Practical Measurement of True Position at RFS in GD&T

In the feature control frame, positional tolerance is assigned with three types of modifiers. They are 

• Regardless of feature size
• Maximum Material Condition
• Least Material Condition

Regardless of Feature size is used

• For critical features like where press fit needed.
• For threaded holes.

Maximum Material condition is used

• To guarantee assembly for non critical feature.
• To allow fixed gage usage when dealing with mass production

Least Material condition is used

• To ensure minimum wall thickness

Now let's discuss about how the practical measurement would be made to confirm the Pass/Fail of the each hole. 

Let's check for each condition

1. Regardless of Feature size

Many people confuse between the position tolerance and the true position.  Below picture will showcase you the difference. 

Position Tolerance & True Position

In the above picture, the red highlighted are the TRUE POSITION & the blue highlighted is the POSITION TOLERANCE.

So in general, the hole specified at RFS are often measured as circles at top & bottom in the CMM. 

Lets assume below are the measurements for the hole 1.1.

• The hole center was measured .506 from B & .504 from C at the top of the hole.
• The hole center was measured .508 from B & .494 from C at the bottom of the hole.

Measurements for the hole 1.1

Here comes the calculation part

Calculate deviations from TRUE POSITION in X & Y

 

X.dev = X measured - X nominal 

 

X.dev =  0.504 - 0.500 = 0.004

 

Y.dev = Y measured - Y nominal 

 

                              Y.dev =   0.506 - 0.500 = 0.006

Calculate Radial deviations 

R.dev = sq.rt((X.dev)^2+(Y.dev)^2)

 

R.dev = sq.rt((0.004)^2+(0.006)^2) = 0.0072

Measured Position Deviation ( M )

 

M = 2 * R.dev = 2 * 0.0072 = 0.0144

The same above calculation should be applied for all the holes. We are going to use the spreadsheet to automate the calculation.

The below table is the format for the calculation of Position Deviation ( M )

The above manual calculation is automated using formulas in the spreadsheet.

Measurements of all the holes

The values highlighted in color in M column fails the results.

The position tolerance is the 0.014. If the measured value is higher than the positional tolerance, then the hole is considered to be Fail

Heat Treatment process & its types

Heat Treatment

Heat treatment is the heating and cooling of metals to change their physical and mechanical properties,without changing its shape.

Grain structure changes with the application of heat and method of cooling. This induces desired properties in the steel.

It is applicable to plain carbon steel, alloy steel as well as non ferrous materials like aluminum and copper.

Heat treatment enhances properties like Hardness, Toughness, Strength & ductility. 

Types of Heat Treatment Processes

• Hardening
• Tempering
• Annealing
• Normalizing 
• Surface Hardening ( Carburizing & Nitriding )

Hardening

Heating Process : The metal is heated at a high temperature and this temperature is maintained until a proportion of carbon has been dissolved in to the metal.

Cooling Process : The metal is quenched, which involves rapidly cooling it in oil or water.

Results : high strength and wear resistance. However hardening will also increase brittleness

Tempering

Heating Process : It is a low temperature heat treatment process normally performed after hardening( double hardening ).

Cooling Process : cooling in air.

Results : Ductility in increased , tougher and less brittle steel.

Annealing

Heating Process : Heating the metal to a specific temperature.

Cooling Process : cooling slowly at a controlled rate.

Results : Annealing is frequently used to soften metals including iron, steel, copper, brass and silver. It increase ductility and reduce hardness. This facilitates shaping, stamping or forming processes, and allows the metal to be cut more easily. Annealing also enhances electrical conductivity.

Normalising

Heating Process : The metal is heated to a predefined temperature.

Cooling Process : cooled by air.

Results : Greater strength and hardness. Typically, the normalising process is performed on materials that will be subjected to machining.

Carburizing

It is a heat treatment process in which iron or steel absorbs carbon while the metal is heated in the presence of a carbon-bearing material such as carbon monoxide. The intent is to make  the metal harder. Not the whole metal-piece but certain outer thickness only can be carburized.

Nitriding

It is a heat treatment process that diffuses nitrogen into the surface of a metal to create a case hardened surface. These processes are most commonly used on low to medium carbon & low-alloy steels.

Virtual Condition & Resultant Condition - Holes & Pins

Virtual Condition

For a shaft that fits into a hole, the shaft virtual condition must be smaller than the hole virtual condition.

For an external feature of size such as a shaft, the virtual condition is equal to the size at MMC plus the size of the position tolerance zone. 

Shaft with MMC applied

Shaft Virtual Condition

For an internal feature of size such as a hole, the virtual condition is equal to the size at MMC minus the size of the position tolerance zone. 

Hole with MMC applied

Hole Virtual Condition

Since the shaft virtual condition is smaller than the hole virtual condition, the two parts will always mate. 

