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**Introduction Limits, fits and tolerances Alignment tests Types of measurements and instruments**

**“Metrology is the science of measurement” (Ostwald and Munoz 1997) Importance terms in metrology: Precision: the repeatability of measurement Accuracy: a measurement proximity to the true value Measurement of dimensions such as length, thickness, diameter, angle, flatness, profile and others.**

**Dimensional tolerance – permissible variation in the dimension of the part Rule of thumb – the smaller the tolerance, the higher the production cost**

**It is impossible to make a part to a exact size and if, by chance, an exact size is achieved it is impossible to measure it accurately enough to prove it. Since a part can not be made to an exact size it is necessary to specify the amount by which the size may deviate from the ideal size. The successful functioning of most manufactured items depends not only upon the individual sizes of the parts but also upon the relationships of those parts in an assembly:**

**A perfect part can not be produced. Therefore it is necessary to specify the amount by which a size may deviate from its ideal size and still fulfill its required functions.**

**Therefore it is necessary to specify the amount by which a size may deviate from its ideal size and still fulfill its required functions.**

Basic Size- size to which limits or deviations are assigned Deviation- algebraic difference between size and corresponding basic size Upper deviation- indicates maximum difference Lower deviation- indicates minimum difference Fundamental deviation- which of the above is closer to the basic size

Tolerance- difference between max. and min. size limits International tolerance grade numbers (IT) designated groups of tolerances that vary depending on basic size Hole basis- system of fits corresponding to hole sizes (H is the fundamental deviation) Shaft basis- system of fits corresponding to shaft size (h is the fundamental deviation)

Tolerances are added to: Control the products that are produced Dimensions can not be reproduced exactly Control the accuracy of the process and to reduce functional or assembly failures.

Create more careful production procedures and more rigorous inspection

There are two different types of conventional tolerances: Unilateral: specify dimensional variation from the basic size in one direction.

Bilateral: specified dimensional variation from the basic size in both directions.

Tighter tolerances improve the quality of the product but generally increase the manufacturing cost.

**Type of fit**

Clearance

**Description**

* Loose running fit*: for wide commercial tolerances or allowances on external members

**Symbol**

H11/c11 Transition * Free running fit*: not for use where accuracy is essential, but good for large temperature variations, high running speeds, or heavy journal pressures

*Locational transitional*

: fit for accurate location, a compromise between clearance and interference

*Locational transitional fit*

for more accurate location where greater interference is permissible H9/d9 H8/f7 H7/g6 H7/h6 H7/k6 H7/n6 Interference

*Locational interference fit*

: for parts requiring rigidity and alignment with prime accuracy of location but without special bore pressure requirements

*Medium drive fit*

: for ordinary steel parts or shrink fits on light sections, the tightest fit useable with cast iron

*Force fit: *

Suitable for parts which can be highly stressed or for shrink fits where the heavy pressing forces are impractical H7/p6 H7/s6 H7/u6

*Clearance fit*: The largest permitted shaft diameter is smaller than the diameter of the smallest hole. LMC of the hole – LMC of the shaft = Clearance *Interference fit*: The minimum permitted diameter of the shaft is larger than the maximum permitted diameter of the hole.

Least amount of Interference is: LMC Shaft = 1.2513

- LMC Hole = 1.2506

Min Interference = .0007

Greatest amount of Interference: MMC Shaft = 1.2519

- MMC Hole = 1.2500

Max Interference = .0019

**Transitional fit: The diameter of the largest permitted hole is greater than that of the smallest permitted shaft and the smallest permitted hole is smaller than the largest permitted shaft. **

LMC Hole = 1.2506

LMC Shaft = 1.2503

Positive Clearance = .0003

MMC Shaft = 1.2509

- MMC Hole = 1.2500

Negative Allowance (Interference) = .0003

**These different types of fits are used in conjunction with two distinct bases: 1. Hole basis system: The desired clearances and interferences in the fit are achieved by combinations of various shaft tolerance zone with the hole tolerance zone “H”. In this system of tolerance and fits, the lower deviation of the hole is always equal to zero. 2. Shaft basis system: The desired clearances and interferences in the fit are achieved in the combination of various hole tolerance zone with the shaft tolerance zone “h”. In this system of tolerance and fits, the upper deviation of the hole is always equal to zero**

**Journal bearings are designed to operate at high rotational speeds.**

**If the clearance between inner and the outer diameter is too small the bearing will sieze.**

**If the clearance is too big the shaft will vibrate.**

**Limits on the size of the shaft and hole provide correct operation.**

**Nominal diameter 20 mm.**

**Close running fit H8 f7 H8 hole= 20,000 to 20.033**

**f7 shaft= 19,980 to 19,959 clearance= 20 to 74 micron**

**Spool valve has a shaft that translates.**

**This time the clearance should be a sliding fit.**

**Nominal diameter 20 mm.**

**Sliding fit H7/g6.**

**g6 shaft= 19,993 to 19,980 H7 hole = 20,000 to 20, 021 Clearance= 7 to 28 microns**

**A 20 mm nominal diameter journal/shaft is to have a clearance, but close accurate running fit. Within what size tolerances should the parts be manufactured? Use “the basic hole system”.**

