Batch of Angle Brackets Out of Tolerance Due to Caliper Zero Error
A student must make 20 identical L-brackets from 40 mm × 40 mm × 4 mm mild steel angle. Each bracket has two 8 mm holes: one in each leg, with hole centres 30 mm from the outside corner and 15 mm from the end. The drawing gives a tolerance of ±0.2 mm on the 30 mm dimension. The student uses a steel rule, scriber, centre punch, and bench drill. The first bracket measures 30.6 mm on a digital caliper; when the caliper jaws are closed, it reads 0.3 mm. The drilled holes are visibly 0.4 mm off the punch marks in different directions. The remaining 19 brackets are due at the end of the week.
1. Identify the sources of error in the first bracket and explain how each contributes to the measured 30.6 mm dimension.
Read the worked answer
The first error is the caliper zero error. With the jaws closed, the caliper reads 0.3 mm, so every reading is 0.3 mm high. The indicated 30.6 mm therefore corresponds to an actual dimension of about 30.3 mm, assuming the zero error is constant. That is still outside the ±0.2 mm tolerance, but the true error is smaller than the raw reading suggests.
Other errors come from marking out and drilling. A steel rule and scriber depend on parallax, line thickness and the student's eye; a scribed line can easily be 0.1 to 0.2 mm wide. The centre punch can drift when struck, especially on the angled leg. The drill then follows the punch mark imperfectly and can wander 0.4 mm, as seen. The combination of measurement error, marking error and drill wander explains why the hole is not in the intended position. The caliper error is systematic, while the punch and drill errors are random, which is why different holes are offset in different directions.
2. Describe a more reliable marking-out and drilling procedure that could achieve ±0.2 mm for the batch.
Read the worked answer
Use a datum-based method rather than measuring each bracket separately with a steel rule. Clamp a stop or fence to the drill table so the outside corner of every bracket locates in the same position. Mark the 30 mm dimension with a vernier height gauge on a surface plate, or use a hardened drill jig or template made from a scrap bracket. The template should have hardened bushes or at least pilot holes so the drill starts in the same place every time.
Centre punch lightly, then check the punch mark with a rule or caliper before drilling. Use a centre drill first to create a rigid start, then drill the 8 mm hole. Clamp the bracket firmly; do not hand-hold it. Drill a test piece and measure it with a calibrated caliper or micrometer before running the batch. Check the first few parts and adjust the stop if needed. For ±0.2 mm, the marking-out line thickness and punch drift are significant, so a jig or stop is more reliable than repeated rule measurement. If the drill still wanders, drill undersize and finish with a reamer or file.
3. How would you check and correct the caliper, and what measurement uncertainty would you assign to the 30 mm dimension? Would you accept the first bracket?
Read the worked answer
Clean the caliper jaws with a lint-free cloth, close them fully and zero the display. Open and close the jaws several times to check that the zero repeats. If the zero error remains, record it and subtract it from every reading, or have the caliper adjusted. Check the caliper against a known gauge block or a micrometer standard if one is available. A digital caliper of this type typically has a resolution of 0.01 mm but a practical uncertainty of about ±0.02 to ±0.05 mm, depending on the user and the condition of the jaws.
The first bracket reads 30.6 mm with a zero error of +0.3 mm, so the corrected dimension is about 30.3 mm. Even allowing ±0.05 mm uncertainty, that is outside the 30 ±0.2 mm tolerance, because the acceptable range is 29.8 to 30.2 mm. I would not accept the first bracket as finished. It could be reworked only if the hole can be moved or the bracket remade, because the hole position cannot be corrected by filing the outside corner without changing the datum. The remaining brackets should be made with the corrected measurement method and a drilling jig.