Patent Publication Number: US-7214036-B2

Title: Screw type vacuum pump

Description:
FIELD OF THE INVENTION 
   The present invention relates to a screw vacuum pump having a pair of multiple-stage-screw rotors to compress a gas sequentially with a plurality of steps. 
   BACKGROUND OF THE INVENTION 
   Recently, it has been desired that a vacuum pump requires a smaller energy (electrical power) to reduce CO 2  emission in view of an environmental control. In Europe (EC), a chemical gas vacuum pump needs to have a discharge side temperature not more than 135° C. according to a safety standard. The temperature corresponds to a temperature grade T4 of the standard, in which acetaldehyde, trimethylamine, ethyl-methyl-ether, diethyl-ether, etc. are listed. These materials need to have a gas temperature not more than 135° C. at an outer surface thereof. 
   A conventional screw vacuum pump is disclosed in Japanese Patent Application Laid-open No. 63-36085, which is a single-stage pump having a pair of screw rotors. Another conventional screw vacuum pump is shown in  FIG. 5 , which is a two-stage pump having a pair of screw rotors. 
   This vacuum pump  61  has a pair of left and right screw rotors  63 ,  64  rotatively engaged with each other in a casing  62 . The screw rotor  63  rotates clockwise while the screw rotor  64  rotates counterclockwise. Each of the rotors  63 ,  64  has helical teeth  65 ,  66  being different from each other in pitch. The helical tooth  65  has a larger pitch and is located in the side of a suction port  67  defined in the casing  62 , while the helical tooth  66  having a smaller pitch is located in the side of a delivery port (not shown) of the casing  62 . 
   Each of the screw rotors  63 ,  64  is supported at each axial end thereof by a bearing  73  or  68 . The screw rotors  63 ,  64  can rotate adversely relative to each other via a timing gear  69  located at one end of thereof. A rotor shaft  70  couples operatively to a drive motor. 
   The rotation of the screw rotors  63 ,  64  compresses a gas introduced into a chamber  71  located in the side of the first helical teeth  65  from the suction port  67 . The compressed gas is transferred into a chamber  72  of the second helical teeth  66 , and the gas is further compressed in the chamber  72  to discharge it from the delivery port under an atmospheric pressure. 
   However, the conventional vacuum pump  61 , as illustrated in a characteristic curve of  FIG. 6 , requires a comparatively larger power (shat driving power La), which disadvantageously increases a delivery gas temperature more than 200° C. In  FIG. 6 , a lower graph shows a shaft driving power (kW) while an upper graph shows a discharge gas flow rate (1/minute). Horizontal coordinates correspond to vacuum degrees (MPaA). Moreover, the gas compressed via the two stages tends to cause a considerable pressure loss due to a gas leak through a gap between the pair of screw rotors  63 ,  64 . This undesirably decreases a discharge gas flow rate S as shown in an upper one of graphs of  FIG. 6 . 
   Screw vacuum pumps having such a property not only require a larger motor power but also compress a gas undesirably to create a gas temperature more than 135° C. Particularly, the screw vacuum pumps take a longer discharging time when a gas is compressed from a vacuum to an atmospheric pressure, which is an undesirable performance of them. 
   In view of the aforementioned situation, an object of the invention is to provide a vacuum pump requiring a reduced power and enhancing a reduced CO 2  emission. The vacuum pump has an inside gas temperature (a temperature in a delivery side) that fulfills an EN standard (not more than 135° C.). The vacuum pump is improved in safety and its gas delivery performance. 
   SUMMARY OF THE INVENTION 
   To achieve the object, a screw vacuum pump of claim  1  of the invention includes a pair of screw rotors rotatively engaged with each other in a pump casing to discharge a gas along a longitudinal direction of the pump. Each rotor has across section with a profile including an epitrochoid curve, a circular arc, and a pseudo-Archimedean spiral curve. Characteristically, each rotor has three types of helical teeth serially located in a longitudinal direction of the rotor, the three types of helical teeth being different from each other in theoretical displacement volume. A bypass conduit communicating with a delivery side of the pump is connected via a check valve to a first intermediate space defined between the first helical teeth and the second helical teeth and to a second intermediate space defined between the second helical teeth and the third helical teeth. 
   In thus configured pump, a gas introduced in the pump casing is compressed at a first stage by the first type of helical teeth, in which a part of the gas is discharged into the bypass conduit via a check valve when the pressure of the gas becomes more than a predetermined value (for example, an atmospheric pressure). The remaining gas is further compressed at a second stage by the second type helical teeth, in which a part of the gas is discharged into the bypass conduit via a check valve when the pressure of the gas becomes more than a predetermined value as well as the first stage. The remaining gas is further compressed at a third stage by the third helical teeth to be discharged outside the pump. Each check valve prevents a gas flow returning from the bypass conduit. 
   This configuration protects the screw rotors not to be under a larger load otherwise exerted during the first to third stages, limiting a temperature increase of the compressed gas. The gas discharges from a port between the first stage and the second stage, a port between the second stage and the third stage, and a discharge outlet of the third stage. Thus, the gas discharge speed is substantially uniform in the first to third stages, decreasing a total time for discharging the gas. 
   A screw vacuum pump of claim  2  is one described in claim  1 , and the screw pump is further characterized in that the three types of helical teeth provides a ratio of 1.4 of a gas flow rate at the first stage to that at the second stage, a ratio of 1.4 of a gas flow rate at the second stage to that at the third stage, and a ratio of 2 of a gas flow rate at the first stage to that at the third stage. 
   In the above-mentioned configuration, a pressure ratio of delivery pressure Pd to suction pressure Ps is equal to 2. When Pd is 760 Torr, Ps is a half of Pd, which is 380 Torr. Meanwhile, a discharge gas temperature Td is equal to Ts (Pd/Ps) n−1/n , where Ts designates a suction gas temperature. When politropic exponent n is 1.6, Td is about 106° C., which is lower than 135° C. to sufficiently fulfill the EN standard. 
   A screw vacuum pump of claim  3  is one described in claim  1  or  2 . The pump is further characterized in that the gas is compressed at the third stage into about a half in quantity to the first stage before a discharge port opens to discharge the gas. This configuration surely achieves a gas flow ratio (approximately 2) of the first stage to the third stage. 

