The present invention relates to an electronic cam control device and an electronic cam curve generating method for generating, as an electronic cam curve, a relation between the position of a main shaft and a position where a driven shaft should operate according to the position of the main shaft.
An electronic cam control device is a device not mounted with a mechanical cam mechanism and configured to output, based on an electronic cam curve set by software, a position where a driven shaft should operate according to the position of a main shaft. The position of the main shaft is, for example, the position of a servomotor of another shaft or the position of a synchronization encoder provided in a certain rotating shaft.
For example, the electronic cam device is used for a rotary cutter apparatus that drives, while continuously sending web-like paper or film, a rotary cutter in synchronization with a flow of the paper or the film and cuts the paper or the film for each fixed dimension. When the electronic cam control device is applied to the rotary cutter apparatus, the main shaft is the position of a motor for sending the paper or the film and the driven shaft is in a rotating position of the rotary cutter.
Such an electronic cam control device generates, based on a plurality of coordinate data that define a relation between a plurality of main shaft positions and a plurality of driven shaft positions, an electronic cam curve for outputting a driven shaft position corresponding to a main shaft position. A command for a position to which the driven shaft should move is calculated such that the electronic cam curve passes a designated plurality of coordinate data and, when the main shaft position is present between coordinate data, by interpolating the coordinate data using a predetermined method. A method of generating the electronic cam curve by interpolating designated coordinates with straight lines has been used. This method has an advantage that it is possible to intuitively grasp, by approximating the designated coordinates with the straight lines, the behavior between the coordinates of the electronic cam curve. In other words, even when the main shaft position is present between the coordinates, it is possible to grasp, with the electronic cam curve, how the driven shaft position is controlled.
However, when the control is performed using the electronic cam curve obtained by connecting the coordinates using the straight lines, cam velocity obtained by differentiating the position of the electronic cam curve with the driven shaft position takes a fixed value for each of regions among designated coordinates. Therefore, when the main shaft operates at certain velocity, the velocity suddenly changes when the main shaft passes a designated coordinate. As a result, an extremely large shock or vibration occurs in a machine driven by a driven shaft motor. To prevent such occurrence of a shock or a vibration, an electronic cam device disclosed in Patent Literature 1 generates a cam curve for setting acceleration in designated coordinates to 0.
However, in the related art, because the cam curve is generated to set acceleration to 0 at a designated coordinate point, large acceleration occurs depending on a section. In particular, when the main shaft passes a first section or a last section, the driven shaft position moves to decelerate toward the next coordinate point after accelerating. Therefore, there is a problem in that the acceleration of the driven shaft tends to be large.
When maximum torque of a driven shaft servomotor is small or when the inertia of a mechanical load connected to the driven shaft servomotor is large, if the driven shaft servomotor is controlled at large acceleration according to a cam curve, the driven shaft servomotor operates exceeding the maximum torque of the driven shaft servomotor. In such a case, a problem occurs in that the position of the driven shaft servomotor cannot sufficiently follow a position commanded by an electronic cam curve or a problem occurs in that a vibration or a shock occurs in the driven shaft.
The present invention has been devised in view of the above and it is an object of the present invention to obtain an electronic cam control device and an electronic cam curve generating method that that makes it possible to generate an electronic cam curve that passes a designated coordinate and with which the acceleration of a driven shaft during driving is suppressed.
There is provided an electronic cam control device comprising: an input unit configured to receive an input of a plurality of designated coordinates that define a relation between a main shaft position and a driven shaft position; an electronic-cam-curve generating unit configured to generate an electronic cam curve to pass the plurality of designated coordinates, the electronic cam curve representing, as a curve, a relation between the main shaft position and the driven shaft position; and an output unit configured to output the driven shaft position corresponding to the main shaft position as a driven shaft position command to an external device, the driven shaft position command confirming to the electronic cam curve, wherein the electronic-cam-curve generating unit generates the electronic cam curve to include a section where a waveform of cam velocity obtained by differentiating the electronic cam curve with respect to the main shaft position changes to fixed cam velocity in each of regions, which are regions among the designated coordinates, and include a monotonous acceleration or deceleration section that connects sections where the waveform of the cam velocity changes to the fixed cam velocity by accelerating or decelerating while monotonously increasing or monotonously decreasing between adjacent regions.
With the electronic cam control device and the electronic cam curve generating method according to the present invention, there is an effect that it is possible to generate an electronic cam curve that passes a designated coordinate and with which the acceleration of a driven shaft during driving is suppressed.
Electronic cam control devices and electronic cam generating methods according to embodiments of the present invention are explained in detail below based on the drawings. The invention is not limited by the embodiments.
The electronic cam control device 1A is a device that generates an electronic cam curve and controls the servo amplifier 3, the servomotor 5, and the load machine 8 using the generated electronic cam curve. In the electronic cam system, the electronic cam control device 1A controls the servo amplifier 3, whereby the servo amplifier 3 controls the servomotor 5. Consequently, the load machine 8 is controlled.
The electronic cam control device 1A generates the electronic cam curve based on coordinate data information 21 and acceleration or deceleration section information 22, which are input by a user in advance, for defining a positional relation between a main shaft position and a driven shaft position.
The coordinate data information 21 is information including N (N is a natural number) coordinate data (designated coordinates). The acceleration or deceleration section information 22 is information including (N+1) acceleration or deceleration sections (section length data). The acceleration or deceleration sections are information indicating the lengths of sections where cam velocity is changed. In the following explanation, the N coordinate data defining a positional relation between a main shaft position and a driven shaft position are represented as coordinate data (X1, Y2), (X2, Y2), . . . , and (XN, YN). It is assumed that, when the main shaft position is Xi (i is a natural number of 1 to N), the driven shaft position passes Yi. The (N+1) acceleration or deceleration sections are represented as acceleration or deceleration sections t0, t1, . . . , and tN.
