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Time：2014-01-19 10:53:14Source：This siteViews：4964
Technical level of machine tools has been an important indicator of a country 's productivity and industrial strength . In the development of machine tools , in order to increase production and processing systems with processing quality , high speed and high accuracy is the key , how to improve the processing speed and precision machine tools has become an important issue of development . Machining tool to enhance productivity , it is necessary to increase the speed of travel within a limited , but as speed increases , the driving force of the drive spindle or a working platform are bound with the increase in the speed feed driving force moment it is easy to cause vibration phenomenon, once the vibration generated during processing , it will result in reduced machining accuracy , thereby affecting the quality of the workpiece , so often unable to taking into account the needs of high speed and high accuracy , precision machining requirements , while you can not improve the processing speed .
Machine tool vibration phenomena instant acceleration and deceleration , causes mainly from the structural rigidity and inertia drive system due to poor matching , so long as the strengthening of the structural rigidity of the feed system can effectively reduce vibration during high-speed feed caused . When feeding system increased structural rigidity , often result in an increase in the quality of the stage base , the greater the system when the feed quality, the driving force must be a corresponding need to increase , due to the limited space of the machine design ( such as a spindle motor configuration space considerations ) , the quality of the base station set is restricted .
Due to the above factors , the machine tools in the design of the drive shaft gradually began to adopt a twin-screw driven architecture , this method can not only increase the structural rigidity of the feed system can also reduce the impact of the driving force of eccentric torque caused by the double motor drive mode, in addition to strengthening the driving force of the system , but also can improve the response speed of the system .
Biaxial synchronous drive advantages:
Biaxial driven applications is usually to get a larger load capacity or used for unloading system containing large span , and therefore the use of demand is not the main focus on the high-speed cutting . But with the development of related technologies, speed and precision machine tool demand continues to increase, dual-axis drive design also began to be used on high-speed machining centers , to suppress vibration caused by high feed when incurred. To sum up the current biaxial driven applications , mainly in the following several advantages , the following will be discussed in more detail for the various advantages.
( A ) suppress the vibration of high speed
( 2 ) improve the rigidity of the system and prolong the service life of the screw
( 3 ) to improve system response
( 1 ) to suppress the vibration of high acceleration and deceleration
As mentioned in the foregoing , in high-speed applications to reduce vibration phenomenon caused by high acceleration and deceleration to improve structural rigidity feed system is the easiest solution , but is often limited by the overall design of parts and electronic control configuration limitations , making the design stage of the base structure is limited . General common machine tool feed a system configuration shown in FIG stage disposed on the X -axis Y -axis of the saddle , the X-axis and Y -axis is connected to drive the movable part is moved . On the configuration, the Y -axis of the screw is set to the intermediate position beneath the saddle , will be the main driving force to avoid the influence of additional torque caused by off-center , as shown in Figure II . Such a configuration, when the X -axis stage of the Y -axis position is located right above the middle of the saddle does effectively reduce the impact of the eccentric , but the stage is moved to the X -axis at both ends , then the overall location of the center of mass system will move with the stage direction of its movement and biased , then the driving force of the Y-axis can not act on the center of mass of the system, the torque generated by the eccentric force will affect the feed system stability.
To solve this problem , the Japanese tool factory Mori Seiki first proposed DCG (Drive at the center of gravity) of the application of concepts , double ball screw driven synchronously by the way , the driving force is applied to the central portion of the overall system quality feed , shown in Figure 3 . Because of the stage relative to the weight , the weight of the workpiece itself to many small , and the vertical axis due to the torque generated by the height difference is not large , so long as the ball screw so that the center of gravity in the same driving force horizontal surface which can effectively suppress vibration phenomena .
According to the test results Mori Seiki raised, shown in Figure IV , so X, Y stage running a rectangular track travel , when to move on stage only when the X -axis ( the long side of the rectangle ) , single-axis drive and no significant difference in comparing the results of biaxial drive , but when Y axis starts driving ( the short side of the rectangle ) , compared to the traditional single-axis drive, dual-axis vibration phenomena driven by a significant improvement .
( 2 ) improve the rigidity of the system and prolong the service life of the screw
Processing center in the mold processing applications, while surface machining , machining trajectory is composed of numerous small segments , shown in Figure 5 , the process of machining , the tool must constantly change direction , in which the process of turning , the drive system needs to provide a large acceleration changes of direction of the tool. With the acceleration of the increase, the driving force of the drive system for the relatively improved, if less rigid feeding system , it is easy to overshoot problems at the turning point occurred at this time too .