   
     BRIEF DESCRIPTIONS OF ACCOMPANIED DRAWINGS 
       FIG. 1  is a longitudinal sectional view showing an embodiment of a screw vacuum pump according to the present invention; 
       FIG. 2  is a cross sectional view showing profiles of a pair of screw rotors of the vacuum pump; 
       FIG. 3  is P-V curves each related to a work done of a screw vacuum pump of the present invention or a conventional screw vacuum pump; 
       FIG. 4  is characteristic curves of a gas discharge rate and a shaft driving power of the screw vacuum pump of the present invention; 
       FIG. 5  is a longitudinal sectional view showing a conventional screw vacuum pump; and 
       FIG. 6  is characteristic curves of a gas discharge rate and a shaft driving power of the conventional screw pump. 
   

   BEST MODE EMBODYING THE INVENTION 
   Referring to the accompanied drawings, an embodiment of the present invention will be discussed. 
     FIG. 1  shows an embodiment of a screw vacuum pump, more definitely of a screw-type dry vacuum pump, according to the present invention. 
   The vacuum pump  1  has a metal casing  2  in which there are a pair of screw rotors  3 ,  4 . The screw rotor  3  has a clockwise helical screw while the screw rotor  4  has a counterclockwise helical screw such that the screws rotatively engage with each other. Each of the screws of the rotors  3 ,  4  has three types of pitches serially in its longitudinal direction. This provides first to third compression stages  7 ,  8 , and  9  between a suction port  5  and a discharge outlet  6  within the casing  2 . More specifically, an intermediate space  10  defined between the first stage  7  and the second stage  8  communicates via a check valve  12  with a pipe conduit (bypass pipe)  14  located outside the casing. Furthermore, an intermediate space  11  defined between the second stage  8  and the third stage  9  communicates via a check valve  13  with the pipe conduit  14 . The pipe conduit  14  communicates with a pipe  15  disposed in the side of the outlet  6 . 
   The casing  2  has a substantially elliptical profile and includes two rotor chambers  16 ,  17  that have a generally spectacle-shaped cross section consisting of two circles partially overlapped with each other. The casing  2  has a cooling (water cooling) jacket  18  outside thereof. The parallel rotor chambers  16  and  17  rotatively accommodate the pair of left and right screw rotors  3  and  4 . Each rotor has an outer peripheral surface positioned adjacent to an inner surface of the rotor chamber  16  or  17  with a little clearance therebetween. The screw rotors  3  and  4  also are positioned adjacent to each other with a small gap therebetween. 
   The screw rotor  3  or  4  has a shaft  19  or  20  which penetrates through a partition wall  21  or  22  positioned at a longitudinally fore or rear side of the casing  2 . The shaft  19  or  20  is rotatively supported by a bearing  25  or  26  within a side case  23  or  24 . The shaft  19  or  20  is secured to the rotor  3  or  4  with a key or the like. The discharge outlet  6  communicates with a discharge port  6   a  in the side of the partition wall  22 . 
   The side case  23  located in the side of the suction port  5  receives a pair of roller bearings  25  secured therein, while the side case  24  located in the side of the discharge outlet  6  receives a pair of ball bearings  26  secured therein. The pump has an end cover  27  in which there are disposed a pair of timing gears  28 . Each of the shafts  19 ,  20  is sealed by a sealing member in the side of the partition wall  22  to keep air tightness. The timing gears  28  engage with each other so that the shafts  19  and  20  can rotate oppositely to each other. 
