interpolation method for the open CNC system is

Transcription

1 DOI.7/s ORIGINAL ARTICLE An interpolation method for the open CNC system based on EPM Yu-an Jin & Yong He & Jian-zhong Fu & Zi-Chen Chen Received: 4 January 3 / Accepted: 9 April 3 # Springer-Verlag London 3 Abstract A typical open computer numerical control (CNC) system should own the capability of being redeveloped easily and effectively, and any improvements of interpolation algorithm or machining technique could be put into practice by users conveniently. However, this is not always available in the current open CNC systems. To solve this problem, an interpolation method based on external profile mode (EPM) is introduced to improve the universality and the performance of an open CNC system in this paper. The method is realized with a rough interpolation in the PC host and a fine interpolation in the slave motion controller. With this method, various interpolation algorithms can be easily realized in the rough interpolation when machining complex contours. Meanwhile, the machining parameters during each interpolation cycle can be wholly determined by the host, so a real-time adjustment of machining parameters can be accomplished during the interpolation. The working principal of EPM is presented in this paper, and the realization of interpolation algorithms with the proposed method is described. A look-ahead algorithm for determining the machining parameters of each segment is implemented based on the length of segments in the rough interpolation. An acceleration/deceleration strategy with confined jounce is proposed in the look-ahead algorithm. The experimental results of specific profile interpolation show that the interpolation method based on EPM can make the open CNC system more universality and high performance. Keywords CNC. External profile mode. Line segments. Look-ahead algorithm Y.<a. Jin : Y. He (*) : J.<z. Fu : Z.<C. Chen The State Key Lab of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 37, China yongqin@zju.edu.cn Introduction In order to give full play to computer technology, open computerized numerical control (CNC) system has become a mainstream direction of research and application in the field of industrial control []. Open CNC systems have the advantages of modularity, standardized, and redevelopment. The performance, including machining efficiency and accuracy of the whole control system, is directly related to the interpolation method of the controller. At present, most interpolation methods in the open CNC system accomplish contours' machining by approaching them with a series of lines or arcs effectively and precisely [ 5]. When machining complicated contours, some special techniques are applied to improve machining performance [6, 7, 4], such as fitting contours into nonuniform rational basis spline (NURBS) and choosing some special acceleration/deceleration (ACC/DEC) strategy. When an open CNC system equipped with a special interpolation algorithm is used in another occasion, some problems may appear during machining. These problems disobey the initial aim of the open CNC system, and a universal interpolation method for the open CNC system is urgently needed. Researchers have done much work to improve machining performance. Yu et al. [8] presented the definition and architecture of an open control system, and pointed out that the open CNC system had been an inevitable trend of the development in industrial field, for it was a key technology to approach unpredictable market changes. Farooq and Wang [9] used a PC-based controller to replace a programmable machine for a real-time direct control of six joints. The concentration of their research was the application of the open system, and the interpolation method was not involved. K.D.et al. [] discussed the design and implementation of an open system for the automatic configuration and dynamic reconfiguration of distributed machine tool control systems. This was the initial attempt on the open CNC system. A realtime look-ahead control algorithm was proposed by Liu []

2 and an ACC/DEC process was considered for the speed planning of the machining profile. However, his algorithm lacked of generalization for arbitrary contours. In addition, many researchers have made efforts on the interpolation methods which can be used widely. Zhang et al. [3]proposed a multiperiod turning method to improve the feed rate at the junctions using linear acceleration and deceleration mode. This method can achieve the maximal acceleration capability of the NC machine and can satisfy the need of real-time interpolation. Wang et al. [6] presented a real-time NURBS interpolator with a look-ahead function to process numerous linear segments. They used a criterion to fit continuous short blocks into NURBS. This interpolation method could be used for irregular contours' machining. However, all these interpolation algorithms were exclusive and were not available in different machining situations, so a CNC system with different interpolation algorithms can boost the universality of itself. In addition, look-ahead