# Cylindrical bush (rotating movement)

## Values for calculation

$F$ $\mathrm{N}$
$D_i$ $\mathrm{mm}$
$B$ $\mathrm{mm}$
$\overline{p}_{sta,max}$ $\mathrm{MPa}$
$\overline{p}_{dyn,max}$ $\mathrm{MPa}$
$U_{max}$ $\mathrm{m/s}$
$\overline{p}U_{max}$ $\mathrm{MPa\cdot m/s}$
$Q$
$N$ $\mathrm{1/min}$
$a_L$
$a_T$
$a_M$

## Calculation

### Specific load limit

$\text{if }\ 10^7\le Q\wedge\text{type }$$\text{of }$$\text{loading}= \text{steady load}$
$$\overline{p}_{lim}=\cfrac{-1/9000000\cdot Q+280/9}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else if }\ 10^7\le Q\wedge\text{type }$$\text{of }$$\text{loading}= \text{dynamic load}$
$$\overline{p}_{lim}=\cfrac{(-1/18000000\cdot Q+140/9)}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else if }\ 10^6\le Q\wedge\text{type }$$\text{of }$$\text{loading}= \text{steady load}$
$$\overline{p}_{lim}=\cfrac{-7/4500000\cdot Q+410/9}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else if }\ 10^6\le Q\wedge\text{type }$$\text{of }$$\text{loading}= \text{dynamic load}$
$$\overline{p}_{lim}=\cfrac{-7/9000000\cdot Q+205/9}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else if }\ 10^5\le Q\wedge\text{type }$$\text{of }$$\text{loading}= \text{steady load}$
$$\overline{p}_{lim}=\cfrac{-2/112500\cdot Q+556/9}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else if }\ 10^5\le Q\wedge\text{type }$$\text{of }$$\text{loading}= \text{dynamic load}$
$$\overline{p}_{lim}=\cfrac{-1/112500\cdot Q+278/9}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else if }\ 10^4\le Q\wedge\text{type }$$\text{of }$$\text{loading}= \text{steady load}$
$$\overline{p}_{lim}=\cfrac{-1/4500\cdot Q+740/9}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else if }\ 10^4\le Q\wedge\text{type }$$\text{of }$$\text{loading}= \text{dynamic load}$
$$\overline{p}_{lim}=\cfrac{-1/9000\cdot Q+370/9}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else if }\ 8000\le Q\wedge\text{type }$$\text{of }$$\text{loading}= \text{steady load}$
$$\overline{p}_{lim}=\cfrac{-0.0025\cdot Q+105}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else if }\ 8000\le Q\wedge\text{type }$$\text{of }$$\text{loading}= \text{dynamic load}$
$$\overline{p}_{lim}=\cfrac{-0.001\cdot Q+50}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else if }\ 6000\le Q\wedge\text{type }$$\text{of }$$\text{loading}= \text{steady load}$
$$\overline{p}_{lim}=\cfrac{-0.005\cdot Q+125}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else if }\ 6000\le Q\wedge\text{type }$$\text{of }$$\text{loading}= \text{dynamic load}$
$$\overline{p}_{lim}=\cfrac{-0.002\cdot Q+58}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else if }\ 4000\le Q\wedge\text{type }$$\text{of }$$\text{loading}= \text{steady load}$
$$\overline{p}_{lim}=\cfrac{-0.01\cdot Q+155}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else if }\ 4000\le Q\wedge\text{type }$$\text{of }$$\text{loading}= \text{dynamic load}$
$$\overline{p}_{lim}=\cfrac{-0.002\cdot Q+58}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else if }\ 2000\le Q\wedge\text{type }$$\text{of }$$\text{loading}= \text{steady load}$
$$\overline{p}_{lim}=\cfrac{-0.0125\cdot Q+165}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else if }\ 2000\le Q\wedge\text{type }$$\text{of }$$\text{loading}= \text{dynamic load}$
$$\overline{p}_{lim}=\cfrac{-0.005\cdot Q+70}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else if }\ \text{type }$$\text{of }$$\text{loading}= \text{steady load}$
$$\overline{p}_{lim}=\cfrac{140}{140}\cdot \overline{p}_{dyn,max}$$
$\text{else}$
$$\overline{p}_{lim}=\cfrac{60}{140}\cdot \overline{p}_{dyn,max}$$

### Specific load

$$\overline{p}=\cfrac{F}{D_i\cdot B}$$

$$\overline{p}\le \overline{p}_{lim}$$

### Sliding speed

$$U=\cfrac{D_i\cdot π\cdot N}{60\cdot 10^3}$$

$$U\le U_{max}$$

### $\overline{p}U$ factor

$$\overline{p}U=\overline{p}\cdot U$$

$$\overline{p}U\le \overline{p}U_{max}$$

### Bearing size factor

$$a_B=1.25\cdot D_i^\left(-0.0445\cdot\ln{D_i}+0.0489\right)$$

### High load factor

$$a_E=\cfrac{\overline{p}_{lim}-\overline{p}}{\overline{p}_{lim}}$$

### Modified $\overline{p}U$ value

$$\overline{p}U_{mod}=\cfrac{5.25\cdot 10^{-5}\cdot F\cdot N}{a_E\cdot B\cdot a_T\cdot a_M\cdot a_B}$$

### Bearing service life

$\text{if }\ \text{type }$$\text{of }$$\text{loading}= \text{steady load}$
$$L_H=\cfrac{615}{\overline{p}U_{mod}}-a_L$$
$\text{else}$
$$L_H=\cfrac{1230}{\overline{p}U_{mod}}-a_L$$

### Total number of cycles

$$Z_T=L_H\cdot N\cdot 60$$

$$Q\le Z_T$$