Rigidity in the axial drive system mainly from the ball screw drive power use, while the outer diameter of the ball screw as the screw outer diameter to increase and upgrade imaginable , hoping the greater rigidity of the drive system , it should be used the larger the outer diameter of a ball screw , but the space limitations on the machine design , the size of the outer diameter of the screw can be used is limited . Biaxial driven design , even a small selection of the screw outer diameter size greater rigidity can be obtained , in the limited space still meet the needs of high rigidity . Figure 6 below , using two 40mm outer diameter ball screw , rigid in the axial direction than the outer diameter of the rigid single improved when 45% 50mm .
Biaxial actuator applications , since the direction of the load shaft is shared equally by the two ball screws , and therefore applied to the load on each screw is driven to approximately half of the uniaxial , can greatly enhance the life of the ball screw , shown in Figure 7 , using two ball screw outer diameter of 40mm , its life is 3.7 times the outer diameter of 50mm single time . In order to achieve greater output and higher life, this design is applied to all-electric injection molding machine injection axis , as shown in Figure 8 JSW large all-electric injection molding machine applications .
( 3 ) to improve system response
Biaxial driven architecture design , because the load average of two screws to share , so even if the choice of screw outer diameter smaller size specifications can also be obtained when life is better than single-axis drive , because the screw outer diameter narrowing, and have two motors simultaneously driven , so in fact single motor output will be less than the required single-motor -driven design , the moment of inertia of the motor will be significantly reduced with the application cases of the table with a biaxial drive application examples comparing single-axis drive , when the load is 500kgf, screw the maximum stroke of 1200mm , the moment of inertia of the drive system down 52 %. Since the moment of inertia of the load is reduced, under the same driving force , the motor can achieve higher acceleration response , with integral drive system is also improved.
Dual-axis ball screw drive needed to resolve the issue :
On the biaxial driven applications , will first encounter the problem is " how to make biaxial screw can be driven synchronously ? " , Although biaxial driver can bring high rigidity , high response and high-thrust advantage , but the two drivers asynchronous system , but likely to cause damage to the transmission mechanism in advance . General screw drive systems are the use of semi-closed loop control mode , with encoder feedback to the servo motor control , but because there are problems with the lead screw errors exist, so the actual amount of displacement of the motor output stage there is a slight difference , usually to make the actual amount of movement of the instruction input by way of the pre- match compensation . In the biaxial actuator applications, the amount of error of two lead screws can not identical, although the control mode can be compensated to achieve a degree of synchronization , but at the same time the two locking screws pedestal seat in a carrier , the two pairs between the number of screw will pull each other 's phenomenon exists if pulling the screw between the two phenomena is too large, the general control can not completely eliminate the compensation synchronization system , drive system and cause instability .
Even using the optical scale approach, while monitoring the compensation can effectively eliminate the two actions are not synchronized between the paired screw phenomenon, but it will result in enhancing the relative cost control , mostly not in this way , so if possible eliminate two pairwise difference between the screw , it can reduce the cost required for the control system , but can also reduce the complexity of the control . Usually the factors affecting the accuracy of the positioning of the screw with the following points , and therefore the manufacture of the screw , as long as the control in this particular number of factors, they can not reduce the synchronization time of the biaxial actuator , the following several factors which will make for a more detailed discussion.
( 1) The difference between the amount of lead errors
( 2 ) changes in preload torque difference
( 3 ) the amount of heat temperature difference
( 1) The difference between the amount of lead errors
Based on the above discussion on the application of the biaxial actuator , even if the drive motor to the instruction in the two are the same, but due to the difference of the screw itself, the actual amount of feed of the drive screw can not both the same pair , by synchronizing require additional in a controlled manner before they can divide the two paired difference between the screw feed . Synchronous control applications , most will set a ball screw shaft MASTER, while the other axis ball screw is set to SLAVE, MASTER and SLAVE amount based on the difference between the two screws , screw in part SLAVE applying a speed correction value thereby achieve speed synchronization control , as shown in Figure IX of Siemens proposed speed / torque coupled from the main control structure , when the compensation value SLAVE side is too large, the heat is likely to cause the motor , the motor temperature heat l phenomenon will directly affect the positioning accuracy SLAVE screw , causing the synchronization delay compensation , thereby affecting the overall stability of the feed system . Figure X shows the all-electric Mitsubishi used in synchronous control method to measure the injection molding machine , its control system, in order to reduce the problem of compensation for delays , and position monitoring system synchronization, the pressure and the speed of synchronization synchronization, than the amount of the difference between the three , choose the smallest amount of difference as compensation benchmark , thereby reducing the instability caused by excessive compensation .