   One  19  of the shafts extends from the end cover  27  to be coupled to a motor (not shown) via a coupler. The turning of the motor rotates the rotor  3  located in the driving side clockwise as shown by an arrowhead A so that the rotor  4  located in a follower side rotates counterclockwise. 
   Each rotor  3  or  4  has a larger helical screw pitch in the side of the suction port  5  and a smaller helical screw pitch in the side of the discharge outlet  6 . Meanwhile, the screw rotor has an intermediate-size helical screw pitch in a longitudinally intermediate part thereof between the suction port  5  and the discharge outlet  6 . The first stage  7  is defied in the side of the suction port  5  by the first type helical teeth  29  having the larger pitch; the second stage  8  is defined in the intermediate part by the second type helical teeth  30  having the intermediate size pitch; and the third stage  9  is defined in the side of the discharge outlet  6  by the third type helical teeth  31  having the smaller size pitch. 
   In the embodiment, the rotor chamber  32  of the first stage  7  has a length axially equal to or a little longer than the rotor chamber  33  of the second stage  8 , while the rotor chamber  34  of the third stage  9  has a length shorter than that of the rotor chamber  33  of the second stage  8 . 
   The suction port  5  is positioned at the first winding of the helical tooth  29  of the first stage  7  to communicate with the rotor chamber  32 , while the discharge port  6   a  of the discharge outlet  6  is positioned in a fore end surface  31   b  of the helical tooth  31  of the third stage  9  to communicate with the rotor chamber  34 . The port  6   a  is connected to the outside of the pump via the pipe  15 . With the rotation of the  4 , the end surface  31   b  of the helical tooth  31  closes and opens alternately the discharge port  6   a . The discharge port  6   a  has, for example, a crescent shape. The crescent may be defined by a smaller radius inner arc, a larger radius outer arc, and a line to connect one end of the inner arc and one end of the outer arc, the other ends of the inner and outer arcs being crossed with each other. 
   The discharge pipe  15  merges with the pipe conduit  14  that extends in a longitudinal direction of the pump casing. The pipe conduit  14  communicates with the intermediate space  11  defined between the second stage  8  and the third stage  9  via the check valve  13  and also with the intermediate space  10  defined between the first stage  7  and the second stage  8  via the check valve  12 . The pipe conduit  14  has an end  14   a  that is bent to have a right angle to communicate with the first check valve  12 . The pipe conduit  14  also has a short pipe  14   b  that is located at a longitudinal middle thereof to communicate with the second check valve  13 . 
   The check valves  12  and  13  are secured each to an outer surface of the pump casing  2  and sealed by a sealing member. The check valves  12  and  13  communicate with the intermediate space  10  or  11  via a passage  35  or  36  of the pump casing  2 . The check valves  12  and  13  allow a gas flow from the intermediate space  10  or  11  to the pipe conduit  14 , while the check valves  12  and  13  prevent a gas flow from the pipe conduit  14  to the intermediate spaces  10  and  11 . The check valves  12  and  13  open so as to flow out a gas from the intermediate space  10  or  11  when the pressure of the gas within the intermediate space  10  or  11  becomes more than a predetermined value (for example, an atmospheric pressure). 