Virtual condition is extremely useful in design of functional gauges. A functional gauge made to virtual condition will ensure that a part will always mate with its counterpart.

In summary, the way to calculate virtual condition (VC) for a shaft and hole is:

SHAFT VC = MMC Diameter + Position Tolerance Zone Diameter

HOLE VC = MMC Diameter - Position Tolerance Zone Diameter

Resultant Condition

For a internal feature of size, the resultant condition is the variable value and outermost boundary.

For a external feature of size, the resultant condition is the variable value and innermost boundary.

The way to calculate resultant condition (RC) for a shaft and hole is:

SHAFT RC = AME - Total Tolerance

HOLE RC = AME + Total Tolerance

Whereas AME is Actual Mating Envelope &

Total Tolerance = Bonus Tolerance + Geometric Tolerance

Lets us consider a case study for Virtual & Resultant condition.

Internal feature of size

Calculation Table Internal feature of size

External feature of size

Calculation Table External feature of size

Summary

Comparison Table for Internal Feature of size

Comparison Table for External Feature of size

Note : virtual condition and resultant condition are applicable only for specification with material condition. Therefore in Regardless of feature size ( RFS ), the similar substitute are inner and outer boundary. 

Terminology and Terms in GD&T - Modifiers - Series 1

Modifiers

Modifiers are symbolic means of communicating information on engineering drawings.

Maximum Material Condition

Maximum material condition (MMC) is the size of a feature of size in a part that contains the maximum amount of material.

• For an internal feature of size, the MMC size is the smallest allowable size.
• For an external feature of size, the MMC size is the largest allowable size.

When the MMC modifier is used, it indicates that the specified tolerance applies when the feature of size is at the MMC size. As the size of the feature of size departs from the MMC size, the tolerance is increased by the amount that the size departs from the MMC size.

Internal & External feature of size

In each of the above case the part will have the maximum amount of material.

GD&T symbols to which MMC applies.

• Straightness (Axis)
• Parallelism
• Perpendicularity
• Angularity
• Position - Very Common

Reason for use

To ensure the two parts never interfere. 

For this you should make the MMC of the shaft is always less than the MMC of the hole, then you can guarantee there will always be clearance between the parts. 

Maximum Material Condition Modifier

Least Material Condition

Least material condition (LMC) is the size of a feature of size in a part that contains the minimum amount of material.

• For an internal feature of size, the LMC size is the largest allowable size.
• For an external feature of size, the LMC size is the smallest allowable size.

When the LMC modifier is used, it indicates that the specified tolerance applies when the feature of size is at the LMC size. As the size of the feature of size departs from the LMC size, the tolerance is increased by the amount that the size departs from the LMC size.

Internal & External feature of size

In each of the above case the part will have the minimum amount of material.

Reason for use

To ensure the two parts is always have a contact or press fit & no clearance. 

Gap between a hole/slot and edge of a part

For this you should make the LMC of the shaft is always larger than the LMC of the hole, then you can guarantee there will always be a tight fit between the parts. 

Least Material Condition Modifier

Regardless of Feature Size

This is the implied condition. All tolerance applies at RFS by default, which means no symbol is needed. 

RFS Modifier

Let us consider a simple example and apply all the above three conditions.

MMC, LMC AND RFS APPLIED

MMC Condition is applied

The geometric tolerance is applied at MMC feature of size. If the hole departs from MMC, additional tolerance is gained. Thus the geometric tolerance is applied to smallest size (MMC) of the hole, If the hole gets larger it gains additional tolerance to the position of the hole.

MMC Modifier is applied

LMC Condition is applied

The geometric tolerance is applied at LMC feature of size. If the hole departs from LMC, additional tolerance is gained. Thus the geometric tolerance is applied to largest size (LMC) of the hole, If the hole gets smaller it gains additional tolerance to the position of the hole.

LMC Modifier is applied

RFS Condition is applied

The geometric tolerance is implied at RFS. The size of the hole can be any, the geometric tolerance remains the same.

RFS Modifier is applied

3-2-1 Principle ( Arresting Degrees of Freedom )

Degrees of Freedom in space

A work-piece free in space can move in an infinite number of direction. For analysis, this motion can be broken down into 12 directional movements or "degrees of freedom". All 12 degrees of freedom must be restricted to ensure proper referencing of a work-piece.

As shown in Fig 1, the 12 degrees of freedom all relate to the central axis of the work-piece. Notice the 6 axial degrees and 6 radial degrees of freedom. The axial degrees of freedom permit straight-line movement in both directions along the 3 principle axis shown as X, Y & Z. The radial degrees of freedom permit rotational movement, in both clockwise & counterclockwise radial directions around the same three axis.