algorithms with an appropriate ACC/DEC strategy can bring significant advancement in high-speed and high-precision CNC machining. The lookahead algorithm can predict the geometrical characteristic of the machining contours and determine the ACC/DEC points, which are essential for smooth machining. Lookahead algorithms are studied by many researchers in recent years [, 5]. Ye et al. [] presented an interpolation method based on the look-ahead algorithm. This look-ahead algorithm was utilized in numerous micro-line segments to improve the machining performance. Related simulation and experiments were performed to verify the efficiency of this method. Tsai et al. [] presented a spline-fitting technique to accomplish the machining of short line segments. The first stage of their algorithm was a look-ahead process, which converted appropriate segments into parametric curves, then a novel ACC/DEC feed rate planning was used to determine the feed rate at the junction between each segments. Tsai et al. [3] proposed an interpolation scheme which integrated ACC/DEC before interpolation and ACC/DEC after interpolation, the look-ahead algorithm planed the profiles' feed rate based on chord errors, command errors, curvatures, and acceleration limits. Liu et al. [4] did a research on the velocity look-ahead algorithm based on the linear ACC/DEC strategy; the result of their research could achieve high-speed and smooth transition between machining blocks. So it could be concluded that the ACC/DEC strategy was the key technology of look-ahead algorithm. Zhang et al. [5] presenteda multiaxis predictive control approach to improve the motion smoothness and contouring precision. The proposed approach contained an improved quadratic performance index, which could guarantee a minimum of errors and a generally predictive control method used for motion smoothness and machining precision. This paper proposes a novel interpolation method based on external profile mode (EPM) in the open CNC system. In this interpolation method, the rough interpolation is undertaken by the PC host, so it is available for users to choose an optimal interpolation algorithm according to the machining situation. A look-ahead algorithm with a novel ACC/DEC strategy which is used in the rough interpolation will be presented. The rough interpolation can be accomplished both off-line to achieve higher machining performance or online for more real-time machining. The machining parameters can be changed online and used for real-time adjustment. Hence, this paper is organized as follows. In Sect., an introduction of the working principle of EPM and the realization of different interpolation algorithms are presented. Besides, a description of an interpolation algorithm, which owns a look-ahead algorithm with a new ACC/DEC strategy based on confined jounce are addressed in this section. A related experiment and the corresponding analysis are provided to demonstrate the feasibility and efficiency of the proposed interpolation method in Section 3. Section 4 concludes with a brief summary. Interpolation method based on EPM. Introduction of EPM In an open CNC system, the motion controller plays an essential role in machining performance. To realize interpolation of various kinds of contours, motion controllers currently support several trajectory control modes, such as S curve point-to-point, trapezoidal point-to-point, contour mode, electronic gear mode, and so on. With these modes, PC host just needs to determine some parameters according to the geometric traits of machining contours or directly send NC codes to the controller. The interpolation process and some other real-time tasks are performed by the controller completely. The schema of a typical control process with these modes is shown in Fig.. The interpolation algorithm under these control modes is wholly decided by the chosen mode itself. After acquiring contours and some necessary machining parameters, the trajectory generator of motion controller plans the parameters in each servo cycle, such as the position, the velocity, the acceleration, and the jerk. These parameters will be converted into command impulses, and then the motors are drove to interpolation. EPM is another control mode of motion controller. Some functions in a general internal trajectory generator can be performed by the PC host with this mode. A common open CNC system means that the PC host mainly undertakes several non real-time control tasks, such as tool management, status watching, and so on. However, with EPM, PC hosts can also determine the machining parameters; that is to say, the work that should have been done in motion controller could be accomplished with PC hosts. Such a change

