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.
- Choose a value for the factor of safety.
- Select the appropriate thread designation from the dropdown menu or leave it as User Defined and enter values for the basic diameter and pitch.
- Select the material of the external thread from the dropdown menu or leave the material designation as User Defined and enter a value for the minimum ultimate tensile stress of the external thread material. The tensile stress value is found under external thread properties.
- 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.
- Select the material of the internal thread or leave the material designation as User Defined and enter a value for the minimum ultimate tensile stress for the internal thread material. The tensile stress value is found under internal thread properties.
- 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
- Materials are homogeneous.
- The surfaces of the thread profiles are within the tolerance limits
Equations
- Height of the Fundamental Triangle
$$H = \frac{\sqrt{3}}{2}p$$
- Truncated Thread Height
$$h_2 = \frac{5}{8}H$$
- 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
$$d_3 = d+\frac{H}{4}$$
- 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
$$d_{min} = d+es-T_d$$
- Minimum Pitch Diameter of the External Thread
$$d_{2_{min}} = d_2+es-T_{d_2}$$
- Base Width of the External Thread
$$w_E = w_2+\left(d_{2_{min}}-D_{1_{max}}\right)\tan 30$$
- Circumference Per Revolution of the External Thread at D2max
$$c_E = \pi \cdot D_{1_{max}}$$
- Arc Length Per Revolution of the External Thread at D2max
$$s_E = \sqrt{\left(\pi D_{1_{max}}\right)^2+p^2}$$
- Tensile Stress Area
$$A_t = \frac{\pi}{4}\left(\frac{d_1+d_2+\frac{H}{6}}{2}\right)^2$$
- Thread Shear Area of the External Thread Based on cE
$$A_{s,c} = w_E \cdot c_E$$
- Thread Shear Area of the External Thread Based on sE
$$A_{s,s} = w_E \cdot s_E$$
- 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
$$EI = 15+11p \:\: for \: T_{POS} = G$$
$$EI = 0 \:\: for \: T_{POS} = H$$
- Maximum Minor Diameter of the Internal Thread
$$D_{1_{max}} = D_1 + EI + T_{D_1}$$
- Maximum Pitch Diameter of the Internal Thread
$$D_{2_{max}} = D_2 + EI + T_{D_2}$$
- Base Width of the Internal Thread
$$w_I = w_2+\left(d_{min}-D_{2_{max}}\right)\tan 30$$
- Circumference Per Revolution of the Internal Thread at Dmin
$$c_I = \pi \cdot d_{min}$$
- Arc Length Per Revolution of the Internal Thread at Dmin
$$s_I = \sqrt{\left(\pi d_{min}\right)^2+p^2}$$
- Thread Shear Area of the Internal Thread Based on cI
$$A_{n,c} = w_I \cdot c_I$$
- Thread Shear Area of the Internal Thread Based on sI
$$A_{n,s} = w_I \cdot s_I$$
- Maximum Allowable Axial Force
$$F_{max} = A_t \cdot \sigma _{t_E}$$
- Minimum Required Number of External Threads
$$N_E = \frac{A_t}{A_{s,c}}$$
- Minimum Required Number of Internal Threads
$$N_I = \left(\frac{\sigma _{t_E}}{\sigma _{t_I}}\right)\left(\frac{A_t}{A_{n,c}}\right)$$
- Minimum Required Number of Threads Engaged
$$N_{min} = max\left(N_E,N_I\right)$$
- Minimum Required Engagement Length
$$L_{e_{min}} = N_{min} \cdot p$$
- Recommended Minimum Number of Threads Engaged Based On FS
$$N = FS \cdot N_{min}$$
- Recommended Minimum Engagement Length Based On FS
$$L_e = N \cdot p$$
Background