Fig 1: The twelve degrees of freedom

Degrees of Freedom of a Rigid Body

Consider the rigid body shown below which is situated in space. It can have 12 degrees of freedom.

Fig 2 : A rigid body on a space

For a rigid body in plane has 6 degrees of freedom (i.e) The motion of a ship at sea has the 6 degrees of freedom .

_Fig 3: A rigid body on a plane 

(1) X+

(2) X-

(3) Y+

(4) Y-

(5) ZCW

(6) ZCCW

Now try to understand 3-2-1 principle of fixturing. The purpose of Fixturing is 

• Resting - Stability
• Locating - W.r.t datum
• Orienting - W.r.t secondary datum
• Clamping - Ensuring above not disturbed.

Primary Locators

First the three locators or supports are placed under the work-piece. It will be positioned on the primary locating surface also known as datum. It will restrict 5 degrees of freedom.

• Axial Movement downward along Z- axis ( No.6 in Fig 2 )
• Rotation about the X & Y axis ( No. 7, 8, 9 & 10 in Fig 2 )

Primary Locators

Secondary Locators

The next two locators are normally placed on the secondary surface, restricting an additional 3 degrees of freedom.

• Axial movement along the Y+ axis ( No.3 in Fig 2 )
• Rotation about the Z axis ( No. 11 & 12 in Fig 2 )

Secondary Locators

Tertiary Locator

This locator is positioned at the end of the part. It restricts 1 degrees of freedom

• Axial movement along the X axis ( No.2 in Fig 2 )

Tertiary Locator

All these 6 locators will restrict a total of 9 degrees of freedom. The remaining 3 degrees of freedom ( 1, 4 & 5 ) will be restricted by the clamps.

Projection methods: 1st angle and 3rd angle projections

Orthographic Projection

Orthographic projection is a way of drawing an 3D object from different directions. Usually a front, side and plan view are drawn so that a person looking at the drawing can see all the important sides. Orthographic drawings are useful especially when a design has been developed to a stage whereby it is almost ready to manufacture.

There are two ways of drawing in orthographic - First Angle and Third Angle.

The principal projection planes and quadrants used to create drawings are shown in Figure 1. The object can be considered to be in any of the four quadrants.

Figure 1. The principal projection planes and quadrants for creation of drawings.

First Angle Projection

• In this the object is assumed to be positioned in the first quadrant and is shown in figure 2. 
• 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 the 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.

Figure 2.  Illustrating the views obtained using  first angle projection technique.

Third Angle Projection

• In the third angle projection method, the object is assumed to be in the third quadrant. i.e the object behind vertical plane and below the horizontal plane. 

• In this projection technique, placing the object in the third quadrant puts the projection plane between the viewer & the object and is shown in figure 3.

Figure 3. Illustrating the views obtained using  first angle projection technique

A summary of  the difference between 1st & 3rd angle projection is shown in Table 1.

Table 1

Note : Second angle projection & fourth angle projection are not used since the drawing becomes complicated.

International Tolerance Grade

An "International Tolerance Grade" establishes the magnitude of the tolerance zone or the amount of part size variation allowed for internal & external dimensions alike. The smaller the grade number the smaller the tolerance zone.

Grade 1-4 are very precise grades Primarily used for Gage making & similar precision works, although grade 4 can be used for precise production works.

Grade 5-16 represent a progressive series suitable for cutting operation such as turning, boring, grinding, milling & sawing. Grade 5 is the most precise grade obtained by fine grinding  & lapping. Grade 16 is the coarsest grade for rough sawing & machining.

Grade 12-16 are intended for manufacturing operation such as pressing, rolling & other forming operations.

Tolerance position letters

Fundamental positions are expressed by "Tolerance position letters". Capital letters are used for internal dimensions (bore) and lower case letters are used for external dimensions (shaft).

There are 28 possible letters.They are A, B, C, CD, D, E, EF, F, FG, G, H, JS, J, K, M, N, P, R, S, T, U, V, X, Y, Z, ZA, ZB, ZC for Internal dimensions.

There are 28 possible letters.They are a, b, c, cd, d, e, ef, f, fg, g, h, js, j, k, m, n, p, r, s, t, u, v, z, y, z, za, zb, zc for External dimensions.


The letters "I, L, O, W, Q" & "i,l, o, w, q" are not used.

Tolerance Grade for Internal & External feature

Fits

Application of International Tolerance Grade range Fig:1

Application of International Tolerance Grade range Fig:2

Below is the ISO Tolerance Chart for reference.

 Find the questions & answers for the tolerance grades using the above ISO  Tolerance Chart.

Question No:1

Answer for Question No:1

Have the below Fit calculation block as reference  and solve the question No:2.

Question No:2

Answers for Question No:2

Answers for Question No:2