PRECISION MEASUREMENT USING VERNIER CALIPER

 

TITLE: PRECISION MEASUREMENT USING VERNIER CALIPER: CALIBRATION, MEASUREMENT OF SLIP GAUGES, AND ERROR ANALYSIS

OBJECTIVES

    1.     To understand and get familiar with the use of the Vernier caliper.

    2.     To determine the least count of the Vernier caliper.

   3.   To measure the dimensions of slip gauges using the Vernier caliper and calculate the measurement errors by comparing the measured values with standard values.

    4.     To analyze the sources of errors and discuss methods to minimize them.

EQUIPMENT USED

    1.     Vernier Caliper

    2.     Set of slip gauges

    3.     Calculator

THEORY

Vernier Caliper

A Vernier caliper is a precision measuring instrument used to measure internal and external dimensions as well as depths. It uses a Vernier scale, pioneered by French mathematician Pierre Vernier in the 17th century.

Figure: Vernier Caliper

Principle: Vernier caliper operates on the principle of alignment of two scales, the main scale and the Vernier scale, to interpolate between the smallest main scale divisions for finer measurements.

Construction: The Vernier caliper consists of two scale: one is fixed and the other is movable. The fixed scale, called main scale is calibrated on L-shaped frame and carries a fixed jaw. The movable scale, called Vernier scale slides over the main scale and carries a movable jaw. The large, external jaws are used to measure external diameter or width of an object and the small internal jaws are used to measure internal diameter of an object. The depth measuring blade extends from one end of the caliper, which is used to measure the depths of an object or a hole. A locking screw is used to stop moveable parts, allowing measurements to be easily transferred.

Least Count: It is the difference between value of main scale division and vernier scale division.

i.e. L.C. = Value of smallest division on main scale – Value of smallest division on Vernier scale

If there are N Vernier scale divisions and N-1 main scale divisions then,

N VSD = (N-1) MSD

1 VSD = (N-1)/N MSD

L.C. = 1 MSD – 1 VSD

        = 1 -  (N-1)/N MSD

L.C.  = 1/N MSD

The total reading of the Vernier caliper = MSR + (VSC * LC)

Errors

                  i.         Zero error occurs if the zero mark on the Vernier scale is not aligned with the main scale zero.

                 ii.         Parallax error is caused by not reading the scale from a perpendicular angle.

               iii.         The error happens due to misalignment of the object between the jaws.

                iv.         Contact pressure either too tight or too loose may lead to inaccurate measurements.

                 v.          Repeated use can wear down the jaws, causing errors.

Slip Gauge

Slip gauges or gauge blocks are universally accepted end standard of length in industry. These were introduced by Johanson and are also called as Johanson Gauges. Slip gauges are rectangular blocks of high-grade steel with exceptionally close tolerances. The cross-sections of these gauges are 9mm x 30 mm for sizes up to 10 mm and 9 mm x 35 mm for larger sizes. Any two slips when perfectly clean may be wrung together. The gap between two wrung slips is only of the order of 0.00635 microns which is negligible.

PROCEDURE

1.     Calibration: The Vernier caliper was calibrated by ensuring it was set to zero when the jaws were fully closed. Our caliper was free from zero error and Vernier zero mark properly coincided with the main scale zero.

2.     Measurement of slip gauges: The two jaws of the Vernier caliper were cleaned and slip gauges were placed in between the measuring jaws. Each of the 10 slip gauges was measured using the Vernier caliper. The main scale reading (MSR) and the Vernier scale reading (VSR) which exactly coincided with any line on the main scale were recorded and the total measurement was calculated.

3.     Error Calculation: The error for each slip gauge was calculated by comparing the measured value with the standard value of the slip gauge.

Error = Measured Value – Standard Value

PRECAUTIONS

    1.     Ensure the Vernier caliper is properly calibrated before use.

    2.     Clean the caliper and the object to be measured to avoid dirt and debris.

    3.     Apply consistent, gentle pressure when closing the jaws to avoid the contact pressure error.

    4.     Read the scale directly from above to avoid parallax error.

    5.     Handle the caliper gently to prevent wear and tear.

OBSERVATION

Observation Table 1

Observation Table 2

CALCULATION

Least Count of Vernier Caliper

One small division of main scale = 1 mm

50 VSD = 49 MSD

1 VSD = 49/50 MSD

L.C. = 1 MSD – 1 VSD

        = 1 - 49/50 MSD

Or, L.C. = 0.02 * 1 mm

∴ L.C.  = 0.02 mm

For Observation Table 1

For slip gauge 1:

Main Scale Reading (MSR) = 1.0 mm

Vernier Scale Reading (VSR) = 5

Least Count (LC) = 0.02 mm

Total Measurement (TM) = 1.0 mm + (5 mm * 0.02 mm) = 1.10 mm

Standard gauge value = 1.10 mm

Error (E) = 1.10 mm – 1.10 mm = 0.00 mm

Similarly, the calculations were performed for each of the slip gauges.

ANALYSIS

The minor errors observed in the measurements (ranging from 0.00 mm to 0.02 mm) suggest that the Vernier caliper is generally accurate but not perfectly so. The least count of 0.02 mm means that any measurement must be rounded to the nearest 0.02 mm. This limitation is particularly evident when measuring gauge blocks with dimensions that fall between the increments that the caliper can measure accurately.

The consistency of the errors suggests that while the caliper may have minor systematic inaccuracies, it is precise within its limitations. The errors, though minor, highlight the importance of understanding and accounting for the limitations of measurement tools. In applications requiring higher precision, alternative tools with a smaller least count or digital calipers might be necessary.

DISCUSSION

The measurements taken using the Vernier caliper showed minor errors ranging from 0.00 mm to 0.02 mm. These errors can be attributed to factors such as slight misalignment, parallax error while reading the scale, and contact pressure error.

The least count of 0.02 mm provided reasonable precision for the measurements. When measuring gauge blocks with an odd hundredths digit, the caliper consistently showed an error due to the least count limitation. Regular calibration and proper handling of the Vernier caliper are essential to maintain accuracy.

CONCLUSION

The experiment successfully demonstrated the use of a Vernier caliper in measuring slip gauges. The calculated least count was 0.02 mm, and the measurement errors were minimal, validating the precision of the instrument. Understanding and mitigating potential sources of error is crucial for obtaining accurate measurements.