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Radial pin for shaft-hub connection

Radial pin for shaft-hub connection d D D h
Radial pin for shaft-hub connection

Values for calculation

$ \{M_T\in\mathbb{R}\mid M_T\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ M_T $ $ \mathrm{Nm} $
$ \{D\in\mathbb{R}\mid D>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ D $ $ \mathrm{mm} $
$ \{d\in\mathbb{R}\mid d>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ d $ $ \mathrm{mm} $
$ \{D_h\in\mathbb{R}\mid D_h>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ D_h $ $ \mathrm{mm} $
$ \{S_{y-shaft}\in\mathbb{R}\mid S_{y-shaft}>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ S_{y-shaft} $ $ \mathrm{MPa} $
$ \{S_{y-pin}\in\mathbb{R}\mid S_{y-pin}>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ S_{y-pin} $ $ \mathrm{MPa} $
$ \{S_{y-hub}\in\mathbb{R}\mid S_{y-hub}>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ S_{y-hub} $ $ \mathrm{MPa} $
$ C_c $
$ \{S_F\in\mathbb{R}\mid S_F>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ S_F $
$ \{M_B\in\mathbb{R}\mid M_B\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ M_B $ $ \mathrm{Nm} $
$ \{F_R\in\mathbb{R}\mid F_R\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ F_R $ $ \mathrm{kN} $
$ \{F_A\in\mathbb{R}\mid F_A\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ F_A $ $ \mathrm{kN} $

Calculation

Allowable axial stress the shaft

$$σ_{all-A-shaft}=\cfrac{0.45 \cdot S_{y-shaft}}{S_F}\cdot C_c$$
$σ_{all-A-shaft}=\cfrac{0.45 \cdot S_{y-shaft}}{S_F}\cdot C_c$
Equations in LaTeX code
σ_{all-A-shaft}=\cfrac{0.45 \cdot S_{y-shaft}}{S_F}\cdot C_c

Allowable bending stress the shaft

$$σ_{all-B-shaft}=\cfrac{0.6 \cdot S_{y-shaft}}{S_F}\cdot C_c$$
$σ_{all-B-shaft}=\cfrac{0.6 \cdot S_{y-shaft}}{S_F}\cdot C_c$
Equations in LaTeX code
σ_{all-B-shaft}=\cfrac{0.6 \cdot S_{y-shaft}}{S_F}\cdot C_c

Allowable shear stress the shaft

$$τ_{all-S-shaft}=\cfrac{0.4 \cdot S_{y-shaft}}{S_F}\cdot C_c$$
$τ_{all-S-shaft}=\cfrac{0.4 \cdot S_{y-shaft}}{S_F}\cdot C_c$
Equations in LaTeX code
τ_{all-S-shaft}=\cfrac{0.4 \cdot S_{y-shaft}}{S_F}\cdot C_c

Allowable bearing stress the shaft

$$P_{all-B-shaft}=\cfrac{0.9 \cdot S_{y-shaft}}{S_F}\cdot C_c$$
$P_{all-B-shaft}=\cfrac{0.9 \cdot S_{y-shaft}}{S_F}\cdot C_c$
Equations in LaTeX code
P_{all-B-shaft}=\cfrac{0.9 \cdot S_{y-shaft}}{S_F}\cdot C_c

Allowable combined stress the shaft

$$σ_{all-C-shaft}=\cfrac{S_{y-shaft}}{S_F}\cdot C_c$$
$σ_{all-C-shaft}=\cfrac{S_{y-shaft}}{S_F}\cdot C_c$
Equations in LaTeX code
σ_{all-C-shaft}=\cfrac{S_{y-shaft}}{S_F}\cdot C_c

Allowable shear stress the pin

$$τ_{all-S-pin}=\cfrac{0.4 \cdot S_{y-pin}}{S_F}\cdot C_c$$
$τ_{all-S-pin}=\cfrac{0.4 \cdot S_{y-pin}}{S_F}\cdot C_c$
Equations in LaTeX code
τ_{all-S-pin}=\cfrac{0.4 \cdot S_{y-pin}}{S_F}\cdot C_c