Based on the above discussion , if the lower two screws lead error difference, can effectively improve the compensation delay occurs, so it can greatly simplify the complexity of the control structure . After pairing is shown in comparison with the control has not been paired control of the ball screw lead C5 level measurement results , A comparison chart eleven screws paired with untreated control screw B , the maximum error of the difference in effective lead inside the tooth length amounted to 40 ? m, with the screw through C special control of the amount of the difference is only 5 ? m, and therefore in a biaxial screw driver pairing , after a special control, on behalf of its cumulative performance difference between the amount of lead can be controlled to at least less than the allowable tolerance of the standard 1/ 4 .
( 2 ) changes in the amount of preload torque difference
Compared to conventional female screw Ike , ball screw friction many smaller , but generally in the application , in order to increase the rigidity of the drive system , a certain degree of pre-pressure is applied on the screw . Compared to the bearing mechanism , ball screw drive track for a spiral track , the track itself, there is a certain size processing error , so the pressure will vary with the pre- nut position vary , as twelve show . In positioning control system, the changes will affect the friction feed system positioning accuracy , so the ball screw preload torque stability for positioning accuracy is very important.
According to JIS B1192 specifications , accuracy grade C5 preload torque allowable amount of variation is ± 35%, and therefore has not been paired two ball screw control , even if the norms are in compliance with JIS difference amount of its maximum possible preload torque up to 70 % of baseline preload torque. One can imagine , in the case of biaxial drive , such differences will inevitably affect the positioning accuracy of the control system, and cause deterioration of synchronicity . In the biaxial screw drive control matching only reduce the amount of difference between the preload torque of the screw pair is not enough to improve the similarity of the two pairs of the screw, also need additional request single screw within the effective preload tooth length torque uniformity, so in biaxial drive synchronous control can get better synchronization , after a period of use , but also to ensure that the two paired comparison differences screw will not change much .
( 3 ) the amount of heat temperature difference
Screw the amount of temperature rise during operation will improve the speed with which gradually increased , so in high-speed applications, the thermal displacement screw driven positioning accuracy is fairly obvious . In the single-axis drive applications, usually in a way calculated to estimate approximately the amount of heat the temperature rise of the screw, so they can compensate for the calculated values ??with the corresponding prior . But in the biaxial -driven applications , the drive system is a coupled architecture , operating conditions will affect the two screws from each other , when the temperature difference between the two conditions paired screw is large, straightness feed platform would continue to deteriorate and cause difficult to estimate the temperature conditions , difficult to advance by way of compensation to improve .
In the biaxial -driven design , the heat temperature control is very important to suppress the temperature difference between the two screw easiest way is to use a hollow screw forced cooling , so you can effectively control the temperature conditions of the screw, if not hollow under cooling conditions, it is necessary to control the synchronization position of the screw , the two screws can be suppressed as long as the mutual pulling phenomenon, an additional frictional force can be avoided . Also preload torque is also a considerable degree of influence on the temperature of the screw , the screw preload torque if the difference between the two is large , the temperature rise of the phenomenon is also bound to vary widely, hot temperature will cause the feed to run different platforms straightness worse, Figure XIII pairing special control screw after screw with general non- paired comparison of temperature rise , through a special control can effectively improve the biaxial drive temperature is not synchronous .
Conclusion :
Past biaxial driven design , mostly based on the design of higher power demand , but with the continuous improvement of industrial technology , high-precision , high- load, high productivity demands of the global development of mechanical equipment constant trend in high-performance lower demand , to enhance the competitiveness of products , processing equipment need to have high-speed and high-precision functions , gradually, biaxial driven design constructs also began to be widely used in high-performance machine tool design.
