UNIVERSITY OF PERPETUAL HELP SYSTEM LAGUNA
STO. NINO, BINAN CITY, LAGUNA
RESEARCH WORK #3
V - Belts
USI, Adam Daryl A. MEE3216/ME3A
ME-3 / 22-0056-469 29 – March – 2025
Bachelor of Science in Mechanical Engineering
College of Engineering, Architecture, and Aviation
A V-belt is a power transmission belt with a trapezoidal
cross-section, designed to fit into corresponding grooves on
pulleys. This design enhances friction and prevents slippage,
making V-belts a reliable choice for transmitting power between
shafts. Their compact design and efficiency have made them
integral components in various mechanical systems.
I. Definition
a. History
The development of V-belts dates back to the early 20th
century, revolutionizing power transmission by offering a more
efficient and compact alternative to flat belts. Their ability to
transmit higher torque with reduced slippage led to widespread
adoption in industrial and automotive applications.
b. Inventor
The specific inventor of the V-belt is not well-documented, as
it evolved over time through contributions from various engineers
and manufacturers aiming to improve power transmission
efficiency.
II. Types/Kinds
V-belts are categorized based on their dimensions and
construction:
1.Classical V-Belts: Featuring a trapezoidal cross-section,
these are the most common type, balancing performance
and affordability.
2.Wedge V-Belts: Designed for limited space applications,
these belts can transmit higher power due to their increased
depth-to-width ratio.
3.Cogged V-Belts: Incorporating notches on the underside,
these belts offer increased flexibility and are suitable for
smaller pulley diameters.
4.Poly V-Belts: Also known as serpentine belts, these thin,
multi-groove belts provide flexibility and are ideal for driving
multiple pulleys in various applications.
5.Double V-Belts: Also known as hexagonal belts, these are
designed to transmit power on both sides, suitable for
serpentine drives.
III. Principle of Operation
V-belts operate on the principle of frictional engagement.
The trapezoidal shape allows the belt to wedge into the pulley
groove, increasing friction and enhancing the belt's grip. This
design minimizes slippage and enables the transmission of
higher torque compared to flat belts.
IV. Applications
V-belts are utilized across various industries due to their
efficiency and versatility:
● Manufacturing: Essential for driving machinery, conveyor
systems, and assembly lines, handling heavy loads with
reliable performance.
● Agriculture: Powering equipment such as tractors, combines,
and irrigation systems, offering durability in demanding
conditions.
● Automotive: Driving components like alternators, water
pumps, and air conditioning compressors, ensuring efficient
vehicle operation.
● Home Appliances: Found in washing machines, dryers, and
other household devices, providing reliable power
transmission.
V. Mathematical Formulas
1. Velocity Ratio of a V-Belt Drive
The velocity ratio (VR) is the ratio of the speed of the driving
pulley to the speed of the driven pulley.
VR = N₁ / N₂ = D₂ / D₁
Where:
● N₁ = Speed of the driving pulley (RPM)
● N₂ = Speed of the driven pulley (RPM)
● D₁ = Diameter of the driving pulley
● D₂ = Diameter of the driven pulley
2. Belt Tension Ratio
The ratio of tensions in the tight and slack sides of the belt is
given by Euler’s Formula:
T₁ / T₂ = e^(μθ)
Where:
● T₁ = Tension in the tight side (N)
● T₂ = Tension in the slack side (N)
● μ = Coefficient of friction between belt and pulley
● θ = Angle of contact (radians)
3. Power Transmitted by a V-Belt
The power transmitted by a V-belt is given by:
P = (T₁ - T₂) × v
Where:
● P = Power transmitted (Watts)
● T₁ = Tension in the tight side (N)
● T₂ = Tension in the slack side (N)
● v = Belt velocity (m/s), given by:
v = (π × D₁ × N₁) / 60
4. Length of a V-Belt (Open Belt Drive)
The total length of the belt required for an open belt drive is given
by:
L = 2C + (π / 2) × (D₁ + D₂) + [(D₂ - D₁)² / (4C)]
Where:
● L = Length of the belt (m)
● C = Center distance between pulleys (m)
● D₁ = Diameter of the driving pulley (m)
● D₂ = Diameter of the driven pulley (m)
5. Centrifugal Tension in a V-Belt
Centrifugal tension occurs due to the belt’s mass and velocity:
Tₐ = m × v²
Where:
● Tₐ = Centrifugal tension (N)
● m = Mass of belt per unit length (kg/m)
● v = Belt velocity (m/s)
Total Tension:
T = T₁ + Tₐ
6. Maximum Power Condition
For maximum power transmission, the centrifugal tension should
be equal to one-third of the total belt tension:
Tₐ = T₁ / 3
Thus, the effective tension equation becomes:
T₁ - T₂ = (2 / 3) × T₁
VI. Summary and Conclusion
V-belts have been pivotal in the advancement of mechanical
power transmission, offering a blend of efficiency, compactness,
and versatility. Their unique design allows for effective power
transfer across various applications, from industrial machinery to
household appliances. Understanding the different types of
V-belts, their operational principles, applications, and the
associated advantages and disadvantages is crucial for selecting
the appropriate belt for specific needs. Proper selection and
maintenance of V-belts ensure optimal performance, longevity,
and cost-effectiveness in mechanical systems.
References
1.Mechanical Power Transmission Association. (2013).
Calculation of V-belt tensions and shaft loads
(MPTA-B7i-2013). Retrieved March 29, 2025, from
https://mpta.org/wp-content/uploads/2016/05/MPTA-B7i-201
3.pdf
2.Optibelt. (n.d.). Technical manual: V-belt drives. Retrieved
March 29, 2025, from
https://www.optibelt.com/fileadmin/pdf/produkte/keilriemen/O
ptibelt-TM-v-belt-drives.pdf
3.RoyMech. (n.d.). Vee belts / V belts. Retrieved March 29,
2025, from
https://roymech.org/Useful_Tables/Drive/Vee_belts.html
4.Engineering LibreTexts. (n.d.). Belt friction. Retrieved March
29, 2025, from
https://eng.libretexts.org/Bookshelves/Mechanical_Engineeri
ng/Mechanics_Map_(Moore_et_al.)/06%3A_Friction_and_Fr
iction_Applications/6.07%3A_Belt_Friction