The electronic cam curve is a function or a table for associating the main shaft position with the driven shaft position in a one-to-one relation. The electronic cam control device 1A outputs the driven shaft position corresponding to the main shaft position as a driven shaft position command 2 according to the electronic cam curve (a waveform corresponding to the function or the table). The main shaft position is, for example, the position of an encoder attached to a servomotor other than the servomotor 5 or a position of an encoder attached to a machine.
The electronic cam control device 1A calculates the driven shaft position from the main shaft position using the generated electronic cam curve and generates the driven shaft position command 2 using the derived driven shaft position. The electronic cam control device 1A is connected to the servo amplifier 3 to output the driven shaft position command 2 to the servo amplifier 3.
The servo amplifier 3 is connected to the servomotor 5 that functions as a driven shaft. The encoder 6 is attached to the servomotor 5. The servo amplifier 3 outputs an electric current 4 for controlling the servomotor 5, which functions as the driven shaft, to the servomotor 5 based on the driven shaft position command 2 output by the electronic cam control device 1A. Specifically, the servo amplifier 3 outputs the electric current 4 by performing feedback control to cause a position 7 of the servomotor 5 output by the encoder 6 to follow the driven shaft position command 2. The load machine 8 is connected to the servomotor 5, which functions as the driven shaft, and driven by the servomotor 5.
The information input unit 11 receives an input of the coordinate data information 21 and the acceleration or deceleration section information 22 and sends the information to the electronic-cam-curve generating unit 12. The electronic-cam-curve generating unit 12 generates an electronic cam curve using the coordinate data information 21 and the acceleration or deceleration section information 22.
The electronic-cam-curve storing unit 13 is a memory or the like that stores the electronic cam curve generated by the electronic-cam-curve generating unit 12. The main-shaft-position input unit 14 receives an input of a main shaft position sent from an external device (an encoder, etc.) and sends the main shaft position to the driven-shaft-position-command generating unit 15. The driven-shaft-position-command generating unit 15 generates, based on the electronic cam curve, the driven shaft position command 2 from the main shaft position. The output unit 16 outputs the driven shaft position command 2 generated by the driven-shaft-position-command generating unit 15 to the servo amplifier 3.
The coordinate data information 21 is information concerning a plurality of designated coordinates for defining a relation between a main shaft position and a driven shaft position. Specifically, the coordinate data information 21 is N coordinate data (X1, Y1), (X2, Y2), . . . , and (XN, YN) for defining positions Yi where the driven shaft should pass when the main shaft passes positions Xi. It is assumed that there is a relation X1<X2<X3< . . . <XN among the main shaft positions X1 to XN. Reference coordinate data is represented as coordinate data (X0, Y0)=(0, 0).
The acceleration or deceleration section information 22 is information representing section length required until cam velocity obtained by differentiating the position of the electronic cam curve with the driven shaft position reaches fixed velocity and is (N+1) acceleration or deceleration sections t0, t1, . . . , and tN. It is assumed that there are limitations explained below (Formulas (1) to (3)) concerning acceleration or deceleration sections ti. In this way, the N coordinate data and the (N+1) acceleration or deceleration sections are input to the information input unit 11 of the electronic cam control device 1A (step ST1).
t
0
+t
1/2≦X1 (1)
t
2/2+ti−1/2≦Xi−Xi−1 (2)
t
N−1/2+tN≦XN−XN−1 (3)
The information input unit 11 inputs the coordinate data information 21 and the acceleration or deceleration section information 22 to the electronic-cam-curve generating unit 12. The electronic-cam-curve generating unit 12 calculates constants αi and ⊖i defined using the coordinate data information 21 and the acceleration or deceleration section information 22 (step ST2). The constants αi and βi are represented by Formulas (4) and (5) below. In Formulas (4) and (5), 0≦i≦N.
αi=⅛·ti (4)
βi=⅜·ti (5)
The electronic-cam-curve generating unit 12 forms, based on the coordinate data information 21, the acceleration or deceleration section information 22, and the calculated constants αi and βi, Formula (6) below as simultaneous linear equations with N unknown variables in which variables are cam velocities Vi (i=1, 2, . . . , and N) of coordinate sections (step ST3).
A coefficient matrix in the formula is a tridiagonal matrix. Coefficients of the coefficient matrix are defined as shown below from coordinate data information, acceleration or deceleration sections, and the calculated constants αi and βi.
C(1,1)=X1−t0/2−α1
C(1,2)=α1
C(N,N−1)=−βN−1+tN−1/2
C(N,N)=βN−1+XN−XN−1−(tN+tN−1)/2
when 2N−1,
C(i,i−1)=−βα−1+ti−1/2
C(i,i)=βi−1−αj+Xi−Xi−1−ti−1/2
C(i,i+1)=αi
The electronic-cam-curve generating unit 12 solves the simultaneous linear equations with N unknown variables of Formula (6), in which the cam velocities Vi (i=1, 2, . . . , and N) are unknown numbers, to thereby calculate the cam velocities Vi (i=1, 2, . . . , and N) (step ST4). The electronic-cam-curve generating unit 12 calculates an electronic cam curve using the calculated cam velocities Vi (step ST5). Specifically, the electronic-cam-curve generating unit 12 calculates, as the electronic cam curve, a driven shaft position Y(X) corresponding to a main shaft position (X) represented by Formulas (7-1) to (7-9) below. The electronic-cam-curve generating unit 12 causes the electronic-cam-curve storing unit 13 to store the calculated electronic cam curve.
With respect to 2≦i≦N−1
Effects of this embodiment are explained.