On the biaxial driven applications , the main key technology is how to remove the two screws pairing operation is not synchronized , although the problem can be improved by extending the drive mechanism differences through electronic control technology to compensate , but this ignores the driver Ruoyin control mechanism on easily extend more additional problems. Therefore, the design of the biaxial actuator , the control characteristic of the screw pair is important , through the control of the screw can effectively improve the matching of the drive system is not synchronized , so that the machine is designed to use the least cost to achieve the best performance.
Machine tool vibration phenomena instant acceleration and deceleration , causes mainly from the structural rigidity and inertia drive system due to poor matching , so long as the strengthening of the structural rigidity of the feed system can effectively reduce vibration during high-speed feed caused . When feeding system increased structural rigidity , often result in an increase in the quality of the stage base , the greater the system when the feed quality, the driving force must be a corresponding need to increase , due to the limited space of the machine design ( such as a spindle motor configuration space considerations ) , the quality of the base station set is restricted .
Due to the above factors , the machine tools in the design of the drive shaft gradually began to adopt a twin-screw driven architecture , this method can not only increase the structural rigidity of the feed system can also reduce the impact of the driving force of eccentric torque caused by the double motor drive mode, in addition to strengthening the driving force of the system , but also can improve the response speed of the system .
Biaxial synchronous drive advantages:
Biaxial driven applications is usually to get a larger load capacity or used for unloading system containing large span , and therefore the use of demand is not the main focus on the high-speed cutting . But with the development of related technologies, speed and precision machine tool demand continues to increase, dual-axis drive design also began to be used on high-speed machining centers , to suppress vibration caused by high feed when incurred. To sum up the current biaxial driven applications , mainly in the following several advantages , the following will be discussed in more detail for the various advantages.
( A ) suppress the vibration of high speed
( 2 ) improve the rigidity of the system and prolong the service life of the screw
( 3 ) to improve system response
( 1 ) to suppress the vibration of high acceleration and deceleration
As mentioned in the foregoing , in high-speed applications to reduce vibration phenomenon caused by high acceleration and deceleration to improve structural rigidity feed system is the easiest solution , but is often limited by the overall design of parts and electronic control configuration limitations , making the design stage of the base structure is limited . General common machine tool feed a system configuration shown in FIG stage disposed on the X -axis Y -axis of the saddle , the X-axis and Y -axis is connected to drive the movable part is moved . On the configuration, the Y -axis of the screw is set to the intermediate position beneath the saddle , will be the main driving force to avoid the influence of additional torque caused by off-center , as shown in Figure II . Such a configuration, when the X -axis stage of the Y -axis position is located right above the middle of the saddle does effectively reduce the impact of the eccentric , but the stage is moved to the X -axis at both ends , then the overall location of the center of mass system will move with the stage direction of its movement and biased , then the driving force of the Y-axis can not act on the center of mass of the system, the torque generated by the eccentric force will affect the feed system stability.
To solve this problem , the Japanese tool factory Mori Seiki first proposed DCG (Drive at the center of gravity) of the application of concepts , double ball screw driven synchronously by the way , the driving force is applied to the central portion of the overall system quality feed , shown in Figure 3 . Because of the stage relative to the weight , the weight of the workpiece itself to many small , and the vertical axis due to the torque generated by the height difference is not large , so long as the ball screw so that the center of gravity in the same driving force horizontal surface which can effectively suppress vibration phenomena .
According to the test results Mori Seiki raised, shown in Figure IV , so X, Y stage running a rectangular track travel , when to move on stage only when the X -axis ( the long side of the rectangle ) , single-axis drive and no significant difference in comparing the results of biaxial drive , but when Y axis starts driving ( the short side of the rectangle ) , compared to the traditional single-axis drive, dual-axis vibration phenomena driven by a significant improvement .
( 2 ) improve the rigidity of the system and prolong the service life of the screw
Processing center in the mold processing applications, while surface machining , machining trajectory is composed of numerous small segments , shown in Figure 5 , the process of machining , the tool must constantly change direction , in which the process of turning , the drive system needs to provide a large acceleration changes of direction of the tool. With the acceleration of the increase, the driving force of the drive system for the relatively improved, if less rigid feeding system , it is easy to overshoot problems at the turning point occurred at this time too .