   The intermediate space  10  is positioned between a fore end surface  29   b  of the helical tooth  29  of the first stage  7  and a rear end surface  30   a  of the helical tooth  30  of the second stage  8 . The intermediate space  11  is positioned between a fore end surface  30   b  of the helical tooth  30  of the second stage  8  and a rear end surface  31   a  of the helical tooth  31  of the third stage  9 . Each intermediate space  10  or  11  has a longitudinal length approximately equal to a half pitch of the helical tooth  30 . In each intermediate space  10  or  11 , there is received an intermediate shaft  38  having the same diameter as a root  37  of the screw rotors  3  and  4 . Each of the shafts  19  and  20  has a diameter smaller than the intermediate shaft  38  or the root  37 . The shafts  19  and  20  extend from a radial central part of the screw rotor  3  or  4 . In a 180° opposite side of the passage  35  or  36  laterally contiguous with the intermediate space  10  or  11 , there is defined a void  39  or  40  that is closed by a lid and sealed by a sealing piece. 
   The pair of screw rotors  3  and  4  have the screws directed oppositely to each other. The driving side clockwise helical screw rotor  3  has serially the smaller pitch helical tooth  31  of the third stage  9 , the middle pitch helical tooth  30  of the second stage  8 , and the larger pitch helical tooth  29  of the first stage  7 . Meanwhile, the driven side counterclockwise helical screw rotor  4  has serially the larger pitch helical tooth  29  of the first stage  7 , the middle pitch helical tooth  30  of the second stage  8 , and the smaller pitch helical tooth  31  of the third stage  9 . Each helical tooth  29  to  31  of the rotor  3  has the same shape as that of the rotor  4 . 
   Referring to  FIG. 2 , cross section curves are provided, in which the pair of screw rotors  3  and  4  have engaged with each other. Each curve of helical teeth  29  to  31  (intermediate helical teeth  30  are illustrated in  FIG. 2 ) consists of a quarter circular arc  43  having a smaller radius corresponding to the root  37 , a pseudo-Archimedean spiral curve  44  contiguous with one end of the circular arc  43 , an epitrochoid curve  45  contiguous with the other end of the circular arc  43 , and a larger radius circular arc  46  corresponding to an outer periphery of the helical tooth. The Archimedean spiral curve  44  is smoothly contiguous with the circular arc  46 , and the epitrochoid curve  45  is tangentially smoothly contiguous with the circular arc  46 . In  FIG. 2 , reference numeral  47  designates a rotation center of each rotor. 
   The pair of screw rotors  3  and  4  rotate oppositely to each other in the casing  2  as shown by arrowheads. A gas moves by a distance in the casing  2  without compression. Then, the gas is compressed after an end surface of the rotor  4  closes the discharge port  6   a  ( FIG. 1 ) defined in the partition wall  22  positioned near the side case  24 . The compression continues during a half turn of the rotor  4  until the discharge port  6   a  opens to discharge the compressed gas. This operation is a known art and its detail is referred to Japanese Patent Application Laid-open No. 63-36085. 
   Next, the operation and theory of the vacuum pump will be discussed. In  FIG. 1 , the rotation of the pair of screw rotors  3  and  4  draws a gas from the suction port  5  of the casing  2  to compress the gas by the pair of helical teeth  29  of the first stage  7 . The compressed gas moves to the second stage  8 . The displacement capacity of the second stage  8  is smaller than that of the first stage  7 . That is, a space defined by helical teeth  30  of the second stage  8  is smaller than that of the helical teeth  29  of the first stage  7 . Thus, the gas is further compressed in the second stage  8 . When the pressure of the compressed gas is larger than a predetermined discharge pressure, a part of the gas is discharged from the intermediate space  10  via the check valve  12  and the pipe conduit  14  while the remaining gas moves to the second stage  8 . 
   A pressure Pm 1  in the intermediate space  10 , which is a pressure of the gas between the first stage  7  and the second stage  8 , is obtained by the following equation:
 
