Trigonometric function feeding speed planning method for four-order continuous tool path

Abstract

The invention discloses a trigonometric function feeding speed planning method for a four-order continuous tool path. According to the method, the added acceleration is restrained through tool path displacement, so that the added acceleration is smooth, continuous and bounded, the added acceleration actually reached by a machine tool in the machining process is smooth, continuous and bounded, speed fluctuation generated at the end of an interpolation period is overcome, and in combination with a four-order continuous smooth tool path, the machining precision is improved. And generating a smooth interpolation point for controlling the motion of the cutter to realize the smooth motion of the cutter. The method is oriented to a numerical control system with high requirements for machining quality, speed fluctuation is effectively eliminated through smooth, continuous and bounded correction and acceleration, smooth motion of a cutter is achieved, and then machining precision is improved.

Description

Technical Field

[0001] The invention relates to the field of feed speed planning of numerical control systems, in particular to a trigonometric function feed speed planning method for a fourth-order continuous tool path. Background Art

[0002] Five-axis CNC machine tools are widely used in CNC machining of complex workpieces such as molds and aviation parts. The speed curve generated by the speed planning method controls the movement of the machine tool. The smooth speed planning method is of great significance for improving machining quality and efficiency. In the CNC machining process, the feed speed planning method of the CNC system has the problem of large speed fluctuations, especially when the last interpolation process is not constrained, it will cause relatively large speed fluctuations, which will cause machine tool chatter and affect the machining quality. Therefore, eliminating speed fluctuations is of great significance for improving machining accuracy, improving machining efficiency, improving machining surface quality, and enhancing tool life. Summary of the invention

[0003] In order to eliminate speed fluctuation and improve machining quality, the present invention provides a trigonometric function feed speed planning method for a fourth-order continuous tool path. The idea of ​​the present invention is based on trigonometric function speed planning, and the jerk is constrained by the tool path displacement, so that the jerk is smooth, continuous and bounded, so that the interpolation time contains an integer number of interpolation cycles, thereby reducing speed fluctuations and obtaining high-precision machining results.

[0004] The trigonometric function feed rate planning method for the fourth-order continuous tool path includes the following steps:

[0005] Step 1: Establish a mathematical expression for the trigonometric function velocity planning with continuous jerk.

[0006] 1) Divide the trigonometric function speed planning into 15 different time periods, T i represents the duration of the i-th (i=1,...,15) stage, where T1-T7 all belong to the acceleration stage, during which the feed speed increases monotonically; T8 belongs to the uniform speed stage, during which the feed speed remains unchanged; T9-T 15 Both belong to the deceleration stage, during which the feed speed decreases monotonically; t i (i=1,...,15) represents the end time of the i-th time stage, t0 represents the start time of the speed planning, then T i =t i -t i-1 ;

[0007] 2) Then, define the kinematic parameters in the trigonometric function velocity planning: d represents the tool path displacement, F crepresents the command speed, V represents the actual speed value of the machine tool during the processing, A represents the actual acceleration reached by the machine tool during the processing, J represents the actual jerk reached by the machine tool during the processing, and S represents the actual jerk reached by the machine tool during the processing; V max Indicates the maximum speed of speed planning; A max , J max and S max Represent the maximum values ​​of acceleration, jerk and jerk allowed by the system, A acc , J acc Indicates the actual acceleration and jerk during the acceleration phase, A dec , J dec Indicates the actual acceleration and jerk during the deceleration phase;

[0008] For any given feed rate planning unit, the starting speed and end speed corresponding to the feed rate planning unit are defined as v s 、v e , v s <v e ;

[0009] Step 2: Under non-integer interpolation cycles, V max =F c , based on the speed stage T included in the feed speed planning unit i Determine the T on the feed speed curve generated on the corresponding speed planning unit i (i=1,2...,15) values, as well as the actual acceleration and jerk A during the acceleration phase acc , J acc The actual acceleration and jerk A during the deceleration phase dec , J dec , the steps are as follows:

[0010] 1) Calculate T during the acceleration phase i (i=1,…,7), as well as the actual acceleration and jerk A during the acceleration phase acc , J acc The steps are as follows:

[0011] 1.1), when A max / J max >J max π / (2S max ) is established, at this time, the system allows the acceleration J max , and there is a constant acceleration stage, that is, T2>0, the feed speed curve generated on the speed planning unit satisfies that the values ​​of T1, T2, T3, T5, T6, and T7 are not zero, that is, T1=T3=T5=T7=J max π / (2S max), T2=T6=A acc / J acc -T1>0;

[0012] 1.1.1) If V max -v s >A max (2T1+T2) holds, then T i (i=1,2,...,7) value, acceleration A acc and jerk J acc The values ​​are as follows,

[0013]

[0014] 1.1.2) Otherwise, V max -v s ≤A max (2T1+T2) is established, the feed speed planning unit will not have a constant acceleration time T4, and the acceleration A acc The acceleration A allowed by the system cannot be reached. max , at this time T i (i=1,2,...,7) value, acceleration A acc and jerk J acc The values ​​are as follows,

[0015]

[0016] 1.2), when A max / J max =J max π / (2S max ) is established, at this time, the system allows the acceleration J max , and there is no constant acceleration, that is, T2 = 0, the feed speed curve generated on the speed planning unit satisfies that the values ​​of T1, T3, T5, and T7 are not zero, that is, T1 = T3 = T5 = T7 = J max π / (2S max ), and determine whether there is a constant acceleration time T4,

[0017] 1.2.1) If V max -v s >2A max If T1 is established, there is a constant acceleration time T4, at which time T i (i=1,2,...,7) value, acceleration A acc and jerk J acc The values ​​are as follows,

[0018]

[0019] 1.2.2), otherwise, V max -v s ≤2A max T1 is established. At this time, the speed curve will not have a constant acceleration time T4, and the acceleration A acc The acceleration A allowed by the system cannot be reached max , at this time T i (i=1,2...,7) value, acceleration A acc and jerk J acc The values ​​are as follows,

[0020]

[0021] 1.3), when A max / J max <J max π / (2S max ) is established. At this time, the jerk J allowed by the system cannot be achieved. max , that is, T2 = 0, the feed speed curve generated on the speed planning unit satisfies that the values ​​of T1, T3, T5, and T7 are not zero. It is necessary to re-solve T1, T3, T5, and T7 and determine whether there is a constant acceleration time T4.

[0022] 1.3.1) When V max -v s >2A max When T1 is established, there is a constant acceleration time T4. At this time, by reducing the acceleration J in the acceleration phase acc Make A max / J acc =T1 is established, and the calculation shows that T i (i=1,2...,7) value, acceleration A acc and jerk J acc The values ​​are as follows,

[0023]

[0024] 1.3.2) When V max -v s ≤2A max When T1 is established, there is no constant acceleration time T4 and jerk time T2, T6. acc and jerk J acc Re-solve and calculate T i (i=1,2...,7) value, acceleration A acc and jerk J acc The values ​​are as follows,

[0025]

[0026] After the above step (1), we can get T in the acceleration stage. i (i=1,…,7) values, and acceleration A acc and jerk J acc The value of

[0027] 2) Calculate T during the deceleration phase i (i=9,…,15), and the actual acceleration A during the deceleration phase dec and jerk J dec The steps are as follows:

[0028] 2.1), when A max / J max >J max π / (2S max ) is established, at this time, the acceleration J dec Reach the system allowed jerk J max , and there is a constant acceleration stage, namely T 10 >0, then T i (i=9,...,15), acceleration A dec and jerk J dec as follows:

[0029]

[0030] 2.2), when A max / J max =J max π / (2S max ) is established, at this time, the acceleration J dec Reach the system allowed jerk J max , and there is no constant acceleration, that is, T 10 =0, then T i (i=9,...,15), acceleration A dec and jerk J dec as follows:

[0031]

[0032] 2.3), when A max / J max <J max π / (2S max ) is established, at this time, the acceleration J dec The jerk J allowed by the system cannot be reached max , that is, T 10 =0, then T i (i=9,...,15), acceleration Adec and jerk J dec as follows:

[0033]

[0034] 3) Calculate the value of uniform speed time T8, when both jerk and acceleration are zero.

