CN114077226A - S-shaped curve speed planning method, control terminal and computer readable storage medium - Google Patents
S-shaped curve speed planning method, control terminal and computer readable storage medium Download PDFInfo
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- G—PHYSICS
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/416—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control of velocity, acceleration or deceleration
- G05B19/4163—Adaptive control of feed or cutting velocity
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract
The invention relates to the technical field of numerical control, and provides an S-shaped curve speed planning method, a control terminal and a computer readable storage medium. The method comprises the following steps: obtaining a speed planning parameter according to a workpiece processing track; calculating the total interpolation period number of the acceleration section according to the speed planning parameters; calculating to obtain the instantaneous speed corresponding to each interpolation period in the acceleration section according to the total interpolation period number, and constructing a speed planning curve of the acceleration section; setting a deceleration point, entering a constant speed section when the instantaneous speed of the acceleration section reaches the maximum speed, moving to the deceleration point at a constant speed and entering the deceleration section, wherein the speed planning curve of the deceleration section is symmetrical to the speed planning curve of the acceleration section; by adopting the planning method, the control terminal and the computer readable storage medium, a smooth S-shaped speed curve can be constructed, the acceleration change is gentle at the initial stage and the final stage of acceleration and deceleration, the motor is not easy to be impacted, the speed curve form can be flexibly adjusted according to various processing technologies, and the application is reasonable and convenient.
Description
Technical Field
The invention belongs to the technical field of numerical control, and particularly relates to an S-shaped curve speed planning method, a control terminal and a computer readable storage medium.
Background
The numerical control machine tool needs to move according to various preset tracks in the working process, so that various machining requirements are met. Therefore, the operation speed of the machine tool must be reasonably planned, so that the machining process can be ensured to be smooth and stable, the flexible impact is small, and the reaction is rapid on the premise of meeting the mechanical motion requirement of the machine tool, so that the machining efficiency of the machine tool can be improved, and the service life and the use safety of the machine tool can be ensured.
The common speed planning method in the existing numerical control system comprises the following steps: trapezoidal curve acceleration and deceleration, S-shaped curve acceleration and deceleration and the like. The trapezoidal acceleration and deceleration is to control the motor in a linear acceleration and deceleration mode, and the motor is increased or decreased in a linear situation from the initial speed to the final speed. The method is simple in calculation and obvious in acceleration and deceleration effect. However, the acceleration sudden change phenomenon exists according to the linear acceleration and deceleration, so that the machine tool is easy to shake, the safe use of the machine tool is not facilitated, and the linear acceleration and deceleration control system is only suitable for a low-speed operation control system. A typical method in S-shaped curve acceleration and deceleration is a seven-section acceleration and deceleration control method, the model structure is relatively complex, the acceleration is continuously changed according to the running state of the machine tool, the acceleration continuity can be realized, and the impact influence of the acceleration change in the motion process on the machine tool is reduced. The disadvantage is that the calculated motion time is not necessarily integral multiple of the interpolation period, which causes sudden change of motion state when the integration time at the end of the motion is less than one period, and the precision is lost if the last displacement less than one interpolation integration time is ignored. The model has complex structure and more parameter limitation, and the phenomenon is difficult to eliminate. The S-type acceleration and deceleration also has a method for building a model by using a trigonometric function, the acceleration and the acceleration are continuous, so the smoothness of the movement is better, but the calculation is realized by a table look-up mode, the calculation efficiency is not high enough, the model only reaches the maximum acceleration at one time point, the movement response is not rapid enough, and the acceleration and deceleration efficiency is relatively low.
Disclosure of Invention
The invention mainly aims to provide an S-shaped curve speed planning method, a control terminal and a computer readable storage medium, which are used for solving the technical problems that the speed change is not smooth enough and the motion response speed is slow in the prior art.