Allowable bearing stress the pin

$$P_{all-B-pin}=\cfrac{0.9 \cdot S_{y-pin}}{S_F}\cdot C_c$$
$P_{all-B-pin}=\cfrac{0.9 \cdot S_{y-pin}}{S_F}\cdot C_c$
Equations in LaTeX code
P_{all-B-pin}=\cfrac{0.9 \cdot S_{y-pin}}{S_F}\cdot C_c

Allowable shear stress the hub

$$τ_{all-S-hub}=\cfrac{0.4 \cdot S_{y-hub}}{S_F}\cdot C_c$$
$τ_{all-S-hub}=\cfrac{0.4 \cdot S_{y-hub}}{S_F}\cdot C_c$
Equations in LaTeX code
τ_{all-S-hub}=\cfrac{0.4 \cdot S_{y-hub}}{S_F}\cdot C_c

Allowable bending stress the hub

$$σ_{all-B-hub}=\cfrac{0.6 \cdot S_{y-hub}}{S_F}\cdot C_c$$
$σ_{all-B-hub}=\cfrac{0.6 \cdot S_{y-hub}}{S_F}\cdot C_c$
Equations in LaTeX code
σ_{all-B-hub}=\cfrac{0.6 \cdot S_{y-hub}}{S_F}\cdot C_c

Allowable bearing stress the hub

$$P_{all-B-hub}=\cfrac{0.9 \cdot S_{y-hub}}{S_F}\cdot C_c$$
$P_{all-B-hub}=\cfrac{0.9 \cdot S_{y-hub}}{S_F}\cdot C_c$
Equations in LaTeX code
P_{all-B-hub}=\cfrac{0.9 \cdot S_{y-hub}}{S_F}\cdot C_c

Allowable axial stress the hub

$$σ_{all-A-hub}=\cfrac{0.45 \cdot S_{y-hub}}{S_F}\cdot C_c$$
$σ_{all-A-hub}=\cfrac{0.45 \cdot S_{y-hub}}{S_F}\cdot C_c$
Equations in LaTeX code
σ_{all-A-hub}=\cfrac{0.45 \cdot S_{y-hub}}{S_F}\cdot C_c

Allowable combined stress the hub

$$σ_{all-C-hub}=\cfrac{S_{y-hub}}{S_F}\cdot C_c$$
$σ_{all-C-hub}=\cfrac{S_{y-hub}}{S_F}\cdot C_c$
Equations in LaTeX code
σ_{all-C-hub}=\cfrac{S_{y-hub}}{S_F}\cdot C_c

Coefficient $ B_T $

$$B_T=4.000-6.055\cdot\cfrac{d}{D}+32.764\cdot\left(\cfrac{d}{D}\right)^2-38.330\cdot\left(\cfrac{d}{D}\right)^3$$
$B_T=4.000-6.055\cdot\cfrac{d}{D}+32.764\cdot\left(\cfrac{d}{D}\right)^2-38.330\cdot\left(\cfrac{d}{D}\right)^3$
Equations in LaTeX code
B_T=4.000-6.055\cdot\cfrac{d}{D}+32.764\cdot\left(\cfrac{d}{D}\right)^2-38.330\cdot\left(\cfrac{d}{D}\right)^3

Coefficient $ B_B $

$$B_B=3.000-6.250\cdot\cfrac{d}{D}+41.000\cdot\left(\cfrac{d}{D}\right)^2-45.000\cdot\left(\cfrac{d}{D}\right)^3$$
$B_B=3.000-6.250\cdot\cfrac{d}{D}+41.000\cdot\left(\cfrac{d}{D}\right)^2-45.000\cdot\left(\cfrac{d}{D}\right)^3$
Equations in LaTeX code
B_B=3.000-6.250\cdot\cfrac{d}{D}+41.000\cdot\left(\cfrac{d}{D}\right)^2-45.000\cdot\left(\cfrac{d}{D}\right)^3

