The Working Principles of Vibratory Hammer
 Amplitude (A), Line Pull (ω), Eccentric Moment (M), Maximum Centrifugal Force (F), Partition Weight (Q), Power (N)

1. The determination of vibratory power N. The formula for vibratory power N:
 N=K•M•n/9550 （kw） In the above formula, n refers rotary speed, and K equals to 1.25.
 2. The determination of eccentric moment M:
 The bigger the eccentric moment of the vibratory hammer is, the more powerful the hammer is to penetrate into hard soil. When amplitude and partition weight Q (the pile weight together with the weight of the hammer) are given,, the eccentric moment can be calculated. The formula goes as follows:
M=Q•A（N•m）
 The bigger the eccentric moment of the vibratory hammer is, the more powerful the hammer is to penetrate into hard soil. When amplitude and partition weight Q (the pile weight together with the weight of the hammer) are given,, the eccentric moment can be calculated. The formula goes as follows:
 3. The determination of pulling frequency ω:
 The pulling frequency of the vibratory hammer is closely related to the inherent frequency of the vibratory system. When the pulling frequency is almost the same as the inherent frequency, the vibratory hammer drives the pile most effectively. The inherent frequency of the vibratory system is related to the parameters not only of the hammer, but also of the soil. The natural frequency of vibration differs greatly in accordance with the soil layers. The following table shows the optimum frequency range for different soil layers.
Reference of Pulling Frequency for Different Soil LayersSoil Layer Optimum Frequency (ω/s) Saturated Sand 100200 Plastic Clay Soil And Sandy Clay Soil 90100 Hard Clay Soil 7075 Gravel Clay Soil 6070 Sandy Gravel Soil 5060 Experimental results show that if other factors remain fixed, liquefaction of the saturated sand can be accelerated by increasing the pulling frequency. As the liquefaction process increases, the friction from the soil reduces, and the acceleration speed of the pile can be more effectively upgraded and the pile driving efficiency can be significantly improved, compared to the mere increase of amplitude. What is worth noticing, however, is that if the pulling frequency if set to high, it will lead to the overload of the output power. Therefore, an overall consideration is needed in determining the pulling frequency.
 The pulling frequency of the vibratory hammer is closely related to the inherent frequency of the vibratory system. When the pulling frequency is almost the same as the inherent frequency, the vibratory hammer drives the pile most effectively. The inherent frequency of the vibratory system is related to the parameters not only of the hammer, but also of the soil. The natural frequency of vibration differs greatly in accordance with the soil layers. The following table shows the optimum frequency range for different soil layers.
 4. The determination of partition weight Q:

Apart from necessary amplitude and acceleration speed, the vibratory hammer requires also some partition weight to overcome the resistance in driving pile. The relationship between the static resistance R and the injection standard value N and section area S is reflected by the below formula:
R=4N•S （KN）
For this reason, when the friction is substantially reduced because of the vibration, the pile would drive to the place where the tip resistance is equal to the partition weight, which can be refected by the formula:
Q=4N•S.

Apart from necessary amplitude and acceleration speed, the vibratory hammer requires also some partition weight to overcome the resistance in driving pile. The relationship between the static resistance R and the injection standard value N and section area S is reflected by the below formula:
 5. The determination of line pull F:

Line pull F is a parameter which reflexes the comprehensive capacity of the vibratory hammer. The line pull F must be larger than the static friction f between the pile and the soil. Under the effect of the line pull, the static friction f will be greatly reduced in driving pile. If the friction between pile and soil during vibration is f′, the rule above can be summarized into the below formula:
F≥f′=μf （KN）
In this formula, μ stands for the reduction coefficient the friction under the vibratory force. The coefficient is determined by the acceleration speed. Experiment shows that when the vibratory acceleration speed is 10 times larger than the gravity acceleration or above, μ changes very subtly, and μ and f′ tends to constant.

Line pull F is a parameter which reflexes the comprehensive capacity of the vibratory hammer. The line pull F must be larger than the static friction f between the pile and the soil. Under the effect of the line pull, the static friction f will be greatly reduced in driving pile. If the friction between pile and soil during vibration is f′, the rule above can be summarized into the below formula:
 6. The determination of amplitude A:
 The larger the amplitude is, the faster the pile drives. The pile will not drive when the amplitude is very small. Only when the amplitude reaches a certain value will the pile drive. The value at which the pile starts driving is called the initial amplitude A0. As the amplitude increases, the pile drives faster, until it reaches the limit value Ac. As a result, the range of the amplitude is:
A0＜A＜Ac
The initial amplitude A0 can be calculated through the following formula which involves the soil injection N: A0≥N/12.5 +3 （mm）
As for the standard value of soil injection, the following table is for your reference.
The Standard Value of Soil InjectionSoil Type N Very Loose Sandy Soil 04 Loose Sandy Soil 410 MediumDensity Sandy Soil 1030 Dense Sandy Soil 3050 Very Dense Sandy Soil ＞50 Soil Type N Soft Clay Soil 24 MediumHardness Clay Soil 48 Hard Clay Soil Very Hard Clay Soil 815 1530 Extremely Hard Clay Soil ＞30 As a professional company, Yong'an Machinery Co., LTD. integrates the researching and developing, manufacturing, selling and leasing of vibratory hammer series products. It has been focusing on producing Yong'an vibratory hammer series products over the past more than 20 years since its establishment in 1986. Yong'an Machinery Co., Ltd. progresses year by year under the support and understanding of its beloved and widespread customers. With outstanding technical expertise and scientific working principle, our vibratory hammer will undoubtedly satisfy your demands.
 The larger the amplitude is, the faster the pile drives. The pile will not drive when the amplitude is very small. Only when the amplitude reaches a certain value will the pile drive. The value at which the pile starts driving is called the initial amplitude A0. As the amplitude increases, the pile drives faster, until it reaches the limit value Ac. As a result, the range of the amplitude is: