in.  Limits:  The stated maximum and minimum dimensions  Tolerance:  The difference between the two limits.  Bilateral tolerance:  The variation in both directions from the basic dimension.  That is, the basic size is between the two limits, for example, 1.005 ± 0.002 in.  The two parts of the tolerance need not be equal.  Unilateral tolerance:  The basic dimension is taken as one of the limits, and variation is permitted in only one direction, for example, 1.005 (+0.004/−0.000) in.  Clearance:  A general term that refers to the mating of cylindrical parts such as a bolt and a hole.  The word clearance is used only when the internal member is smaller than the external member.  The diametral clearance is the measured difference in the two diameters. The radial clearance is the difference in the two radii.  Interference:  The opposite of clearance, for mating cylindrical parts in which the internal member is larger than the external member.  Allowance:  The minimum stated clearance or the maximum stated interference for mating parts.  When several parts are assembled, the gap (or interference) depends on the dimensions and tolerances of the individual parts.