Let's break down and solve the problem step by step. --- ## **Question Recap** Design a **Go** and **No-Go plug gauge** for a **hole of 25D8** with: - \( i = 0.45(D)^{1/3} + 0.001D \) in microns - Fundamental deviation for hole: \( E_S = 16D^{0.44} \) - IT8 = \( 25i \) - D = 25 mm (since 25 falls in 18–30 mm step) --- ## **Step 1: Calculate the Standard Tolerance Unit, \( i \)** Given: - \( D = 25 \) mm - \( i = 0.45(D)^{1/3} + 0.001D \) (in microns) Calculate \( (25)^{1/3} \): \[ 25^{1/3} \approx 2.924 \] Now, \[ i = 0.45 \times 2.924 + 0.001 \times 25 \] \[ i = 1.316 + 0.025 \] \[ i = 1.341 \text{ microns} \] --- ## **Step 2: Calculate IT8 Tolerance** \[ IT8 = 25i = 25 \times 1.341 = 33.525 \text{ microns} \] --- ## **Step 3: Fundamental Deviation (for D8 hole)** For hole (D8), the fundamental deviation for holes is generally **zero** (for H holes) but for D holes, use: \[ E_S = 16D^{0.44} \] Calculate \( D^{0.44} \): \[ D^{0.44} = 25^{0.44} \] \[ \ln(25) = 3.21888 \] \[ 0.44 \times 3.21888 = 1.417 \] \[ e^{1.417} \approx 4.13 \] \[ E_S = 16 \times 4.13 \approx 66.08 \text{ microns} \] --- ## **Step 4: Limits of Hole (D8)** - **Lower Limit** = Basic Size + Fundamental Deviation = \( 25 + 66.08 \) microns = \( 25.06608 \) mm - **Upper Limit** = Lower Limit + IT8 Tolerance = \( 25.06608 + 0.033525 \) mm = \( 25.099605 \) mm --- ## **Step 5: Go and No-Go Plug Gauge Design** ### **Go Gauge:** - **Go Gauge** should enter the hole, so must be made to the lower limit (minimum size): - **Go Plug Gauge size = Lower Limit = 25.066 mm** ### **No-Go Gauge:** - **No-Go Gauge** should not enter if the hole is too large, i.e., made to the upper limit (maximum size): - **No-Go Plug Gauge size = Upper Limit = 25.100 mm** --- ## **Step 6: Final Answers (rounded to suitable decimal places)** - **Standard tolerance unit, \( i \) = 1.34 µm** - **IT8 Tolerance = 33.53 µm** - **Fundamental deviation (D8) = 66.08 µm** - **Hole limits = 25.066 mm to 25.100 mm** - **Go Plug Gauge size = 25.066 mm** - **No-Go Plug Gauge size = 25.100 mm** --- ## **Summary Table** | Parameter | Value | |--------------------------|--------------| | Standard unit (\(i\)) | 1.34 µm | | IT8 Tolerance | 33.53 µm | | Fundamental deviation | 66.08 µm | | Hole Lower Limit | 25.066 mm | | Hole Upper Limit | 25.100 mm | | **Go Plug Gauge** | 25.066 mm | | **No-Go Plug Gauge** | 25.100 mm | --- ### **Explanation** - **Go gauge** ensures the hole is not smaller than the minimum acceptable size. - **No-Go gauge** ensures the hole is not larger than the maximum acceptable size. - Calculations follow ISO tolerance system for plug gauge design. --- **Let me know if you need a diagram or further explanation!**