[0035] When T8>0, the uniform speed time T8 is as follows:

[0036]

[0037] When T8≤0, there is no uniform time, that is, T8=0;

[0038] Step 3: In order to reduce the speed fluctuation during the interpolation process, the T obtained in step 2 is i (i=1,…,7,9,…,15) to make corrections under the constraints of integer interpolation cycle so that T i (i=1,…,7,9,…,15) all contain an integer number of interpolation cycles T; at the same time, the jerk is constrained by the tool path displacement, and the constant feed speed time stage T8 and the command speed F are constrained by the tool path displacement. c The acceleration A, jerk J, and jerk S actually reached by the machine tool are corrected to make the jerk S smooth, continuous and bounded, and eliminate speed fluctuations. The specific steps are as follows:

[0039] Define T as the interpolation cycle of the CNC system,

[0040] T i ' represents the adjusted integer interpolation period T i ,

[0041] v' e is the adjusted terminal velocity v e ,

[0042] V′ max The maximum speed V planned for the adjusted speed max , V′ max Do not exceed the command speed F c

[0043] A' acc and A' dec is the acceleration A of the adjusted acceleration and deceleration phases acc and A dec ,

[0044] J i ' is the adjusted jerk J i , where J'2=-J'6,J' 10 =-J′14 , J i is the extreme value of the acceleration,

[0045] S′ i is the adjusted jerk S i , where S′1=-S′3=S′5=-S′7, S′9=-S′ 11 =S′ 13 =-S′ 15 ,S i is the extreme value of jerk;

[0046] 1) The trigonometric function feed speed planning only contains the acceleration and uniform speed stages.

[0047] In this case, the deceleration time stage is zero, that is, T i = 0 (i = 9, ..., 15), so the duration of the acceleration and uniform speed phase T based on the tool path displacement i (i=1,2,...,8) is modified to make T i (i=1,2,...,8) contains an integer number of interpolation periods T,

[0048] 1.1) First, the duration of the acceleration phase T i (i=1,2,...,7) is adjusted, and T is obtained after adjustment. i '(i=1,2,...,7) value,

[0049] T′ i =ceil(T i / T)T (11)

[0050] Among them, ceil means rounding up.

[0051] Then, according to the adjusted T i '(i=1,2,...,7) values, calculate the tool path displacement d' in the acceleration phase after integer interpolation cycle constraint acc :

[0052] d' acc =(v s +V max )(2T′1+T′2+T′4 / 2) (12)

[0053] Among them, d' acc represents the tool path displacement in the acceleration phase after the integer interpolation cycle constraint,

[0054] 1.2) The tool path displacement d' in the acceleration phase after the integer interpolation cycle constraint acc Tool path length d with speed planning unit segmentCompare and determine the value of constant speed time T8, where d segment represents the tool path length of the velocity planning unit, and then, based on the adjusted time T i '(i=1,2,...,8) and tool path length d segment , the actual acceleration A during the acceleration phase acc , acceleration J i (i=2,6) and jerk S i ,i=(1,3,5,7) correction, so that the jerk is smooth and continuously bounded, eliminating the speed fluctuations generated at the end of interpolation,

[0055] 1.21) When d' acc <d segment When the situation is established, there is a duration phase T8 of constant feed rate, and T8 is constrained by integer interpolation cycle to obtain the adjusted duration phase T8' of constant feed rate:

[0056]

[0057] Since the tool path displacement d cannot exceed the length d of the velocity planning unit segment , based on the integer interpolation cycle constraint, the maximum speed V max correction,

[0058]

[0059] Because the adjusted time T i '(i=1,2,...,8) and the adjusted maximum speed V′ max Different from the initial speed planning stage time T i (i=1,2,...,8) and maximum speed V max , while the tool path displacement d is constant, the adjusted terminal speed v' e Equal to the adjusted maximum speed V' max ;

[0060] Therefore, the actual acceleration A during the acceleration phase is acc , jerk constraint J i (i=2,6) and jerk constraint S i (i=1,3,5,7) to adjust and correct the acceleration A' acc , jerk constraints (J'2, J'6) and jerk constraints (S'1, S'3, S'5, S'7) to make the jerk continuous and eliminate the velocity fluctuations generated at the end of interpolation.

[0061]

[0062] 1.22) When d' acc ≥d segment When it is established, there will be no constant speed stage, that is, T8 = 0. In order to ensure that the tool path displacement in the acceleration stage does not exceed the displacement generated by the speed planning unit, the acceleration stage time is first adjusted to the integer interpolation cycle time T i '=ceil(T i / T)T(i=1,2...,7), for the maximum speed V max Correction is made to obtain the maximum speed V′ max :

[0063]

[0064] At this time, the corrected terminal velocity v' e Equal to the adjusted maximum speed V' max ,

[0065] The actual acceleration A during the acceleration phase acc , jerk constraint J i (i=2,6) and jerk constraint S i (i=1,3,5,7) to adjust and correct the acceleration A' acc , the values ​​of jerk constraints J'2, J'6 and jerk constraints S'1, S'3, S'5, S'7 are:

[0066]

[0067] 2) The trigonometric function feed speed planning only contains the acceleration and deceleration stages, that is, T8 = 0.

[0068] 2.1) First, the acceleration time T of the trigonometric function speed planning i (i=1,...,7) and deceleration time T i (i=9,...,15) is corrected to the integer interpolation cycle time, and the adjusted T i '=ceil(T i / T)T,(i=1,...,7),T8=0,T i '=ceil(T i / T)T,(i=9,...,15);

[0069] 2.2) Based on the tool path displacement and the maximum speed V max , acceleration J i and jerk S i Correct and adjust to calculate the adjusted maximum speed V' max , acceleration J'2, J'6, J' 10, J′ 14 and jerk S′1, S′3, S′5, S′7, S′9, S′ 11 , S′ 13 , S′ 15 , and the actual acceleration A' of the adjusted acceleration phase acc and the actual acceleration A' during the deceleration phase dec , eliminate speed fluctuations,

[0070]

[0071] Among them, a' and b' are intermediate parameters, a'=v s (2T1'+T′2+T′4 / 2)+v e (2T′9+T′ 10 +T′ 12 / 2), b'=2(T1'+T'9)+(T'2+T' 10 )+(T′4+T′ 12 )...2;

[0072] 3) The trigonometric function feed speed planning includes acceleration, uniform speed and deceleration stages.

[0073] 3.1) Set the time parameter T i (i=1,...,15) rounded up to an integer interpolation cycle time T i '=ceil(T i / T)T(i=1,...,15), the total displacement d1' of the acceleration and deceleration stages is expressed as:

[0074] d′1=(v s +V max )(2T′1+T′2+T′4 / 2)+(v e +V max )(2T′9+T′ 10 +T′ 12 / 2) (19)

[0075] 3.2) Based on tool path displacement d segmemnt Calculate the corrected constant speed time T′8, and adjust the maximum speed, jerk and acceleration in the acceleration, constant speed and deceleration stages to obtain the adjusted maximum speed V′ max , acceleration A' acc , A' dec , acceleration J'2, J'6, J' 10 , J′ 14 and jerk S′1, S′3, S′5, S′7, S′9, S′ 11 , S′13 , S′ 15 , eliminate the speed fluctuations generated at the end of interpolation,

[0076] When d′1<d segmemnt When the situation is established, the corrected constant speed time T′8 is:

[0077]

[0078] Among them, c' and d' are intermediate parameters.

[0079] c'=v s (2T′1+T′2+T′4 / 2)+v e (2T′9+T′ 10 +T′ 12 / 2),d'=2T′1+T′2+T′4 / 2+2T′9+T′ 10 +T′ 12 / 2,

[0080] At this time, the terminal velocity v e The value remains unchanged, the corrected maximum speed V′ max and jerk J'2, J'6, J' 10 ,J′ 14 and jerk S′1, S′3, S′5, S′7, S′9, S′ 11 , S′ 13 , S′ 15 Calculated as:

[0081]

[0082] When d′1≥d segmemnt When the situation is established, the adjusted speed curve does not contain a constant speed phase, that is, T8 = 0.