 Pm   1   =Ps   1   ×Qs   1   /Qs   2   ×Tm   1   /Ts   1   (1)
 
   where 
   Ps 1 : pressure of suction port  5   
   Qs 1 : gas suction rate of first stage  7   
   Qs 2 : gas suction rate of second stage  8   
   Tm 1 : gas temperature between first stage  7  and second stage  8   
   Ts 1 : gas temperature (absolute temperature) at suction port  5   
   Before Pm 1  becomes a value obtained by the equation (1), the gas is partially discharged into the side of the discharge outlet  6  via the check valve  12  and the pipe conduit  14 , and the remaining gas moves to the second stage  8 . When Pm 1  becomes equal to a value obtained by the equation (1), the check valve  12  closes so that all the gas drawn from the suction port  5  moves to the second stage  8 . 
   Similarly to the first stage  7 , a pressure Pm 2  in the intermediate space  11 , which is a pressure of the gas between the second stage  8  and the third stage  9 , is obtained by the following equation: 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         P 
                         m2 
                       
                       = 
                         
                       ⁢ 
                       
                         
                           P 
                           m1 
                         
                         × 
                         
                           
                             Q 
                             s2 
                           
                           / 
                           
                             Q 
                             s3 
                           
                         
                         × 
                         
                           
                             T 
                             m2 
                           
                           / 
                           
                             T 
                             s3 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           
                             P 
                             s1 
                           
                           × 
                           
                             
                               Q 
                               s1 
                             
                             / 
                             
                               Q 
                               s2 
                             
                           
                           × 
                           
                             
                               T 
                               m1 
                             
                             / 
                             
                               T 
                               s1 
                             
                           
                           × 
                           
                             
                               Q 
                               s2 
                             
                             / 
                             
                               Q 
                               s3 
                             
                           
                           × 
                           
                             
                               T 
                               m2 
                             
                             / 
                             
                               T 
                               m1 
                             
                           
                         
                         = 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           P 
                           s1 
                         
                         × 
                         
                           
                             Q 
                             s1 
                           
                           / 
                           
                             Q 
                             s3 
                           
                         
                         × 
                         
                           
                             T 
                             m2 
                           
                           / 
                           
                             T 
                             s1 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 2 
                 ) 
               
             
           
         
       
     
   
   where
         Qs 3 : gas suction rate of third stage  9     Tm 2 : gas temperature between second stage  8  and third stage  9     Ps 1 , Qs 1 , Qs 2 , Tm 1 , and Ts 1  are the same as those defined above.       