To achieve the above object, in one aspect, a S-curve speed planning method is provided, which includes the steps of:
obtaining a speed planning parameter of workpiece processing according to a workpiece processing track, wherein the speed planning parameter comprises a path total length STotalMaximum velocity vmaxAnd maximum acceleration amax；
Calculating to obtain the total interpolation period number T of the acceleration section through a preset speed planning model according to the speed planning parameters;
calculating to obtain an instantaneous speed V corresponding to each interpolation period T in the acceleration section through the speed planning model according to the total interpolation period number T, and constructing a speed planning curve of the acceleration section;
setting a deceleration point according to the total length of the path, and when the instantaneous speed V of the acceleration section reaches the maximum speed VmaxThen entering a constant speed section, moving at a constant speed to the deceleration point and entering a deceleration section, wherein the speed planning curve of the deceleration section is symmetrical to the speed planning curve of the acceleration section;
wherein the velocity planning model comprises the following formula:
the calculation formula of the instantaneous speed of the acceleration section is as follows:
where f (T) is the instantaneous speed at the time of interpolation T, T represents the interpolation period, n is half of the total interpolation period T, vminIs the initial velocity of the acceleration section.
In one embodiment, the calculation formula of the instantaneous acceleration is obtained by taking the derivative of formula (1):
according to the acceleration reaching a maximum value in the middle of the acceleration section, at a known initial velocity vminTerminal velocity vmaxMaximum acceleration amaxAnd when T is 2n, obtaining a calculation formula of the total interpolation period number T of the acceleration section according to the formula (2):
in one embodiment, the calculation formula of the instantaneous displacement is obtained by integrating the formula (1)
Calculating the motor feed amount of each interpolation period according to the formula (4), wherein the calculation formula is
F(i)＝F(ti)-F(ti-1) (5)
Wherein F (i) is tiAnd (5) the distance which the motor needs to run in the time interpolation period.
In one embodiment, the displacement amount S of the acceleration section is calculated according to the formula (3) and the formula (4)upAnd the displacement amount S of the acceleration sectionupEqual to the displacement S of the deceleration sectiondownTotal length of route STotal≥2SupThe amount of displacement by which the machine has been operated is SmovedWhen said S ismoved＝STotal-SupAnd the time is the deceleration point, and the machine tool starts to enter a deceleration section for deceleration after passing through the deceleration point.
In one embodiment, the total length of the path S is determined according toTotalAnd the displacement amount S of the acceleration sectionupCalculating the displacement S of the constant velocity sectionstay：
Sstay＝STotal-Sup-Sdown (6)
According to the displacement S of the uniform velocity sectionstayAnd calculating the interpolation period of the uniform velocity section by the maximum velocityNumber Tstay：
Tstay＝Sstay/Vmax (7)
For the interpolation period number TstayInteger value correction is carried out to obtain the corrected actual interpolation period number T'stay
And according to the actual interpolation period number T'stayTo calculate the corrected speed v of the uniform speed sectionstay：
vstay＝Sstay/T′stay (8)
Making the uniform speed segment at the corrected speed vstayAnd running at a constant speed until the speed reduction point is reached, and starting to reduce the speed and enter the speed reduction section.
In another aspect, a control terminal is provided, including:
at least one processor; and the number of the first and second groups,
a memory communicatively coupled to the at least one processor; wherein the content of the first and second substances,
the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method of velocity planning numerical control of the above embodiments.
In still another aspect, a computer-readable storage medium is provided, which stores a computer program, and when the computer program is executed by a processor, the speed planning numerical control method according to the foregoing embodiment is implemented.
The embodiment of the present invention described above has the following advantages:
by carrying out deformation processing on the Sigmoid function, a smooth S-shaped speed curve can be constructed, the acceleration change is gentle at the initial stage and the final stage of acceleration and deceleration, the motor is not easy to be impacted, and in the middle stage of acceleration and deceleration, the acceleration and deceleration process is accelerated due to the fact that the specified maximum acceleration can be reached, the efficiency is higher, and meanwhile, the characteristics of smoothness, quick response and the like required by the motor are met; and the speed planning model is simple, the speed curve form can be flexibly adjusted according to various processing technologies, and the application is reasonable and convenient.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without inventive exercise.