[0083] At this time, the terminal velocity v e The value remains unchanged, and the adjusted maximum speed V′ max , acceleration A' acc , A' dec , acceleration J'2, J'6, J′ 10 ,J′ 14 and jerk S′1, S′3, S′5, S′7, S′9, S′ 11 , S′ 13 , S′ 15 Corrected to:

[0084]

[0085] Where, e'=v s (2T′1+T′2+T′4 / 2)+ve (2T′9+T′ 10 +T′ 12 / 2),

[0086] f'=2(T'1+T'9)+(T'2+T' 10 )+(T′4+T′ 12 ) / 2;

[0087] At this point, the time parameter T of the trigonometric function speed planning has been i Adjusted to an adjusted integer interpolation period T′ containing an integer number of interpolation periods i , and the corrected jerk S′ is obtained based on the integer interpolation cycle and tool path displacement constraints i , acceleration J′ i , acceleration A′ i and maximum speed V′ max , which are the jerk S, jerk J, acceleration A and speed V actually reached by the machine tool during the machining process, and make the jerk actually reached by the machine tool during the machining process smooth, continuous and bounded, overcoming the speed fluctuation generated at the end of the interpolation cycle, and combining the fourth-order continuous smooth tool path to generate smooth interpolation points for controlling the tool motion, thereby achieving smooth motion of the tool.

[0088] Preferably, after adjustment, the feed speed V' allowed by the system max Less than or equal to the adjusted terminal velocity v' e , then V′ max To solve this problem, it is necessary to recalculate the feed rate V′ allowed by the adjusted system. max , the kinematic parameters also need to be re-solved, the steps are as follows:

[0089] Let T′8=T′8+T′9+T′ 10 +T′ 11 +T′ 12 +T′ 13 +T′ 14 +T′ 15 At this time, the tool path length d of the speed planning unit segment It is expressed as:

[0090]

[0091] In order to ensure that the tool path length d does not exceed the path length d of the velocity planning unit segment , for the adjusted maximum speed V′ max Calculate again to get the maximum speed V″ after the second adjustment max :

[0092]

[0093] Then, based on the adjusted time T i '(i=1,2,...,7) and the maximum speed V″ after secondary adjustment max For maximum speed V max , acceleration J i and jerk S i Correction adjustment, the actual acceleration of the acceleration phase after adjustment A' acc , jerk J'2, J'6 and jerk S'1, S'3, S'5, S'7,

[0094]

[0095] The above is the actual acceleration A' in the adjusted acceleration phase. acc , jerk J'2, J'6 and jerk S'1, S'3, S'5, S'7.

[0096] Beneficial Effects

[0097] In order to further improve the processing quality, compared with the S-curve speed planning method commonly used in CNC machine tools, the trigonometric function feed speed planning method of the fourth-order continuous tool path of the present invention further improves the flexibility of the feed speed curve by constraining the jerk in the processing process and realizing the smooth, bounded and continuous jerk, thereby improving the processing quality; in the CNC system, the servo motor runs with an integer interpolation cycle, and the current speed planning method does not take into account the speed fluctuation problem caused by the constraints of the interpolation process. The present invention innovatively uses the tool path displacement to correct the jerk, so that the jerk is smooth, bounded and continuous, and the interpolation time includes an integer interpolation cycle, which effectively eliminates the feed speed fluctuation, thereby improving the processing quality.

[0098] Therefore, the present invention is aimed at numerical control systems with higher requirements on machining quality. By correcting the jerk to be smooth, continuous and bounded, the speed fluctuation is effectively eliminated, the smooth movement of the tool is achieved, and the machining accuracy is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] The accompanying drawings provide a further understanding of the technical solution of the present invention and constitute a part of the specification. Together with the specific embodiments of the present application, they are used to explain the technical solution of the present invention and do not constitute a limitation on the technical solution of the present invention.

[0100] Figure 1 , three Schematic diagram of the angular function speed planning method,

[0101] Figure 2(a), only T2=T4=T6=T8=T9=T 10=T 11 =T 12 =T 13 =T 14 =T 15 = 0 and the acceleration does not reach the maximum value allowed by the system, the trigonometric function speed plans the speed, acceleration and jerk curves.

[0102] Figure 2(b), only T8=T9=T 10 =T 11 =T 12 =T 13 =T 14 =T 15 = 0, the trigonometric function speed plans the speed, acceleration and jerk curves,

[0103] Figure 2(c), only T2 = T4 = T6 = T8 = T9 = T 10 =T 11 =T 12 =T 13 =T 14 =T 15 = 0 and the acceleration can reach the maximum value allowed by the system, the trigonometric function speed plans the speed, acceleration and jerk curves,

[0104] Figure 2(d), only T4=T8=T9=T 10 =T 11 =T 12 =T 13 =T 14 =T 15 = 0, the trigonometric function speed plans the speed, acceleration and jerk curves,

[0105] Figure 2(e), only T2=T4=T6=T9=T 10 =T 11 =T 12 =T 13 =T 14 =T 15 = 0 and the acceleration does not reach the maximum value allowed by the system, the trigonometric function speed plans the speed, acceleration and jerk curves.

[0106] Figure 2(f), only T9 = T 10 =T 11 =T 12 =T 13 =T 14 =T 15 = 0, the trigonometric function speed plans the speed, acceleration and jerk curves,

[0107] Figure 2(g), only T2 = T4 = T6 = T9 = T 10 =T11 =T 12 =T 13 =T 14 =T 15 = 0 and the acceleration can reach the maximum value allowed by the system, the trigonometric function speed plans the speed, acceleration and jerk curves,

[0108] Figure 2(h), only T4=T9=T 10 =T 11 =T 12 =T 13 =T 14 =T 15 = 0, the trigonometric function speed plans the speed, acceleration and jerk curves,

[0109] Figure 2(i) shows the velocity, acceleration and jerk curves of trigonometric function velocity planning only when T8=0.

[0110] Figure 2(j), only T4=T8=T 12 = 0, the trigonometric function speed plans the speed, acceleration and jerk curves,

[0111] Figure 2(k), only T2=T4=T6=T8=T 10 =T 12 =T 14 = 0, the trigonometric function speed plans the speed, acceleration and jerk curves,

[0112] Figure 2(l), only T2=T6=T8=T 10 =T 14 = 0, the trigonometric function speed plans the speed, acceleration and jerk curves,

[0113] Figure 2(m) contains the velocity, acceleration and jerk curves of the trigonometric velocity planning for all time stages.

[0114] Figure 2(n), only T4 = T 12 = 0, the trigonometric function speed plans the speed, acceleration and jerk curves,

[0115] Figure 2(o), only T2=T4=T6=T 10 =T 12 =T 14 = 0, the trigonometric function speed plans the speed, acceleration and jerk curves,

[0116] Figure 2(p), only T2 = T6 = T 10 =T 14 = 0, the trigonometric function speed plans the speed, acceleration and jerk curves,

[0117] Figure 3, experimental tool path diagram,

[0118] Fig. 4(a) Speed ​​comparison of method 1 and method 2.

[0119] Figure 4(b) is an enlarged view of Part A in Figure 4(a). Specific implementation methods

[0121] The present invention will be described in more detail below with reference to the accompanying drawings, in which preferred embodiments of the present invention are shown. It should be understood that those skilled in the art can modify the present invention described herein and still achieve the beneficial effects of the present invention. Therefore, the following description should be understood as being widely known to those skilled in the art and not as a limitation of the present invention. In order to make the objects and features of the present invention more obvious and understandable, the specific embodiments of the present invention are further described below in conjunction with the accompanying drawings. It should be noted that the drawings are all in a very simplified form and use non-precise ratios, which are only used to conveniently and clearly assist in explaining the purpose of the embodiments of the present invention.

[0122] A trigonometric function feed rate planning method for a fourth-order continuous tool path comprises the following steps:

[0123] Step 1: Establish a mathematical expression for the trigonometric function velocity planning with continuous jerk.

