Understanding Dimensional Metrology and Tolerances in Manufacturing
Dimensional Metrology and Tolerances
Precision and Range
When a set of readings of a measurement has a wide range, it indicates low precision. The difference between the lower and higher values that an instrument is able to measure is called range.
Uncertainty Factors
When determining the uncertainty for a particular measurement device, the common uncertainty factors that should be included are: technician’s error, errors in the measurement technique and method, and random variability of the measurement process.
Accuracy and Traceability
Accuracy is defined as the closeness of a measured value to the real value. Conformity of a physical quantity to the national standard of measurement is known as traceability.
Maximum and Least Material Limits
MML corresponds to the lower limit of a hole and higher limit of the shaft. LML corresponds to the higher limit of a hole and lower limit of the shaft.
ISO Tolerance Grades
The most appropriate reason for specifying grades of tolerances in the ISO system is to improve the accuracy of manufacture. In the hole and shaft pair designation of 40 H7/d9, the numbers 7 and 9 indicate tolerance grade. In a shaft basis system, the upper deviation of the size of the shaft is 0.
Measurement Principles and Instruments
The degree to which an instrument conforms to Abbe’s Law determines its inherent accuracy. The foundation for all dimensional measurements is the datum plane. The preferred instrument for measuring holes, grooves, and recesses is a depth gauge.
Bevel Protractor
While measuring the angle of a workpiece using a universal bevel protractor in a clockwise direction, the angle can be read directly from the scale in quadrants 1 and 3. The following statement is false with respect to a bevel protractor: The angle measured in quadrant IV is always an acute angle. Type A bevel protractor has a vernier scale as well as an acute angle attachment.
Measurement Errors
The measurement error is the incompatibility of the obtained result with the value of the measured value. The absolute measurement error (deviation) is the difference between the measurement result and the actual value. The relative error is determined by the ratio of the absolute error to the actual value of the measured quantity. Environmental conditions and parallax errors are controllable errors, while linearity and hysteresis are non-controllable errors.
Micrometer
For an Abbe principle micrometer, a good result is graduations located along the same axis as the measurement. Scale errors can be reduced or eliminated by:
- Choosing a setting master whose size is as close to that of the gauge being checked as possible.
- Using as short a length scale as possible.
- Calibrating the scale against known standards of length.
The following statement with reference to a micrometer is false: It is not as precise as a vernier caliper.
Comparators
A scribing tool comprising one divider leg and one caliper leg is known as a hermaphrodite caliper. In comparison measurement, precision depends on the least count of the standard. In the case of a comparator, measurement is done by the interchange method. The precision of a dial comparator is determined by the dispersal of a series of readings. A spherical contact point is most preferred in dial gauges since it presents point contact to the mating surface irrespective of whether it is flat or cylindrical. Solex pneumatic gauge can give amplification of up to 50,000. With respect to the Johansson mikrokator, the following statement is true: Magnification varies inversely with the number of turns and width of the metal strip. In a Sigma mechanical comparator, magnification is obtained in two stages. Double reflection of light using a pair of mirrors is a unique feature of a Zeiss Ultra-Optimeter.
Data Plot Lines
- Best fit line: The line midway between the two closest parallel straight lines that enclose all the data points.
- End point line: A line drawn between the end points of a data plot.
- Terminal line: A line drawn from the origin to the farthest data point.
- Least square line: The line for which the sum of the squares of the deviations of the data points from the line being fit is minimized.
Geometric Tolerances
Geometric tolerances are standards that control the shape, orientation, position, and profile of features on manufactured parts. They communicate design intent and ensure parts function correctly. While they require precise interpretation and may need advanced technology, they are essential for quality and efficiency in manufacturing.
Limits, Fundamental Deviation, and Tolerance
Limits: In engineering and manufacturing, limits refer to the maximum and minimum allowable dimensions, usually specified by a tolerance. For example, if a hole diameter is specified as 25 ± 0.1 mm, the limits are 24.9 mm (lower limit) and 25.1 mm (upper limit).
Fundamental Deviation: Fundamental deviation is the deviation from the basic size of a dimension, expressed as a positive or negative value. It indicates whether the actual dimension is larger or smaller than the basic size. Fundamental deviations are defined in standards such as ISO 286 and ASME Y14.5 to simplify the selection of fits between mating parts.
Fundamental Tolerance: Fundamental tolerance is the basic tolerance associated with a specific fundamental deviation. It represents the maximum allowable variation in the dimension from the basic size. Fundamental tolerances are typically defined in tables within engineering standards and are used in conjunction with fundamental deviations to establish the tolerance zone for a given dimension.
Hole Basis System: Tolerance primarily allocated to the hole. Hole serves as the reference feature. Hole dimensions vary; shaft dimensions remain constant. Fits determined based on relationship between shaft and hole sizes.
Shaft Basis System: Tolerance primarily allocated to the shaft. Shaft serves as the reference feature. Shaft dimensions vary; hole dimensions remain constant. Fits determined based on relationship between hole and shaft sizes.