FIG. 1 is a flow chart of a method for S-curve speed planning in accordance with an embodiment of the present invention;
FIG. 2 is a velocity profile and an acceleration profile of an entire path in an embodiment of the present invention;
FIG. 3 is a jerk curve in an embodiment of the present invention.
Detailed Description
In order to make the objects, features and advantages of the present invention more obvious and understandable, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, an embodiment of the present invention discloses a method for planning speed of an S-shaped curve, including the steps of:
s1, obtaining the speed planning parameter of the workpiece processing according to the workpiece processing track, wherein the speed planning parameter comprises the total path length STotalMaximum velocity vmaxAnd maximum acceleration amax。
It should be noted that the workpiece processing track is a motion track requiring speed planning, and this embodiment exemplifies that the initial speed and the final speed of the whole path are both 0, that is, in the whole path of the workpiece processing track planned into an acceleration section, a uniform speed and a deceleration section, the initial speed of the acceleration section and the final speed of the deceleration section are 0. Of course, the initial speed and the final speed of the whole path may be defined according to the actual requirement of the workpiece machining track, that is, in other embodiments, the initial speed of the acceleration section and the final speed of the deceleration section may not be 0.
And S2, calculating the total interpolation period number T of the acceleration section through a preset speed planning model according to the speed planning parameters. As shown in FIG. 2, when the machine tool is at a standstill, i.e. at an initial speed vminWhen the acceleration is started to be 0, the acceleration is gradually increased from 0 according to an interpolation period, so that the problem of machine tool vibration caused by sudden acceleration can be avoided; the middle segment of the S curve can be according to the maximum acceleration amaxThe instantaneous slope is changed in size, so that the processing response time can be flexibly adjusted; meanwhile, when the acceleration reaches the second half stage of the acceleration section, the acceleration is decreased to 0 from the middle moment according to the interpolation period, and the machine tool can stably reach the maximum speed; that is to say that the total number of interpolation cycles T passes through the maximum speed vmaxAnd maximum acceleration amaxCalculated according to the speed planning model.
S3, calculating to obtain the instantaneous speed V corresponding to each interpolation period T in the acceleration section through a speed planning model according to the total interpolation period number T, and constructing a speed planning curve of the acceleration section; the speed planning model carries out deformation processing on a Sigmoid function and comprises the following calculation formula of the instantaneous speed of an acceleration section:
where f (T) is the instantaneous speed at the time of interpolation T, T represents the interpolation period, n is half of the total interpolation period T, and v is the speed of the acceleration sectionminRepresents the initial speed of the acceleration section and is equal to 0; according to the maximum speed v obtainedmaxAnd calculating the instantaneous speed V corresponding to each interpolation period T in the acceleration section by the total interpolation period number T through a formula (1), thereby constructing a smooth S-shaped speed curve of the acceleration section as shown in fig. 2, and meeting the characteristics of smoothness, quick response and the like required by the motor.
S4, setting a deceleration point according to the total length of the path, and when the instantaneous speed V of the acceleration section reaches the maximum speed VmaxThen entering a constant speed section, moving at a constant speed to a deceleration point and entering a deceleration section, wherein the speed planning curve of the deceleration section is symmetrical to the speed planning curve of the acceleration section. Specifically, an instantaneous speed calculation formula of the deceleration section is as follows:
it is distinguished from the formula for calculating the instantaneous speed of the acceleration section in that v in the formula for the deceleration sectionminRepresenting the final speed and equal to 0, i.e. the speed of the machine tool from the point of deceleration at a constant speed section (i.e. the maximum speed v)max) Stopping running after the speed is reduced to 0; in the S-shaped speed curve for constructing the deceleration section, when the speed is reduced to the second half stage of the deceleration section, the acceleration is reduced to 0 from the middle moment according to the interpolation period, and the machine tool can be stopped smoothly.