[0124] First, the trigonometric function speed planning is divided into 15 different time periods, T i represents the duration of the i-th (i=1,...,15) stage, where T1-T7 all belong to the acceleration stage, during which the feed speed increases monotonically; T8 belongs to the uniform speed stage, during which the feed speed remains unchanged; T9-T 15 Both belong to the deceleration stage, during which the feed speed decreases monotonically; t i (i=1,...,15) represents the end time of the i-th time stage, t0 represents the start time of the speed planning, then T i =t i -t i-1 ;

[0125] Then, the kinematic parameters in the trigonometric function velocity planning are defined: d represents the tool path displacement, F c represents the command speed, V represents the actual speed value of the machine tool during the processing, A represents the actual acceleration reached by the machine tool during the processing, J represents the actual jerk reached by the machine tool during the processing, and S represents the actual jerk reached by the machine tool during the processing;

[0126] V max Indicates the maximum speed of speed planning; A max , J max and S maxRepresent the maximum values ​​of acceleration, jerk and jerk allowed by the system, A acc , J acc Indicates the actual acceleration and jerk during the acceleration phase, A dec , J dec Indicates the actual acceleration and jerk during the deceleration phase;

[0127] For any given feed rate planning unit, the starting speed and end speed corresponding to the feed rate planning unit are defined as v s 、v e , v s <v e ;

[0128] Finally, by constraining the jerk S that the machine tool actually reaches during the processing, the jerk J, acceleration A, and maximum speed V that the machine tool actually reaches during the processing are obtained. max and tool path displacement d, a trigonometric function speed planning model is established to describe the feed speed curve. The schematic diagram of trigonometric function speed planning is shown in Figure 1 shown.

[0129] 1) First, the kinematic expression of the acceleration phase is solved.

[0130] 1.1) At the maximum jerk S max Under the constraint of , the expression of jerk Jounce(t) in the trigonometric function feed rate planning method is established as follows:

[0131]

[0132] 1.2) Integrate the jerk in the time domain to get the jerk expression Jerk(t):

[0133]

[0134] In the formula, the value of T1 is: T1 = J max π / (2S max ).

[0135] 1.3) Perform a second integration of the jerk in the time domain to obtain the acceleration parameters. The results are shown in Table 1:

[0136] Table 1 Trigonometric function speed planning acceleration formula

[0137]

[0138]

[0139] For Table 1 A maxThe value of is simplified to obtain the constant jerk time T2 in the acceleration phase:

[0140] T2=A acc / J acc -T1 (3)

[0141] 1.4) By integrating the jerk acceleration curve three times in the time domain, the expression of the trigonometric function feed speed curve V(t) can be obtained, as shown in Table 2:

[0142] Table 2 Trigonometric function speed planning speed formula

[0143]

[0144] In Table 2, v i (i=1,2...,7) represents the time node t i The feed speed at time (i=1,2...,7) is shown in Table 3:

[0145] Table 3 Speed ​​formula for each time node in the acceleration phase of trigonometric speed planning

[0146]

[0147]

[0148] In Table 3, when the equation V=v7 for the maximum speed holds, the constant acceleration time T4 can be obtained by simplifying the v7 formula:

[0149]

[0150] 1.5) Integrate the jerk four times in the time domain to obtain the tool path displacement formula, as shown in Table 4:

[0151] Table 4 Tool path displacement formula in trigonometric function acceleration stage

[0152]

[0153] Table 4d i (i=1,2...,7) represents the time node t i The tool path displacement at time (i=1,2...,7) is shown in Table 5:

[0154] Table 5 Displacement formula for each time node in the trigonometric function acceleration stage

[0155]

[0156]

[0157] 2) Solve the kinematic expression of the deceleration stage to obtain the kinematic parameters of the deceleration stage;

[0158] 2.1) The jerk expression during the deceleration phase is as follows:

[0159]

[0160] 2.2) Integrate the jerk in the time domain to get the jerk expression Jerk(t):

[0161]

[0162] Where T9 = J max π / 2S max .

[0163] 2.3) Perform a second integration of the jerk in the time domain to obtain the acceleration expression A(t) as shown in Table 6:

[0164] Table 6 Trigonometric function speed planning acceleration formula for deceleration stage

[0165]

[0166]

[0167] Simplifying Table 6, we can get T 10 =A max / J max -T9.

[0168] 2.4) Integrate the jerk three times in the time domain to obtain the velocity expression V(t) of trigonometric velocity planning, as shown in Table 7:

[0169] Table 7 Trigonometric function speed planning speed formula for deceleration stage

[0170]

[0171] In Table 7, v i Represents each time node t i The specific values ​​of the feed speed at time (i=9,10...,15) are shown in Table 8:

[0172] Table 8 Trigonometric function speed planning speed formula for each acceleration and deceleration time node stage

[0173]

[0174] Through v 15 Simplifying the formula, we can get the constant acceleration time T 12=(Vv e ) / A max -2T9-T 10 .

[0175] 2.5) By integrating the velocity curve in the time domain, the tool path displacement curve can be obtained, which is represented by Table 9:

[0176] Table 9 Trigonometric function speed planning deceleration stage displacement formula

[0177]

[0178] where d i It represents the path length of each time node in the speed planning process, i=9,10...,15, and its formula is shown in Table 10:

[0179] Table 10 Displacement formulas for each deceleration time node stage of trigonometric functions

[0180]

[0181] 3) In the uniform speed stage, the jerk S, jerk J and acceleration A of the trigonometric function velocity planning method are all zero, and its velocity and displacement parameters are expressed in the time interval (t7, t8) as follows:

[0182]

[0183] Wherein t7≤t<t8.

[0184] Step 2: Under non-integer interpolation cycles, V max =F c , based on the speed stage T included in the feed speed planning unit i Determine the T on the feed speed curve generated on the corresponding speed planning unit i (i=1,2...,15) values, as well as the actual acceleration and jerk A during the acceleration phase acc , J acc The actual acceleration and jerk A during the deceleration phase dec , J dec , the steps are as follows:

[0185] 1) Calculate T during the acceleration phase i (i=1,…,7), as well as the actual acceleration and jerk A during the acceleration phase acc , J acc The steps are as follows:

[0186] 1.1), when A max / J max >J max π / (2S max) is established, at this time, the system allows the acceleration J max , and there is a constant acceleration stage, that is, T2>0, the feed speed curve generated on the speed planning unit satisfies that the values ​​of T1, T2, T3, T5, T6, and T7 are not zero, that is, T1=T3=T5=T7=J max π / (2S max ), T2=T6=A acc / J acc -T1>0;

[0187] 1.1.1) If V max -v s >A max (2T1+T2) holds, then T i (i=1,2,...,7) value, acceleration A acc and jerk J acc The values ​​are as follows,

[0188]

[0189] 1.1.2) Otherwise, V max -v s ≤A max (2T1+T2) is established, the feed speed planning unit will not have a constant acceleration time T4, and the acceleration A acc The acceleration A allowed by the system cannot be reached. max , at this time T i (i=1,2,...,7) value, acceleration A acc and jerk J acc The values ​​are as follows,

[0190]

[0191] 1.2), when A max / J max =J max π / (2S max ) is established, at this time, the system allows the acceleration J max , and there is no constant acceleration, that is, T2 = 0, the feed speed curve generated on the speed planning unit satisfies that the values ​​of T1, T3, T5, and T7 are not zero, that is, T1 = T3 = T5 = T7 = J max π / (2S max ), and determine whether there is a constant acceleration time T4,

[0192] 1.2.1) If V max -v s >2A max If T1 is established, there is a constant acceleration time T4, at which time Ti (i=1,2,...,7) value, acceleration A acc and jerk J acc The values ​​are as follows,

[0193]

[0194] 1.2.2), otherwise, V max -v s ≤2A max T1 is established. At this time, the speed curve will not have a constant acceleration time T4, and the acceleration A acc The acceleration A allowed by the system cannot be reached max , at this time T i (i=1,2...,7) value, acceleration A acc and jerk J acc The values ​​are as follows,

[0195]

[0196] 1.3), when A max / J max <J max π / (2S max ) is established. At this time, the jerk J allowed by the system cannot be achieved. max , that is, T2 = 0, the feed speed curve generated on the speed planning unit satisfies that the values ​​of T1, T3, T5, and T7 are not zero. It is necessary to re-solve T1, T3, T5, and T7 and determine whether there is a constant acceleration time T4.

