At Hydraulic Power Systems, Inc. (HPSI), we understand that technical data on vibratory pile hammers can often be useful when selecting a machine for a particular application. It is very useful to select a machine with the right combination of eccentric moment, amplitude, dynamic force, hydraulic horsepower, engine horsepower and total weight for a particular application. The following information may be valuable in your selection of equipment for your job.

Eccentric Moment
A value in inch pounds equal to the weight of the eccentric multiplied by the distance from the center of rotation to the center of gravity of the eccentric.

Eccentric Moment = Weight x Radius (to C.G.)

Centrifugal Force
A weight rotating about a center of rotation at a fixed radius equal to outward force.

Centrifugal Force, lbs. =
Weight x Radius x RPM x RPM / 35204

Clamp Force
The area of the piston rod head of the clamp multiplied by the available clamp pressure of the Power Pack. Clamp force is very important to the life of the jaws of the clamp.

Clamp Force Tons = Dia2 x .7854 x Pressure / 2000

Hydraulic Horsepower
Output horsepower of the hydraulic motors is equal to the actual gallons per minute of hydraulic oil being delivered multiplied by the maximum relief setting of the hydraulic system. It is important when reviewing hammer specifications that the diesel engine horsepower is capable of providing more power than is required to achieve the required hydraulic horsepower. Without this horsepower available, it is not possible to maintain frequency to obtain maximum driving forces.

Hydraulic Horsepower =
GPM x Pressure / 1714 x Motor Efficiency

Dynamic Forces
Also sometimes known as driving force, is the force generated by the rotation of the eccentrics. The driving force is the product of the eccentric moment multiplied by a constant multiplied by the steady state frequency squared.

Force Tons =
Eccentric Moment x .0142 x Frequency2 / 1,000,000

Driving Amplitude
The total vertical travel of the vibrating mass including the vibrating portion of the Exciter and the weight of the pile being driven.

Amplitude in inches =
Eccentric Moment / Vibrating Mass x 2

Vibrating Mass
In determining the drivability of very heavy pile such as caissons, it is helpful to know the vibrating mass of the particular machine you are using. With known factors of eccentric moment and amplitude, the vibrating mass may be expressed as follows.

Vibrating Mass =
Eccentric Moment x 2 / Amplitude

Caisson Weight
To calculate the total vibrating mass for determining available amplitude, it is necessary to know the weight of the caisson. The simplified formula for pipe is shown as follows.

Weight per Foot =
O.D. of Pipe — Wall Thickness x Wall Thickness x 10.68