| Dynamic synthesis of hydraulic devices - Examples 
 
  
   
    Examples of dynamic synthesis of the throttle brake device of the  hydro cylinder
   
  
 
 
 
 
 
  As  examples of dynamic synthesis of throttle brake devices of hydro cylinders we’ll  consider two simplified schemes: braking of the piston at action of impeding  force and retraction of a rod (Fig. 2
  
   а
  
  ) and at action of passing force  at promotion of a rod (Fig. 3
  
   а
  
  ).
 
 
 
  E x  a m p l e 1. Let’s consider a variant of the simplified scheme (Fig. 2
  
   а
  
  ).  Input data for calculation:
 
 
 
  
   D
  
 
 
  =140 mm;
  
   d
  
  = 90 mm;
  
   L
  
  =1000 mm;
   = 90.32 cm²;  =153.94 cm²;  = 12.64 cm²;  =7.7 cm²;  = 3480 N;
 
 
  
   т
  
 
 
  
  
 
 
  = 46550 kg;  =0.5 m/s;
  
   R
  
  =112.7 kN (impeding load);  = 31.4
 
 
  М
 
 
  P
 
 
  а
 
 
  ;  = 31.4
 
 
  М
 
 
  P
 
 
  а
 
 
  ;  = 0.735
 
 
  М
 
 
  P
 
 
  а
 
 
  ;  = 3.92
 
 
  М
 
 
  P
 
 
  а
 
 
  ;  = 0;  = 271 l/min;  = 980
 
 
  МPа;  =14 mm;  25 cm³;  = 1.96·10
  
   5
  
  МPа. 
 
  S o  l u t i o n.    For given values of  parameters we’ll receive: from the formula (6)
   = – 815.2 cm/s²; from the formula (16)  let’s assume
 
 
  
   Т
  
 
 
  = 0.11s, then  = 3.3 cm;  = 96.7 cm.
 
 
  Coefficients  of the polynomial (9) are equal: 
   
 
  Results  of dynamic synthesis of the characteristic of the throttle brake device of the  hydro cylinder
   for a  considered simplified variant are resulted on Fig. 2
  
   b
  
  . In the same place  diagrams of change of pressures  and piston speed
  
   v
  
  are resulted at braking accordingly  the planned law of movement. 
 
 
 
 
    
 
  Fig. 2. The simplified scheme (
  
   a
  
  ) and results (
  
   b
  
  ) of dynamic
 
 
 
  synthesis of the throttle brake device
 
 
 
 
 
 
  E x  a m p l e  2. At synthesis of the  characteristic
   of hydraulic damper for the second simplified case (Fig.  3
  
   а
  
  ) the following input data have been accepted:  =153.94  cm²;  = 90.32 cm²;  = 7.7 cm²;  =12.64 cm²;
 
 
  
   т
  
 
 
  
  
 
 
  = 63700 kg;
  
   R
  
  = –112.7 kN (passing force);  = 0 (otherwise in view of differential of areas of the  hydro cylinder for maintenance of the piston braking it is necessary to raise much  );  = 39.2
 
 
  М
 
 
  P
 
 
  а
 
 
  ;  =461.8 l/min; the rest parameters are as in the first simplified  case. 
 
  S o  l u t i o n.    From the formula (6)
 
 
  it is found:
   = – 462.2 cm/s²; from the formula (16)  let’s assume
 
 
  
   Т
  
 
 
  
  
 
 
  = 0.2 s, then  = 6 cm;  = 94.0 cm.
 
 
  Coefficients  of the polynomial (9) are equal: 
   
 
  Results  of dynamic synthesis of the characteristic of the throttle brake device of the  hydro cylinder
   for the second simplified  variant are resulted on Fig. 3
  
   b
  
  . In the same place diagrams of change of  pressure  and piston speed
  
   v
  
  are resulted at braking accordingly  the planned law of movement. 
 
    
 
  Fig. 3. The simplified scheme (
  
   a
  
  ) and results (
  
   b
  
  ) of dynamic
 
 
 
  synthesis of the throttle brake device
 
 
 
 
 
 
  The characteristics  of throttle brake devices
   received at
  
   certain
  
  parameters of the hydraulic system it is necessary then to survey at change of  the reduced masses and loadings in all working range of the projected machine to  define a degree of influence of each varied parameter to dynamics and basic  parameters of braking process, otherwise, to define "scope" of the  synthesized devices at change of external conditions. |