In a graph shown on the upper side of
When the main shaft position increases at a fixed rate, the velocity of the servomotor 5 (the driven shaft) is a value proportional to the cam velocity. The servomotor 5 operates according to the waveform of the cam velocity. When the electronic cam curve according to this embodiment is formed, the cam velocity changes to fixed cam velocities Vi for each of regions i, which are regions among designated coordinates. The cam velocity is accelerated or decelerated to cam velocities Vi+1 and Vi−1 adjacent to the cam velocities Vi while monotonously increasing or monotonously decreasing. In this way, the cam velocity in this embodiment has the waveform formed by straight lines.
Consequently, coordinate sections assuming straight lines that linearly monotonously increase or monotonously decrease are acceleration or deceleration sections ti (i=0, 1, . . . , and N) input to the information input unit 11. The designated coordinates pass coordinates right in middle points of the acceleration or deceleration sections. The limitations of Formulas (1) to (3) are applied to the acceleration or deceleration sections ti to prevent the sections assuming the fixed cam velocities Vi from having negative velocity. When the main shaft position is 0 and XN (a first designated coordinate and a last designated coordinate), the cam velocity is 0 in the designated positions.
Effects explained below are obtained by using the electronic curve in which the waveform of the cam velocity is such a shape (pattern). Because the cam velocity is continuous, even when the main shaft operates at fixed velocity, the velocity of the driven shaft does not suddenly change at designated coordinate points. Therefore, a sudden velocity change does not occur in the servomotor 5, which is a driven shaft motor), either. There is an effect that, even if the driven shaft operates according to the electronic cam curve, a shock less easily occurs.
When the main shaft moves from a certain coordinate (Xi, Yi) to another coordinate (Xi+1, Yi+1) while operating at the fixed velocity, the driven shaft assumes the cam velocity Vi for each of the regions i among the designated coordinates and moves such that the cam velocity Vi changes to another cam velocity Vi+1 while monotonously increasing or monotonously decreasing between the regions i. Therefore, a useless acceleration or deceleration action does not occur in the movement among the designated coordinates. As a result, there is an effect that it is possible to reduce the torque of the servomotor 5, which is the driven shaft motor, during driving.
In the electronic cam curve in the past, because only coordinate data is simply input, the electronic cam curve is uniquely determined. Therefore, depending on coordinate data and the velocity in the main shaft position, when the driven shaft is driven according to the electronic cam curve, the torque of the driven shaft sometimes exceeds the maximum torque. In this embodiment, the electronic-cam-curve generating unit 12 uses, besides the coordinate data, the acceleration or deceleration sections ti in which the magnitude of the torque of the driven shaft can be changed. Therefore, the acceleration or deceleration of the servomotor 5 is changed to gentle motion by increasing the acceleration or deceleration sections ti. Therefore, there is an effect that it is possible to prevent the torque of the servomotor 5, which is the driven shaft motor, from exceeding the maximum torque during driving.
There are a large number of methods of interpolating a plurality of coordinate data to form a curve. In the methods, it is guaranteed that the curve passes designated coordinates. However, when the main shaft position takes a value between the coordinate data, it is difficult to grasp what kind of a value the driven shaft position takes. According to this embodiment, the cam velocity has a characteristic that the cam velocity is formed by the fixed velocity and the straight lines on which the cam velocity monotonously increases (monotonous acceleration or deceleration sections). Therefore, the electronic cam curve assumes a waveform close to a curve obtained by connecting the coordinate data using the straight lines. Therefore, there is an effect that, even when the main shaft position is the position between the designated coordinates, it is easy to intuitively understand an output driven shaft position according to the electronic cam curve.
When the main shaft position is in a range of 0≦X≦XN, the electronic cam curve is calculated using Formulas (7-1) to (7-9). However, with respect to the main shaft position in a range of XN≦X≦2XN, the driven shaft position is calculated according to values obtained by substituting X-XN in X of Formulas (7-1) to (7-9). In other words, when the main shaft position X exceeds XN, the electronic-cam-curve generating unit 12 applies Formula (7-1) to (7-9) using, as the main shaft position, the remainder left by dividing the main shaft position X by one cycle length XN and calculates the driven shaft position.
Even when the electronic cam control device 1A performs the operation explained above (the operation in which the main shaft position exceeds the main shaft position XN of the last coordinate), according to this embodiment, as shown in
The electronic cam curve having the waveform of the cam velocity shown in
First, as shown in
u={(V−v)·X/T}+v
The cam velocity is velocity obtained by differentiating a position command for the driven shaft with respect to the main shaft position. Therefore, the driven shaft position is obtained by integrating the cam velocity with respect to the main shaft position. Specifically, a driven shaft position y(X) can be represented by a formula below using the main shaft position X (0≦X≦T).
y(X)={(V−v)·X2/2T}+vX+D
where, D is the driven shaft position in the main shaft position 0.
An amount the driven shaft position moves while the main shaft position shifts from 0 to T/2 (an amount of movement A1) can be calculated by y(T/2)−y(0) as indicated by Formula (8) below. In Formula (8), α is α=(⅛)T.
A1=(V−v)·α+v·T/2 (8)
An amount the driven shaft position moves while the main shaft position moves from T/2 to T (an amount of movement A2) can be calculated by y(T)−y(T/2) as indicated by Formula (9) below. In Formula (9), β is β=(⅜)T.
A2=(V−v)·β+v·T/2 (9)
Further, an amount the driven shaft position moves while the main shaft position moves from 0 to T (an amount of movement A3) can be calculated by α+β as indicated by Formula (10) below.
Conditions that need to be satisfied between an amount of movement of the main shaft and an amount of movement of the driven shaft to obtain the electronic cam curve according to this embodiment are explained.
