1. INTRODUCTION TO MEASUREMENTS

 For 4th Semester Polytechnic ME Students

Written by Garima Kanwar | Blog: Rajasthan Polytechnic

📢 🔔 Important:
👉 Full PDF available in our WhatsApp Group | Telegram Channel
👉 Subscribe YouTube Channel: BTER Polytechnic Classes

Course Code : ME 4001(Same in MA 4001)
Course Title : MEASUREMENTS & METROLOGY

1.1 Measurement and Its Significance

Definition:
Measurement is the process of determining the size, quantity, or degree of something. It involves comparing an unknown quantity to a known standard.

Significance:

• Accuracy & Consistency: It allows us to ensure precision in processes, ensuring products meet quality standards.
• Decision Making: In fields like engineering, science, and medicine, accurate measurements are crucial for designing systems, developing products, and diagnosing conditions.
• Scientific Discovery: Measurements help in the advancement of knowledge by quantifying natural phenomena.

---

1.2 Standards of Measurements: Primary & Secondary

Primary Standards:

• Primary standards are the highest form of measurement and cannot be improved upon by direct comparison.
• Example: The definition of the meter in terms of the speed of light.
• These are internationally agreed-upon values used for calibrating secondary standards.

Secondary Standards:

• These are instruments or measurements that have been calibrated against primary standards.
• Example: A laboratory thermometer calibrated by comparison with a standard platinum resistance thermometer.

---

1.6 Factors Influencing Selection of Measuring Instruments

When selecting a measuring instrument, the following factors must be considered:

1. Accuracy: How close the instrument reading is to the true value.
2. Precision: The degree of reproducibility of measurements.
3. Range: The span of values over which an instrument can operate.
4. Resolution: The smallest change in the measured quantity that an instrument can detect.
5. Environment: Factors like temperature, humidity, and pressure that may affect the instrument’s performance.
6. Cost: Budget constraints may limit the choice of instruments.
7. Ease of Use: Simple and intuitive instruments are preferred for practical use.
8. Durability: Instruments need to be robust enough for long-term use in specific environments.

---

1.7 Terms Applicable to Measuring Instruments

1. Precision and Accuracy:

   • Precision: Refers to the closeness of two or more measurements to each other (reproducibility).
     • Example: A clock showing 12:05, 12:06, 12:05 over several trials has high precision.
   • Accuracy: Refers to how close a measurement is to the true or accepted value.
     • Example: A thermometer reading 98.6°F when the true temperature is 98.6°F is accurate.

2. Sensitivity and Repeatability:

   • Sensitivity: The smallest detectable change in the measured quantity.
     • Example: A digital scale that can detect a change in weight of 0.01g is more sensitive than one that detects 1g.
   • Repeatability: The ability of an instrument to provide the same result when the same measurement is repeated under the same conditions.
     • Example: A ruler measuring the length of a table gives the same result every time; it shows high repeatability.

3. Range:

   • The range refers to the minimum and maximum limits of a measurement instrument.
     • Example: A thermometer with a range from -10°C to 110°C.

4. Threshold:

   • The minimum measurable value an instrument can detect.
     • Example: A scale that can detect 1g but not anything below that is said to have a threshold of 1g.

5. Hysteresis:

   • This is the difference in measurements when the input is increasing vs. when it is decreasing.
   • Example: A pressure gauge may read 5 units when pressure is increasing and 4.8 units when decreasing—this difference is hysteresis.

6. Calibration:

   • Calibration refers to adjusting and setting an instrument to the correct value by comparing it to a standard.
     • Example: A digital thermometer is calibrated against a standard to ensure accurate temperature readings.

---

1.8 Errors in Measurements

Types of Errors:

1. Systematic Errors: These errors occur consistently in the same direction. They can be corrected by calibration.

   • Example: An incorrectly zeroed scale.

2. Random Errors: These errors are due to unpredictable factors and vary with each measurement.

   • Example: Slight differences in the time of taking a measurement due to human reaction time.

3. Human Errors: These errors arise from misreading or misunderstanding of instruments or poor measurement techniques.

   • Example: Misreading a dial gauge or making a mistake in the units of measurement.

Error Analysis:

• Absolute Error: The difference between the measured value and the true value.
• Relative Error: The absolute error divided by the true value.
• Percentage Error: Relative error expressed as a percentage.

---

1.9 Surface Finish Measurements

Surface Finish:
Refers to the texture of the surface, which is critical in determining the performance, wear, and aesthetic quality of an object.

Methods of Measurement:

1. Roughness: The fine irregularities of the surface, which affect how an object moves or seals.
   • Example: Roughness can be measured using a profilometer.
2. Waviness: Larger, periodic variations in the surface.
   • Example: A ripple-like pattern on a surface that is measured using a long-wavelength measuring instrument.
3. Flatness: The extent to which a surface deviates from a flat plane.

Instruments:

• Stylus-based instruments: A fine stylus moves over the surface to measure roughness.
• Optical instruments: Used for measuring surface features without contact.
• Surface texture analyzers: Can measure roughness, waviness, and other features.

---

Important Questions and Example Numericals

Example 1: Calculating Absolute and Relative Error

Given:

• True Value = 50.0 cm
• Measured Value = 49.7 cm

Absolute Error = |Measured Value - True Value|
= |49.7 - 50.0|
= 0.3 cm

Relative Error = Absolute Error / True Value
= 0.3 / 50.0
= 0.006 or 0.6%

---

Example 2: Precision vs Accuracy

• Example 1 (High Precision, Low Accuracy):
  A thermometer consistently reads 90°F for a body temperature measurement, but the true value is 98.6°F. This shows high precision (repeatability) but low accuracy.

• Example 2 (High Accuracy, High Precision):
  A digital caliper consistently measures the length of a rod as 10.0 cm, and the actual length is also 10.0 cm. This shows both high precision and high accuracy.

---

Important Questions for Exam Preparation:

1. Define measurement and explain its significance in engineering.
2. Differentiate between primary and secondary standards with examples.
3. What factors influence the selection of measuring instruments?
4. Explain the terms: precision, accuracy, range, and sensitivity.
5. What is the difference between systematic and random errors?
6. How do you measure surface finish, and why is it important in manufacturing?
7. Explain calibration and why it is important in measurement.
8. What is hysteresis, and how can it affect the readings of an instrument?

---

Diagrams to Consider:

• Measurement Error Diagram: A diagram showing accuracy vs precision (e.g., a target with shots spread out for low precision vs. tightly clustered for high precision).
• Surface Finish Measurement Diagram: Profilometer reading showing roughness and waviness.

---

These notes should help you prepare well for your exam. Be sure to understand the key concepts and practice solving example problems!

📢 🔔 Download PDF & Join Study Groups:
📥 WhatsApp Group: Join Now
📥 Telegram Channel: Join Now
📺 Watch Lecture on YouTube: BTER Polytechnic Classes
📍 Stay connected for more study materials! 🚀