Page 192 - Compression Machinery for Oil and Gas

Reciprocating Compressors Chapter 5 181

crosshead, gas forces at the cylinder nozzle due to pressure pulsations, gas
forces in the pulsation bottle.
Unbalance inertia forces are the vector addition of the acceleration forces of
the rotating and reciprocating mass of all throws. The rotating mass are the
unbalance portion of each crank throw plus the rotating portion of the connect-
ing rod. The reciprocating mass is the reciprocating portion of the connecting
rod, crosshead, piston, and rod.
2
For vertical force F ¼ m rot rw sin(ωt) where m rot is the rotating mass, r is
crank radius, w is angular velocity in rad/s, ωt is the crank angle (0¼outer dead
center).
For horizontal force (axis of piston rod)
2
2
F ¼(m rot + m rec )rω cos(ωt)+ mrω r/Lcos(2ωt) where L is the connecting
rod length.
For the reciprocating mass there are a 1 and a 2 component. Ratio r/L is
the crank radius/connecting rod length and is typically about 20%.
However the acceleration forces of each throw act at each throw and so are
local forces. So for example, consider a six-throw compressor with all cylinders
of equal mass. At each throw there will be a local force due to the gas force
acting on the piston this will apply as an equal and opposite force at the cylinder
head and at the crankshaft. So while the force is in balance it does cause elastic
stretch of the frame, distance piece, and cylinder. The elastic stretch will be
approximately 0.1mm p-p per meter of distance from the center of the frame
to the center of the cylinder. In addition, the inertia force acting on the frame
and crosshead must be accounted for. Over the entire machine the inertia forces
will sum to zero for a fully balanced six throw; however, the local forces will
cause the frame to distort elastically and shake by an amount that does not
exceed the same value of 0.1mm p-p per meter along the frame.
The forces, both local and global will cause cyclic elastic deformation of the
compressor, bottles and piping, plus the skid, and foundation.
Normal practice is that for small skid-mounted compressor and for
foundation-mounted compressors just the global forces, that is, the unbalance
forces and moments are reported and considered in the design of the compressor
base and foundation (sometimes called the “rigid frame assumption”). How-
ever, for certain large skid-mounted compressors it may be appropriate to con-
sider the more complete picture of the local gas forces and shaking forces acting
at each throw. This is sometimes called the “flexible frame analysis” and is a
much more complicated analysis comprising an finite element analysis
(FEA) model of the frame and cylinder train along with the support structure.
This allows the skid to be analyzed including the complex elastic distortion of
the frame under load and how those loads are transmitted into the skid and
foundation.
Allowable limits for compressor vibrations are contained in ISO 10816. This
provides good, acceptable, and marginal levels of vibration in displacement,
velocity, and acceleration units, rms. Velocity units tend to be the most useful