   Before Pm 2  becomes a value obtained by the equation (2), the gas is partially discharged into the side of the discharge outlet  6  via the check valve  13  and the pipe conduit  14 , and the remaining gas moves to the third stage  9 . When Pm 2  becomes equal to a value obtained by the equation (2), the check valve  13  closes so that all the gas drawn into the second stage  8  moves to the third stage  9 . 
     FIG. 3  shows two P-V (work done) curves of vacuum pumps of the present invention and a conventional art in parallel. A P-V curve of a conventional pump consists of lines or curves serially connecting points 0, V1, 1, 4, and Pd. Meanwhile, A P-V curve of the vacuum pump  1  of the present invention consists of lines or curves serially connecting points 0, V1, 1, 2, m, 3, 4, and Pd. 
   In  FIG. 3 , P designates a pressure; V a specific volume; Pd a discharge pressure; Pm 1  a pressure between the first stage  7  and the second stage  8  (of the intermediate space  10 ); Pm 2  a pressure between the second stage  8  and the third stage  9  (of the intermediate space  11 ); V 1  a specific volume at a point of the suction side (compression initiating point); V 2  a specific volume at the intermediate space  10 ; V 3  a specific volume at the intermediate space  11 ; and V 4  a specific volume at a point of the discharge side. 
   The pressure of the conventional vacuum pump increases along a quadratic curve, which is approximately a line, from a suction side (numeral  1  of  FIG. 3 ) to a discharge side (numeral  4  of  FIG. 3 ). In the meantime, the vacuum pump  1  ( FIG. 1 ) of the present invention partially discharges a gas into the pipe conduit  14  via the check valve  12  from the intermediate space  10  when the gas pressure of the chamber  32  at the first stage  7  becomes more than a predetermined pressure. Thus, the gas pressure (Pm 1 ) in the chamber  32  at the first stage  7  is constant from point  1  to point  2  ( FIG. 3 ). Then, the gas in the chamber  33  at the second stage  8  is compressed up to Pm 2  as shown a line between point  2  and point m. The gas is partially discharged into the pipe conduit  14  via the check valve  13  from the intermediate space  11  when the gas pressure of the chamber  33  at the second stage  8  becomes more than another predetermined pressure. Next, the gas pressure (Pm 2 ) in the chamber  33  at the second stage  8  is constant from point m to point  3  ( FIG. 3 ). Then, the gas in the chamber  34  at the third stage  9  is compressed along an approximately quadratic curve from point  3  to point  4  of  FIG. 3 . 
   Accordingly, the vacuum pump of the present invention saves a power (energy) by hatching areas of  FIG. 3  as compared with the conventional vacuum pump. 
   When a suction side temperature Ts 1  is 40° C. (313° K.), a discharge gas temperature tm 1  at the first stage is obtained by the following equation: 
   
     
       
         
           
             
               
                 
                   t 
                   m1 
                 
                 = 
                   
                 ⁢ 
                 
                   
                     
                       T 
                       s1 
                     
                     × 
                     
                       
                         ( 
                         
                           
                             P 
                             m1 
                           
                           / 
                           
                             P 
                             s1 
                           
                         
                         ) 
                       
                       
                         n 
                         - 
                         
                           1 
                           / 
                           n 
                         
                       
                     
                   
                   - 
                   273 
                 
               
             
           
           
             
               
                 = 
                   
                 ⁢ 
                 
                   
                     
                       313 
                       × 
                       
                         1.4 
                         
                           06 
                           / 
                           1.6 
                         
                       
                     
                     - 
                     273 
                   
                   = 
                   
                     82 
                     ⁢ 
                     
                       ( 
                       
                         °C 
                         . 
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
   
   where n: politropic exponent 
   The discharge gas temperature tm 1  of 82° C. at the first stage is less than 135° C. This fulfills the EN standard. 
   Similarly, a discharge gas temperature tm 2  at the second stage is obtained by the following equation: 
   
     
       
         
           
             
               
                 
                   t 
                   m2 
                 
                 = 
                   
                 ⁢ 
                 
                   
                     
                       T 
                       s2 
                     
                     × 
                     
                       
                         ( 
                         
                           
                             P 
                             m2 
                           
                           / 
                           
                             P 
                             m1 
                           
                         
                         ) 
                       
                       
                         n 
                         - 
                         
                           1 
                           / 
                           n 
                         
                       
                     
                   
                   - 
                   273 
                 
               
             
           
           
             
               
                 = 
                   
                 ⁢ 
                 
                   
                     
                       
                         ( 
                         
                           273 
                           + 
                           82 
                         
                         ) 
                       
                       × 
                       
                         1.4 
                         
                           06 
                           / 
                           1.6 
                         
                       
                     
                     - 
                     273 
                   
                   ⁢ 
                   
                     = 
                     . 
                     . 
                   
