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Radial pin for shaft-hub connection

Radial_pin_for_shaft-hub_connection
Radial pin for shaft-hub connection

Values for calculation

$M_T$ $\mathrm{Nm}$
$D$ $\mathrm{mm}$
$d$ $\mathrm{mm}$
$D_h$ $\mathrm{mm}$
$S_{y-shaft}$ $\mathrm{MPa}$
$S_{y-pin}$ $\mathrm{MPa}$
$S_{y-hub}$ $\mathrm{MPa}$
$C_c$
$S_F$
$M_B$ $\mathrm{Nm}$
$F_R$ $\mathrm{kN}$
$F_A$ $\mathrm{kN}$

Calculation

Allowable axial stress the shaft

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

Allowable bending stress the shaft

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

Allowable shear stress the shaft

$$T_{all-S-shaft}=\cfrac{0.4 \cdot S_{y-shaft}}{S_F}\cdot C_c$$

Allowable bearing stress the shaft

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

Allowable combined stress the shaft

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

Allowable shear stress the pin

$$T_{all-S-pin}=\cfrac{0.4 \cdot S_{y-pin}}{S_F}\cdot C_c$$

Allowable bearing stress the pin

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

Allowable shear stress the hub

$$T_{all-S-hub}=\cfrac{0.4 \cdot S_{y-hub}}{S_F}\cdot C_c$$

Allowable bending stress the hub

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

Allowable bearing stress the hub

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

Allowable axial stress the hub

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

Allowable combined stress the hub

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

Coefficient $ B_T $

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

Coefficient $ B_B $

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

Coefficient $ B_A $

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

Coefficient $ B_{1B-hub} $

$$B_{1B-hub}=3.000$$

Coefficient $ B_{2B-hub} $

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

Coefficient $ B_{3B-hub} $

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

Coefficient $ B_{4B-hub} $

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

Coefficient $ B_{B-hub} $

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

Coefficient $ B_{1A-hub} $

$$B_{1A-hub}=3.000$$

Coefficient $ B_{2A-hub} $

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

Coefficient $ B_{3A-hub} $

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

Coefficient $ B_{A-hub} $

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

Coefficient $ B_{1T-hub} $

$$B_{1T-hub}=4.000$$

Coefficient $ B_{2T-hub} $

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

Coefficient $ B_{3T-hub} $

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

Coefficient $ B_{4T-hub} $

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

Coefficient $ B_{T-hub} $

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

Shear stress in the pin

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

Torsion stress in the shaft

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

Bending stress in the shaft

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

Shear stress in the shaft

$$T_{S-shaft}=\cfrac{10^3 \cdot F_R}{\cfrac{π \cdot D^2}{4}-D \cdot d}$$$$T_{S-shaft}\le T_{all-S-shaft}$$

Axial stress in the shaft

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

Combined stress in the shaft

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

Torsion stress in the hub

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

Bending stress in the hub

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

Shear stress in the hub

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

Axial stress in the hub

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

Combined stress in the hub

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

Bearing stress in the pin and shaft

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

Bearing stress in the pin and hub

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

Requirements

$$\cfrac{d}{D_h}\le 0.4$$$$\cfrac{D}{D_h}\le 0.8$$$$\cfrac{d}{D}\le 0.7$$