Rigidity in the axial drive system mainly from the ball screw drive power use, while the outer diameter of the ball screw as the screw outer diameter to increase and upgrade imaginable , hoping the greater rigidity of the drive system , it should be used the larger the outer diameter of a ball screw , but the space limitations on the machine design , the size of the outer diameter of the screw can be used is limited . Biaxial driven design , even a small selection of the screw outer diameter size greater rigidity can be obtained , in the limited space still meet the needs of high rigidity . Figure 6 below , using two 40mm outer diameter ball screw , rigid in the axial direction than the outer diameter of the rigid single improved when 45% 50mm .
Biaxial actuator applications , since the direction of the load shaft is shared equally by the two ball screws , and therefore applied to the load on each screw is driven to approximately half of the uniaxial , can greatly enhance the life of the ball screw , shown in Figure 7 , using two ball screw outer diameter of 40mm , its life is 3.7 times the outer diameter of 50mm single time . In order to achieve greater output and higher life, this design is applied to all-electric injection molding machine injection axis , as shown in Figure 8 JSW large all-electric injection molding machine applications .
( 3 ) to improve system response
Biaxial driven architecture design , because the load average of two screws to share , so even if the choice of screw outer diameter smaller size specifications can also be obtained when life is better than single-axis drive , because the screw outer diameter narrowing, and have two motors simultaneously driven , so in fact single motor output will be less than the required single-motor -driven design , the moment of inertia of the motor will be significantly reduced with the application cases of the table with a biaxial drive application examples comparing single-axis drive , when the load is 500kgf, screw the maximum stroke of 1200mm , the moment of inertia of the drive system down 52 %. Since the moment of inertia of the load is reduced, under the same driving force , the motor can achieve higher acceleration response , with integral drive system is also improved.
Dual-axis ball screw drive needed to resolve the issue :
On the biaxial driven applications , will first encounter the problem is " how to make biaxial screw can be driven synchronously ? " , Although biaxial driver can bring high rigidity , high response and high-thrust advantage , but the two drivers asynchronous system , but likely to cause damage to the transmission mechanism in advance . General screw drive systems are the use of semi-closed loop control mode , with encoder feedback to the servo motor control , but because there are problems with the lead screw errors exist, so the actual amount of displacement of the motor output stage there is a slight difference , usually to make the actual amount of movement of the instruction input by way of the pre- match compensation . In the biaxial actuator applications, the amount of error of two lead screws can not identical, although the control mode can be compensated to achieve a degree of synchronization , but at the same time the two locking screws pedestal seat in a carrier , the two pairs between the number of screw will pull each other 's phenomenon exists if pulling the screw between the two phenomena is too large, the general control can not completely eliminate the compensation synchronization system , drive system and cause instability .
Even using the optical scale approach, while monitoring the compensation can effectively eliminate the two actions are not synchronized between the paired screw phenomenon, but it will result in enhancing the relative cost control , mostly not in this way , so if possible eliminate two pairwise difference between the screw , it can reduce the cost required for the control system , but can also reduce the complexity of the control . Usually the factors affecting the accuracy of the positioning of the screw with the following points , and therefore the manufacture of the screw , as long as the control in this particular number of factors, they can not reduce the synchronization time of the biaxial actuator , the following several factors which will make for a more detailed discussion.
( 1) The difference between the amount of lead errors
( 2 ) changes in preload torque difference
( 3 ) the amount of heat temperature difference
( 1) The difference between the amount of lead errors
Based on the above discussion on the application of the biaxial actuator , even if the drive motor to the instruction in the two are the same, but due to the difference of the screw itself, the actual amount of feed of the drive screw can not both the same pair , by synchronizing require additional in a controlled manner before they can divide the two paired difference between the screw feed . Synchronous control applications , most will set a ball screw shaft MASTER, while the other axis ball screw is set to SLAVE, MASTER and SLAVE amount based on the difference between the two screws , screw in part SLAVE applying a speed correction value thereby achieve speed synchronization control , as shown in Figure IX of Siemens proposed speed / torque coupled from the main control structure , when the compensation value SLAVE side is too large, the heat is likely to cause the motor , the motor temperature heat l phenomenon will directly affect the positioning accuracy SLAVE screw , causing the synchronization delay compensation , thereby affecting the overall stability of the feed system . Figure X shows the all-electric Mitsubishi used in synchronous control method to measure the injection molding machine , its control system, in order to reduce the problem of compensation for delays , and position monitoring system synchronization, the pressure and the speed of synchronization synchronization, than the amount of the difference between the three , choose the smallest amount of difference as compensation benchmark , thereby reducing the instability caused by excessive compensation .