Coefficient $ B_A $

$$B_A=3.000+0.427\cdot\cfrac{d}{D}+11.357\cdot\left(\cfrac{d}{D}\right)^2$$
$B_A=3.000+0.427\cdot\cfrac{d}{D}+11.357\cdot\left(\cfrac{d}{D}\right)^2$
Equations in LaTeX code
B_A=3.000+0.427\cdot\cfrac{d}{D}+11.357\cdot\left(\cfrac{d}{D}\right)^2

Coefficient $ B_{1B-hub} $

$$B_{1B-hub}=3.000$$
$B_{1B-hub}=3.000$
Equations in LaTeX code
B_{1B-hub}=3.000

Coefficient $ B_{2B-hub} $

$$B_{2B-hub}=-6.250-0.585\cdot\cfrac{D}{D_h}+3.115\cdot\left(\cfrac{D}{D_h}\right)^2$$
$B_{2B-hub}=-6.250-0.585\cdot\cfrac{D}{D_h}+3.115\cdot\left(\cfrac{D}{D_h}\right)^2$
Equations in LaTeX code
B_{2B-hub}=-6.250-0.585\cdot\cfrac{D}{D_h}+3.115\cdot\left(\cfrac{D}{D_h}\right)^2

Coefficient $ B_{3B-hub} $

$$B_{3B-hub}=41.000-1.071\cdot\cfrac{D}{D_h}-6.746\cdot\left(\cfrac{D}{D_h}\right)^2$$
$B_{3B-hub}=41.000-1.071\cdot\cfrac{D}{D_h}-6.746\cdot\left(\cfrac{D}{D_h}\right)^2$
Equations in LaTeX code
B_{3B-hub}=41.000-1.071\cdot\cfrac{D}{D_h}-6.746\cdot\left(\cfrac{D}{D_h}\right)^2

Coefficient $ B_{4B-hub} $

$$B_{4B-hub}=-45.000+1.389\cdot\cfrac{D}{D_h}+13.889\cdot\left(\cfrac{D}{D_h}\right)^2$$
$B_{4B-hub}=-45.000+1.389\cdot\cfrac{D}{D_h}+13.889\cdot\left(\cfrac{D}{D_h}\right)^2$
Equations in LaTeX code
B_{4B-hub}=-45.000+1.389\cdot\cfrac{D}{D_h}+13.889\cdot\left(\cfrac{D}{D_h}\right)^2

Coefficient $ B_{B-hub} $

$$B_{B-hub}=B_{1B-hub}+B_{2B-hub}\cdot\cfrac{d}{D_h}+B_{3B-hub}\cdot\left(\cfrac{d}{D_h}\right)^2+B_{4B-hub}\cdot\left(\cfrac{d}{D_h}\right)^3$$
$B_{B-hub}=B_{1B-hub}+B_{2B-hub}\cdot\cfrac{d}{D_h}+B_{3B-hub}\cdot\left(\cfrac{d}{D_h}\right)^2+B_{4B-hub}\cdot\left(\cfrac{d}{D_h}\right)^3$
Equations in LaTeX code
B_{B-hub}=B_{1B-hub}+B_{2B-hub}\cdot\cfrac{d}{D_h}+B_{3B-hub}\cdot\left(\cfrac{d}{D_h}\right)^2+B_{4B-hub}\cdot\left(\cfrac{d}{D_h}\right)^3

Coefficient $ B_{1A-hub} $

$$B_{1A-hub}=3.000$$
$B_{1A-hub}=3.000$
Equations in LaTeX code
B_{1A-hub}=3.000

Coefficient $ B_{2A-hub} $

$$B_{2A-hub}=0.427-6.770\cdot\cfrac{D}{D_h}+22.698\cdot\left(\cfrac{D}{D_h}\right)^2-16.670\cdot\left(\cfrac{D}{D_h}\right)^3$$
$B_{2A-hub}=0.427-6.770\cdot\cfrac{D}{D_h}+22.698\cdot\left(\cfrac{D}{D_h}\right)^2-16.670\cdot\left(\cfrac{D}{D_h}\right)^3$
Equations in LaTeX code
B_{2A-hub}=0.427-6.770\cdot\cfrac{D}{D_h}+22.698\cdot\left(\cfrac{D}{D_h}\right)^2-16.670\cdot\left(\cfrac{D}{D_h}\right)^3