The cam velocity in this embodiment is formed by fixed cam velocities V1, . . . , and VN (N=5) and monotonous acceleration or deceleration that linearly accelerates or decelerates while monotonously increasing or monotonously decreasing with respect to fixed cam velocities of adjacent regions. In other words, the electronic cam curve is generated such that a waveform of the cam velocity has a section where the cam velocity is the fixed cam velocity for each of regions, which are regions among designated coordinates, and has a monotonous acceleration or deceleration section that connects sections, where the cam velocity is the fixed cam velocity, by accelerating or decelerating while monotonously increasing or monotonously decreasing between adjacent regions.
In this case, it is considered what kinds of conditions the fixed cam velocities V1, . . . , and VN of the cam velocity need to satisfy to pass designated coordinates (Xi, Yi) (i=1, 2, . . . , and N) right in the middles of the acceleration or deceleration sections ti.
An amount the driven shaft moves while the main shaft position moves from 0 to X1 can be represented by a sum of amounts of movement A11 to A13 described below.
The amount of movement A11 of the driven shaft that moves when the main shaft position moves from 0 to t0 (equivalent to (a) in
The amount of movement A12 of the driven shaft that moves when the main shaft moves from t0 to X1−t1/2 (equivalent to (b) in
The amount of movement A13 of the driven shaft that moves when the main shaft position moves from Xl−t1/2 to X1 (equivalent to (c) in
The amounts of movement A11, A12, and A13 of (a), (b), and (c) in
A12=V1(X1−t0−t1/2)
A13=α1(V2−V1)+V1t1/2
In the above, α1 is a value obtained by substituting t=t1 in α of Formula (8). α1 conforms to the definition of Formula (4). In the following explanation, it is assumed that α1 and β1 represent values obtained by substituting t=t1 in α and β of Formulas (8) and (9). α1 and β1 conform to the definition of Formulas (4) and (5). A total of (a), (b), and (c) (an amount of movement A14) can be represented by Formula (11) below.
A14=(X1−t0/2−α1)V1+α1V2 (11)
To set an amount of movement of the driven shaft position to Y1 when the driven shaft position passes the coordinate (X1, Y1) (when the main shaft position moves from 0 to X1), the amount of movement A14 of Formula (11) needs to be equal to Y1. This is equal to an expression of a first row of Formula (6).
Similarly, an amount the driven shaft moves while the main shaft position moves from X1 to X2 can be represented by a total of amounts of movement A21 to A23 described below.
The amount of movement A21 of the driven shaft that moves when the main shaft position moves from X1 to X1+t1/2 (equivalent to (d) in
The amount of movement A22 of the driven shaft that moves when the main shaft position moves from X1+t1/2 to X2−t2/2 (equivalent to (e) in
The amount of movement A23 of the driven shaft that moves when the main shaft position moves from X2−t2/2 to X2 (equivalent to (f) in
The amounts of movement A21, A22, and A23 of (d), (e), and (f) in
A21=β1(V2−V1)+V1t1/2
A22=V2{X2−X1−(t1/2)−(t2/2)}
A23=β2(V2−V2)+V2t2/2
A total of (d), (e), and (f) (an amount of movement A24) can be represented by Formula (12) below.
A24=(−β1+t1/2)V1+(β1+X2−X1−t1/2−α2)V2+α2V3 (12)
To set the driven shaft position to Y2 when the driven shaft position passes the coordinate (X2, Y2) (when the main shaft position moves from X1 to X2), the amount of movement A24 of Formula (12) needs to be equal to Y2−Y1. This is equal to an expression of a second row of Formula (6).
Similarly, concerning i of 2≦i≦N−1, an amount of movement of the driven shaft position is Y1−Yi−1 when the driven shaft position passes the coordinate (Xi, Yi) (when the main shaft position moves from Xi−1 to Xi). Therefore, a relation shown below needs to be satisfied.
(−βi−1+ti−1/2)Vi−1+(βi−1+Xi−Xi−1−ti−1/2−αi)Vi+αiVi+1=Yi−Yi−1
These are equal to an ith row (2≦i≦N−1) of Formula (6).
Further, an amount the driven shaft moves while the main shaft position moves from XN−1 to XN can be represented by a total of amounts of movement An1 to An3 described below.
The amount of movement An1 of the driven shaft that moves when the main shaft position moves from XN−1 to tN−1/2 (equivalent to (g) in
The amount of movement An2 of the driven shaft that moves when the main shaft position moves from XN−1+tN−1/2 to XN−tN (equivalent to (h) in
The amount of movement An3 of the driven shaft that moves when the main shaft position moves from XN−tN to XN (equivalent to (i) in
The amounts of movement An1, An2, and An3 of (g), (h), and (i) in
An1=βN−1(VN−VN−1)+VN−1tN−1/2
An2=VN(XN−tN−tN−1/2)
An3=(½)VNtN
A total of (g), (h), and (i) (an amount of movement An4) can be represented by Formula (13) below.
An4=(−βN−1+tN−1/2)VN−1+(βN1+XN−XN−1−tN−1/2−tN/2)VN (13)
To set an amount of movement of the driven shaft position to YN-YN−1 when the driven shaft position passes the coordinate (XN, YN) (when the main shaft position moves from XN−1 to XN), An4 of Formula (13) needs to be equal to YN YN−1. This is represented by an Nth row of Formula (6).
Consequently, to pass all the designated coordinates (Xi, Yi) (i=1, 2, . . . , and N), the fixed cam velocities Vi need to satisfy Formula (6). By solving Formula (6), when the fixed cam velocities V1, . . . , and VN are determined, a waveform of cam velocity that linearly connects the predetermined cam velocities Vi, the cam velocities adjacent to the cam velocities Vi on one side, and the cam velocities Vi+1 adjacent to the cam velocities Vi on the other side are sectionally determined. Therefore, an expression of cam velocity for the main shaft position X can be represented using the fixed cam velocities Vi, the designated coordinate data (Xi, Yi) (i=1, 2, . . . , and N), and the acceleration or deceleration sections ti (i=0, 1, . . . , and N). Further, a relational expression (an electronic cam curve) with the driven shaft position with respect to an arbitrary main shaft position X can be calculated using Formulas (7-1) to (7-9) by integrating the cam velocity with respect to the main shaft position X.