3 Fig. Schema of control process of internal trajectory generator CAM PC host NC code File process NC interpreter Motion Controller Trajectory genertator Position velocity Acceleration Jerk Servo/Step drive Servo/Step motors brings a plenty of benefits. For example, the computation burden of controller's CPU can be relived; the interpolation efficiency can be improved accordingly. Besides, with more autonomy, the host computer can realize specific interpolation algorithm to satisfy the given machining requirements. After the planning of trajectory parameters in the PC host, these data are saved in the external RAM of motion controller for the further use. Then, the trajectory generator of motion controller acquires the command values of these parameters successively from the external RAM and transfers them into command impulses, which are able to drive motors. In order to realize contours' interpolation with EPM, machining parameters, including the position, the velocity, the acceleration, the jerk, and the period of sampling points, are needed to be determined in the PC host. The period is the sampling interval of rough interpolation in the PC host. For example, if the period is one, servo/step drive obtains periodical parameters directly from external RAM in each servo cycle, i.e., those parameters are just kept in one servo cycle. When the period is larger than one, a data intensive process needs to be applied on the planned data, which are stored in the RAM. The trajectory generator takes parameters from RAM and calculates the intermediate parameters. Parameters of each servo cycle are calculated as follows: In general, the jerk is known; thus, the acceleration A n can be expressed. A n ¼ a n þ j n n ¼ ; ; 3 t ðþ where a n presents the acceleration of the former servo cycle, j n is the jerk of the former servo cycle, t is the period. The integral calculus is applied in Eq. (); the equation on velocity can be given as Eq. () V n ¼ v n þ a n þ j n n ¼ ; ; 3 t ðþ where v n is the velocity of the former servo cycle. The equation on position can be shown in Eq. (3) with the same principle. P n ¼ p n þ v n þ a n n ¼ ; ; 3 t þ j n 6 ð3þ where p n is the position of the former servo cycle. If period (t) is larger, the final interpolation data are mostly calculated by trajectory generator in the controller. Since the above calculation algorithm (Eqs. (), (), and (3)) is unchangeable, a deviation may appear between the data calculated by trajectory generator and the expecting data. In contrast, if t is too small, the amount of parameters calculated by the PC host is very large, especially when the machining contour is quite complex. This is time-consuming, and a very large storage of buffer is needed for these data. So the value of t is different in different machining situations. After acquiring needed parameters for driving a motor, the drive module will transfer these values into corresponding command impulses just as it does in other control modes. Figure shows the schema of control process with EPM... Interpolation method based on EPM Considering the limited applicable range of current interpolation methods of an open CNC system that has been mentioned in Sect., this paper proposes an interpolation method based on EPM to solve this problem. In this method, a rough interpolation with a look-ahead algorithm is implemented in the PC host to take full use of PC's highperformance hardware. Any interpolation algorithms can be realized in the rough interpolation, which is suitable for specific machining situations. Fig. Schema of control process of external profile mode PC host CAM NC code File process Trajectory plan NC interpreter Position velocity Acceleration Jerk RAM Motion Controller Trajectory genertator Position velocity Acceleration Jerk Servo/Step drive Servo/Step motors

4 The proposed interpolation method can realize machining of arbitrary contours within two steps. The first stage is implemented in the PC host, with various machining segments going through a rough interpolation. A look-ahead algorithm is used to determine the points where acceleration/deceleration should begin based on the geometrical characteristic of segments. Without a look-ahead algorithm may result in unexpected problems, such as severe vibration or great errors. It will be discussed in detail in Sect.. about the look-ahead algorithm. Besides, in the lookahead process, picking out enough sampling points in contours for calculating their parameters for fine interpolation is also helpful. So, the procedure in PC hosts contains three parts: obtaining original data from NC code file; choosing an appropriate ACC/DEC strategy to make a look-ahead process for machining trajectory; and lastly, a rough calculation needs to be implemented to calculate parameters of each sampling point. The planned data will be stored in the buffer of PC hosts for the further use. The second stage is a real-time machining; the external RAM of motion controller is filled with data from PC host buffer. After further process by the trajectory generator in motion controller, the driven module obtains command values and transfers them into command impulses to drive motors. A workflow about the interpolation method is show in Fig. 3. The rough interpolation is executed in the PC host. The amount of data after rough interpolation is so large that it is impossible to send all of them to the RAM of the motion controller only once. These data should be parted into enough groups for sending. However, during machining, only a few microseconds delay of data transmission can bring an interruption of impulses, which may lead to terrible results. So the delay must be avoided. This paper introduces a buffer mechanism which can provide enough memory space for data transmission. Firstly, an initialization is applied in the RAM of controller for EPM interpolation. In the initialization process, buffer space is divided into two same parts for usage in turn. This buffer mechanism can increase the efficiency of data transmission and guarantee the continuity of the fine interpolation. Furthermore, another benefit of the proposed interpolation method based on EPM is the changeable parameters during machining. That means machining parameters can be adjusted online if the current parameters is not the best. As long as the changed interpolation data are sent to the external RAM of motion controller in time, the machining trajectory can be adjusted adaptively, which may be used in online error compensation [6]. Figure 4 shows a flow chart of data transmission in the interpolation. Supposing the data amount after rough interpolation is EntitySize, the memory space in the controller for interpolation buffer is BufferSize. At the beginning, a judgment of EntitySize is implemented to decide how to process those data in the following step. If the amount of data (EntitySize) from rough interpolation is less than BufferSize, these data will be sent to memory buffer of the controller wholly. Otherwise, the data of BufferSize from PC's buffer are sent to RAM in the controller. On the start of fine interpolation, the trajectory generator obtains data from RAM for further data intensive and sends results to the driven module continuously, and the free space of memory (Freesize) of controller is gradually larger and larger; when it increases to BufferSize/, the data of BufferSize/ in PC's buffer are sent to controller's RAM for the next fine interpolation cycle. Just like this, when the data in the PC buffer are taken out completely, the interpolation is accomplished. Obtaining information of segments File of NC code Fine interpolation in controller Look-ahead algorithm Calculation of parameters save data to PC buffer RAM of controller Buffer for data Rough interpolation in PC host Trajectory generator for fine calculation Motion platform Driven module obtains data for fine interpolation Servo controller Sending command impulses Fig. 3 Schema of interpolation based on EPM

5 Fig. 4 Flow chart of data in interpolation based on EPM Initialization of RAM of controller Buffersize Amount of rough interpolation from PC Entitysize Entitysize>Buffersize? YES NO Sending data of rough interpolation wholly Entitysize= Taking data of Buffersize out from PC s buffer to RAM of controller EntitySize=EntitySize-Buffersize Fine interpolation begins Entitysize>? YES NO End While loop Freesize>Buffersize/? NO Waiting YES Entitysize>Buffersize/? NO Remaining data to RAM Entitysize= YES Taking remaining data of Buffersize/ to RAM EntitySize=EntitySize-Buffersize/ Actually, this interpolation method can realize any other interpolation algorithms for any contours. Because of EPM, rough interpolation with a look-ahead algorithm can be implemented in the PC host. As long as enough sampling points for fine interpolation based on specific interpolation algorithms are produced in the rough interpolation, this technique can realize the corresponding algorithm. This characteristic of EPM can provide enough autonomy for users to develop new interpolation algorithms.. An Interpolation algorithm based on EPM The interpolation method based on EPM is just as described in Sect...; the machining for arbitrary contours includes speed planning (rough interpolation) and command impulses sending (fine interpolation). It can be easily understood that fine interpolation is accomplished in the motion controller, which possesses the capability of high-speed calculation. So it can achieve a high-precision in fine interpolation. Hence, the rough interpolation is the key factor of this interpolation method. A look-ahead algorithm, which can guarantee the machining efficiency and accuracy, is necessary in the rough interpolation. During the look-ahead process, the geometrical characteristic of machining contour is analyzed for determining the speed of sampling points according to an ACC/DEC strategy. The traditional ACC/DEC strategies affect machining efficiency, and the quality of workpiece will be deteriorated because of high on off frequency. Hence, a better ACC/DEC strategy is proposed in this paper. The universality of this interpolation method is increased because of the rough interpolation. This paper will set the interpolation with numerous micro-line segments to demonstrate the benefits of this method. A known complex contour can be split into a large number of micro-line segments by computer-aided manufacturing (CAM) system, and the profile of any appearances can be rebuilt with micro-line segments with the development of reverse engineering. So the research on

6 interpolation of micro-line segments is meaningful. The interpolation algorithm proposed in this paper can realize the machining of arbitrary profiles approximated with large tiny line segments. Faced with a large number of segments, it is very essential to adopt a proper method to transit the junction between segments. The sharp alteration of some kinetic parameters, such as velocity and acceleration, can bring vibration and impact which deteriorate the machining quality. The ACC/DEC control strategy is one of effective methods to solve this problem [7]. At present, there are some ACC/DEC control strategies, such as linear ACC/DEC strategy, S curve ACC/DEC strategy, and exponential ACC/DEC strategy. Linear ACC/DEC strategy is easy to realize, while the value of acceleration is constant and changes violently, which may result in serve vibration because of saltus step of velocity at the beginning (end) of a motion process. S curve ACC/DEC strategy avoid the uncontinuity of acceleration, but it brings the complex of algorithm because there are seven possible phases during machining process, and the short lines make the motion process more complicated. Meanwhile, the jerk in S curve ACC/DEC strategy is not continuous. Saltus step of acceleration also exists in exponential ACC/DEC strategy. This paper proposes a confined jounce ACC/DEC strategy according to the characteristic of EPM. This method can make velocity, acceleration, and jerk continuous with which motors can keep moving smoothly. At the same time, some simplified procedures make this algorithm simple to realize... ACC/DEC model based on confined jounce The jerk of each interpolation cycle can be planned with EPM, so guaranteeing the continuity of jerk is feasible. By doing this, the stationarity during motion can be improved comparing with S curve ACC/DEC strategy. It can avoid the slight change of jerk, which may lead to vibration in machining. Defining jounce (J) as differential coefficient of jerk, and the relationship among position, velocity, acceleration, jerk, and jounce can be given as Eqs.(4), (5), (6), (7), and (8). For simplifying the algorithm, the periods during which the jerk and the acceleration speed keep constant are not considered. The acceleration period is divided into four average parts. Supposing that jounce is positive in the first and fourth parts, while negative in second and third parts. 8 < J ð; t Š Jounce ¼ J ðt ; 3t Š ð4þ : J ð3t ; 4t Š 8 < Jt ð; t Š Jerk ¼ Jt Jt ðt ; 3t Š : Jt 4Jt ð3t ; 4t Š ð5þ Acceleration 8 Jt ð; t Þ ð; t Š >< ¼ Jt þ Jt t Jt ðt ; 3t Þ ðt ; 3t Š >: Jt 4Jt t þ 8Jt ð3t ; 4t Þ ð3t ; 4t Š 8 6 Jt3 ð; t Š >< Velocity ¼ 6 Jt3 þ Jt t Jt t þ 3 Jt 3 ðt ; 3t Š >: 6 Jt3 Jt t þ 8Jt t 6 3 Jt 3 ð3t ; 4t Š ð6þ ð7þ Position 8 4 Jt4 ð; t Š >< ¼ 4 Jt4 þ 3 Jt t 3 Jt t þ 3 Jt 3 t Jt 4 ðt ; 3t Š >: 4 Jt4 3 Jt t 3 þ 4Jt t 6 3 Jt 3 t þ 6 4 Jt 4 ð3t ; 4t Š ð8þ The initial condition of the ACC/DEC strategy is that the initial and terminal value of acceleration is. Figure 5 shows the plots of every parameter during acceleration period according to the above Eqs. It can be seen that the acceleration and the jerk is continuously changing during acceleration process, and the stability can be increased accordingly. At the same time, velocity changes slowly at the beginning, which benefits the transition between line segments. From Eqs. (4), (5), (6), (7), and (8), the maximal value of jerk, acceleration, and velocity during acceleration can be deduced as the following Eqs: Jerk max ¼ Jerkðt Þ ¼ Jt Acceleration max ¼ Accelerationðt Þ ¼ Jt 3 ΔVelocity max ¼ Velocityð4t Þ ¼ Jt ð9þ ðþ ðþ where ΔVelocity max = Velocity max V s ; When Jerk max, Acceleration max, and Velocity max have been know, the maximum value of t during acceleration process can be calculated as Eq. (). t ðmaxþ ¼ min Jerk max ; J max rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir Acceleration max J max ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; ΔVelocity 3 max J max ðþ The total displacement (position (t (max) ) can be worked out according to t (max). So necessary parameters during

7 J ounce (m/s 4 ) - - t 4t time/s Velocity (m/s) 4 Jerk (m/s 3 ) acceleration period can be figured out in ACC/DEC strategy, when Jounce (J max ), Jerk max, Acceleration max,and Velocity max are known. The process of a look-ahead algorithm can be realized based on the ACC/DEC strategy... ACC/DEC strategy of line segments with different length - - t 4t time/s - t 4t time/s Position(m) The look-ahead algorithm is for determining the position where the velocity starts to accelerate (decelerate) according to the lengths of line segments, which vary in a large range because of the complication of machining contours. So the length needs to be taken into consideration in discussion on the ACC/DEC strategy. According to the length of lines, the ACC/DEC strategy with confined jounce can be classified into three cases. In the first case, the machining process of a line contains three stages including acceleration stage, constant speed stage, and deceleration stage. The length of the line in this case is long enough for accelerating to the maximal speed. In the second case, machining process does not have the constant speed stage comparing to the first case because of the shortage of the length. In the third case, the maximal speed is the initial one or the terminal one. The velocity profiles of three cases are shown in Fig. 6. Where S is the 4 Acceleration(m/s ) - - t 4t time/s Fig. 5 Model of ACC/DEC based on confined jounce - t 4t time/s displacement during acceleration stage, S 3 is the displacement during deceleration stage, and S is the remaining length of the line where the velocity keeps constant. (.) Define the length of the line as L, initial velocity and terminal velocity as V s and V e. The maximal velocity is V max, and then the change of velocity during acceleration is ΔV = V max V s. The time of the first part in the acceleration stage can be worked out as Eq. (3). ΔV.3 t ¼ J max ð3þ where t can be determined after verification with Eq. (). And then the displacement during acceleration can be determined as Eq. (4). S ¼ Positionð4t ÞþV s 4t ¼ ð V s þ V max Þ4t ¼ ðv s þ V max Þt ð4þ Using the same approach to analyze the deceleration process, the time and displacement of deceleration can be determined as Eqs. (5) and (6). Define the change of velocity during deceleration is = V max V e.. 3 t ¼ ΔV ð5þ J max S 3 ¼ Positionð4t ÞþV s 4t ¼ V ð s þ V max Þ4t ¼ ðv s þ V max Þt ð6þ The length of the second part of the line is obtained as Eq. (7), the machining velocity is V max. S ¼ L ðs þ S 3 Þ > ð7þ (.) The speed cannot increase to the maximal one because the length is not long enough in this case, so the maximum velocity should decrease to meet the length condition. This can be fulfilled with an easy algorithm: Fig. 6 Three cases of ACC/DEC based on length

8 assuming that the maximum velocity is the one in the (.) case, and working out the corresponding S and S 3. Compare the length of line (L) ands +S 3 ;ifl is less than S +S 3 minus maximum speed by a little value, then work out the corresponding S and S 3. Repeat the last step continuously as long as L is less than S +S 3.Atlast, the parameters can be obtained according to Eqs. (3), (4), (5), and (6) afterv max has been determined. (3.) This case is a complement for the second case. When V max has decreased to max (V s, V e ), L is still not less than S +S 3. When this happens, it becomes a special case where acceleration stage and deceleration stage does not exist together. If V max is equal to V s, deceleration stage disappears, otherwise, acceleration stage disappears. Setting V e as V max for example to analyze this case here. According to Eqs. (3) and (4), Eq. (8) can be worked out: t ¼ V.3 e V s J max S ¼ ðv s þ V e Þt S 3 ¼ ð8þ Length of line segments should be taken into consideration for verifying the feasibility of the parameters, if L is less than S +S 3, V max needs to decrease to V e. Repeat the above operation until L equals with S + S 3. In this case, V s or V e changes, so velocity of the profile needs to be planned again. Fig. 7 Flow chart of look-ahead algorithm

9 Fig. 8 Architecture of experimental platform Mition controller PC Ethernet motor drive..3 Look-ahead algorithm for determination of parameters In the above ACC/DEC strategy, the initial and terminal velocityofeachlineshouldbedeterminedinadvance,andtherearea lot of relevant researches on velocity determination in the junction between segments [8]. Supposing the allowed maximal acceleration is A max, the complementary angle between two adjacent lines is α. The change of velocity should be finished within only one interpolation cycle, so the velocity at the junction should meet the condition as following Eq. (9): v A max T sin α ð9þ Y-axis Position (mm) Direction of machining X-axis Position (mm) Fig. 9 Profile of machining contour When A max and interpolation period T are known, the initial/terminal velocity of every line are decided by the angle between lines. The transition velocity can be worked out according to Eq. (9). For a steady transition, terminal velocity of the prior line equals with initial velocity of the subsequent line. This is the first look-ahead calculation. An iterative algorithm is applied to all the segments to determine the initial/terminal velocity of each line with Eq. (9). Subsequently, as mentioned before, because of the different length of segments, a further look-ahead algorithm is performed to solve the problem of some too short lines. The planned velocity max (V s, V e ) in the first look-ahead calculation probably needs to be changed for satisfying ACC/DEC strategy. The further look-ahead algorithm with all line segments can make the initial/terminal velocity of every line available for interpolation. The flow chart of this algorithm is shown in Fig. 7. When finding a transition point needed to plan again, decrease the initial/terminal velocity little by little. Considering efficiency, max (V s, V e ) is the priority to decrease, and S +S 3 is calculated to compare with L repeatedly, until L= S + S 3. After completing the revision of initial/terminal velocity, change the terminal velocity of the prior line and the initial velocity of the next line. In the look-ahead algorithm, when the initial velocity V s is picked out to be changed, the terminal velocity V e of the prior line should be changed to the same value, which may result in the velocity plan of lines before this point becomes unavailable. As to this problem, there are two advised solutions. The first is available, when the number of line segments is not so large, or time-consuming is not a problem. All the lines need to go through the look-ahead algorithm to make all of them meet the ACC/DEC condition. However, this iteration of calculation may cost too much time. Except