**Solution: A H8/f7 fit is suitable. From the BS chart, for a 20 mm diameter nominal size the H8 limits are + 0.033 and – 0.000 and the f7 limits are 0.020 and -0.041 mm. Hence the hole diameter should be between 20.000 and 20.003 mm and the shaft diameter should be between 19.959 and 19.980 mm.**

**A fit is designated as diameter 130 H 7 p 6 1.**

**State the classification of fit produced 2.**

**3.**

**Determine the limits of size both the shaft and the hole.**

**State the extremes of fit i.e. the maximum or minimum interference or clearance.**

**4.**

**Determine the fundamental deviations on both the hole and the shaft.**

**5.**

**State the tolerance grades for both the hole and shaft.**

**1.**

**Classification of fit: Interference 2.**

**Hole: + 0.040 Shaft: + 0.068, + 0.043**

**Hole: 130.040 shaft: 130.068, 130.043**

**3. Maximum interference occurs between the smallest hole and the largest shaft; i.e. 130.000 – 130.068 = - 0.068 mm Minimum interference occurs between the largest hole and the smallest shaft; i.e. 130.040 – 130.043 = - 0.003 mm**

**4. Fundamental deviation for Hole = + 0.040 and + 0.000, Fundamental deviation for shaft = + 0.068, + 0.043**

**5. Tolerance grade for Hole is IT7 = 0.040**

**Tolerance grade for shaft is IT6= 0.025**

Determine the “loose running fit” tolerances for a shaft and hole that have a basic diameter of 32 mm. 32H11/32c11 Tolerance Grade Hole Shaft Upper deviation Lower deviation Max Diameter Min Diameter Average Diameter Max Clearance Min Clearance Dimensions tolerance in drawing 0.160 mm 0.000 mm 32.160 mm 32.000

32.080 mm Dmax- dmin=0.44 mm Dmin-dmax=0.12 mm Hole 32.080 +0.080 - 0.080

-0.120 mm -0.280 mm 31.880 mm 31.720 mm 31.800 mm Shaft 31.800 +0.080 – 0.080

Determine the “medium drive force fit” tolerances for a shaft and hole that have a basic diameter of 32 mm. 32H7/32s6 Tolerance Grade Hole Shaft Upper deviation Lower deviation Max Diameter Min Diameter Average Diameter Max Clearance Min Clearance 0.025 mm 0.000 mm 32.025 mm 32.000 mm 32.013 mm Dmax-dmin= - 0.018 mm Dmin-dmax= - 0.059 mm 0.059 mm 0.043 mm 32.059 mm 32.043 mm 32.051 mm

Measurement Linear Angle Comparative length Straightness Flatness roundness Profile GO NOT GO Instrument Steel rule, vernier caliper, micrometer Bevel protractor with vernier Sine bar Dial indicator Gauge blocks Autocollimator Interferometry Dial indicater circular tracing Dial indicator Optical comparator Sensitivity µm 0.5 mm 25 2.5

5 min 1 1 0.05

2.5

0.03

0.03

1 125

**The limits for GO and NOT GO gauges for an internal diameter component are found as follows: The workpiece tolerance is 0.200 mm. From the column 4 of Table 1, the limits for GO gauges are: + 0.021, +0.012, therefore, the size of the GO gauge is: +75.021 mm, + 75.012 mm.**

**The limits for GO and NOT GO gauges for an internal diameter component are found as follows: The workpiece tolerance is 0.200 mm. From the column 5 of Table 1, the limits for NOT GO gauges are: + 0.0, -0.009, therefore, the size of the NOT GO gauge is: +75.200 mm, + 74.991 mm.**

**The limits for GO and NOT GO gauges for a shaft are found as follows: The workpiece tolerance is 0.040 mm. From the column 6 of Table 1, the limits for GO gauge are: -0.002 mm, - 0.005 mm + 0.0, -0.009, therefore, the size of the GO gauge is: +44.928 mm, + 44.925 mm.**

**The limits for GO and NOT GO gauges for a shaft are found as follows: The workpiece tolerance is 0.040 mm. From the column 7 of Table 1, the limits for NOT GO gauge are: +0.003 mm, - 0.000 mm therefore, the size of the NOT GO gauge is: +44.893 mm, + 44.890 mm.**

1. S. Kalpakjian, S.R. Schmid: Manufacturing Engineering & Technology, 5 th edition, Prentice-Hall International, 2006.

2. E. Paul Degarmo, J. R. Black, R. A. Kohser; Materials and Processes in Manufacturing, 9 th edition, John Wiley & Sons, Inc, 3.

2003.

R. L. Timings, S. P. Wilkinson: Manufacturing Technology, 2 nd edition, Pearson Education Limited, London, 2000.

4. J. F. W. Galyer, C. R. Shotbolt: Metrology for Engineers, Cassell & Co. Ltd, 3 rd edition, 1977.

5. Data Sheet BS 4500A: 1970