# Interference fit

## Values for calculation

$M_T$ $\mathrm{Nm}$
$D$ $\mathrm{mm}$
$D_0$ $\mathrm{mm}$
$D_h$ $\mathrm{mm}$
$l$ $\mathrm{mm}$
$μ$
$S_{y-shaft}$ $\mathrm{MPa}$
$E_{shaft}$ $\mathrm{MPa}$
$ν_{shaft}$
$S_{y-hub}$ $\mathrm{MPa}$
$E_{hub}$ $\mathrm{MPa}$
$ν_{hub}$
$C_c$
$S_F$
$F_A$ $\mathrm{kN}$
$Δ_{max}$ $\mathrm{mm}$

## Calculation

### Allowable combined stress the hub

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

### Allowable combined stress the shaft

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

### Dimensional characteristics of the connection on diameter $D_0$

$$C_{D_0}=\cfrac{D^2+D_0^2}{D^2-D_0^2}$$

### Dimensional characteristics of the connection on diameter $D$

$$C_{D}=\cfrac{D_h^2+D^2}{D_h^2-D^2}$$

### Min. contact pressure

$$p_{min}=\left(\cfrac{2\cdot M_T\cdot 10^3}{π\cdot D^2\cdot l\cdot μ}+\cfrac{F_A\cdot 10^3}{π\cdot D\cdot l\cdot μ}\right)\cdot\cfrac{S_F}{C_c}$$

### Max. contact pressure

$$p_{max}=\cfrac{Δ_{max}}{D\cdot\left(\cfrac{C_{D_0}-ν_{shaft}}{E_{shaft}}+\cfrac{C_{D}+ν_{hub}}{E_{hub}}\right)}$$

$$p_{max}\geq p_{min}$$

### Min. Interference

$$Δ_{min}=p_{min}\cdot D\cdot\left(\cfrac{C_{D_0}-ν_{shaft}}{E_{shaft}}+\cfrac{C_{D}+ν_{hub}}{E_{hub}}\right)$$

### Radial stress in the hub on diameter $D$

$$σ_{R-hub-D}=-p_{max}$$

### Tangential stress in the hub on diameter $D$

$$σ_{T-hub-D}=p_{max}\cdot C_{D}$$

### Torsion stress in the hub on diameter $D$

$$τ_{T-hub-D}=\cfrac{10^3\cdot M_T}{\cfrac{π}{16}\cdot\cfrac{D_h^4-D^4}{D}}$$

### Shear stress in the hub on diameter $D$

$$τ_{S-hub-D}=\cfrac{10^3\cdot F_A}{π\cdot D\cdot l}$$

### Combined stress in the hub on diameter $D$

$$σ_{tresca-hub-D}=\sqrt{σ_{T-hub-D}^2+σ_{R-hub-D}^2-\left(σ_{T-hub-D}\cdot σ_{R-hub-D}\right)+4\cdot(τ_{T-hub-D}^2+τ_{S-hub-D}^2)}$$

$$σ_{tresca-hub-D}\le σ_{all-C-hub}$$

### Radial stress in the shaft on diameter $D$

$$σ_{R-shaft-D}=-p_{max}$$

### Tangential stress in the shaft on diameter $D$

$$σ_{T-shaft-D}=-p_{max}\cdot C_{D_0}$$

### Torsion stress in the shaft on diameter $D$

$$τ_{T-shaft-D}=\cfrac{10^3\cdot M_T}{\cfrac{π}{16}\cdot\cfrac{D^4-D_0^4}{D}}$$

### Shear stress in the shaft on diameter $D$

$$τ_{S-shaft-D}=τ_{S-hub-D}$$

### Combined stress in the shaft on diameter $D$

$$σ_{tresca-shaft-D}=\sqrt{σ_{T-shaft-D}^2+σ_{R-shaft-D}^2-\left(σ_{T-shaft-D}\cdot σ_{R-shaft-D}\right)+4\cdot(τ_{T-shaft-D}^2+τ_{S-shaft-D}^2)}$$

$$σ_{tresca-shaft-D}\le σ_{all-C-shaft}$$

### Radial stress in the shaft on diameter $D_0$

$\text{if }\ D_0=0$
$$σ_{R-shaft-D_0}=-p_{max}$$
$\text{else}$
$$σ_{R-shaft-D_0}=0$$

### Tangential stress in the shaft on diameter $D_0$

$\text{if }\ D_0=0$
$$σ_{T-shaft-D_0}=-p_{max}$$
$\text{else}$
$$σ_{T-shaft-D_0}=-p_{max}\cdot\left(C_{D_0}+1\right)$$

### Torsion stress in the shaft on diameter $D_0$

$\text{if }\ D_0=0$
$$τ_{T-shaft-D_0}=0$$
$\text{else}$
$$τ_{T-shaft-D_0}=\cfrac{10^3\cdot M_T}{\cfrac{π}{16}\cdot\cfrac{D^4-D_0^4}{D_0}}$$

### Combined stress in the shaft on diameter $D_0$

$$σ_{tresca-shaft-D_0}=\sqrt{σ_{T-shaft-D_0}^2+σ_{R-shaft-D_0}^2-\left(σ_{T-shaft-D_0}\cdot σ_{R-shaft-D_0}\right)+4\cdot τ_{T-shaft-D_0}^2}$$

$$σ_{tresca-shaft-D_0}\le σ_{all-C-shaft}$$