[0197] 1.3.1) When V max -v s >2A max When T1 is established, there is a constant acceleration time T4. At this time, by reducing the acceleration J in the acceleration phase acc Make A max / J acc =T1 is established, and the calculation shows that T i (i=1,2...,7) value, acceleration A acc and jerk J acc The values ​​are as follows,

[0198]

[0199] 1.3.2) When V max -v s ≤2A max When T1 is established, there will be no constant acceleration time T4 and jerk time T2, T6, for acceleration A acc and jerk Jacc Re-solve and calculate T i (i=1,2...,7) value, acceleration A acc and jerk J acc The values ​​are as follows,

[0200]

[0201] After the above step (1), we can get T in the acceleration stage. i (i=1,…,7) values, and acceleration A acc and jerk J acc The value of

[0202] 2) Calculate T during the deceleration phase i (i=9,…,15), and the actual acceleration A during the deceleration phase dec and jerk J dec The steps are as follows:

[0203] 2.1), when A max / J max >J max π / (2S max ) is established, at this time, the acceleration J dec Reach the system allowed jerk J max , and there is a constant acceleration stage, namely T 10 >0, then T i (i=9,...,15), acceleration A dec and jerk J dec as follows:

[0204]

[0205] 2.2), when A max / J max =J max π / (2S max ) is established, at this time, the acceleration J dec Reach the system allowed jerk J max , and there is no constant acceleration, that is, T 10 =0, then T i (i=9,...,15), acceleration A dec and jerk J dec as follows:

[0206]

[0207] 2.3), when A max / J max <Jmax π / (2S max ) is established, at this time, the acceleration J dec The jerk J allowed by the system cannot be reached max , that is, T 10 =0, then T i (i=9,...,15), acceleration A dec and jerk J dec as follows:

[0208]

[0209] 3) Calculate the value of uniform speed time T8, when both jerk and acceleration are zero.

[0210]

[0211] When T8>0, the uniform time T8 is the formula. When T8≤0, there is no uniform time, that is, T8=0;

[0212] Step 3: In order to reduce the speed fluctuation during the interpolation process, the T obtained in step 2 is i (i=1,…,7,9,…,15) to make corrections under the constraints of integer interpolation cycle so that T i (i=1,…,7,9,…,15) all contain an integer number of interpolation cycles T; at the same time, the jerk S is constrained by the tool path displacement, and the constant feed speed time stage T8 and the command speed F are constrained by the tool path displacement. c The acceleration A, jerk J, and jerk S actually reached by the machine tool are corrected to make the jerk S smooth, continuous and bounded, and eliminate speed fluctuations. The specific steps are as follows:

[0213] Define T as the interpolation cycle of the CNC system,

[0214] T i ' represents the adjusted integer interpolation period T i ,

[0215] v' e is the adjusted terminal velocity v e ,

[0216] V′ max The maximum speed V planned for the adjusted speed max , V′ max Do not exceed the command speed F c ,

[0217] A' acc and A' dec is the acceleration A of the adjusted acceleration and deceleration phases acc and Adec ,

[0218] J′ i is the adjusted jerk J i , where J'2=-J'6,J' 10 =-J′ 14 , J i is the extreme value of the acceleration,

[0219] S′ i is the adjusted jerk S i , where S′1=-S′3=S′5=-S′7, S′9=-S′ 11 =S′ 13 =-S′ 15 ,S i is the extreme value of jerk;

[0220] 1) When the trigonometric function feed speed planning only contains the acceleration and uniform speed stages, the corresponding speed curves are shown in Figure 2(a)-(h).

[0221] In this case, the deceleration time stage is zero, that is, T i = 0 (i = 9, ..., 15), so the duration of the acceleration and uniform speed phase T based on the tool path displacement i (i=1,2,...,8) is modified to make T i (i=1,2,...,8) contains an integer number of interpolation periods T,

[0222] 1.1) First, the duration of the acceleration phase T i (i=1,2,...,7) is adjusted, and T′ is obtained after adjustment i (i=1,2,...,7) value,

[0223] T′ i =ceil(T i / T)T (18)

[0224] Among them, ceil means rounding up.

[0225] Then, according to the adjusted T′ i (i=1,2,...,7) values, calculate the tool path displacement d' in the acceleration phase after integer interpolation cycle constraint acc :

[0226] d' acc =(v s +V max )(2T′1+T′2+T′4 / 2) (19)

[0227] Among them, d'acc represents the tool path displacement in the acceleration phase after the integer interpolation cycle constraint,

[0228] 1.2) The tool path displacement d' in the acceleration phase after the integer interpolation cycle constraint acc Tool path length d with speed planning unit segment Compare and determine the value of constant speed time T8, where d segment represents the tool path length of the velocity planning unit,

[0229] 1.21) When d' acc <d segment When the situation is established, there is a duration stage T8 of constant feed speed. The corresponding speed curve, acceleration curve and jerk curve are shown in Figure 2(e)-(h). The integer interpolation cycle constraint is applied to T8 to obtain the adjusted duration stage T′8 of constant feed speed:

[0230]

[0231] Since the tool path displacement d cannot exceed the length d of the velocity planning unit segment , based on the integer interpolation cycle constraint, the maximum speed V max correction,

[0232]

[0233] Because the adjusted time T i '(i=1,2,...,8) and the adjusted maximum speed V′ max Different from the initial speed planning stage time T i (i=1,2,...,8) and maximum speed V max , and the tool path displacement d segment is constant, therefore, the adjusted terminal velocity v' e Equal to the adjusted maximum speed V' max .

[0234] Therefore, the actual acceleration A during the acceleration phase is acc , jerk constraint J i (i=2,6) and jerk constraint S i (i=1,3,5,7) to adjust and correct the acceleration A' acc , jerk constraints (J'2, J'6) and jerk constraints (S'1, S'3, S'5, S'7) to make the jerk continuous and eliminate the velocity fluctuations generated at the end of interpolation.

[0235]

[0236] 1.22) When d' acc ≥d segment When it is established, there will be no constant speed stage, that is, T8 = 0. The corresponding speed curve, acceleration curve, and jerk curve are shown in Figure 2(a)-(d). In order to ensure that the tool path displacement in the acceleration stage does not exceed the displacement generated by the speed planning unit, the acceleration stage time is first adjusted to the integer interpolation cycle time T i '=ceil(T i / T)T(i=1,2...7), for maximum speed V max Correction is made to obtain the maximum speed V′ max :

[0237]

[0238] At this time, the corrected terminal velocity v' e Equal to the adjusted maximum speed V' max ,

[0239] The actual acceleration A during the acceleration phase acc , jerk constraint J i (i=2,6) and jerk constraint S i (i=1,3,5,7) to adjust and correct the acceleration A' acc , the values ​​of jerk constraints J'2, J'6 and jerk constraints S'1, S'3, S'5, S'7 are:

[0240]

[0241] 2) When the trigonometric function feed speed planning only contains the acceleration and deceleration stages, that is, T8 = 0, the corresponding speed curve, acceleration curve and jerk curve are shown in Figure 2 (i)-(l).