According to the technical scheme of the embodiment, a smooth S-shaped speed curve can be constructed by performing deformation processing on the Sigmoid function, the acceleration change is gentle at the initial stage and the final stage of acceleration and deceleration, the motor is not easy to be impacted, and in the middle stage of acceleration and deceleration, the specified maximum acceleration can be achieved, so that the acceleration and deceleration process is accelerated, the efficiency is higher, and the characteristics of smoothness, quick response and the like required by the motor are met; and the speed planning model is simple, the speed curve form can be flexibly adjusted according to various processing technologies, and the application is reasonable and convenient.
In one embodiment of the invention, the calculation formula of the instantaneous acceleration is obtained by taking the derivative of formula (1):
according to the acceleration reaching a maximum value in the middle of the acceleration section, at a known initial velocity vminTerminal velocity vmaxMaximum acceleration amaxWhen T is 2n, the formula for calculating the total interpolation cycle number T of the acceleration stage in step S2 is obtained from formula (2):
it should be noted that the instantaneous acceleration and the total interpolation cycle number of the deceleration section are also obtained by the above equations (2) and (3), except that in the deceleration section, v ismaxIs an initial velocity, vminIs the final velocity; and according to the characteristics of the formula (3), the velocity planning method of the embodiment can pass the maximum acceleration amaxTo limit the acceleration and deceleration time, i.e. according to the maximum acceleration amaxThe instantaneous slope is adjusted by changing the size of the machining center, and the machining response time is flexibly adjusted.
Fig. 3 is a graph showing the jerk curve in the present embodiment, as can be seen from fig. 3, in the acceleration section, the machine tool starts to accelerate from a static state according to the processing track of the workpiece, the acceleration in the first half of the acceleration section is gradually increased to the maximum acceleration, and the jerk is gradually increased and then gradually decreased to 0; the acceleration of the first half section of the acceleration section is gradually reduced to 0, and the jerk becomes a negative value and is gradually reduced and then gradually increased to 0; the change of the acceleration at the initial stage and the final stage of acceleration is smooth, so that the motor is not easy to be impacted, and the smooth transition of the change of the speed required by the motor is met. Similarly, in the deceleration section, the acceleration changes in the initial and final deceleration stages are also gradual.
In one embodiment of the invention, the calculation formula of the instantaneous displacement is obtained by integrating formula (1):
calculating the motor feed amount of each interpolation period, namely the instantaneous displacement difference value of two adjacent interpolation periods according to the formula (4), wherein the calculation formula is as follows:
F(i)＝F(ti)-F(ti-1) (5)
wherein F (i) is tiThe motor needs to run the distance in the interpolation period at any moment, and the numerical control system is positioned at an acceleration stageIn a segment, T has a value range of [0, T](ii) a When the numerical control system is in a deceleration stage, the value range of T is [ T, 0 ]]。
In one embodiment of the present invention, the deceleration point in step S4 is calculated by: calculating the displacement S of the acceleration section according to the formula (3) and the formula (4)upSince the velocity planning models of the acceleration section and the deceleration section are the same, and the initial and final velocities and the maximum acceleration are also the same, the displacement S of the acceleration section can be knownupEqual to the displacement S of the deceleration sectiondownTotal length of route STotal≥2SupThe amount of displacement by which the machine has been operated is SmovedWhen the machine tool finishes running STotalTotal time of TnThe speed curves for the acceleration phase and the deceleration phase then relate to T ═ Tn2 is symmetrical, and when Smoved＝STotal-SupAnd the machine tool starts to enter a deceleration section for deceleration after passing through the deceleration point, and stops running until the speed is 0.
In an embodiment of the present invention, before the step S4 enters the constant velocity segment, the method further includes the following steps:
according to the total length S of the pathTotalAnd displacement S of acceleration stageupCalculating the displacement S of the set uniform velocity segmentstay：
Sstay＝STotal-Sup-Sdown (6)
According to the displacement S of the uniform velocity sectionstayAnd calculating the interpolation period number T of the uniform speed section by the maximum speedstay：
Tstay＝Sstay/Vmax (7)
For interpolation period number TstayInteger value correction is carried out to obtain the corrected actual interpolation period number T'stay
According to the actual interpolation period number T'stayTo calculate the correction velocity v of the uniform velocity sectionstay：
vstay＝Sstay/T′stay (8)
The constant speed segment in the step S4 is corrected by the corrected speed vstayRun at constant speed until reaching the speed reductionThe speed point begins to decelerate into the deceleration section. The approximation method can effectively ensure that the error between the whole speed planning path and the given distance is small, can ensure that the acceleration fluctuation is small, the speed change is smooth, and reduces the motor vibration.