In the example explained in this embodiment, the electronic cam curve is formed to pass the designated coordinate right in the middle point between the acceleration or deceleration sections. However, the electronic cam curve can be formed such that the designated coordinate (the cam velocity) passes an arbitrary halfway point (middle point) between the acceleration or deceleration sections. In this case, as in the embodiment, effects same as the effects explained above can be obtained.
As explained above, according to the first embodiment, the electronic cam curve is generated such that the cam curve is formed by the fixed velocity, the monotonous acceleration or deceleration that linearly accelerates or decelerates while monotonously increasing or monotonously decreasing with respect to the adjacent fixed velocity. Therefore, it is possible to suppress the acceleration of the driven shaft during driving while causing the driven shaft to pass a designated coordinate.
A second embodiment of the present invention is explained with reference to
The electronic cam system according to this embodiment includes an electronic cam control device 1B instead of the electronic cam control device 1A. Like the electronic cam control device 1A, the electronic cam control device 1B includes the information input unit 11, the electronic-cam-curve generating unit 12, the electronic-cam-curve storing unit 13, the main-shaft-position input unit 14, the driven-shaft-position-command generating unit 15, and the output unit 16.
The coordinate data information 21 and one parameter R are input to the information input unit 11 in this embodiment. The electronic-cam-curve generating unit 12 in this embodiment generates an electronic cam curve using the coordinate data information 21 and the one parameter R. The parameter R in this embodiment is a parameter for adjusting the magnitude of cam acceleration explained below.
The electronic-cam-curve generating unit 12 calculates cam velocities Vi′ (i=1, 2, . . . , and N) obtained when the N coordinate data input as designated coordinates are connected by only straight lines (step ST11). Specifically, the electronic-cam-curve generating unit 12 connects the N coordinate data using only the straight lines and calculates the cam velocities Vi′ based on the coordinate data connected by the straight lines. At this point, the electronic-cam-curve generating unit 12 calculates the cam velocities Vi′ using Formula (14) below. It is assumed that X0=0 and Y0=0.
The electronic-cam-curve generating unit 12 calculates (N+1) acceleration or deceleration sections ti using the parameter R, the N coordinate data, and the cam velocities Vi′ (step ST12). Specifically, the electronic-cam-curve generating unit 12 calculates a variable G shown below using the calculated cam velocities Vi′ and the coordinate data. The electronic-cam-curve generating unit 12 calculates the variable G using Formula (15) shown below. It is assumed that min[A1, A2, . . . , and AN] represents a function that takes a smallest value among A1, A2, . . . , and AN.
Further, the electronic-cam-curve generating unit 12 calculates acceleration or deceleration sections as indicated by Formula (16) below using the calculated variable G.
t
0
=R×G×|V
1′|
t
i
=R×G×|V
i
′−V
i−1′|2≦i ≦N
t
N
=R×G×|V
N′| (16)
Formula (16) is equivalent to setting the acceleration or deceleration sections to be proportional to absolute values of differences between the cam velocities Vi′ and cam velocities Vi−1′ of adjacent regions obtained when the designated coordinates are connected by the straight lines. Concerning t0 and tN, Formula (16) is equivalent to setting t0 and tN regarding adjacent cam velocities as 0. In other words, concerning t0 and tN, Formula (16) is equivalent to setting the acceleration or deceleration sections to be proportional to a difference value of a main shaft position between the designated coordinates.
Thereafter, the electronic-cam-curve generating unit 12 performs processing at steps ST13 to ST16. The processing at steps ST13 to ST16 is processing same as the processing at steps ST2 to ST5 explained with reference to
Effects of this embodiment are explained. The first embodiment and this embodiment are different only in whether the acceleration or deceleration sections are directly input or only the parameter R is input and the acceleration or deceleration sections are calculated from the parameter R. Therefore, this embodiment has effects same as the effects of the first embodiment. Effects not obtained in the first embodiment and obtained in the second embodiment are explained.
The cam velocity differentiated with respect to the main shaft position is referred to as cam acceleration. The cam acceleration is equivalent to a value obtained by multiplying the acceleration of a driven shaft with a constant when the main shaft position increase at a fixed rate. The cam acceleration is a factor for determining in which degree the acceleration of the driven shaft motor is.
In the first embodiment, the magnitude of the cam acceleration can be adjusted by changing the sizes of the acceleration or deceleration sections ti. If the acceleration or deceleration sections ti are increased in size, when a main shaft passes the acceleration or deceleration sections ti, the acceleration of the driven shaft decreases. According to the decrease in the acceleration, the torque of the driven shaft motor also decreases.
In this embodiment, acceleration or deceleration sections for generally uniformalizing cam accelerations can be automatically calculated from the one parameter R. Further, the magnitudes of the cam accelerations can be adjusted by adjusting the magnitude of the parameter R. Specifically, the cam accelerations can be reduced by increasing the parameter R. Consequently, there is an effect that, when the driven shaft motor is driven according to the electronic cam curve, it is possible to easily prevent the driven shaft motor from being driven exceeding maximum torque.