[0242] 2.1) First, the acceleration time T of the trigonometric function speed planning i (i=1,...,7) and deceleration time T i (i=9,...,15) is corrected to the integer interpolation cycle time, and the adjusted T i '=ceil(T i / T)T,(i=1,...,7),T8=0,T i '=ceil(T i / T)T,(i=9,…,15);

[0243] 2.2) Based on the tool path displacement and the maximum speed V max , acceleration J i and jerk S iCorrect and adjust to calculate the adjusted maximum speed V' max , acceleration J'2, J'6, J' 10 , J′ 14 and jerk S′1, S′3, S′5, S′7, S′9, S′ 11 , S′ 13 , S′ 15 , and the actual acceleration A' of the adjusted acceleration phase acc and the actual acceleration A' during the deceleration phase dec ,

[0244]

[0245] Among them, a' and b' are intermediate parameters, a'=v s (2T′1+T′2+T′4 / 2)+v e (2T′9+T′ 10 +T′ 12 / 2), b'=2(T′1+T′9)+(T′2+T′ 10 )+(T′4+T′ 12 ) / 2;

[0246] When the feed speed V' allowed by the system after adjustment appears max Less than or equal to the adjusted terminal velocity v' e , then V′ max When it becomes an infeasible solution, recalculate the feed rate V′ allowed by the adjusted system max At this time, the kinematic parameters also need to be re-solved, and the solution steps are as follows:

[0247] Let T′8=T′8+T′9+T′ 10 +T′ 11 +T′ 12 +T′ 13 +T′ 14 +T′ 15 At this time, the tool path length d of the speed planning unit segment It is expressed as:

[0248]

[0249] In order to ensure that the tool path length d does not exceed the path length d of the velocity planning unit segment , for the adjusted maximum speed V′ max Calculate again to get the maximum speed V″ after the second adjustment max :

[0250]

[0251] Then, based on the adjusted time T i '(i=1,2,...,7) and the maximum speed V″ after secondary adjustment max For maximum speed V max , acceleration J i and jerk S i Correction adjustment, the actual acceleration of the acceleration phase after adjustment A' acc The values ​​of jerk J'2, J'6 and jerk S'1, S'3, S'5, S'7 are as follows,

[0252]

[0253] The above is the actual acceleration A' in the acceleration phase after adjustment. acc , jerk J'2, J'6 and jerk S'1, S'3, S'5, S'7.

[0254] 3) The trigonometric function feed speed planning includes acceleration, uniform speed and deceleration stages. The corresponding speed curve, acceleration curve and jerk curve are shown in Figure 2(m)-(p).

[0255] 3.1) Set the time parameter T i (i=1,...,15) rounded up to an integer interpolation cycle time T i '=ceil(T i / T)T(i=1,…,15), the total displacement d1' of the acceleration and deceleration stages is expressed as:

[0256] d′1=(v s +V max )(2T′1+T′2+T′4 / 2)+(v e +V max )(2T′9+T′ 10 +T′ 12 / 2) (29)

[0257] 3.2) Based on tool path displacement d segmemnt Calculate the corrected constant speed time T′8, as well as the maximum speed, jerk and jerk correction adjustments for the acceleration, constant speed and deceleration stages. segmemnt When the situation is established, the corresponding velocity curve, acceleration curve and jerk curve are shown in Figure 2(m)-(p), and the corrected constant speed time T′8 is:

[0258]

[0259] Among them, c' and d' are intermediate parameters.

[0260] c'=vs (2T′1+T′2+T′4 / 2)+v e (2T′9+T′ 10 +T′ 12 / 2),d'=2T′1+T′2+T′4 / 2+2T′9+T′ 10 +T′ 12 / 2,

[0261] At this time, the terminal velocity v e The value remains unchanged, the corrected maximum speed V′ max and jerk J'2, J'6, J' 10 ,J′ 14 and jerk S′1, S′3, S′5, S′7, S′9, S′ 11 , S′ 13 , S′ 15 Calculated as:

[0262]

[0263] When d′1≥d segmemnt When the situation is established, the adjusted speed curve does not contain a constant speed stage, that is, T8 = 0, that is, when it does not contain a uniform speed stage, the corresponding speed curve, acceleration curve and jerk curve are shown in Figure 2 (i)-(l).

[0264] At this time, the terminal velocity v e The value remains unchanged, and the adjusted maximum speed V′ max , acceleration A' acc , A' dec , acceleration J'2, J'6, J′ 10 ,J′ 14 and jerk S′1, S′3, S′5, S′7, S′9, S′ 11 , S′ 13 , S′ 15 Corrected to:

[0265]

[0266] Where, e'=v s (2T′1+T′2+T′4 / 2)+v e (2T′9+T′ 10 +T′ 12 / 2), f'=2(T′1+T′9)+(T′2+T′ 10 )+(T′4+T′ 12 ) / 2;

[0267] At this point, the time parameter T of the trigonometric function speed planning has been iAdjust to a new parameter T containing an integer number of interpolation cycles i ', and the corrected jerk S' is obtained based on the integer interpolation cycle and tool path displacement constraints i , acceleration J′ i , acceleration A′ i and speed V′ i , which is the actual jerk S, jerk J, acceleration A and speed V reached by the machine tool during the processing, and makes the actual jerk reached by the machine tool during the processing smooth and continuous and bounded, overcomes the speed fluctuation generated at the end of the interpolation cycle, combines the fourth-order continuous smooth tool path, generates smooth interpolation points to control the tool movement, and then realizes the smooth movement of the tool. This process effectively eliminates speed fluctuations and improves the processing quality of the machine tool.

[0268] Simulation experiment

[0269] In order to verify the performance of the method proposed in the present invention, the trigonometric function speed planning method proposed in this patent is referred to as Method 1 (i.e., the trigonometric function speed planning method for the fourth-order continuous path of the present invention), and the trigonometric function speed planning method for the non-fourth-order continuous path is referred to as Method 2 (Z. Wu, J. Chen, D. Zhang, J. Wang, L. Zhang, F. Xu. A novel multi-point trajectory generator for robotic manipulators based on piecewise motion profile and series-parallel analytical strategy [J]. Mechanism and Machine Theory, 2023, 181: 105201.). The experiment verifies that the feed speed planning method with continuous jerk is implemented on a five-axis CNC machining center. The machining center is equipped with a high-end CNC device with a system interpolation period of 1 ms. In order to verify the performance of the method proposed in the present invention, the trigonometric function speed planning method for the non-fourth-order continuous path is referred to as Method 2 (Z. Wu, J. Chen, D. Zhang, J. Wang, L. Zhang, F. Xu. A novel multi-point trajectory generator for robotic manipulators based on piecewise motion profile and series-parallel analytical strategy [J]. Mechanism and Machine Theory, 2023, 181: 105201.). Figure 3 The tool path shown is processed: Set the system command speed F c , the acceleration A allowed during CNC machining max , acceleration J max and jerk S max 40mm / s and 2500mm / s respectively 2 , 40000mm / s 3 ,4000000mm / s 4 .

[0270] The trigonometric function speed planning method was experimented with by method 1 and method 2 respectively. The experimental results are as follows: The maximum tracking error is shown in Table 11:

[0271] Table 11 Comparison of the extreme values ​​of tracking errors of each axis between method 1 and method 2

[0272]

[0273] The comparison images of Method 1 and Method 2 are shown in Figure 4(a). The speed curve (Part A) of 6-6.2s in the speed planning is compared, and the result is shown in Figure 4(b). Compared with the method of non-fourth-order continuous path (Method 2), the trigonometric function speed planning method of the fourth-order continuous path proposed in the present invention (Method 1) can effectively eliminate speed fluctuations and has a smaller tracking error extreme value, so it has better processing quality; Method 2 cannot ensure that the jerk is smooth, continuous and bounded, so there will be large speed fluctuations.

[0274] Compared with the prior art, the above implementation verification shows that the feed speed curve generated when the above method of the present invention is used for speed planning can achieve smooth, continuous and bounded jerk. Therefore, the method proposed by the present invention can generate a high-order smooth feed speed curve, improve the processing quality, and can be applied to high-end CNC devices. The reason for the analysis is that the present invention uses the maximum jerk provided by the user as a constraint to plan the tool motion feed curve during the processing process. The maximum processing speed, maximum acceleration and maximum jerk corresponding to the generated feed speed curve all meet the system constraints. Each stage of the generated feed speed curve is rounded. The key is to correct the kinematic parameters that change during the speed planning process through the tool path displacement. The jerk curve contains an integer number of interpolation cycles, which eliminates the speed fluctuation at the end of the last interpolation cycle. Therefore, compared with the prior art, the method of the present invention further improves the processing quality and reduces the tracking error.