Simulation verification:
the machine tool parameters in the numerical control system are set as follows: interpolation period Ts0.5ms, maximum speed of 60m/min, and maximum acceleration of 5m/s2. After converting into time and distance units adopted in the numerical control system, the maximum speed is 1mm/ms, and the maximum acceleration is 0.005mm/ms2And the total displacement is 5000 mm. The result of planning by the speed planning method of the above embodiment is shown in table 1, and the deviation of the planned total displacement from the actual path is only 0.0006 due to the deviation caused by the calculation process data type.
TABLE 1 speed planning result of acceleration and deceleration section
The embodiment of the invention also relates to a control terminal, which comprises at least one processor; and a memory communicatively coupled to the at least one processor; wherein the memory stores instructions executable by the at least one processor to enable the at least one processor to perform embodiments of the above speed planning numerical control method.
Where the memory and processor are connected by a bus, the bus may comprise any number of interconnected buses and bridges, the buses connecting together one or more of the various circuits of the processor and the memory. The bus may also connect various other circuits such as peripherals, voltage regulators, power management circuits, and the like, which are well known in the art, and therefore, will not be described any further herein. A bus interface provides an interface between the bus and the transceiver. The transceiver may be one element or a plurality of elements, such as a plurality of receivers and transmitters, providing a means for communicating with various other apparatus over a transmission medium. The data processed by the processor is transmitted over a wireless medium via an antenna, which further receives the data and transmits the data to the processor.
The processor is responsible for managing the bus and general processing and may also provide various functions including timing, peripheral interfaces, voltage regulation, power management, and other control functions. And the memory may be used to store data used by the processor in performing operations.
An embodiment of the present invention relates to a computer-readable storage medium storing a computer program. The computer program, when executed by the processor, implements the above-described speed planning numerical control method embodiments.
In the above embodiments, the descriptions of the respective embodiments have respective emphasis, and for parts that are not described in detail in a certain embodiment, reference may be made to related descriptions of other embodiments.
In view of the above description of the technical solutions provided by the present invention, those skilled in the art will recognize that there may be variations in the technical solutions and the application ranges according to the concepts of the embodiments of the present invention, and in summary, the content of the present specification should not be construed as limiting the present invention.
Claims (7)
1. A S-shaped curve speed planning method is characterized by comprising the following steps:
obtaining a speed planning parameter of workpiece processing according to a workpiece processing track, wherein the speed planning parameter comprises a path total length STotalMaximum velocity vmaxAnd maximum acceleration amax；
Calculating to obtain the total interpolation period number T of the acceleration section through a preset speed planning model according to the speed planning parameters;
calculating to obtain an instantaneous speed V corresponding to each interpolation period T in the acceleration section through the speed planning model according to the total interpolation period number T, and constructing a speed planning curve of the acceleration section;
setting a deceleration point according to the total length of the path, and when the instantaneous speed V of the acceleration section reaches the maximum speed VmaxThen enters into the uniform velocity sectionMoving to the deceleration point at a constant speed and entering a deceleration section, wherein a speed planning curve of the deceleration section is symmetrical to a speed planning curve of the acceleration section;
wherein the velocity planning model comprises the following formula:
the calculation formula of the instantaneous speed of the acceleration section is as follows:
where f (T) is the instantaneous speed at the time of interpolation T, T represents the interpolation period, n is half of the total interpolation period T, vminIs the initial velocity of the acceleration section.