An electronic cam curve for uniformalizing the cam accelerations irrespective of acceleration or deceleration sections can be generated by the calculation at steps ST10 and ST11 explained in the flowchart of
In the first embodiment, as explained with reference to
From the definition of the cam acceleration, absolute values of cam accelerations in the acceleration or deceleration sections are calculated by a value obtained by dividing an absolute value of a difference between adjacent velocities by the acceleration or deceleration sections. Therefore, in a cam curve in which cam accelerations are equal in the acceleration or deceleration sections (absolute values of the cam accelerations at this point are represented as “a”), Formula (17) shown below holds.
When Formula (17) is used, the acceleration or deceleration sections ti (i=1, 2, . . . , N) can be represented by Formula (18) using “a” and Vi (i=1, . . . , and N).
When Formula (18) is substituted in Formulas (1), (2), and (3) representing the limitations on the coordinate data and the acceleration or deceleration sections, Formula (19) shown below can be obtained. Therefore, inverses of the cam accelerations need to satisfy all limitations indicated by Formula (20) below.
Because Vi and Vi′ can be regarded as substantially equal as explained above, when Vi=Vi′ is substituted in Formula (20), Formula (21) below can be obtained.
Right sides of Formula (21) respectively correspond to arguments of the function min of Formula (15). Therefore, G is a value for uniformalizing absolute values of the cam accelerations in the acceleration or deceleration sections and can be regarded as an upper limit of the inverses of the cam accelerations that can be set. RxG obtained by multiplying the upper limit with the parameter R (0<R<1) is also a value for uniformalizing the absolute values of the cam accelerations and can be the inverses of the absolute values of the cam accelerations. A formula obtained by substituting Vi=Vi′ in Formula (18) and substituting 1/a=R×G as the inverses of the absolute values of the can accelerations is Formula (16).
For example, when R is increased, the acceleration or deceleration section increases from Formula (16). Therefore, the cam acceleration and the acceleration of the driven shaft motor decrease. The driving torque decreases according to the decrease in the cam acceleration and the acceleration of the driven shaft motor. On the other hand, when R is reduced, the acceleration or deceleration section decreases. Therefore, the cam acceleration and the acceleration of the driven shaft motor increase. The driving torque increases according to the increase in the cam acceleration and the acceleration of the driven shaft motor.
As explained above, according to the second embodiment, it is possible to automatically calculate acceleration or deceleration sections for generally uniformalizing cam accelerations from one parameter R. It is possible to adjust the magnitudes of the cam accelerations by adjusting the magnitude of the parameter R. Therefore, when the driven shaft motor is driven according to the electronic cam curve, it is possible to easily prevent the driven shaft motor from being driven exceeding the maximum torque.
A third embodiment of the present invention is explained with reference to
The electronic cam system according to this embodiment includes an electronic cam control device 1C instead of the electronic cam control device 1A. Like the electronic cam control device 1A, the electronic cam control device 1C includes the information input unit 11, the electronic-cam-curve generating unit 12, the electronic-cam-curve storing unit 13, the main-shaft-position input unit 14, the driven-shaft-position-command generating unit 15, and the output unit 16.
The coordinate data information 21, the acceleration or deceleration section information 22, and S-shape section information 24 are input to the information input unit 11 in this embodiment. The electronic-cam-curve generating unit 12 in this embodiment generates an electronic cam curve using the coordinate data information 21, the acceleration or deceleration section information 22, and the S-shape section information 24. The S-shape section information 24 is information indicating a section where cam velocity draws an S curve. The S-shape section information 24 includes information indicating (N+1) S-shape sections.
(N+1) acceleration or deceleration sections t0, t1, t2, . . . , and tN representing section lengths required until cam velocity reaches fixed velocity are input as acceleration or deceleration section information 22. Further, (N+1) S-shape sections d0, d1, d2, . . . , and dN representing sections for smoothing acceleration and deceleration during the start and during the end in the acceleration or deceleration sections are input as the S-shape section information 24. It is assumed that a limitation of 0≦diti/2 is applied to S-shape sections di (i=0, . . . , and N).
The electronic-cam-curve generating unit 12 calculates αi and βi according to Formulas (22) and (23) below using the acceleration or deceleration sections ti and the S-shape sections di (step ST21).
Thereafter, the electronic-cam-curve generating unit 12 performs processing at steps ST22 and ST23. The processing at steps ST22 and ST23 is processing similar to the processing at step ST3 and ST4 explained with reference to
Specifically, the electronic-cam-curve generating unit 12 forms, based on the coordinate data information 21, the acceleration or deceleration section information 22, and the constants αi and βi, simultaneous linear equations with N unknown variables of Formula (6) in which variables are the cam velocities Vi (i=1, 2, . . . , and N) of coordinate sections (step ST22).
As explained in the first embodiment, Formula (6) represents an equation for defining that, with respect to the input coordinates (Xi, Yi) (i=1, 2, . . . , and N) and acceleration or deceleration sections ti (i=0, 1, . . . , and N), designated coordinates pass coordinates (Xi, Yi) (i=1, 2, . . . , and N−1) right in middle points of the acceleration or deceleration sections ti and pass (XN, YN) at the end point of the acceleration or deceleration section tN.
After forming the equation of Formula (6), the electronic-cam-curve generating unit 12 solves the simultaneous linear equations with N unknown variables of Formula (6) to thereby calculate the cam velocities Vi (i=1, 2, . . . , and N) (step ST23).
The electronic-cam-curve generating unit 12 calculates, based on the calculated cam velocities Vi, a driven shaft position Y(X) corresponding to a main shaft position X (step ST24) according to Formulas (24-1) to (24-16) below (step ST24).
With respect to 2≦i≦n,
Effects of this embodiment are explained.