Coefficient $ B_{3A-hub} $

$$B_{3A-hub}=11.357+15.665\cdot\cfrac{D}{D_h}-60.929\cdot\left(\cfrac{D}{D_h}\right)^2+41.501\cdot\left(\cfrac{D}{D_h}\right)^3$$
$B_{3A-hub}=11.357+15.665\cdot\cfrac{D}{D_h}-60.929\cdot\left(\cfrac{D}{D_h}\right)^2+41.501\cdot\left(\cfrac{D}{D_h}\right)^3$
Equations in LaTeX code
B_{3A-hub}=11.357+15.665\cdot\cfrac{D}{D_h}-60.929\cdot\left(\cfrac{D}{D_h}\right)^2+41.501\cdot\left(\cfrac{D}{D_h}\right)^3

Coefficient $ B_{A-hub} $

$$B_{A-hub}=B_{1A-hub}+B_{2A-hub}\cdot\cfrac{d}{D_h}+B_{3A-hub}\cdot\left(\cfrac{d}{D_h}\right)^2$$
$B_{A-hub}=B_{1A-hub}+B_{2A-hub}\cdot\cfrac{d}{D_h}+B_{3A-hub}\cdot\left(\cfrac{d}{D_h}\right)^2$
Equations in LaTeX code
B_{A-hub}=B_{1A-hub}+B_{2A-hub}\cdot\cfrac{d}{D_h}+B_{3A-hub}\cdot\left(\cfrac{d}{D_h}\right)^2

Coefficient $ B_{1T-hub} $

$$B_{1T-hub}=4.000$$
$B_{1T-hub}=4.000$
Equations in LaTeX code
B_{1T-hub}=4.000

Coefficient $ B_{2T-hub} $

$$B_{2T-hub}=-6.055+3.184\cdot\cfrac{D}{D_h}-3.461\cdot\left(\cfrac{D}{D_h}\right)^2$$
$B_{2T-hub}=-6.055+3.184\cdot\cfrac{D}{D_h}-3.461\cdot\left(\cfrac{D}{D_h}\right)^2$
Equations in LaTeX code
B_{2T-hub}=-6.055+3.184\cdot\cfrac{D}{D_h}-3.461\cdot\left(\cfrac{D}{D_h}\right)^2

Coefficient $ B_{3T-hub} $

$$B_{3T-hub}=32.764-30.121\cdot\cfrac{D}{D_h}+39.887\cdot\left(\cfrac{D}{D_h}\right)^2$$
$B_{3T-hub}=32.764-30.121\cdot\cfrac{D}{D_h}+39.887\cdot\left(\cfrac{D}{D_h}\right)^2$
Equations in LaTeX code
B_{3T-hub}=32.764-30.121\cdot\cfrac{D}{D_h}+39.887\cdot\left(\cfrac{D}{D_h}\right)^2

Coefficient $ B_{4T-hub} $

$$B_{4T-hub}=-38.330+51.542\cdot \sqrt {\cfrac{D}{D_h}} -27.483\cdot\cfrac{D}{D_h}$$
$B_{4T-hub}=-38.330+51.542\cdot \sqrt {\cfrac{D}{D_h}} -27.483\cdot\cfrac{D}{D_h}$
Equations in LaTeX code
B_{4T-hub}=-38.330+51.542\cdot \sqrt {\cfrac{D}{D_h}} -27.483\cdot\cfrac{D}{D_h}

Coefficient $ B_{T-hub} $

$$B_{T-hub}=B_{1T-hub}+B_{2T-hub}\cdot\cfrac{d}{D_h}+B_{3T-hub}\cdot\left(\cfrac{d}{D_h}\right)^2+B_{4T-hub}\cdot\left(\cfrac{d}{D_h}\right)^3$$
$B_{T-hub}=B_{1T-hub}+B_{2T-hub}\cdot\cfrac{d}{D_h}+B_{3T-hub}\cdot\left(\cfrac{d}{D_h}\right)^2+B_{4T-hub}\cdot\left(\cfrac{d}{D_h}\right)^3$
Equations in LaTeX code
B_{T-hub}=B_{1T-hub}+B_{2T-hub}\cdot\cfrac{d}{D_h}+B_{3T-hub}\cdot\left(\cfrac{d}{D_h}\right)^2+B_{4T-hub}\cdot\left(\cfrac{d}{D_h}\right)^3

