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Flat Belt Drive Design Calculator and Equations
Flat Belt Design Engineering Data
Flat Belt Drive Design Calculator and Equations
Flat belts have high strength, can be used for large speed ratios (>8:1), have a low pulley cost, produce low noise levels, and are good at absorbing torsional vibration. The belts are typically made from multiple plies, with each layer serving a special purpose. A typical threeply belt consists of a friction ply made from synthetic rubber, polyurethane, or chrome leather, a tension ply made from polyamide strips or polyester cord, and an outer skin made from polyamide fabric, chrome leather, or an elastomer. The corresponding pulleys are made from cast iron or polymer materials and are relatively smooth to limit wear. The driving force is limited by the friction between the belt and the pulley. Applications include manufacturing tools, saw mills, textile machinery, food processing machines, multiple spindle drives, pumps, and compressors.
Preview Flat Belt Drive Design Calculator
Figure 1, Belt drive geometry definition
For the simple belt drive configuration shown in Figure 1, the angles of contact between the belt and the pulleys are given by
Eq. 1
$\theta}_{d}=\pi 2\cdot si{n}^{1}\cdot \frac{Dd}{2C$$}^{$Eq. 2
$\theta}_{D}=\pi +2\cdot si{n}^{1}\cdot \frac{Dd}{2C$where
d = diameter of the small pulley (m),
D = diameter of the large pulley (m),
C = distance between the pulley centers (m),
θ_{d} = angle of contact between the belt and the small pulley (rad),
θ_{D} = angle of contact between the belt and the large pulley (rad).
The length of the belt can be obtained by summing the arc lengths of contact and the spanned distances and is given by
Eq. 3
$L=\sqrt{4\cdot {C}^{2}{(Dd)}^{2}}+\frac{1}{2}(D{\theta}_{D}+d\cdot {\theta}_{d})$
The power transmitted by a belt drive is given by
Eq. 4
P = ( F_{1} F_{2} ) ·V
where
P = power (watts)
F_{1} = belt tension in the tight side (N),
F_{2} = belt tension in the slack side (N),
V = belt speed (per ms).
The torque is given by
Eq. 5
T = ( F_{1} F_{2} ) · r
Assuming that the friction is uniform throughout the arc of contact and ignoring centrifugal effects, the ratio of the tensions in the belts can be modeled by Eytlewein's formula
Eq. 6
$\frac{{F}_{1}}{{F}_{2}}={e}^{\mu \theta}$where
µ = coefficient of friction,
θ = angle of contact (rad), usually taken as the angle for the smaller pulley.
The centrifugal forces acting on the belt along the arcs of contact reduce the surface pressure. The centrifugal force is given by
Eq. 7
$F}_{c}=\rho \cdot {V}^{2}\cdot A=m\cdot {V}^{2$
where
ρ = density of the belt material (kg/m^{3}),
A = crosssectional area of the belt (m^{2}),
m = mass per unit length of the belt (kg/m).
The centrifugal force acts on both the tight and the slack sides of the belt, and Eytlewein’s formula can be modified to model the effect:
Eq. 7a
e^{µθ} = (F_{1}  F_{c} ) / ( F_{2}  F_{c} )
The maximum allowable tension, F_{1,max}, in the tight side of a belt depends in the allowable stress of the belt material, smax. Typical values for the maximum permissible stress are given in Table 1
Eq. 8
F_{1,max} = σ_{max} · A
The required crosssectional area for a belt drive can be found from
Eq. 9
$A=\frac{{F}_{1}{F}_{2}}{{\sigma}_{1}{\sigma}_{2}}$ $\frac{}{}$where
σ_{1} = stress belt tight side, M·N/m^{2}
σ_{2} = stress belt slack side, M·N/m^{2}
Typical values for the maximum permissible stress for highperformance flat belts.
Multiply structure 
Maximum permissible stress (MN/m^{2}) 

Friction surface coating 
Core 
Top surface 

Elastomer 
Polyamide sheet 
Polyamide fabric 
8.3 19.3 
Elastomer 
Polyamide sheet 
Elastomer 
6.613.7 
Chrome leather 
Polyamide sheet 
None 
6.311.4 
Chrome leather 
Polyamide sheet 
Polyamide fabric 
5.714.7 
Chrome leather 
Polyamide sheet 
Chrome leather 
48 
Elastomer 
Polyester cord 
Elastomer 
Up to 21.8 
Chrome leather 
Polyester cord 
Polyamide fabric 
5.212 
Chrome leather 
Polyester cord 
Chrome leather 
3.18 
Mechanical Design Engineering Handbook
Peter R. N. Childs
2014
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