In a graph shown on the upper side of
The can velocity in this embodiment includes the fixed cam velocities Vi, monotonous acceleration or deceleration that monotonously increases or monotonously decreases with respect to adjacent fixed cam velocities, and S-shape change velocity for performing acceleration or deceleration to draw an S curve with respect to an increase in the main shaft position. In other words, the waveform of the cam velocity includes, for each of regions, which are regions among designated coordinates, a section of a fixed cam velocity, a monotonous acceleration or deceleration section, and the S-shape change velocity. The monotonous acceleration or deceleration section is arranged between sections where the cam velocity accelerates or decelerates while monotonously increasing or monotonously decreasing and is the fixed cam velocity between adjacent regions. The S-shape change velocity accelerates or decelerates to draw an S curve with respect to an increase in the main shaft position. The S-shape change velocity is arranged to connect the section of the fixed cam velocity and the monotonous acceleration or deceleration section.
The electronic cam curve is generated such that the lengths of acceleration or deceleration sections are ti (i=1, 2, . . . , and N) and to pass designated coordinates (Xi, Yi) (i=1, 2, . . . , and N−1) in the middles of the sections and pass (XN, YN) at the end of acceleration.
In the electronic cam curve according to this embodiment, the S-shape sections di are provided at the starts and the ends of the acceleration or deceleration sections ti (ends of the sections). In the S-shape sections, acceleration and deceleration is gentle. The waveform of the cam acceleration in the first and second embodiment in which there is no S-shape section is rectangular. On the other hand, in this embodiment, because the S-shape sections are provided in the cam velocity, the waveform of the cam acceleration of the electronic cam curve is a trapezoidal waveform between the acceleration or deceleration sections.
In this embodiment, the fixed cam velocities Vi and Vi+1 are connected to monotonously increase or monotonously decrease in an S shape. Therefore, this embodiment has effects similar to the effects of the first embodiment. In this embodiment, the cam velocity is accelerated and decorated such that the waveform of the cam velocity draws an S curve rather than a straight line. Therefore, there is an effect that acceleration and torque required for driving are smoothed and a shock of a machine driven by the driven shaft motor is further reduced.
Formulas (24-1) to (24-16) used in this embodiment are derived by a procedure similar to the procedure in the first embodiment. Specifically, a formula representing overall cam velocity is calculated from input coordinate data, the acceleration or deceleration sections, the S-shape sections, and the fixed cam velocities Vi calculated from Formula (6). The electronic cam curve is obtained by integrating once the formula representing the overall cam velocity.
In the example explained in this embodiment, the acceleration or deceleration sections ti are directly input. However, as explained in the second embodiment, it is also possible to input the parameter R and automatically determine acceleration or deceleration sections using the parameter R. In this case, the S-shape sections di can be set at a ratio corresponding to the sizes of the acceleration or deceleration sections ti. In other words, it is also possible to input a parameter r (0≦r≦1), which is information for designating S-shape sections, and set the S-shape sections as di=r/2×ti (i=1, 2, . . . , and N). Consequently, it is possible to automatically calculate acceleration or deceleration sections for generally uniformalizing cam velocity and obtain a cam curve in which the cam velocity is smooth.
As explained above, according to the third embodiment, the cam velocity is accelerated or decelerated such that the waveform of the cam velocity draws the S curve at the ends of the acceleration or deceleration sections. Therefore, acceleration and torque required for driving are smoothed. It is possible to reduce a shock of a machine driven by the driven shaft motor.
A fourth embodiment of the present invention is explained with reference to
The electronic-cam-curve generating unit 12 generates electronic cam curves with respect to the divided coordinate data. At this point, with respect to a region where the driven shaft positions of the adjacent designated coordinates are the same, the electronic-cam-curve generating unit 12 generates electronic cam curves in which the driven shaft positions are the same value. Further, the electronic-cam-curve generating unit 12 generates an electronic cam curve with respect to all the coordinate data by connecting the generated electronic cam curves. Consequently, the electronic cam system according to the fourth embodiment generates an electronic cam curve in which the driven shaft position can be stopped.
The electronic cam system according to this embodiment has components similar to the components of the electronic cam systems according to the first to third embodiments. Therefore, explanation of the components is omitted. In the following explanation, a generation processing procedure in which the electronic cam control device 1A generates an electronic cam curve according to this embodiment is explained.
The parameter R explained in the second embodiment can be input instead of the (N+1) acceleration or deceleration section information 22. The (N+1) S-shape section information 24 explained in the third embodiment can be input in addition to the coordinate data information 21 and the acceleration or deceleration section information 22. The parameter r for determining S-shape sections can be input as S-shape section information.
The electronic-cam-curve generating unit 12 performs initialization of a variable k and a variable i necessary for calculation processing. Specifically, the electronic-cam-curve generating unit 12 sets the variable k to 0 and sets the variable i to 1 (step ST31).
The electronic-cam-curve generating unit 12 checks whether coordinate data Yi representing a driven shaft position is equal to adjacent coordinate data Yi−1. In other words, the electronic-cam-curve generating unit 12 determines whether Yi=Yi−1 holds (step ST32). If adjacent driven shaft positions of the input coordinate data are equal (Yes at step ST32), the electronic-cam-curve generating unit 12 calculates an electronic cam curve w(X), which is a part of the electronic cam curve (step ST33). A driven shaft position corresponding to the main shaft position X is represented by w(X).
Specifically, the electronic-cam-curve generating unit 12 calculates the electronic cam curve w(X) using coordinate data (Xk+1−Xk, Yk+1−Yk), (Xk+2−Xk, Yk+2−Yk), . . . , and (Xi−1−Xk, Yi−1−Yk) and acceleration or deceleration sections tk, tk+1, . . . , and ti−1 such that the electronic cam curve w(X) passes the coordinate data (Xk+1−Xk, Yk+1−Yk), (Xk+2−Xk, Yk+2−Yk), . . . , and (Xi−1−Xk, Yi−1−Yk). At this point, the electronic-cam-curve generating unit 12 calculates the electronic cam curve w(X) according to the processing at steps ST2 to ST5 and the like explained in the first embodiment.
