Angular Measurement
•No absolute standard is required for angular
measurement.
•Units of measurement
–Degrees (°): defined as 1/360 of a circle
–Radians (rad): defined as 1/(2π) of a circle.
•1 radian = 57.29578°
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Hardened and precision ground tools used for: – Measuring known angles or locating any work to a given angle. – Checking of unknown angles.
Typology: Slides
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Angular Measurement
- No absolute standard is required for angular
measurement.
- Units of measurement
- Degrees (°): defined as 1/360 of a circle
- Radians (rad): defined as 1/(2π) of a circle.
- 1 radian = 57.29578°
Angular Measurement
Common Instruments Used:
- Protractors
- Sine Bars & Sine Centers
- Angle Gauges
- Spirit Level
- Autocollimator
- Angle Dekkor
Optical Bevel Protractor
- It has a glass circle fitted inside the main body
- Glass circle is divided into 10’ throughout its 360 0 .
- Provision for magnification is available.
- By approximation, it may read upto 2’.
Sine Bars
- Hardened and precision ground tools used for:
- Measuring known angles or locating any work to a given angle.
- Checking of unknown angles.
- Used in conjunction with slip gauges and dial
indicator.
- Depending on the accuracy they may be
- Grade A: 0.01 mm/m of length
- Grade B: 0.02 mm/m of length
Sine Bar: Principle
- If sine bar is the hypotenuse of right angled triangle and h the height of slip gauges as shown in Figure h = Height in mm L = Center distance in mm Sinθ = Opp / Hyp = (h/ L)
Use of Sine Bar
Sine Bar Error
- Accuracy of an angle set by a sine bar depends on:
- Error in spacing of roller centers (dL)
- error in or errors in combination of slip gauges (dh)
- The height of slip gauge combination (h) required to set angle (ϴ) is given by: h = L sin ϴ Partial differentiation of the above equation yields: dh/dϴ = (sin ϴ) (dL /dϴ) + L cos ϴ or dh = (sin ϴ) dL + (L cos ϴ) dϴ or dϴ = tan ϴ ((dh/h) - (dL /L))
- As the angle increases, the error (dϴ) in the angular measurement increases. Above 45 °, t he graph for dϴ vs. ϴ rises sharply, so a sine bar is never used beyond 45 °.
Limitation of Sine Bar
- Sine bars are not used beyond 45 0
because:
- It is difficult to handle & position on slip gauges.
- Large angular error may result due to slight error in length.
- Long gauge stacks are not as accurate as short ones
- Different deformation is observed at the two rollers because at large angles, weight load gets shifted towards the fulcrum roller
Sine Plate
- Allow angles to be measured and set in each of two orthogonal planes.
- A work piece is secured to the top plate and the bottom plate is secured to a machine tool table using clamps or a magnetic chuck.
Angle Gauges
Wedge shaped block used as standards for
angle measurement.
Large number of combinations by adding or
subtracting gauges are possible
Nominal angles of combination angle gauges
Degrees 1 3 9 27 41 Minutes 1 3 9 27 Seconds 3 6 18 30
- Square block is also available
Angle Gauges
Spirit Level
- Principle: When the base of the level is moved out of the horizontal, the bubble moves along the scale. Thus, l = Rα = Rh/L (For small values of α)
- Thus sensitivity of the level increases as - Radius of curvature (R)increases - Length of the base (L) decreases
- Scale division values:
- For precise measurements: 4 to 10
- For ordinary purposes: 10 to 40
- Very sensitive to variation in surroundings temperature
Types of Spirit Level (Contd.)
According to BS 1958, three types of spirit levels are recommended.
- Type 1.:
- It has an unrelieved flat base of steel, hardened and lapped.
- The base length of spirit level varies between 100 to 200 mm.
- Effective length of the level can be varied by wringing two gauge blocks on the base at the desired distance apart.
- Type 2
- It is mounted in cast iron or steel body, having a base formed with feet bearing surfaces at the two ends (middle portion being relieved).
- Base length 250- 500 mm
- The bearing surface may be plain or contain a longitudinal 120 ° V- groove for use on cylindrical surfaces.
- Type 3:
- It is a square block level about 200 mm square and made of cast iron.
- The four bearing surfaces are flat and may have the middle portion relieved. Alternatively, the base and one adjacent-surface may contain a longitudinal 120° vee groove for use on cylindrical surfaces in which case a short cross-level is provided.