List of formulae

Terms, definitions

Circumferential force Fu [N]   Centre distance a [mm]
specific tooth force FUspez [N/cm]   Belt length LB [mm]
admissible tensile force Fzul [N]   Belt width b [mm]
Pre-tension force Fv [N]   Pulley width B [mm]
Shaft force Fw [N]   Bore, pulley d [mm]
Torque M [Nm]   Pitch circle diameter d0 [mm]
Accelleration torque MB [Nm]   Crown diameter dK [mm]
specific torque Mspez [Ncm/cm]   Span length LT [mm]
Power P [kW]   Pitch t [mm]
specific power Pspez [W/cm]   Number of belt teeth zB  
Load bearing torque J [kgm²]   Number of teeth with i=1 z  
Load m [kg]   Number of teeth in mesh ze  
Density ρ [kg/dm³]   No. of teeth, small pulley z1  
Speed v [m/s]   No. of teeth, large pulley z2  
Rotational speed n [min-1]   Transmission i  
Angular speed ω [s-1]   Accelleration time tB [s]
Frequency fe [s-1]

 

\begin{align} F_U & = {2 \cdot 10^3 \cdot M \over d_0} \\ & ={19,1 \cdot 10^6 \cdot P \over n \cdot d_0} \\ & ={10^3 \cdot P  \over v} \end{align}

Circumferencial force

\begin{align} M & ={d_0 \cdot F_U  \over 2 \cdot 10^3} \\ & ={9,55 \cdot 10^3  \cdot P \over n} \\ & ={d_0 \cdot P  \over 2 \cdot v} \end{align}

Torque

\begin{align} P & ={M \cdot n \cdot F_U \over 9,55 \cdot 10^3} \\ & ={F_U \cdot d_0 \cdot n \over 19,1 \cdot 10^6} \\ & ={F_U \cdot v   \over 10^3} \end{align}

Power

\begin{align} L_B & = 2a + \pi \cdot d_0 \\  & = 2a + z \cdot t \end{align}

Belt Length for i=1

\[d_0={z \cdot t  \over  \pi }\]

Pitch circle diameter

\[\omega={\pi \cdot n \over 30}\]

Angular speed

\[n = {19,1 \cdot 10^3 \cdot v \over d_0}\]

Rotational speed

\[v={d_0 \cdot n  \over  19,1 \cdot 10^3 }\]

Peripheral speed

\[M_B={J \cdot \Delta n \over 9,55 \cdot t_B}\]

Acceleration torque

\[J={98,2 \cdot 10^{-15} \cdot B \cdot \rho \cdot (d_k^4 - d^4) }\]

Load bearing torque

Apply all equations with the dimensions mentioned here.