[0275] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A trigonometric function feed rate planning method for a fourth-order continuous tool path, characterized in that it comprises the following steps: Step 1: Establish a mathematical expression for the trigonometric function velocity planning with continuous jerk. 1) Divide the trigonometric function speed planning into 15 different time periods, T i represents the duration of the i-th (i=1,...,15) stage, where T1-T7 all belong to the acceleration stage, during which the feed speed increases monotonically; T8 belongs to the uniform speed stage, during which the feed speed remains unchanged; T9-T 15 Both belong to the deceleration stage, during which the feed speed decreases monotonically; t i (i=1,...,15) represents the end time of the i-th time stage, t0 represents the start time of the speed planning, then T i =t i -t i-1 ; 2) Define the kinematic parameters in trigonometric function speed planning: d represents the tool path displacement, F c represents the command speed, V represents the actual speed value of the machine tool during the processing, A represents the actual acceleration reached by the machine tool during the processing, J represents the actual jerk reached by the machine tool during the processing, S represents the actual jerk reached by the machine tool during the processing, V max Indicates the maximum speed of speed planning, A max , J max and S max They represent the maximum values ​​of acceleration, jerk and jerk allowed by the system, A acc , J acc Indicates the actual acceleration and jerk during the acceleration phase, A dec , J dec Indicates the actual acceleration and jerk during the deceleration phase; For any given feed rate planning unit, the starting speed and end speed corresponding to the feed rate planning unit are defined as v s 、v e , v s <v e ; Step 2: Under non-integer interpolation cycles, V max =F c , based on the speed stage T included in the feed speed planning unit i Determine the T on the feed speed curve generated on the corresponding speed planning unit i (i=1,2...,15) values, as well as the actual acceleration and jerk A during the acceleration phase acc , J acc The actual acceleration and jerk A during the deceleration phasedec , J dec , the steps are as follows: 1) Calculate T during the acceleration phase i (i=1,…,7), as well as the actual acceleration and jerk A during the acceleration phase acc , J acc The steps are as follows: 1.1), when A max / J max >J max π / (2S max ) is established, at this time, the system allows the acceleration J max , and there is a constant acceleration stage, that is, T2>0, the feed speed curve generated on the speed planning unit satisfies that the values ​​of T1, T2, T3, T5, T6, and T7 are not zero, that is, T1=T3=T5=T7=J max π / (2S max ), T2=T6=A acc / J acc -T1>0; 1.1.1) If V max -v s >A max (2T1+T2) holds, then T i (i=1,2,...,7) value, acceleration A acc and jerk J acc The values ​​are as follows, 1.1.2) Otherwise, V max -v s ≤A max (2T1+T2) is established, the feed speed planning unit will not have a constant acceleration time T4, and the acceleration A acc The acceleration A allowed by the system cannot be reached. max , at this time T i (i=1,2,...,7) value, acceleration A acc and jerk J acc The values ​​are as follows, 1.2), when A max / J max =J max π / (2S max ) is established, at this time, the system allows the acceleration J max , and there is no constant acceleration, that is, T2 = 0, the feed speed curve generated on the speed planning unit satisfies that the values ​​of T1, T3, T5, and T7 are not zero, that is, T1 = T3 = T5 = T7 = Jmax π / (2S max ), and determine whether there is a constant acceleration time T4, 1.2.1) If V max -v s >2A max If T1 is established, there is a constant acceleration time T4, at which time T i (i=1,2,...,7) value, acceleration A acc and jerk J acc The values ​​are as follows, 1.2.2), otherwise, V max -v s ≤2A max If T1 is true, there will be no constant acceleration time T4, and the acceleration A acc The acceleration A allowed by the system cannot be reached max , at this time T i (i=1,2...,7) value, acceleration A acc and jerk J acc The values ​​are as follows, 1.3), when A max / J max <J max π / (2S max ) is established. At this time, the jerk J allowed by the system cannot be achieved. max , that is, T2 = 0, the feed speed curve generated on the speed planning unit satisfies that the values ​​of T1, T3, T5, and T7 are not zero. It is necessary to re-solve T1, T3, T5, and T7 and determine whether there is a constant acceleration time T4. 1.3.1) When V max -v s >2A max When T1 is established, there is a constant acceleration time T4. At this time, by reducing the acceleration J in the acceleration phase acc Make A max / J acc =T1 is established, and the calculation shows that T i (i=1,2...,7) value, acceleration A acc and jerk J acc The values ​​are as follows, 1.3.2) When V max -v s ≤2A max When T1 is established, there will be no constant acceleration time T4 and jerk time T2, T6, for acceleration A acc and jerk J acc Re-solve and calculate T i (i=1,2...,7) value, acceleration A acc and jerk J acc The values ​​are as follows, After the above step 1), we can get the T in the acceleration stage: i (i=1,…,7) values, and acceleration A acc and jerk J acc The value of 2) Calculate T during the deceleration phase i (i=9,…,15), and the actual acceleration A during the deceleration phase dec and jerk J dec The steps are as follows: 2.1), when A max / J max >J max π / (2S max ) is established, at this time, the acceleration J dec Reach the system allowed jerk J max , and there is a constant acceleration stage, namely T 10 >0, then T i (i=9,...,15) value, acceleration A dec and jerk J dec as follows: 2.2), when A max / J max =J max π / (2S max ) is established, at this time, the acceleration J dec Reach the system allowed jerk J max , and there is no constant acceleration, that is, T 10 =0, then T i (i=9,...,15) value, acceleration A dec and jerk J dec as follows: 2.3), when A max / J max <J max π / (2S max ) is established, at this time, the acceleration J dec The jerk J allowed by the system cannot be reached max , that is, T 10 =0, then T i (i=9,...,15) value, acceleration A dec and jerk J dec as follows: After the above step 2), we can get the T of the deceleration stage: i (i=9,…,15), and the actual acceleration A during the deceleration phase dec and jerk J dec The value of 3) Calculate the value of uniform speed time T8, at which the jerk and acceleration in the uniform speed stage are both zero. When T8>0, the value of uniform speed time T8 is as follows: When T8≤0, there is no uniform time, that is, T8=0; Step 3: In order to reduce the speed fluctuation during the interpolation process, the T obtained in step 2 is i (i=1,…,7,9,…,15) to make corrections under the constraints of integer interpolation cycle so that T i (i=1,…,7,9,…,15) all contain an integer number of interpolation cycles T; at the same time, the jerk S is constrained by the tool path displacement, and the constant feed speed time stage T8 and the command speed F are constrained by the tool path displacement. c The acceleration A, jerk J, and jerk S actually reached by the machine tool are corrected to make the jerk S smooth, continuous and bounded, eliminate speed fluctuations, and achieve smooth tool motion. The steps are as follows: Define T as the interpolation cycle of the CNC system, T i ' represents the adjusted integer interpolation period T i , v' e is the adjusted terminal velocity v e , V′ max The maximum speed V planned for the adjusted speed max , V′ max Do not exceed the command speed F c , A' acc and A' dec is the acceleration A of the adjusted acceleration and deceleration phases acc and A dec , J′ i is the adjusted jerk J i , J i is the extreme value of jerk, where J'2 = -J'6, J1'0 = -J' 14 , S i ' is the adjusted jerk S i ,S i is the extreme value of jerk, where S1' = -S'3 = S'5 = -S'7, S'9 = -S' 11 =S′ 13 =-S′ 15 ; 1) The trigonometric function feed speed planning only contains the acceleration and uniform speed stages. In this case, the deceleration time stage is zero, that is, T i = 0 (i = 9, ..., 15), so the duration of the acceleration and uniform speed phase T based on the tool path displacement i (i=1,2,...,8) is modified to make T i (i=1,2,...,8) contains an integer number of interpolation periods T, 1.1) Duration of the acceleration phase T i (i=1,2,...,7) is adjusted, and T is obtained after adjustment. i '(i=1,2,...,7) value, T i '=ceil(T i / T)T (11) in, Ceil means round up. Then, according to the adjusted T i '(i=1,2,...,7) values, calculate the tool path displacement d' in the acceleration phase after integer interpolation cycle constraint acc : d' acc =(v s +V max )(2T1'+T2'+T4' / 2) (12) Among them, d' acc represents the tool path displacement in the acceleration phase after the integer interpolation cycle constraint, 1.2) The tool path displacement d' in the acceleration phase after the integer interpolation cycle constraint acc Tool path length d with speed planning unit segment Compare and determine the value of constant speed time T8, where d segment represents the tool path length of the velocity planning unit, and then, based on the adjusted time T i '(i=1,2,...,8) and tool path length d segment , the actual acceleration A during the acceleration phase acc , acceleration J i (i=2,6) and jerk S i ,i=(1,3,5,7) correction, so that the jerk is smooth and continuously bounded, eliminating the speed fluctuations generated at the end of interpolation, 1.21) When d' acc <d segment When the situation is established, there is a duration phase T8 of constant feed rate, and T8 is constrained by integer interpolation cycle to obtain the adjusted duration phase T8' of constant feed rate: Since the tool path displacement d cannot exceed the length d of the velocity planning unit segment , based on the integer interpolation cycle constraint, the maximum speed V max correction, The tool path displacement d is constant, and the adjusted terminal speed v' e Equal to the adjusted maximum speed V' max ; Then, based on the adjusted time T i '(i=1,2,...,8) and the adjusted maximum speed V′ max , the actual acceleration A during the acceleration phase acc , acceleration J i (i=2,6) and jerk S i ,i=(1,3,5,7) correction, make the jerk continuous, eliminate the speed fluctuation generated at the end of interpolation, and adjust the corrected acceleration A' acc , jerk J'2, J'6 and jerk S'1, S'3, S'5, S'7, 1.22) When d' acc ≥d segment When it is established, there will be no constant speed stage, that is, T8 = 0. In order to ensure that the tool path displacement in the acceleration stage does not exceed the displacement generated by the speed planning unit, the acceleration stage time is first adjusted to the integer interpolation cycle time T i '=ceil(T i / T)T(i=1,2...,7), for the maximum speed V max Correction is made to obtain the maximum speed V′ max : At this time, the adjusted terminal velocity v' e Equal to the adjusted maximum speed V' max , Based on the adjusted time T i '(i=1,2,...,7) and the adjusted maximum speed V′ max , the actual acceleration A during the acceleration phase acc , jerk constraint J i (i=2,6) and jerk constraint S i (i=1,3,5,7) to make the jerk continuous, eliminate the speed fluctuation at the end of interpolation, and adjust the corrected acceleration A' acc , the values ​​of jerk constraints J'2, J'6 and jerk constraints S'1, S'3, S'5, S'7 are: 2) The trigonometric function feed speed planning only contains the acceleration and deceleration stages, that is, T8 = 0. 2.1) First, the acceleration time T of the trigonometric function speed planning i (i=1,...,7) and deceleration time T i (i=9,...,15) is corrected to the integer interpolation cycle time, and the adjusted T i '=ceil(T i / T)T,(i=1,...,7),T8=0,T i '=ceil(T i / T)T,(i=9,...,15); 2.2) Based on the tool path displacement and the maximum speed V max , acceleration J i and jerk S i Correct and adjust to make the jerk continuous, eliminate the speed fluctuation at the end of interpolation, and calculate the adjusted maximum speed V' max , acceleration J'2, J'6, J' 10 , J′ 14 and jerk S′1, S′3, S′5, S′7, S′9, S′ 11 , S′ 13 , S′ 15 , and the actual acceleration A' of the adjusted acceleration phase acc and the actual acceleration A' during the deceleration phase dec , eliminate speed fluctuations, Among them, a' and b' are intermediate parameters, a'=v s (2T1'+T′2+T′4 / 2)+v e (2T9'+T′ 10 +T′ 12 / 2), b'=2(T1'+T′9)+(T′2+T′ 10 )+(T′4+T′ 12 ) / 2; 3) The trigonometric function feed speed planning includes acceleration, uniform speed and deceleration stages. 3.1) Set the time parameter T i (i=1,...,15) rounded up to an integer interpolation cycle time T i '=ceil(T i / T)T(i=1,...,15), defines the total displacement d′1 during the acceleration and deceleration phases, d′1=(v s +V max )(2T1'+T′2+T′4 / 2)+(v e +V max )(2T′9+T′ 10 +T′ 12 / 2) (19) 3.2) Based on tool path displacement d segmemnt The constant speed duration stage T8' is corrected, and the maximum speed, jerk and acceleration of the acceleration, uniform speed and deceleration stages are corrected and adjusted to obtain the adjusted maximum speed V' max , acceleration A' acc , A' dec , acceleration J'2, J'6, J' 10 , J′ 14 and jerk S′1, S′3, S′5, S′7, S′9, S′ 11 , S′ 13 , S′ 15 , eliminate the speed fluctuations generated at the end of interpolation, When d′1<d segmemnt When this condition holds true, the corrected constant speed duration phase T8' is: Among them, c' and d' are intermediate parameters. c'=v s (2T1'+T′2+T′4 / 2)+v e (2T′9+T′ 10 +T′ 12 / 2),d'=2T1'+T′2+T′4 / 2+2T′9+T′ 10 +T′ 12 / 2, At this time, the terminal velocity v e The value remains unchanged, the corrected maximum speed V′ max and jerk J'2, J'6, J' 10 , J′ 14 and jerk S′1, S′3, S′5, S′7, S′9, S′ 11 , S′ 13 , S′ 15 for: When d′1≥d segmemnt When the condition is established, the constant speed stage is not included, that is, T8 = 0. At this time, the terminal velocity v e The value remains unchanged, and the maximum speed after adjustment is V′ max , acceleration A' acc , A' dec , acceleration J'2, J'6, J' 10 , J′ 14 and jerk S′1, S′3, S′5, S′7, S′9, S′ 11 , S′ 13 , S′ 15 Corrected to: Where, e' = v s (2T1'+T′2+T′4 / 2)+v e (2T′9+T′ 10 +T′ 12 / 2), f'=2(T1'+T′9)+(T′2+T′ 10 )+(T′4+T′ 12 ) / 2; At this point, the time parameter T of the trigonometric function speed planning has been i Adjusted to an adjusted integer interpolation period T containing an integer number of interpolation periods i ', and the corrected jerk S' is obtained based on the integer interpolation cycle and tool path displacement constraints i , acceleration J′ i , acceleration A′ i and maximum speed V′ max , which are the jerk S, jerk J, acceleration A and speed V actually reached by the machine tool during the machining process, and make the jerk actually reached by the machine tool during the machining process smooth, continuous and bounded, overcoming the speed fluctuation generated at the end of the interpolation cycle, and combining the fourth-order continuous smooth tool path to generate smooth interpolation points for controlling the tool motion, thereby achieving smooth motion of the tool.

