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Cylindrical bush (oscillating movement)

Cylindrical bush D i B
Cylindrical bush
Oscillating cycle (and36)φ(and36) 2 1 3 4 φ φ
Oscillating cycle $φ$

Values for calculation

$ \{F\in\mathbb{R}\mid 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.
$ F $ $ \mathrm{N} $
$ \{D_i\in\mathbb{R}\mid D_i>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_i $ $ \mathrm{mm} $
$ \{B\in\mathbb{R}\mid B>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.
$ B $ $ \mathrm{mm} $
$ \{\overline{p}_{sta,max}\in\mathbb{R}\mid \overline{p}_{sta,max}>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.
$ \overline{p}_{sta,max} $ $ \mathrm{MPa} $
$ \{\overline{p}_{dyn,max}\in\mathbb{R}\mid \overline{p}_{dyn,max}>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.
$ \overline{p}_{dyn,max} $ $ \mathrm{MPa} $
$ \{U_{max}\in\mathbb{R}\mid U_{max}>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.
$ U_{max} $ $ \mathrm{m/s} $
$ \{\overline{p}U_{max}\in\mathbb{R}\mid \overline{p}U_{max}>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.
$ \overline{p}U_{max} $ $ \mathrm{MPa\cdot\ m/s} $
$ \{Q\in\mathbb{R}\mid Q>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.
$ Q $
$ \{N_{osz}\in\mathbb{R}\mid N_{osz}>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.
$ N_{osz} $ $ \mathrm{1/min} $
$ \{φ\in\mathbb{R}\mid φ>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.
$ φ $ $ \mathrm{°} $
$ \{a_L\in\mathbb{R}\mid a_L>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.
$ a_L $
$ \{a_T\in\mathbb{R}\mid a_T>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.
$ a_T $
$ \{a_M\in\mathbb{R}\mid a_M>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.
$ a_M $

Calculation

Specific load limit

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

Specific load

$$\overline{p}=\cfrac{F}{D_i\cdot B}$$
$\overline{p}=\cfrac{F}{D_i\cdot B}$
Equations in LaTeX code
\overline{p}=\cfrac{F}{D_i\cdot B}
$$\overline{p}\le \overline{p}_{lim}$$
$\overline{p}\le \overline{p}_{lim}$
Equations in LaTeX code
\overline{p}\le \overline{p}_{lim}

Rotational speed

$$N=\cfrac{4\cdot φ\cdot N_{osz}}{360}$$
$N=\cfrac{4\cdot φ\cdot N_{osz}}{360}$
Equations in LaTeX code
N=\cfrac{4\cdot φ\cdot N_{osz}}{360}

Sliding speed

$$U=\cfrac{D_i\cdot π\cdot N}{60\cdot 10^3}$$
$U=\cfrac{D_i\cdot π\cdot N}{60\cdot 10^3}$
Equations in LaTeX code
U=\cfrac{D_i\cdot π\cdot N}{60\cdot 10^3}
$$U\le U_{max}$$
$U\le U_{max}$
Equations in LaTeX code
U\le U_{max}

$ \overline{p}U $ factor

$$\overline{p}U=\overline{p}\cdot U$$
$\overline{p}U=\overline{p}\cdot U$
Equations in LaTeX code
\overline{p}U=\overline{p}\cdot U
$$\overline{p}U\le \overline{p}U_{max}$$
$\overline{p}U\le \overline{p}U_{max}$
Equations in LaTeX code
\overline{p}U\le \overline{p}U_{max}

Bearing size factor

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

High load factor

$$a_E=\cfrac{\overline{p}_{lim}-\overline{p}}{\overline{p}_{lim}}$$
$a_E=\cfrac{\overline{p}_{lim}-\overline{p}}{\overline{p}_{lim}}$
Equations in LaTeX code
a_E=\cfrac{\overline{p}_{lim}-\overline{p}}{\overline{p}_{lim}}

Modified $ \overline{p}U $ value

$$\overline{p}U_{mod}=\cfrac{5.25\cdot 10^{-5}\cdot F\cdot N}{a_E\cdot B\cdot a_T\cdot a_M\cdot a_B}$$
$\overline{p}U_{mod}=\cfrac{5.25\cdot 10^{-5}\cdot F\cdot N}{a_E\cdot B\cdot a_T\cdot a_M\cdot a_B}$
Equations in LaTeX code
\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}$
$\text{if }\ \text{type }$$\text{of }$$\text{loading}= \text{steady load}$
Equations in LaTeX code
\text{if }\ \text{type }$$\text{of }$$\text{loading}= \text{steady load}
$$L_H=\cfrac{615}{\overline{p}U_{mod}}-a_L$$
$L_H=\cfrac{615}{\overline{p}U_{mod}}-a_L$
Equations in LaTeX code
L_H=\cfrac{615}{\overline{p}U_{mod}}-a_L
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$L_H=\cfrac{1230}{\overline{p}U_{mod}}-a_L$$
$L_H=\cfrac{1230}{\overline{p}U_{mod}}-a_L$
Equations in LaTeX code
L_H=\cfrac{1230}{\overline{p}U_{mod}}-a_L

Total number of cycles

$$Z_T=L_H\cdot N_{osz}\cdot 60$$
$Z_T=L_H\cdot N_{osz}\cdot 60$
Equations in LaTeX code
Z_T=L_H\cdot N_{osz}\cdot 60
$$Q\le Z_T$$
$Q\le Z_T$
Equations in LaTeX code
Q\le Z_T
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