Shear stress in the pin

$$τ_{S-pin}=\cfrac{4\cdot 10^3\cdot M_T}{π\cdot d^2 \cdot D}+\cfrac{2\cdot 10^3\cdot F_A}{π\cdot d^2}$$
$τ_{S-pin}=\cfrac{4\cdot 10^3\cdot M_T}{π\cdot d^2 \cdot D}+\cfrac{2\cdot 10^3\cdot F_A}{π\cdot d^2}$
Equations in LaTeX code
τ_{S-pin}=\cfrac{4\cdot 10^3\cdot M_T}{π\cdot d^2 \cdot D}+\cfrac{2\cdot 10^3\cdot F_A}{π\cdot d^2}
$$τ_{S-pin}\le τ_{all-S-pin}$$
$τ_{S-pin}\le τ_{all-S-pin}$
Equations in LaTeX code
τ_{S-pin}\le τ_{all-S-pin}

Torsion stress in the shaft

$$τ_{T-shaft}=\cfrac{16\cdot 10^3 \cdot M_T\cdot B_T}{π \cdot D^3}$$
$τ_{T-shaft}=\cfrac{16\cdot 10^3 \cdot M_T\cdot B_T}{π \cdot D^3}$
Equations in LaTeX code
τ_{T-shaft}=\cfrac{16\cdot 10^3 \cdot M_T\cdot B_T}{π \cdot D^3}
$$τ_{T-shaft}\le τ_{all-S-shaft}$$
$τ_{T-shaft}\le τ_{all-S-shaft}$
Equations in LaTeX code
τ_{T-shaft}\le τ_{all-S-shaft}

Bending stress in the shaft

$$σ_{B-shaft}=\cfrac{32\cdot 10^3 \cdot M_B \cdot B_B}{π \cdot D^3}$$
$σ_{B-shaft}=\cfrac{32\cdot 10^3 \cdot M_B \cdot B_B}{π \cdot D^3}$
Equations in LaTeX code
σ_{B-shaft}=\cfrac{32\cdot 10^3 \cdot M_B \cdot B_B}{π \cdot D^3}
$$σ_{B-shaft}\le σ_{all-B-shaft}$$
$σ_{B-shaft}\le σ_{all-B-shaft}$
Equations in LaTeX code
σ_{B-shaft}\le σ_{all-B-shaft}

Shear stress in the shaft

$$τ_{S-shaft}=\cfrac{10^3 \cdot F_R}{\cfrac{π \cdot D^2}{4}-D \cdot d}$$
$τ_{S-shaft}=\cfrac{10^3 \cdot F_R}{\cfrac{π \cdot D^2}{4}-D \cdot d}$
Equations in LaTeX code
τ_{S-shaft}=\cfrac{10^3 \cdot F_R}{\cfrac{π \cdot D^2}{4}-D \cdot d}
$$τ_{S-shaft}\le τ_{all-S-shaft}$$
$τ_{S-shaft}\le τ_{all-S-shaft}$
Equations in LaTeX code
τ_{S-shaft}\le τ_{all-S-shaft}

Axial stress in the shaft

$$σ_{A-shaft}=\cfrac{4\cdot 10^3 \cdot F_A \cdot B_A}{π \cdot D^2}$$
$σ_{A-shaft}=\cfrac{4\cdot 10^3 \cdot F_A \cdot B_A}{π \cdot D^2}$
Equations in LaTeX code
σ_{A-shaft}=\cfrac{4\cdot 10^3 \cdot F_A \cdot B_A}{π \cdot D^2}
$$σ_{A-shaft}\le σ_{all-A-shaft}$$
$σ_{A-shaft}\le σ_{all-A-shaft}$
Equations in LaTeX code
σ_{A-shaft}\le σ_{all-A-shaft}

