Title:

United States Patent 3920968

Abstract:

A system for controlling the eccentricity of a roll especially of a reversing mill such as a plate mill is disclosed wherein the eccentricity and phase of eccentricity of a roll are measured from the rolling pressure and applied as the correcting signal to a roll gap control unit so that the variation in thickness due to the eccentricity of the roll may be eliminated.

Inventors:

Imai, Isao (Yokohama, JA)

Shiozaki, Hiroyuki (Yokohama, JA)

Shiozaki, Hiroyuki (Yokohama, JA)

Application Number:

05/483415

Publication Date:

11/18/1975

Filing Date:

06/26/1974

Export Citation:

Assignee:

ISHIKAWAJIMA-HARIMA JUKOGYO KABUSHIKI KAISHA

Primary Class:

Other Classes:

72/10.3, 72/10.4

International Classes:

Field of Search:

235/151

View Patent Images:

US Patent References:

3709009 | METHOD FOR DETECTING ECCENTRICITY AND PHASE ANGLE OF WORKING OR BACKING ROLL IN ROLLING MILL | 1973-01-09 | Shiozaki et al. | |

3580022 | ROLLING MILL INCLUDING GAUGE CONTROL | 1971-05-25 | Waltz et al. | |

3543549 | ROLLING MILL CONTROL FOR COMPENSATING FOR THE ECCENTRICITY OF THE ROLLS | 1970-12-01 | Howard | |

3478551 | CONTROL SYSTEMS | 1969-11-18 | Alsop | |

3194035 | System for eliminating cyclic variations in rolling mill gauge errors | 1965-07-13 | Smith | |

3100410 | Control systems | 1963-08-13 | Hulls et al. |

Primary Examiner:

Ruggiero, Joseph F.

Attorney, Agent or Firm:

Scrivener Parker Scrivener & Clarke

Claims:

What is claimed is

1. In an apparatus for controlling the eccentricity of a first roll of a rolling mill having upper and lower rolls, including

2. Apparatus as defined in claim 1, and further including gate means (21) connected between said first and second arithmetic units, and means (18, 10) responsive to rolling pressure for isolating said first arithmetic unit from said second arithmetic unit in the absence of rolling pressure.

3. Apparatus as defined in claim 1, wherein said means for deriving the corrected eccentricity and phase signals further includes second pulse generator means (4) for generating pulses in accordance with the other roll of the rolling mill, second counter means (6) for counting the pulses of said second pulse generator means, said third arithmetic unit providing a signal which is one half of the angle eccentricity provided by signals from said first and second counters, and sine and cosine generator means (24) and weighing calculator means (26) connected between said third arithmetic unit and said eccentricity computer means.

1. In an apparatus for controlling the eccentricity of a first roll of a rolling mill having upper and lower rolls, including

2. Apparatus as defined in claim 1, and further including gate means (21) connected between said first and second arithmetic units, and means (18, 10) responsive to rolling pressure for isolating said first arithmetic unit from said second arithmetic unit in the absence of rolling pressure.

3. Apparatus as defined in claim 1, wherein said means for deriving the corrected eccentricity and phase signals further includes second pulse generator means (4) for generating pulses in accordance with the other roll of the rolling mill, second counter means (6) for counting the pulses of said second pulse generator means, said third arithmetic unit providing a signal which is one half of the angle eccentricity provided by signals from said first and second counters, and sine and cosine generator means (24) and weighing calculator means (26) connected between said third arithmetic unit and said eccentricity computer means.

Description:

BRIEF DESCRIPTION OF THE PRIOR ART

The accuracy in thickness of the materials rolled by the metal rolling mills has been recently much improved, but the problem of the eccentricity of the roll or rolls of the rolling mills which adversely affects the accuracy in thickness has not been solved yet. The eccentricity of the rolls presents the serious problem not only in the two-high mills but also the four-high mills having backup rolls. When the work rolls in the two-high mills and the backup rolls in the four-high mills have any eccentricity, the roll gap varies as the rolls make one rotation, resulting in the variation in the thickness of materials rolled.

Recently the reduction response speed of the rolling mills have been much improved so that if the eccentricity of the roll is detected, the variation in thickness due to the roll eccentricity may be substantially eliminated.

SUMMARY OF THE INVENTION

Briefly stated, according to the present invention the eccentricity of the work or backup roll is detected by measuring the rolling pressure, not by directly sensing the eccentricity of the roll by a sensor disposed around the roll so that the signal for correcting the variation in thickness may be applied to a roll gap control unit of the rolling mills.

First the underlying principle of the present invention for sensing the eccentricity and phase of the work or backup roll in a rolling mill will be described. The correlation between the eccentricity of a roll and the variation in load (i.e. rolling pressure) is given by ##EQU1## where ΔP = variation in rolling pressure;

ΔS = eccentricity of roll,

K = mill modulus; and

M = plasticity modulus depending upon rolling conditions.

Since ΔS is the roll eccentricity, it corresponds to the period of a backup roll in the case of a four-high mill.

That is,

where

A = eccentricity of a backup roll;

ω = angular velocity of the backup roll;

t = time; and

β = phase angle, that is an angle between a predetermined angular position of the backup roll to a point at which the roll eccentricity is maximum.

Substituting Eq. 2 into Eq. 1, we have ##EQU2## Therefore, A and β may be measured from the value ΔP measured during one rotation of the backup roll.

The rolling pressure and the rotation of the backup roll are measured. The measured rolling pressure is sampled at a predetermined time interval so as to be converted into the digital signals. Based upon the digital signals the eccentricity and phase are obtained by an arithmetic unit and held by a holding circuit. The eccentricity or both eccentricity and phase are converted into the analog signals again which are used as the signals for correcting the variation in thickness due to the eccentricity of the roll.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph illustrating the variation in rolling pressure;

FIG. 2 is a graph illustrating that the rolling pressure shown in FIG. 1 is sampled;

FIG. 3 is a graph illustrating that the deviations of the sampled signals shown in FIG. 2 are obtained and the averages of these deviations are obtained; and

FIG. 4 is a block diagram of one preferred embodiment of the present invention.

DETAILED DESCRIPTION

The present invention will be described hereinafter with reference to a four-high rolling mill. According to the present invention, first the rolling pressure and the rotation of a backup roll are measured. FIG. 1 shows the rolling pressure curve a, the rolling pressure P being plotted along the ordinate while the time, along the abscissa. The rolling pressure P is sampled as shown in FIG. 2 at a time interval in which is equal to T/n, where T is a time required for the back roll to make one rotation and n, an integer. The sampled digital quantities or signals are stored. In general, the rolling pressure P_{1} and P_{n}_{+1} are not equal as shown in FIG. 2. The deviations of the rolling pressures from a straight line (the chain line L shown in FIG. 1) are obtained and their average is obtained as shown in FIG. 3 where ΔP_{1}, ΔP_{2}, . . . , and ΔPn are deviations. Deviations are detected on the basis of the line L (which connects the beginning of time T and the end thereof) because it is the prerequisite that the original value and the final value of the sine wave are to be identical with each other if deviations should arise along the sine wave. From these deviations an eccentricity A of the backup roll and a phase β from a predetermined position of the backup roll and the maximum eccentricity of the backup roll are based upon the following formula: ##EQU3## Thus, from the rolling pressure the eccentricity and the phase angle may be detected. However, in order to use them as the signal for correcting the variation in thickness of a rolled steel or the like due to the eccentricity of the backup roll in a strip mill where the rolling mill rolls continuously a steel strip in the same direction, the averages of A and β during a predetermined number of rotations of the backup roll must be obtained. That is, the averages of A and β for a number of N rotations of the backup roll are obtained and used as the signal for correcting the eccentricity of the backup roll in the next rotation. A and β obtained in the next rotation are compared with the averages A and B, and the deviations are added to A and β, respectively, so that the correction signal for the next rotation may be obtained. However, in case of a plate mill where rolling is made intermittently and reversed in direction, the arithmetic control circuits must be switched when the direction of rotation is reversed. Furthermore, the rolling mill must be controlled depending upon whether the material enters or leaves the working rolls. Moreover the arithmetic operation is carried out only when the rolling pressure is produced. When the rolling pressure is intermittently produced, the intermittently obtained data must be made into "the continuous data," and in some cases the slip angle between the upper and lower rolls must be corrected when the direction of rotation of the rolls is reversed.