2. The method according to claim 1, characterized in that Step 2 of step 3) When the trigonometric function feed speed planning only contains the acceleration and deceleration stages, the maximum speed V′ after adjustment max Less than or equal to the adjusted terminal velocity v' e When the tool path is used, the feed rate, jerk and acceleration allowed by the system during the acceleration phase need to be adjusted based on the tool path displacement. The steps are as follows: Let T′8=T′8+T′9+T′ 10 +T′ 11 +T′ 12 +T′ 13 +T′ 14 +T′ 15 At this time, the tool path length d of the speed planning unit segment It is expressed as: In order to ensure that the tool path length d does not exceed the path length d of the velocity planning unit segment , for the adjusted maximum speed V′ max Adjust again to get the maximum speed V″ after the second adjustment max , and the adjusted terminal velocity v' e Equal to the maximum speed V after secondary adjustment m ” ax , Then, based on the adjusted time T i '(i=1,2,...,7) and the maximum speed V″ after secondary adjustment max For maximum speed V max , acceleration J i and jerk S i Correction adjustment, the actual acceleration of the acceleration phase after adjustment A' acc , jerk J'2, J'6 and jerk S'1, S'3, S'5, S'7, The above is the actual acceleration A' in the adjusted acceleration phase. acc , jerk J'2, J'6 and jerk S'1, S'3, S'5, S'7.

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