Gears
Cylindrical Gears
Gear Ratio (i)
Where:
and are the rotational speeds and are the diameters of the gears
Torque transmitted
Where:
is the power in watts is the speed in revolutions per minute (RPM)
Power transmitted
Where:
is the angular speed in radians per second
Linear Speed
Where:
is the linear speed (in m/s)
Stress on the Teeth (Lewis formula)
Where:
is the tangential force is the face width, is the tooth module is the tooth form factor
Conical Gears
Gear Ratio
Where:
and are the radii of the conical gears
Helical Gears
Axial Force
Where:
is the tangential force is the helix angle
Torque in Helical Gears
Where:
is the tangential force is the gear radius
Gear Ratio with Helix Angle
Where:
and are the helical angles of the gears
Pulleys and Belts
Simple Pulleys
Gear Ratio
Where:
and are the diameters of the pulleys
Multiple Pulleys
Efficiency of the Pulley System
Calculation of Tension in the Ropes
Where:
is the mass of the object is the gravitational acceleration is the number of rope segments
Belts
Gear Ratio in Belts
Length of the Belt in a Pulley System
Where:
is the length of the belt is the distance between the centers of the pulleys
Contact Angle in Belts
Transmission Efficiency
Screws
Threaded Screws
Thread Pitch (p)
Where:
is the length of the thread is the number of threads
Clamping Force (F)
Where:
is the applied pressure is the cross-sectional area of the screw
Torque in Screws
Torque Required to Tighten a Screw
Where:
is the coefficient of friction is the axial force is the diameter of the screw
Efficiency of a Power Screw
Where:
is the lead angle of the thread is the friction angle
Torque Required to Lift a Load with a Power Screw
Where:
is the mean diameter of the screw is the axial load, is the lead angle is the coefficient of friction
Shafts and Bearings
Shafts
Calculation of Moment of Inertia (I) of a Circular Shaft
Where:
is the diameter of the shaft.
Shear Stress in the Shaft
Where:
is the torque is the radius of the shaft is the polar moment of inertia.
Critical Speed of a Shaft
Where:
is the critical speed of the shaft is the gravity is the static deflection of the shaft
Bearings
Contact Load in a Bearing
Where:
is the tangential force is the contact angle
Basic Nominal Life of a Bearing
Where:
is the life in number of revolutions is the dynamic load capacity of the bearing is the equivalent load applied to the bearing
Couplings and Clutches
Torque Transmitted by a Friction Coupling
Where:
is the torque, is the coefficient of friction is the normal force applied is the radius of the coupling.
Maximum Allowable Angular Misalignment in a Flexible Coupling
Where:
is the angular misalignment is the maximum allowable radial displacement is the radius of the coupling.
Brakes
Braking Torque in Drum Brakes
Where:
is the braking torque is the coefficient of friction is the normal force of the shoes on the drum is the effective radius of the drum
Vibrations and Damping
Natural Frequency of a System
Where:
is the stiffness of the system is the mass