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

Fits in Mechanical design

FITS

A fit is defined as the condition of clearance or interference between two parts.

Terminology associated with fits

Allowance - The amount of clearance or interference that exists between two parts

Maximum Allowance - The greatest amount of clearance or interference that can exist between mating parts. ( i.e) Largest female size ( upper limit ) minus the smallest male size ( lower limit )

Minimum Allowance - The least amount of clearance or interference that can exist between mating parts. ( i.e) Smallest female size ( lower limit ) minus the largest male size ( upper limit )

Types of fits

There are three types. They are

• Clearance fit
• Interference fit
• Transition fit

Clearance Fit

• There will always be some amount of space between mating parts
• No force required to put these parts together.
• When calculation is performed the allowance values will be positive.

Clearance Fit

Interference Fit

• There will always be some amount of contact between mating parts.
• Usually force will be required to put these parts together.
• When calculation is performed the allowance values will be negative.

Interference Fit

Transition Fit

• There could exist between mating parts sometimes a condition of clearance or interference.
• Force depends on how the parts were toleranced.
• When calculation is performed the allowance values will be positive & negative.

Transition Fit

Tolerance in Mechanical design

History of Tolerance

• In the 1800's manufacturing used the " cut & try, file & fit " approach.
• The plus-minus or co-ordinate system of tolerance was next developed.
• In the 1900's the first GD&T standards came out to improve quality & utility of engineering drawings.
• In 1966, the united GD&T standards was published " ANSI - Y14.5M".

Definition of Tolerance

A tolerance is the acceptable difference between the maximum and minimum size of a mechanical part as a basis for determining the accuracy of its fit with another part.

Tolerance

For Example: A dimension gives as Ø 28±0.2 means that the manufactured part may be Ø 28.2 or Ø 27.8, or anywhere between these limit dimensions.

Terminology

Nominal Dimension - The dimension that the tolerance are applied to.

Upper Limit - The maximum allowable size of the part based on the tolerance given

Lower Limit - The minimum allowable size of the part based on the tolerance given.

Interval of Tolerance - The upper limit minus lower limit, also known as range of  tolerance.

WHY Tolerance

No one cannot manufacture a part to its accurate dimension. If you leave a dimension without a tolerance, no one else will know the importance or the unimportant of that dimension. Not only a lack of tolerance lead to improper fits, it will also add to delay and higher costs.

Unit price vs Tolerance

How Effective tolerance helps

• The part functions correctly.
• Fabrication cost is minimum.

Types of Tolerance

• Special tolerance
• General workshop tolerance

Special Tolerance

• Limit Allowance
• Unilateral Tolerance
• Bilateral Tolerance

Examples

Examples of Special Tolerance

General workshop tolerance

General workshop tolerance are usually found in the tittle block of a detail drawing. These tolerance set the acceptable limits when the fabricator or machinist has no other tolerances given on the drawings.