the hydraulic hammer is in the lowest working position, the gas pressure of the
high-pressure accumulator is the highest and the volume is the smallest, which are
p ha2 and V ha2 , respectively. Assuming that the gas in the high-pressure accumulator
is adiabatic, the equation of state is
p ha0 V
n 1
ha0 ¼ p ha1 V
n 1
ha1 ¼ p ha2 V
n 1
ha2
ð12:27Þ
where n 1 —Gas variability index of high-pressure accumulator.
When the hydraulic hammer is in the highest working position, the gas pressure
of the nitrogen chamber of hydraulic cylinder is the highest and the volume is the
smallest, which are p a1 and V a1 , respectively. When the hydraulic hammer is in the
lowest working position, the gas pressure of the nitrogen chamber of hydraulic
cylinder is the lowest and the volume is the largest, which are p a2 and V a2 ,
respectively. Assuming that the gas in the nitrogen chamber is adiabatic, the
equation of state is
p a1 V
n 2
a1 ¼ p a2 V
n 2
a2
ð12:28Þ
where n 2 —Gas variability index of nitrogen chamber.
The dynamic equation of hammer body is
p d A d À p u A u À mg ¼ m
d
2 y
dt 2 þ B
dy
dt
þ k y þ y 0
ð
Þ
ð12:29Þ
where
m Mass of hammer body;
g Gravity acceleration;
y Rising stroke of hammer body;
t Time of hammer body rises;
B Viscous damping coefficient;
k Spring stiffness;
y 0 Spring precompression.
The initial conditions are yð0Þ ¼ 0; dy
dt
t¼0
¼ 0;
d
2 y
dt 2
t¼0
¼ 0.
12.3.2.2 Hammer Body Descending Stage
As shown in Fig. 12.12, during the descending stage, the hammer body falls with
variable acceleration under the action of gas pressure in the nitrogen chamber and
the weight of the hammer body.
12.3 Mathematical Model of High-Speed Pneumatic–Hydraulic Composite Hammer
291