Based on the above discussion , if the lower two screws lead error difference, can effectively improve the compensation delay occurs, so it can greatly simplify the complexity of the control structure . After pairing is shown in comparison with the control has not been paired control of the ball screw lead C5 level measurement results , A comparison chart eleven screws paired with untreated control screw B , the maximum error of the difference in effective lead inside the tooth length amounted to 40 ? m, with the screw through C special control of the amount of the difference is only 5 ? m, and therefore in a biaxial screw driver pairing , after a special control, on behalf of its cumulative performance difference between the amount of lead can be controlled to at least less than the allowable tolerance of the standard 1/ 4 .
( 2 ) changes in the amount of preload torque difference
Compared to conventional female screw Ike , ball screw friction many smaller , but generally in the application , in order to increase the rigidity of the drive system , a certain degree of pre-pressure is applied on the screw . Compared to the bearing mechanism , ball screw drive track for a spiral track , the track itself, there is a certain size processing error , so the pressure will vary with the pre- nut position vary , as twelve show . In positioning control system, the changes will affect the friction feed system positioning accuracy , so the ball screw preload torque stability for positioning accuracy is very important.
According to JIS B1192 specifications , accuracy grade C5 preload torque allowable amount of variation is ± 35%, and therefore has not been paired two ball screw control , even if the norms are in compliance with JIS difference amount of its maximum possible preload torque up to 70 % of baseline preload torque. One can imagine , in the case of biaxial drive , such differences will inevitably affect the positioning accuracy of the control system, and cause deterioration of synchronicity . In the biaxial screw drive control matching only reduce the amount of difference between the preload torque of the screw pair is not enough to improve the similarity of the two pairs of the screw, also need additional request single screw within the effective preload tooth length torque uniformity, so in biaxial drive synchronous control can get better synchronization , after a period of use , but also to ensure that the two paired comparison differences screw will not change much .
( 3 ) the amount of heat temperature difference
Screw the amount of temperature rise during operation will improve the speed with which gradually increased , so in high-speed applications, the thermal displacement screw driven positioning accuracy is fairly obvious . In the single-axis drive applications, usually in a way calculated to estimate approximately the amount of heat the temperature rise of the screw, so they can compensate for the calculated values ??with the corresponding prior . But in the biaxial -driven applications , the drive system is a coupled architecture , operating conditions will affect the two screws from each other , when the temperature difference between the two conditions paired screw is large, straightness feed platform would continue to deteriorate and cause difficult to estimate the temperature conditions , difficult to advance by way of compensation to improve .
In the biaxial -driven design , the heat temperature control is very important to suppress the temperature difference between the two screw easiest way is to use a hollow screw forced cooling , so you can effectively control the temperature conditions of the screw, if not hollow under cooling conditions, it is necessary to control the synchronization position of the screw , the two screws can be suppressed as long as the mutual pulling phenomenon, an additional frictional force can be avoided . Also preload torque is also a considerable degree of influence on the temperature of the screw , the screw preload torque if the difference between the two is large , the temperature rise of the phenomenon is also bound to vary widely, hot temperature will cause the feed to run different platforms straightness worse, Figure XIII pairing special control screw after screw with general non- paired comparison of temperature rise , through a special control can effectively improve the biaxial drive temperature is not synchronous .
Conclusion :
Past biaxial driven design , mostly based on the design of higher power demand , but with the continuous improvement of industrial technology , high-precision , high- load, high productivity demands of the global development of mechanical equipment constant trend in high-performance lower demand , to enhance the competitiveness of products , processing equipment need to have high-speed and high-precision functions , gradually, biaxial driven design constructs also began to be widely used in high-performance machine tool design.
On the biaxial driven applications , the main key technology is how to remove the two screws pairing operation is not synchronized , although the problem can be improved by extending the drive mechanism differences through electronic control technology to compensate , but this ignores the driver Ruoyin control mechanism on easily extend more additional problems. Therefore, the design of the biaxial actuator , the control characteristic of the screw pair is important , through the control of the screw can effectively improve the matching of the drive system is not synchronized , so that the machine is designed to use the least cost to achieve the best performance.
