Directions
This calculator is designed to resemble a spreadsheet calculator that can be printed as a report for project recordkeeping. The term project, with regards to Precision Mindset calculators, refers to engineered designs, homework problems, tutorial problems, hobby designs or self-study.
Cells with a border are inputs and cells without a border are outputs. An external thread refers to a bolt, screw, or threaded rod. An internal thread refers to a nut or tapped hole.
- Select the thread designation from the dropdown menu or leave it as User Defined and enter values for the basic diameter and pitch.
- Choose the three values that define the tolerance grade of the external thread. These variables are automatically populated, but their values can be changed by selecting the appropriate value from their respective dropdown menus.
- Choose the three values that define the tolerance grade of the internal thread. These variables are automatically populated as well, but they can also be changed by selecting the appropriate value from their respective dropdown menus.
- Select the calculate button to complete the analysis.
- Print a report for your project recordkeeping by pressing the print button.
Assumptions
- The thread profile is for an ISO metric screw.
Equations
- Height of the Fundamental Triangle
$$H = \frac{\sqrt{3}}{2}p$$
- External Thread Clearance Height
$$h_1 = \frac{H}{4}$$
- Truncated Thread Height
$$h_2 = \frac{5}{8}H$$
- Internal Thread Clearance Height
$$h_3 = \frac{H}{8}$$
- External Thread Clearance Diameter
$$d_0 = d-\frac{7}{8}H$$
- Basic Minor Diameters
$$d_1 = D_1 = d-2\cdot h_2$$
- Basic Pitch Diameter
$$d_2 = D_2 = d-\frac{3}{4}H = d-\frac{3}{8}\sqrt{3}\cdot p$$
- Internal Thread Clearance Diameter
$$d_3 = d+\frac{H}{4}$$
- Crest Width
$$f_1 = \frac{p}{8}$$
- Root Width
$$f_2 = \frac{p}{4}$$
- Base Width
$$w_1 = \frac{3}{4}p$$
- Pitch Diameter Width
$$w_2 = \frac{p}{2}$$
- Tolerance for Major Diameter External Thread
$$T_d\left(4\right) = 0.63T_d\left(6\right) \: for \: G_d = 4$$
$$T_d\left(6\right) = 180\sqrt[3]{p^2}-\frac{3.15}{\sqrt{p}} \: for \: G_d = 6$$
$$T_d\left(8\right) = 1.6T_d\left(6\right) \: for \: G_d = 8$$
- Tolerance for Pitch Diameter External Thread
$$T_{d_2}\left(3\right) = 0.5T_{d_2}\left(6\right) \: for \: G_p = 3$$
$$T_{d_2}\left(4\right) = 0.63T_{d_2}\left(6\right) \: for \: G_p = 4$$
$$T_{d_2}\left(5\right) = 0.8T_{d_2}\left(6\right) \: for \: G_p = 5$$
$$T_{d_2}\left(6\right) = 90p^{0.4}d^{0.1} \: for \: G_p = 6$$
$$T_{d_2}\left(7\right) = 1.25T_{d_2}\left(6\right) \: for \: G_p = 7$$
$$T_{d_2}\left(8\right) = 1.6T_{d_2}\left(6\right) \: for \: G_p = 8$$
$$T_{d_2}\left(9\right) = 2T_{d_2}\left(6\right) \: for \: G_p = 9$$
- Fundamental Deviaion of the External Thread
$$es = -\left(50+11p\right) \: for \: T_{pos} = e$$
$$es = -\left(30+11p\right) \: for \: T_{pos} = f$$
$$es = -\left(15+11p\right) \: for \: T_{pos} = g$$
$$es = 0 \: for \: T_{pos} = h$$
- Adjustment Variable y
$$y = \frac{p}{8}\left\{1-\cos\left[\frac{\pi}{3}-cos^{-1}\left(1-\frac{2T_{d_2}}{p}\right)\right]\right\}$$
- Adjustment Variable z
$$z = \frac{H}{4}+\frac{T_{d_2}}{2}-\frac{p}{8}$$
- Minimum Major Diameter of the External Thread
$$d_{min} = d_{max}-T_d$$
- Maximum Major Diameter of the External Thread
$$d_{max} = d + es$$
- Minimum Minor Diameter of the External Thread
$$d_{1_{min}} = d_1-es-2z$$
- Maximum Minor Diameter of the External Thread
$$d_{1_{max}} = d_1-es-2y$$
- Minimum Pitch Diameter of the External Thread
$$d_{2_{min}} = d_{2_{max}}-T_{d_2}$$
- Maximum Pitch Diameter of the External Thread
$$d_{2_{max}} = d_2+es$$
- Tolerance for Minor Diameter Internal Thread
$$T_{D_1}\left(4\right) = 0.63T_{D_1}\left(6\right) \:\: for \: G_D = 4$$
$$T_{D_1}\left(5\right) = 0.8T_{D_1}\left(6\right) \:\: for \: G_D = 5$$
$$T_{D_1}\left(6\right) = 433p-190p^{1.22} \:\: for \: p \le 0.8 \: \& \: G_D = 6$$
$$T_{D_1}\left(6\right) = 230p^{0.7} \:\: for \: p \ge 1 \: \& \: G_D = 6$$
$$T_{D_1}\left(7\right) = 1.25T_{D_1}\left(6\right) \:\: for \: G_D = 7$$
$$T_{D_1}\left(8\right) = 1.6T_{D_1}\left(6\right) \:\: for \: G_D = 8$$
- Tolerance for Pitch Diameter Internal Thread
$$T_{D_2}\left(4\right) = 0.85\left(90p^{0.4}d^{0.1}\right) \:\: for \: G_P = 4$$
$$T_{D_2}\left(5\right) = 1.06\left(90p^{0.4}d^{0.1}\right) \:\: for \: G_P = 5$$
$$T_{D_2}\left(6\right) = 1.32\left(90p^{0.4}d^{0.1}\right) \:\: for \: G_P = 6$$
$$T_{D_2}\left(7\right) = 1.7 \left(90p^{0.4}d^{0.1}\right) \:\: for \: G_P = 7$$
$$T_{D_2}\left(8\right) = 2.12\left(90p^{0.4}d^{0.1}\right) \:\: for \: G_P = 8$$
- Fundamental Deviation of the Internal Thread
$$EI = 15+11p \:\: for \: T_{POS} = G$$
$$EI = 0 \:\: for \: T_{POS} = H$$
- Minimum Major Diameter of the Internal Thread
$$D_{min} = D + EI$$
- Minimum Minor Diameter of the Internal Thread
$$D_{1_{min}} = D_1 + EI$$
- Maximum Minor Diameter of the Internal Thread
$$D_{1_{max}} = D_{1_{min}}+T_{D_1}$$
- Minimum Pitch Diameter of the Internal Thread
$$D_{2_{min}} = D_2+EI$$
- Maximum Pitch Diameter of the Internal Thread
$$D_{2_{max}} = D_{2_{min}}+T_{D_2}$$
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