2. A S-curve velocity planning method according to claim 1, characterized in that the calculation formula of the instantaneous acceleration is obtained by taking the derivative of formula (1):
according to the acceleration reaching a maximum value in the middle of the acceleration section, at a known initial velocity vminTerminal velocity vmaxMaximum acceleration amaxAnd when T is 2n, obtaining a calculation formula of the total interpolation period number T of the acceleration section according to the formula (2):
3. a S-curve velocity planning method according to claim 2, characterized in that the calculation formula of the instantaneous displacement is obtained by integrating the formula (1)
Calculating the motor feed amount of each interpolation period according to the formula (4), wherein the calculation formula is
F(i)＝F(ti)-F(ti-1) (5)
Wherein F (i) is tiAnd (5) the distance which the motor needs to run in the time interpolation period.
4. A S-curve velocity planning method according to claim 3, wherein the displacement amount S of the acceleration section is calculated according to formula (3) and formula (4)upAnd the displacement amount S of the acceleration sectionupEqual to the displacement S of the deceleration sectiondownTotal length of route ST otal≥2SupThe amount of displacement by which the machine has been operated is SmovedWhen said S ismoved＝STotal-SupAnd the time is the deceleration point, and the machine tool starts to enter a deceleration section for deceleration after passing through the deceleration point.
5. A sigmoidal speed planning method according to claim 4, wherein said path total length S is based onTotalAnd the displacement amount S of the acceleration sectionupCalculating the displacement S of the constant velocity sectionstay：
Sstay＝STotal-Sup-Sdown (6)
According to the displacement S of the uniform velocity sectionstayAnd calculating the interpolation period number T of the uniform speed section by the maximum speedstay：
Tstay＝Sstay/Vmax (7)
For the interpolation period number TstayInteger value correction is carried out to obtain the corrected actual interpolation period number T'stayAnd according to the actual interpolation period number T'stayTo calculate the corrected speed v of the uniform speed sectionstay：
vstay＝Sstay/T′stay (8)
Making the uniform speed segment at the corrected speed vstayAnd running at a constant speed until the speed reduction point is reached, and starting to reduce the speed and enter the speed reduction section.
6. A control terminal, comprising:
at least one processor; and the number of the first and second groups,
a memory communicatively coupled to the at least one processor; wherein the content of the first and second substances,
the memory stores instructions executable by the at least one processor to enable the at least one processor to perform a method of velocity planning numerical control according to any one of claims 1 to 5.
7. A computer-readable storage medium, storing a computer program, wherein the computer program, when executed by a processor, implements the method of velocity planning numerical control of any of claims 1 to 5.
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| CN115016559A (en) * | 2022-08-04 | 2022-09-06 | 深圳市杰美康机电有限公司 | Full closed loop multi-path planning line feeding method and device |
| CN115328032A (en) * | 2022-10-11 | 2022-11-11 | 济南邦德激光股份有限公司 | B-spline speed look-ahead control method, device and medium based on S-shaped acceleration and deceleration |
| CN115922687A (en) * | 2022-05-23 | 2023-04-07 | 以诺康医疗科技（苏州）有限公司 | S-shaped speed curve-based motion trajectory planning method and device |
| CN116954280A (en) * | 2023-09-21 | 2023-10-27 | 北京一控软件技术有限公司 | Speed control system of metal rolling post-treatment process line |
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| CN115016559A (en) * | 2022-08-04 | 2022-09-06 | 深圳市杰美康机电有限公司 | Full closed loop multi-path planning line feeding method and device |
| CN115328032A (en) * | 2022-10-11 | 2022-11-11 | 济南邦德激光股份有限公司 | B-spline speed look-ahead control method, device and medium based on S-shaped acceleration and deceleration |
| CN115328032B (en) * | 2022-10-11 | 2023-03-31 | 济南邦德激光股份有限公司 | B-spline speed look-ahead control method, device and medium based on S-shaped acceleration and deceleration |
| CN116954280A (en) * | 2023-09-21 | 2023-10-27 | 北京一控软件技术有限公司 | Speed control system of metal rolling post-treatment process line |
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