ANGULAR MEASUREMENT USING SINE BAR

TITLE: ANGULAR MEASUREMENT USING SINE BAR

OBJECTIVES

1. To understand and get familiar with the use of the sine bar.
2. To use trigonometric relationship to set up exact measurements on a workpiece.
3. To understand and use sine bar, and make it reliable tool.
4. To get familiar with the use of dial indicator.
5. To discuss the sources of errors and discuss methods to minimize them.

APPARATUS REQUIRED

1. Sine bar
2. Dial indicator
3. Indicator Stand
4. Set of slip gauges
5. Metal surface plate

THEORY

Sine Bar

A sine bar consists of a hardened, precision ground body with two precision ground cylinders fixed at the ends. The distance between the centers of the cylinders is precisely controlled, and the top of the bar is parallel to a line through the centers of the two rollers. The distance between the centers of the rollers is standardized (for ease of later calculations) and forms the hypotenuse of a triangle when in use.

                            

Figure: Sine Bar

 Principle

Angles are measured using a sine bar with the help of slip gauge and a dial indicator. The aim of a measurement is to measure the surface on which the dial gauge is placed horizontally. The principle of operation of sine bar depends upon trigonometry.

sinθ = (perpendicular)/(hypotenuse)

Construction

The sine bar is made of high carbon steel, high chromium (corrosion resistance) and hardened. It consists of two rollers with steel bars. The two rollers are very precise and highly accurate and are equal in diameter. When the sine bar placed on a flat surface, the axes of the two rollers are parallel to each other and also parallel to the above face of the sine bar. The steel bar has the appearance of relief holes to easily handle the sine bar and also to reduce overall weight.

 Dial Indicator

A dial indicator is an instrument with either jeweled or plain bearings, precisely finished gears, pinions, and other precision parts designed to produce accurate measurements. It is possible to take measurements ranging from one-thousandth (0.001 inch or one mil) to 50 millionths of an inch.

   Figure: Dial Indicator

Construction

 A dial indicator has a dial display similar to a clock face with clock hands; the hands point to graduations in circular scales on the dial which represent the distance of the probe tip from a zero setting. The internal works of a mechanical dial indicator are similar to the precision clockworks of a mechanical wristwatch, employing a rack and pinion gear to read the probe position, instead of a pendulum escapement to read time. The side of the indicator probe shaft is cut with teeth to provide the rack gear. When the probe moves, the rack gear drives a pinion gear to rotate, spinning the indicator "clock" hand. Springs preload the gear mechanism to minimize the backlash error in the reading. Precise quality of the gear forms and bearing freedom determines the repeatable precision of measurement achieved. Since the mechanisms are necessarily delicate, rugged framework construction is required to perform reliably in harsh applications such as machine tool metalworking operations, similar to how wristwatches are ruggedized.

Indicator Stand

The dial indicator is used in conjunction with stands for holding them so that the stand itself may be placed on a datum surface or machine tools.

                            Figure: Indicator Stand

 

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.

 

Surface Plate

Surface plate is a solid, flat plate used as the main horizontal reference plane for precision inspection, marking out (layout), and tooling setup. The surface plate is often used as the baseline for all measurements to a workpiece, therefore one primary surface is finished extremely flat with tolerances below 11.5 μm or 0.0115 mm per 2960 mm for a grade 0 plate. Surface plates are a common tool in the manufacturing industry and are often fitted with mounting points so that it can be an integrated structural element of a machine such as a coordinate measuring machine precision optical assembly, or other high precision scientific & industrial machine. Plates are typically square or rectangular, although they may be cut to any shape. 

PROCEDURE

1. We used a perfectly flat and clean surface plate.

2. We placed one roller on the surface plate and the other roller on slip gauge block of height 'H'.

3. Let the sine bar set at angle ''.

4. We slid the dial indicator horizontally on an object whose angle was to be determine.

5. If dial indicator showed any deflection, then we adjusted the height 'H' by adding or removing slip gauge.

6. We repeated the procedure until the dial indicator showed zero deflection.

7. We calculated the required angle using the sine trigonometric function.

CALCULATION

Height of slip gauge (H) = (3+1.10+1.01) mm

Length between the rollers (L) = 127 mm

Now,

sin⁡θ = (Height of slip gauge)/(Length between the roller)

Or, sinθ = 5.11/127

Or, θ = 2.305^°

Or, θ = 2^° + 0.305*60 minutes

Or, θ = 2^° 18.3 minutes

Or,  θ = 2^° 18 minutes + 0.3*60 seconds

∴ θ = 2^° 18 minutes 18 seconds

RESULT AND ANALYSIS

In our experiment, we determined the angle of the workpiece to be 2 degrees 18 minutes and 18 seconds. The performed measurements suggest that the sine bar is an accurate measuring instrument for angular measurements. The precision of the gauge blocks and sine bar setup allows for accurate determination of angles. The primary factors contributing to measurement inaccuracies included the lack of flatness of the slip gauges, vibrations during working and uneven surface plate. Despite these issues, the sine bar provided reliable results due to its simplicity and the accurate application of trigonometric relationships.

DISCUSSION

During the experiment, we ensured that the sine bar and the workpiece were properly aligned to avoid any errors in the angle measurement. Misalignment of the sine bar or the gauge blocks can introduce significant errors. We also considered potential sources of error, such as alignment error, human error, parallax error and flatness of the upper surface of the bar. Careful handling of the sine bar, slip gauges and dial indicator, as well as ensuring a stable setup without any vibrations, were crucial in obtaining accurate measurements.

Sine bar is fairly reliable for angles less than 15 degrees and becomes increasingly inaccurate as the angle increases. So, the workpiece with very small angle was measured during the lab. The precision of the gauge blocks, no deflection on dial indicator and the correct calculation of the required height for the angle were key to achieving an accurate result.

CONCLUSION

In conclusion, the sine bar proved to be a highly reliable and precise instrument for measuring angles. While various sources of error were identified, proper alignment, careful handling, and regular calibration can significantly reduce these errors. The experiment demonstrates the importance of the sine bar in applications requiring high accuracy in angular measurements. The result of 2 degrees 18 minutes and 18 seconds for the angle of the workpiece confirms the sine bar's effectiveness in angular measurements.

PRECAUTIONS

1. Clean the sine bar and workpiece by wiping of oil, dirt and dust with a clean piece of cloth.

2. Ensure the height of the gauge blocks is correct and dial indicator shows no deflection.

3. Place the sine bar on a stable and flat surface, preferably a surface plate.

4. Align the sine bar correctly with the workpiece.

5. Inspect the sine bar for any signs of wear or damage.

6. Ensure the experiment is conducted without vibration, as any movement can cause errors.