                   ⁢ 
                   
                     130 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ( 
                       
                         °C 
                         . 
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
   
   The discharge gas temperature tm 2  of 130° C. at the second stage is less than 135° C. This also fulfills the EN standard. 
   At the third stage, almost all the calorie generated can be used to increase a temperature of a cooling water in the jacket  18 . Thus, a discharge gas temperature Td at the third stage is approximately equal to the discharge gas temperature Tm 2  at the second stage. Accordingly, all the gases discharged from the first and third stages are less than 135° C. to fulfill the EN standard. 
   Next, features of the vacuum pump  1  according to the present invention will be summarily discussed. 
   The conventional vacuum pump compresses a gas by two stages. However, an intermediate pressure between the first stage and the second stage exerts on the screw rotors, which requires an extra energy. To eliminate the disadvantage, the embodiment of the present invention employs the bypass pipe conduit  14  and the check valves  12 ,  13  to discharge partially the gas to keep the gas at a pressure not more than the predetermined pressure. This prevents a pressure more than the predetermined pressure from exerting on the screw rotors  3  and  4  between the first stage  7  and the second stage  8  or between the second stage  8  and third stage  9 . 
   Each rotor has the helical tooth  29  of the first stage  7 , the helical tooth  30  of the second stage  8 , and the helical tooth  31  of the third stage  9  serially from the suction side. The discharge gas temperature (inside temperature) is determined to be less than 135° C. The gas is compressed at the first to third stages such that a ratio of a pressure of the finally discharged gas at the third stage to that at the suction side is determined to be 2. 
   Pm 1  designates a pressure between the first stage  7  and the second stage  8 ; Pm 2  a pressure between the second stage  8  and the third stage  9 ; Ps a suction pressure; Pd a discharge pressure; Q 1  a volume of the chamber  32  at the first stage  7 ; Q 2  a volume of the chamber  33  at the second stage  8 ; T 1  a temperature in the chamber  32 ; T 2  a temperature in the chamber  33 ; R 1  a ratio of a gas flow rate of the first stage  7  to the second stage  8 ; and R 2  a ratio of a gas flow rate of the second stage  8  to the third stage  9 :
 
 R   1   =Pm   1   /Ps=Q   1   /Q   2   ×T   2   /T   1   (3)
 
 R   2   =Pm   2   /Ps=Q   2   /Q   3   ×T   3   /T   2 ,  (4)
 
thus,
 
 R   1   ×R   2   =Pm   2   /Ps=Q   1   /Q   3   ×T   3   /T   1   ≈Qth   1   /Qth   3   (5)
 
   Actually, R 1 ×R 2 =2, 
   that is, Qth 3  is a half of Qth 1 , 
   where
         Qth 1 : theoretical displacement volume of helical teeth  29  at first stage  7     Qth 3 : theoretical displacement volume of helical teeth  31  at third stage  9 ,       

   furthermore, R 1 ×R 2 =R 2 =2, 
   thus, R 1 =R 2 =R=√{square root over ( )}2≈1.4. 
   A ratio of a theoretical displacement volume of the first stage  7  to that of the second stage  8  is 1.4, and a ratio of a theoretical displacement volume of the second stage  8  to that of the third stage  9  is 1.4. That is, the theoretical displacement volume ratio of the first to third stages  7 ,  8 , and  9  is 2:1.4:1. 
   Thus, a ratio of a gas flow rate of the first stage  7  to that of the second stage  8  is 1.4, and a ratio of a gas flow rate of the second stage  8  to that of the third stage  9  is 1.4. Accordingly, a ratio of a gas flow rate of the first stage  7  to that of the third stage  9  is approximately 2. The discharge port  6   a  ( FIG. 1 ) is configured so as to open to discharge the gas at the third stage  9  after the gas is compressed into about a half in volume. 
   When a pressure ratio of Pd/Ps is 2 and Pd is 760 Torr (or 0.1 MPaA or 1 atm), Ps=Pd/2=380 Torr (or 0.05 MpaA), where Ps designates a discharge pressure and Ps designates a suction pressure. 
   Generally, a discharged gas temperature Td Ts (Pd/Ps) n−1/n  where n (politropic exponent)=1.6
 
 Td= 293×2 0.375 ≈106(° C.)
 
