Introduction

Often when a part is being machined, is it least likely that we will get anexact size as required in the design. We will get an accurate but not precisedimensions. For example, the diameter of a shaft in the design is 2.000Ó butwhen the machinist machined the shaft, the diameter may not be 2.000Ó, itcould be 2.002Ó or 1.998Ó. If the machinist were to machine multiple shaftof the same diameter (2.000Ó), we will have a series of dimension thatranges from 1.998Ó to 2.002Ó. These ranges are called tolerancing. Most ofthe time tolerances are determined by the resolution of the machines thatproduce the parts. i.e a laser cutting will have better precision than an oxy-cutting.

Depending on the application, some application may require a higherprecision and some may not. A fan blade that is being used in the turbinemay need a higher precision than the fan blade used in normal householdfan. Higher precision would mean lower tolerance and better machines areneeded to manufacture the parts and thus, this will increase the cost tomanufacture the parts.

Mechanical Tolerancing

Tolerance is a key factor in determining the cost of a part. As mentionedearlier lower tolerance will results in a higher cost of producing the parts.The relationship between tolerance and manufacturing cost is shown in thefigure.

The manufacturing cost is divided into machining and scraps cost.

- The machining cost is the cost of first producing the part.

- The scrap cost is the cost encountered due to rejecting some parts that fall outside the specified tolerance range.

In this chapter we will look at the concepts of tolerance and how geometrictolerancing is applied to manufacturing.

1. Tolerance Concepts

2. Geometric Tolerancing

Machining

Scrap Cost

Manufacturing Cost

Cost

Tolerance

Tolerance Concepts

Basic size: theoretical size from which limits of size are derived by theapplication of

allowance and tolerances.

Tolerance: is the total amount by which a dimension might vary

Tolerance can expressed in either two ways:

Bilateral tolerance: is specified as plus or minus deviation frombasic size.

Example: 1.75 ± 0.002 in.

Unilateral tolerance: variation is permitted only in one directionfrom the basic size

Example: 000.0

004.0750.1

−+

004.0

003.0750.1

−−

Fits between mating parts can be identified as:

1. Cylindrical fits: shaft and hole

2. Location fits: location of mating parts

Both cylindrical and location fits can be divided into three types of fits:

1. clearance fit:

One part is always loosed in relative to the other.

2. Interference fit:

One part is force tight into the other during assembly

3. Transition fits

May result in either a clearance or interference condition.

System for calculating the limits and tolerance dimensions:

1. The basic hole system (most widely used)

2. Basic shaft system

Both systems assume unilateral tolerance h and s for the hole and the shaft

In the basic hole system, the minimum hole is taken as the basic size.

h

dhmin

dhma

Basic size

ANSI has established eight classes of cylindrical fit that specify the amountof allowance a, the hole tolerance h, and the shaft tolerance s as functions ofthe basic size (diameter) d.

d hmin = d

d hmax = d + h

d smax = d Ð a

d smin = d Ð a Ð s

In these equations the allowance a is an algebraic value; it is positive forclearance fit and negative for interference fit.

The tolerance h and s are always positive:

a = d hmin - d smax

For each IT number there is a tolerance value ∆d and for each shaft class

there is a fundamental deviation δF

Based on those two values:

h = ∆ dh

s = ∆ ds

∆+=

ds F

F δ

δa

Example:

Fil class RC2, basic size is 3.000 in.

H6 / g5

ANSI the rearranged this table and extended it to include location fits:

The result: five classes of fit with several grades

The five classes are:

1. running or sliding fit RC

2. location fits

2.1 location clearance LC2.2 location transition LT2.3 location interference LN

3. force or shrink fit

How to read the table:

H ; describe the classes of holes

Small letters ( g, f, e, d, k, n É) describe the classes of shaft.

ITnumber

IT numberfor shaft

Example:

grade ISO symbolHole Shaft

Class LC1 H6 h5Location LC2 H7 h6

Clearance fits : : :

Geometrical Tolerancing

Conventional tolerancing is capable of controlling all aspects ofthe shape of a part, (straightness, flatness, parallelism orangularity of specific portions of a part)

Types of geometric tolerances:

1. size2. location3. from tolerance

Geometric tolerancing permits an explicit definition of datums.

IT number(tolerance gradenumber)

ANSI symbols for Geometric Tolerancing

There are five categories of geometric characteristic symbology

1. Form: Flatness

StraightnessNot related to datum

Circularity

Cylindricity

2. Profile: Profile of a line

Profile of a surface

3. Orientation: Perpendicularity

Parallelism requires a datum

Angularity

4. Runout: Circular runout

Total runout requires a datum

5. Location Position Controls :

Symmetry requires a datum

Concentricity

ANSI modifying symbols

1. Maximum Material Condition meaning and uses:

Maximum material condition is the condition of a feature where in thefeature contains the most material. It is often thought of as the heaviestfeature. It is the smallest hole or the largest shaft.

The MMC concept is usually used for mating features. If a shaft is to beinserted into a hole, the shaftÕs geometry, orientation or location is need notbe as perfect if the shaft is made at a smaller size.

Just as the holeÕs geometry can be less perfect if the hole is produced at alarger size.

This additional geometric tolerance based on size departure from maximummaterial condition is often termed Òbonus toleranceÓ.

2. Least Material condition Meaning and Uses

Least material condition is the condition of a feature where in featurecontains the least material. It is often thought of as the lightest feature. It isthe largest hole or the smallest shaft.

The LMC concept is usually used for features when preservation of materialis great importance. It is used when wall thickness is thought to beendangered and the holes stand a chance of approaching a breakoutcondition.

3. Regardless of feature size conditions or

This condition implies that geometric tolerance is to remain the same nomatter what size hole or shaft is produced.

The concept is often used where balance is important.

Μ

L

SRFS

RFS

For example: Spinning parts could be functionally endangered if tolerance oflocation, such as centering, were allowed to vary with a size of the feature.

How to read a feature Control Frame

The symbol in a feature control frame can be read as one would read asentence to describe how a part is to be made.

0.625 + 0.005 - 0.005

A

1.500 + 0.005 - 0.005

1.750 +0.005

0.75

B

C0.87

φ 0.250 Ð 0.260

φ 0.010 M A B C

Interpretation:

The axis fo the hole

: May be out of position

φ : a diameter of

: if the hole is produced at maximum material condition(diameter of 0.250Ó)

A : to datum A for perpencularity

B : and B for location (holding the 0.875Ó dimension)

C : and C for location (holding the 0.750Ó dimension)

The complete sentence reads:

The axis of the hole may be out of position a diameter of 0.010Ó if the holeis produces at a diameter of 0.250Ó while holding perpendicularity to datumA, and location to datum B and C.

φ 0.250 Ð 0.260

M

Example:

φ 1.600

5x φ 0.570 Ð 0.590

M A MB

0.625 + 0.005 - 0.005

0.001

A

φ 2.990 2.960

φ 0.020

φ 0.004 M A

B