Combined stress in the shaft

$$σ_{tresca-shaft}=\sqrt{σ_{B-shaft}^2+σ_{A-shaft}^2+4\cdot\left(τ_{T-shaft}^2+τ_{S-shaft}^2\right)}$$
$σ_{tresca-shaft}=\sqrt{σ_{B-shaft}^2+σ_{A-shaft}^2+4\cdot\left(τ_{T-shaft}^2+τ_{S-shaft}^2\right)}$
Equations in LaTeX code
σ_{tresca-shaft}=\sqrt{σ_{B-shaft}^2+σ_{A-shaft}^2+4\cdot\left(τ_{T-shaft}^2+τ_{S-shaft}^2\right)}
$$σ_{tresca-shaft}\le σ_{all-C-shaft}$$
$σ_{tresca-shaft}\le σ_{all-C-shaft}$
Equations in LaTeX code
σ_{tresca-shaft}\le σ_{all-C-shaft}

Torsion stress in the hub

$$τ_{T-hub}=\cfrac{16\cdot 10^3 \cdot M_T \cdot B_{T-hub}}{π\cdot\left(D_h^4-D^4\right)}\cdot D$$
$τ_{T-hub}=\cfrac{16\cdot 10^3 \cdot M_T \cdot B_{T-hub}}{π\cdot\left(D_h^4-D^4\right)}\cdot D$
Equations in LaTeX code
τ_{T-hub}=\cfrac{16\cdot 10^3 \cdot M_T \cdot B_{T-hub}}{π\cdot\left(D_h^4-D^4\right)}\cdot D
$$τ_{T-hub}\le τ_{all-S-hub}$$
$τ_{T-hub}\le τ_{all-S-hub}$
Equations in LaTeX code
τ_{T-hub}\le τ_{all-S-hub}

Bending stress in the hub

$$σ_{B-hub}=\cfrac{32\cdot 10^3 \cdot M_B \cdot D_h \cdot B_{B-hub}}{π \cdot \left(D_h^4-D^4\right)}$$
$σ_{B-hub}=\cfrac{32\cdot 10^3 \cdot M_B \cdot D_h \cdot B_{B-hub}}{π \cdot \left(D_h^4-D^4\right)}$
Equations in LaTeX code
σ_{B-hub}=\cfrac{32\cdot 10^3 \cdot M_B \cdot D_h \cdot B_{B-hub}}{π \cdot \left(D_h^4-D^4\right)}
$$σ_{B-hub}\le σ_{all-B-hub}$$
$σ_{B-hub}\le σ_{all-B-hub}$
Equations in LaTeX code
σ_{B-hub}\le σ_{all-B-hub}

Shear stress in the hub

$$τ_{S-hub}=\cfrac{10^3 \cdot F_R}{\cfrac{π \cdot \left(D_h^2-D^2\right)}{4}-\left(D_h-D\right)\cdot d}$$
$τ_{S-hub}=\cfrac{10^3 \cdot F_R}{\cfrac{π \cdot \left(D_h^2-D^2\right)}{4}-\left(D_h-D\right)\cdot d}$
Equations in LaTeX code
τ_{S-hub}=\cfrac{10^3 \cdot F_R}{\cfrac{π \cdot \left(D_h^2-D^2\right)}{4}-\left(D_h-D\right)\cdot d}
$$τ_{S-hub}\le τ_{all-S-hub}$$
$τ_{S-hub}\le τ_{all-S-hub}$
Equations in LaTeX code
τ_{S-hub}\le τ_{all-S-hub}

Axial stress in the hub

$$σ_{A-hub}=\cfrac{4\cdot 10^3 \cdot F_A \cdot B_{A-hub}}{π \cdot \left(D_h^2-D^2\right)}$$
$σ_{A-hub}=\cfrac{4\cdot 10^3 \cdot F_A \cdot B_{A-hub}}{π \cdot \left(D_h^2-D^2\right)}$
Equations in LaTeX code
σ_{A-hub}=\cfrac{4\cdot 10^3 \cdot F_A \cdot B_{A-hub}}{π \cdot \left(D_h^2-D^2\right)}
$$σ_{A-hub}\le σ_{all-A-hub}$$
$σ_{A-hub}\le σ_{all-A-hub}$
Equations in LaTeX code
σ_{A-hub}\le σ_{all-A-hub}