10 a 5 b 5 Velocity (mm/s) 4 3 Velocity (mm/s) Position (mm) ACC/DEC with confined jounce strategy Position (mm) ACC/DEC with linear strategy Fig. Velocity curve of different ACC/DEC strategy this solution, setting an appropriate number of line segments for look-ahead and parting all the line segments into several groups for this algorithm is a better choice. This solution has an advantage of rapid calculating, but it may bring the discontinuation between different groups, which could lead to the deterioration of machining quality. So a balance between machining efficiency and precision has to be stricken according to their importance. 3 Experiment and analysis 3. Experimental platform The experimental platform of this paper is an open CNC system including a host PC and an EMAC- multiaxis motion controller as slave computer. The EMAC- is an independent motion controller developed by E-Motion America Co. The controller has the advantage of highspeed, generality, high-performance, and so on, which enable the open CNC system to satisfy most industrial occasions. The rough interpolation with the look-ahead algorithm is finished in the host PC, and the EMAC- motion controller drives the motors with command impulses through fine interpolation based on the data from rough interpolation. The cooperation of the host and the slave computer can realize the plan and calculation of trajectory parameters of every servo cycle. The bridge between them is Ethernet, which can transmit data rapidly to satisfy the requirement of high-speed transmission for interpolation. The performing machines in this experimental platform are MR-E serial servo drives and the corresponding motors from Mitsubishi. The whole architecture of the platform can be seen in Fig. 8. The algorithm of look-ahead algorithm and rough interpolation in host software is realized with C Practical experiment There are two aims in this experiment. The first is to evaluate the feasibility of the interpolation method and the second is to demonstrate the benefits of the ACC/DEC method with confined jounce compared with traditional a 3 b 3 Acceleration (mm/s ) 5-5 Acceleration (mm/s ) Position(mm) Position(mm) ACC/DEC with confined jounce strategy ACC/DEC with linear strategy Fig. Acceleration curve of different ACC/DEC strategy

11 ACC/DEC methods. Take the profile shown in Fig. 9 for example; this profile is a -D contour of a letter y. CAM system process the profile with G codes according to a specific accuracy requirement. The square points in Fig. 9 are the results after processing by CAM system. In the midst of those points, the red one is the starting point, namely the G point. The processing profile consists of 5 points, so the profile is split into 5 line segments with different lengths. The look-ahead algorithm in the host software is implemented with setting parameters: federate of V max = 5 mm/s assigned by CAM in code file, maximal acceleration of a max =3 mm/s, and maximal jerk of Jerk max = mm/s 3, maximal jounce of Jounce max = mm/s 4. The cycle of rough interpolation is ms. Figure a is the velocity profile after rough interpolation with confined jounce method. From the graphic, it is concluded that the fluctuations happen when a lot of short lines accumulate to shape a curve. Velocity profile of longer lines is comparatively steady. As a whole, the velocity curve does not change sharply within a very short period, let alone saltus step of velocity. It can satisfy the requirements of stability and efficiency of an open CNC system. In contrast, Fig. b shows the velocity profile with linear ACC/DEC strategy. When it comes to extremely short segments, the feed rate variation is completed within a very tiny period, which will deteriorate the machining quality. It can obviously find that the proposed ACC/DEC method for machining of micro-line segments is more suitable for high-speed CNC system. In addition, Fig. shows the acceleration profiles of two different ACC/DEC strategy. In Fig. a, the acceleration variation of ACC/DEC method with confined jounce strategy is smaller than that of ACC/DEC method with linear strategy. And the acceleration profile is always continuous. According to the knowledge of kinetics, the load endured by the machine tools from the workpiece is continuous; it can keep machine tools from vibrating by a large margin. In contrast, the acceleration profile with linear strategy in Fig. b jumps between maximum value + A max and minimum value m max, which deteriorates the machining quality of the machining tool. Data from rough interpolation are stored in the buffer of the PC host firstly. When the machining process begins, the slave motion controller obtains data from the buffer and sends to the trajectory generator group by group according to the memory space of motion controller. The fine interpolation is accomplished by the motion controller through producing command pulses to drive motors. The machining results and the status of machine tool during machining are quite satisfying. 