Unilateral Tolerance examples are generally observed in** **interchangeable manufacturing processes specially where precision fits are required.

**A Unilateral Tolerance basically signifies a nominal size and either a plus or a minus tolerance. In Unilateral Tolerance the allowable size variation is only in one direction, it can be positive or negative and zero value is also permitted.**

**Tolerance** or permissible variation of dimension is always allowed during machining of a mating component or any engineering parts to avoid high cost and long time consumption.

The permissible deviation of true dimension of a mating part without hindering any functional accuracy and useful for actual working is known as tolerance.

Tolerance zone indicates the difference between the upper and lower limit of deviation.

There different types of tolerances are listed below:

**Unilateral Tolerance****Bilateral Tolerance****Compound Tolerance****Geometric Tolerance**

Here we are going to discuss mainly about Unilateral Tolerance

The diagram shows us that the tolerance lies only on one side of the basic size. It may be above or below the nominal dimension.

Some examples of Unilateral Tolerances are given below to get a clear idea:

- 12.0mm +0/+0.5mm
- 5.5″ +0.010″/+0.015″
- 5.325″ +0/-0.002″
- 7.1mm -0.5/-0.6mm

The above examples can be illustrated elaborately as below:

Nominal Size | Bottom Tolerance | Top Tolerance |

12.0mm | 12.0mm | 12.5mm |

5.5″ | 5.51″ | 5.515″ |

5.325″ | 5.325″ | 5.323″ |

7.1mm | 6.6mm | 6.5mm |

**What is Unilateral Tolerance?**

During machining of mating parts Unilateral Tolerance assist the operators to calculate the deviation in a easy and simple way.

**In Unilateral tolerance the variation from the original profile is only allowed in one direction i.e tolerance limits lie only above or below the basic size. Here the variation in dimension is permitted only in one direction, not in both the directions.**

Unilateral Tolerance is most widely used especially in case of precision fits due to its simplicity in determining the deviations.

Example of Unilateral Tolerance for machining a shaft:

Here we try to achieve a diameter of 25 cm, known as basic or nominal size. The deviation from the basic size is permitted as +0.02 cm as upper limit and +0.01 cm as lower limit. Here the variation in dimension is allowed only in positive direction or above the basic size.

Basic size: 25 cm

Upper limit: 25+.02=25.02cm

Lower limit: 25+.01=25.01cm

**How to calculate Cpk for Unilateral Tolerance?**

Unilateral or one-sided tolerances impose only an upper limit or a lower limit on the process, and leave the specification unbounded on the other side.

The Process Capability Indices Cp & Cpk can be calculated by using the following formulae:

*Cp = USL-LSL/6σ*

Where USL=Upper Specification Limit

LSL=Lower Specification Limit

The process capability index Cpk is used in manufacturing industry to calculate the ability of the process to meet customers’ expectations. In this competitive world to sustain in the market the good knowledge of Cp and Cpk value is a powerful strategy.

In general, higher the Cpk value, the better the product or process that means the process or the product has a higher ability to satisfy the customers. In other words an improvement in the process results a higher Cpk value.

Cpk is calculated by determining the difference between mean value and specification(upper and lower), then this difference is divided by 3 x standard deviation. The value obtained indicates the process capability, higher value means better product or process.

Cpk=Zmin/3

Zmin=Smaller of Zupper or Zlower

Zupper=[(USL-Mean)/Estimated sigma*]

Zlower=[(Mean-LSL)/Estimated sigma*]

Estimated sigma=average range/d2

In case of** Unilateral** Tolerance we have only one specification or tolerance either upper tolerance or lower tolerance. For example in our example we have only upper tolerance value but no lower tolerance.

In this case we can go for two options

- Considering LSL as 0
- Lower specification or tolerance is missing and calculation is done without considering it.

Let here USL=0.5

And estimated sigma=0.15

In case of the 1^{st} option,

We consider LSL=0

Z_{upper} = [0.5-0.0025/0.15] = 3.316

Z_{lower} = [0.0025-0/0.15] = 0.01667

Z_{min }= 0.01667

C_{pk} = 0.01667/3 = 0.005

This value of Cpk i.e. 0.005 cann not satisfy a customer .

In case of the 2nd option,

Here we assume that lower specification or tolerance is missing, without LSL, obliviously Z lower value is also missing.

Zupper=3.316(from above)

Cpk=3.316/3=1.10

A Cpkof 1.10 is more realistic than one of 0.005.

From the above example it is clear that Cpk can be calculated when only one deviation exists, using only the available specification and the other one specification is considered as missing. Now consider either the upper limit( Z_{upper}) or the lower limit( Z_{lower}).

If we consider lower specification as zero it will give a lower value of Cpk which is not advisable.

**How to convert Unilateral Tolerance to Bilateral Tolerance?**

A bilateral tolerance is plus **AND **minus whereas a unilateral tolerance is a plus **OR **minus tolerance.

In case of Bilateral Tolerance variation from the true profile is permitted in both directions whereas in case of Unilateral Tolerance variation is allowed only in one direction.

Let us consider an example of a Unilateral Tolerance is

Here Basic size: 40.0

Upper Tolerance:40.0+0.0=40.0

Lower Tolerance:40.0-0.5=39.5

Now if we try to convert this Unilateral Tolerance into Bilateral Tolerance, then it will be:

Divide the total tolerance by 2, -0.5/2= -0.25

Determine the mean dimension, 40.0-0.25= 39.75

Now write as a bilateral tolerance ,

For this new bilateral form

Basic size: 39.75

Upper Tolerance:39.75+.25=40.0

Lower Tolerance:39.75-0.25=39.5

We can convert Unilateral tolerance into Bilateral Tolerance keeping the Tolerance zone same and including both +ve and –ve tolerance.

**How to find Unilateral Tolerance?**

Unilateral Tolerance is a unequally disposed tolerance where deviations lie only in one direction of the nominal size.

**Unilateral Tolerance consists of one nominal size or basic size and a plus or minus deviation. Using these values we can easily calculate the Unilateral Tolerance given for a component.**

Considering an example of Unilateral Tolerance ,

1)

Basic size: 25 cm

Upper limit: 25+.02=25.02cm

Lower limit: 25+.01=25.01cm

Tolerance Zone=25.02-25.01=0.01cm

2)

Basic size: 25 cm

Upper limit: 25-.01=24.90cm

Lower limit: 25-.02=24.80cm

Tolerance Zone=24.90-24.80=0.10cm

I am Sangeeta Das. I have completed my Masters in Mechanical Engineering with specialization in I.C Engine and Automobiles. I have around ten years of experience encompassing industry and academia. My area of interest includes I.C. Engines, Aerodynamics and Fluid Mechanics. You can reach me at