Combined stress in the hub

$$σ_{tresca-hub}=\sqrt{σ_{B-hub}^2+σ_{A-hub}^2+4\cdot\left(τ_{T-hub}^2+τ_{S-hub}^2\right)}$$
$σ_{tresca-hub}=\sqrt{σ_{B-hub}^2+σ_{A-hub}^2+4\cdot\left(τ_{T-hub}^2+τ_{S-hub}^2\right)}$
Equations in LaTeX code
σ_{tresca-hub}=\sqrt{σ_{B-hub}^2+σ_{A-hub}^2+4\cdot\left(τ_{T-hub}^2+τ_{S-hub}^2\right)}
$$σ_{tresca-hub}\le σ_{all-C-hub}$$
$σ_{tresca-hub}\le σ_{all-C-hub}$
Equations in LaTeX code
σ_{tresca-hub}\le σ_{all-C-hub}

Bearing stress in the pin and shaft

$$P_{B-pin-shaft}=\cfrac{6\cdot 10^3 \cdot M_T}{D^2\cdot d}+\cfrac{10^3 \cdot F_A}{D\cdot d}$$
$P_{B-pin-shaft}=\cfrac{6\cdot 10^3 \cdot M_T}{D^2\cdot d}+\cfrac{10^3 \cdot F_A}{D\cdot d}$
Equations in LaTeX code
P_{B-pin-shaft}=\cfrac{6\cdot 10^3 \cdot M_T}{D^2\cdot d}+\cfrac{10^3 \cdot F_A}{D\cdot d}
$$P_{B-pin-shaft}\le \min\left(P_{all-B-shaft}, P_{all-B-pin}\right)$$
$P_{B-pin-shaft}\le \min\left(P_{all-B-shaft}, P_{all-B-pin}\right)$
Equations in LaTeX code
P_{B-pin-shaft}\le \min\left(P_{all-B-shaft}, P_{all-B-pin}\right)

Bearing stress in the pin and hub

$$P_{B-pin-hub}=\cfrac{4\cdot 10^3 \cdot M_T}{d\cdot \left(D_h^2-D^2\right)}+\cfrac{10^3 \cdot F_A}{d\cdot \left(D_h-D\right)}$$
$P_{B-pin-hub}=\cfrac{4\cdot 10^3 \cdot M_T}{d\cdot \left(D_h^2-D^2\right)}+\cfrac{10^3 \cdot F_A}{d\cdot \left(D_h-D\right)}$
Equations in LaTeX code
P_{B-pin-hub}=\cfrac{4\cdot 10^3 \cdot M_T}{d\cdot \left(D_h^2-D^2\right)}+\cfrac{10^3 \cdot F_A}{d\cdot \left(D_h-D\right)}
$$P_{B-pin-hub}\le \min\left(P_{all-B-hub}, P_{all-B-pin}\right)$$
$P_{B-pin-hub}\le \min\left(P_{all-B-hub}, P_{all-B-pin}\right)$
Equations in LaTeX code
P_{B-pin-hub}\le \min\left(P_{all-B-hub}, P_{all-B-pin}\right)

Requirements

$$ \cfrac{d}{D_h}\le 0.4 $$
$\cfrac{d}{D_h}\le 0.4$
Equations in LaTeX code
\cfrac{d}{D_h}\le 0.4
$$ \cfrac{D}{D_h}\le 0.8 $$
$\cfrac{D}{D_h}\le 0.8$
Equations in LaTeX code
\cfrac{D}{D_h}\le 0.8
$$ \cfrac{d}{D}\le 0.7 $$
$\cfrac{d}{D}\le 0.7$
Equations in LaTeX code
\cfrac{d}{D}\le 0.7
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