4 Conclusion The rapid development of open CNC systems boosts the need for high-performance interpolation of various contours. With more and more complex machining contours, the traditional interpolation methods of motion controller cannot reach satisfying precision and efficiency because of their limitation in range of application. A universal interpolation method for the open CNC system is needed urgently for trajectory interpolation. This paper presents an interpolation method for open CNC systems based on EPM. This technique can realize interpolation of various contours by a rough interpolation with a look-ahead algorithm in the PC host. With the lookahead algorithm, the planning parameters of trajectory can obtain satisfying results. The ACC/DEC strategy with confined jounce in the look-ahead algorithm guarantees machining process to be smooth and free from vibration. Meanwhile, interpolation experiment of a contour is conducted to demonstrate the feasibility and generalization of this interpolation method. Actually, the proposed interpolation method can be applied to machining of many kinds of curves, such as line, arc, spline, and any other curves. As long as the interpolation algorithm can be realized in the PC host, the interpolation of any complicated contours can be accomplished by the motion controller with fine interpolation. Hence, an intelligible interpolation algorithm for complex contours based on the proposed interpolation method will be developed in our future research. Acknowledgments This paper is sponsored by the science fund for creative research groups of National Natural Science Foundation of China (54), National Natural Science Foundation of China (57546) and Fundamental Research Funds for the Central Universities (3QNA47), the Program for Zhejiang Leading Team of S&T Innovation (No. 9R58). References. Zhao CH, Qin XS, Tang H (5) Research on open-cnc system based on PC. Mech Sci Technol 4(9):8 3. Ye PQ, Shi C, Yang KM, Lv Q (8) Interpolation of continuous micro-line segment trajectories based on look-ahead algorithm in high-speed machining. Int J Adv Manuf Technol 37: Zhang LX, Sun RY, Gao XS, Li HB () High-speed interpolation for micro-line trajectory and adaptive real-time look-ahead scheme in CNC machining. Sci China Technol Sci 54(6): Zhang LB, You YP, He J, Yang XF () The transition algorithm based on parametric spline curve for high-speed machining of continuous short line segments. Int J Adv Manuf Technol 5: Shi C, Ye PQ () The look-ahead function-based interpolation algorithm for continuous micro-line trajectories. Int J Adv Manuf Technol 54: Wang JB, Yau HT (9) Real-time NURBS interpolator application to short linear segments. Int J Adv Manuf Technol 4: Yong T, Narayanaswami R (3) A parametric interpolator with confined chord errors, acceleration, and deceleration for NC machining. Computer-Aided Design 35(3):49 59

12 8. Yu D, Hu Y, XuXW HY, Du SH (9) An open CNC system based on component technology. IEEE Trans Autom Eng 6(): Farooq M, Wang DB (7) Implementation of a new PC based controller for a PUMA robot. J Zhejiang Univ 8(): Oldknow KD, Yellowley I () Design, implementation and validation of a system for the dynamic reconfiguration of open architecture machine tool controls. Int J Mach Tool Manuf 4: Liu QS, Gao L (9) A look-ahead algorithm for feed-rate control in CNC with a motion control card. Mech Sci Technol Aerosp Eng 8(9): Tsai MS, Nien HW, Yau HT () Development of a real-time look-ahead interpolation methodology with spline-fitting technique for high-speed machining. Int J Adv Manuf Technol 47: Tsai MS, Nien HW, Yau HT () Development of integrated acceleration/deceleration look-ahead interpolation technique for multi-blocks NURBS curves. Int J Adv Manuf Technol 56: Liu JQ, Xu D, Wu JR, Xu Y, Li X () Research on the velocity look-ahead algorithm in the NC system. Adv Mater Res 3 33: Zhang LB, You YP, Yang XF (3) A control strategy with motion smoothness and machining precision for multiaxis coordinated motion CNC machine tools. Int J Adv Manuf Technol 64: Shen HY, Fu JZ, He Y, Yao XH () On-line asynchronous compensation methods for static/quasi-static error implemented on CNC machine tools. Int J Mach Tool Manuf 6: Yeh SS (999) The speed-controlled interpolator for machining parametric curves. Computer-Aided Design 3(5): Wang YH, Xiao LJ, Zeng SS, Wu ZY, Zhong SB (4) An optimal feed rate model and solution for high-speed machining of small line blocks with look-ahead. J Shanghai JiaoTong Univ 38(6):9 94