In this embodiment, the electronic-cam-curve generating unit 12 calculates the electronic cam curve w(X) using data obtained by subtracting (Xk, Yk) respectively from the coordinate data (Xk, Yk) to (Xi−1, Yi−1). This is equivalent to calculating the electronic cam curve with reference to the coordinate data (Xk, Yk), in which adjacent driven shaft positions are equal, in this embodiment, whereas the electronic cam curve is calculated with reference to (0, 0) in the first to third embodiments. Because the electronic cam curve w(X) passes (Xi−1−Xk, Yi−1−Yk), Formula (25) below holds.
w(Xi−1−Xk)=Yi−1−Yk (25)
The electronic-cam-curve generating unit 12 calculates, according to Formula (26) below, a portion corresponding to a main shaft position Xk≦X≦Xi in the electronic cam curve Y(X) that passes N coordinate data (step ST34).
X
k
≦X≦X
i−1
y(X)=w(X−Xk)+Yk
X
i−1
<X≦X
i
y(X)=Yi (26)
The electronic-cam-curve generating unit 12 calculates the electronic cam curve by adding the reference coordinate data (Xk, Yk) subtracted at step ST33 to the electronic cam curve w(X).
Thereafter, the electronic-cam-curve generating unit 12 substitutes i in the variable k (step ST35). The electronic-cam-curve generating unit 12 increases the variable i by +1 (i=i+1) (step ST36).
On the other hand, if Yi=Yi−1 does not hold (No at step ST32), the electronic-cam-curve generating unit 12 increases the variable i by +1 (i=i+1) without calculating the electronic cam curve w(X) (step ST36).
After increasing the variable i by +1 (i=i+1), the electronic-cam-curve generating unit 12 determines whether the variable i is equal to N (step ST37). If the variable i is not equal to N (if i<N) (No at step ST37), the electronic-cam-curve generating unit 12 executes the processing at steps ST32 to ST36 again.
On the other hand, if the variable i is equal to N (Yes at step ST37), the electronic-cam-curve generating unit 12 determines whether the variable k is equal to 0 (step ST38). When k=0 holds, this represents that coordinates of adjacent driven shaft positions are not equal at all in the processing at step ST32. When k=0 hold (Yes at step ST38), the electronic-cam-curve generating unit 12 generates an overall electronic cam curve from all the coordinate data (X1, Y1), . . . , and (XN, YN) (step ST39). Specifically, the electronic-cam-curve generating unit 12 generates the overall electronic cam curve as explained in the first to third embodiments.
On the other hand, when k=0 does not hold (No at step ST38), the electronic-cam-curve generating unit 12 shifts to step ST40. At step ST40, the electronic-cam-curve generating unit 12 generates the electronic cam curve w(X) with respect to the main shaft position 0≦X≦XN−YN from (Xk+1−Xk, Yk+1−Yk), (Xk+2−Xk, Yk+2−Yk), . . . , and (XN−Xk, YN−Yk).
Thereafter, at step ST41, the electronic-cam-curve generating unit 12 forms an electronic cam curve with respect to Xk≦X≦KN as y=w(X−Xk)+Yk using the electronic cam curve calculated at step ST39. The processing for generating the electronic cam curve ends.
Effects of this embodiment are explained.
In
In other words, data in which driven shaft positions of adjacent designated coordinates are equal is input, whereby it is possible to obtain an electronic cam curve in which the driven shaft position can be stopped when the main shaft position is present between designated coordinates (in
As explained above, according to the fourth embodiment, in addition to the effects of the first to third embodiments, when the coordinate data Yi, Yi−1 representing the driven shaft position are equal, the coordinate data are divided before and after the coordinate data and the electronic cam curves are generated with respect to the divided coordinate data and combined. Therefore, it is possible to obtain an electronic cam curve in which the driven shaft position can be stopped.
Effects of the electronic cam curve having such characteristics are typically displayed in an application example explained below. It is conceivable to apply the electronic cam control to a liquid filling machine including a driving shaft that moves a conveying unit to thereby convey bottles arranged at a fixed interval to right under a nozzle and a driving shaft that drives an action for pushing down the nozzle to the bottle placed right under the nozzle and pushing up the nozzle after liquid is injected into the bottle, the liquid filling machine injecting the liquid into a large number of bottles in order using one nozzle.
The action of the driving shaft for controlling the up down movement of the nozzle needs to be synchronized with the action of the driving shaft for controlling the conveying unit. Therefore, the electronic cam control is performed using, as a main shaft, the driving shaft that controls the conveying unit and using, as a driven shaft, the shaft that controls the up down movement of the nozzle. When the electronic cam control is performed, the liquid spills if the nozzle is pushed down before the bottom moves to right under the nozzle. Therefore, it is desired that the shaft that moves up and down the muzzle maintains a stopped state until the shaft that controls the conveying unit moves from a position immediately before a position right under the bottle to the position right under the bottle.
When the electronic cam control device according to this embodiment is used, if the position immediately before the position right under the bottle is set as Xi−1, the position right under the bottle is set as Xi, and a position to which the nozzle is pushed up straight is set as Yi=Yi−1, the driven shaft can maintain the stopped state while the main shaft position is in a certain range (i.e., a range from the position immediately before the position right under the bottle to the position right under the bottle). Therefore, there is an effect that it is possible to realize a filling action without spilling the liquid.
As explained above, the electronic cam control device and the electronic cam curve generating method according to the present invention are suitable for generation of an electronic cam curve in which acceleration of the driven shaft is suppressed.
Filing Document | Filing Date | Country | Kind | 371c Date |
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PCT/JP12/63366 | 5/24/2012 | WO | 00 | 3/5/2013 |