   This temperature of 106° C. is lower than 135° C., fulfilling the EN standard. 
   The discharged gas temperature may be lower than 135° C. based on a thermal conversion calculation when the gas pressure in the suction side is about 380 Torr. When the vacuum pump operates with the suction side of the pump being closed, a cooling gas is introduced into a discharge side of the pump to cool its inside. The cooling gas is supplied from a port (not shown) defined in an inner surface of the casing into the casing, the port being opened and closed by the movement of the helical tooth. This cooling method is referred to Japanese Patent Application Laid-open No. 63-36085. 
   As illustrated in a characteristic curve of  FIG. 4 , the vacuum pump according to the present invention requires a discharging time considerably less than that ( FIG. 6 ) of the conventional pump, achieving an energy saved pump. In  FIG. 4 , a lower graph shows a shaft driving power La (kW), and an upper graph shows a discharge gas flow rate S (1/minute). Lateral coordinates correspond to vacuum degrees (MPaA). 
   In  FIG. 4 , a shaft driving power La ranged from point  1  and point  2  corresponds to one for compressing the gas by the helical teeth  29  at the first stage  7 . A shaft driving power La ranged from point  2  and point  3  corresponds to one for compressing the gas by the helical teeth  30  at the second stage  8 . A shaft driving power La ranged from point  3  and point  4  corresponds to one for compressing the gas by the helical teeth  31  at the third stage  9 . Unlike the conventional pump, the pipe conduit  14  partially discharges the gas so that the shaft driving power of the second stage  8  is kept in a lower range. The shaft driving power graph is generally a trapezoid with an upper flat line as a whole. 
   Furthermore, as shown in the discharge gas flow rate curve of the upper graph of  FIG. 4 , the provision of the pipe conduit  14  enables that a discharge gas rate obtained the helical teeth  29  at the first stage  7  is kept until the gas is compressed up to the predetermined pressure at the third stage  9 . The displacement capacity does not decease in the discharge side unlike the conventional pump (the upper graph of  FIG. 6 ). This considerably decreases a time for discharging the gas to allow an efficient pump operation particularly when the gas is discharged under an atmospheric pressure. 
   The vacuum pump  1  ( FIG. 1 ) may be modified to be another embodiment that has a pair of upper and lower screw rotors in place of the left and right screw rotors  3 ,  4 . The screw rotors  3 ,  4  may have helical teeth of the three stages which are separately formed to be assembled in one body. The timing gears  28  may be positioned not in the discharge side but in the suction side. The concept that the gas is compressed at the three stages  7  to  9  may be applied to another vacuum pump having screw rotors using a gear profile different from the one of  FIG. 2 . Air may be selected as the gas. 
   INDUSTRIAL APPLICABILITY OF THE INVENTION 
   As mentioned above, according to the present invention of claim  1 , the provision of the three types of helical teeth, the bypass conduit, and the check valves protects the screw rotors not to be under a larger load otherwise exerted during the first to third stages. This enables a reduced shaft driving power to be better in energy saving, contributing a deduction of CO 2  emission in a heat power plant. The pump casing keeps a comparatively lower inner pressure unlike the conventional art, limiting a temperature increase of the delivered gas. Thereby, the vacuum pump can be used more safely, for example, as a chemical vacuum pump. Furthermore, the gas discharge rate at the first stage  7  is kept until the gas is finally discharged, considerably decreasing a time taken for discharging the gas to allow an efficient pump operation, particularly when the gas is discharged under an atmospheric pressure. 
   The invention of claim  2  limits a temperature increase of the delivered gas, fulfilling the EN temperature standard for a chemical vacuum pump. This prevents a danger such as inflammation of the chemical gas, improving the pump in safety. 
   The invention of claim  3  determines the gas flow rates of the first to third stages to surely have the advantageous effects of the inventions of claims  1  and  2 .