The present invention will be described in more detail hereinafter with reference to FIG. 4. A first pulse generator 3 is coupled to an upper backup roll 1 while a second pulse generator 4, to a lower backup roll 2. A discriminator or sensor 8 is coupled to the rotary shaft of a motor 7, which drives an upper work roll 28 and a lower work roll 29, so as to sense the reverse in direction of the rotary shaft and hence the work rolls. The rolling pressure P is picked up as the analog signal by a load cell 10, and the analog signal is transmitted to a first converter 19 to be converted into the digital signal which in turn is transmitted to a first arithmetic unit 20. Thus, the deviation ΔPk is obtained. Meanwhile the pulses generated by the first pulse generator 3 are counted by a first counter 5, and the output signal of the counter 5 is transmitted to the first arithmetic unit 20 as the value K used in Eq. 3. Consequently, the first arithmetic unit 20 obtains B and C in Eq. 3 based upon Pk and K. A comparator 18 detects whether the rolling pressure signal exists or not so as to control a gate 21.

The angle of the upper backup roll 1 is detected by a third arithmetic unit 9. That is, the output K of the counter 5 is applied to the third arithmetic unit 9 so that 2π/n . K in Eq. 3 is obtained. In like manner, the angle of the lower backup roll 2 is detected by the third arithmetic unit 9. That is, the pulses generated by the second pulse generator 4 are counted by a second counter 6, and the output K' of the counter 6 is applied to the third arithmetic unit 9, so that 2π/n . K' may be derived. Furthermore the third arithmetic unit 9 derives one half of the angular deviation, i.e. ##EQU4## in order to correct the relative slip angle between the backup rolls. The output of the third arithmetic unit 9 is applied to a sine-cosine generator 24 which produces sin ##EQU5## and cos ##EQU6##

In addition to transmitting the output K to the first arithmetic unit 20, the counter 5 has a function to transmit to a second arithmetic unit 22 the signal representing one rotation of the upper back roll 1.

The output of the first arithmetic unit 20 is controlled by the gate 21. That is, when there is no rolling pressure P, the gate 21 is closed in response to the output of the comparator 18 so that no output signal is transmitted from the first arithmetic unit 20 to the second arithmetic unit 22, but when there exists the rolling pressure P, the gate 21 is opened so that the output signal of the first arithmetic unit 20 is transmitted to the second arithmetic unit 22.

In response to the output signal from the counter 5, the first arithmetic unit 20 transmits the signals representing B and C in Eq. 3 to the second arithmetic unit 22 during one rotation of the upper backup roll 1 when and only when the rolling pressure P exists. The first arithmetic unit 20 has a function of adding the minus (-) sign to the signal C in response to the output signal of the sensor 8 when the rotation is reversed as indicated by the dotted line in FIG. 4.

The values B and C required for computing the eccentricity A and the phase angle β are applied to the second arithmetic unit 22 in the manner described above. When these intermittent values are made into the continuous data or values in one direction of rotation, the continuous data may be derived from the second arithmetic unit 22. Therefore, the averages of the values B and C for a predetermined number of rotations are used as the correcting signals for the next rotation as described hereinbefore with reference to a continuous rolling mill. The values B and C obtained in the next rotation are compared with the average values B and C, and the deviations are added to the average values B and C, respectively, so that the correcting signals for the next rotation may be derived. In other words, the optimum values Bo and Co may be derived from the second arithmetic unit 22.

The second arithmetic unit 22 is connected to a multiplier 25 through a sign controller 23 which in response to the output signal from the sensor 8 adds the positive or negative sign to the optimum value Co depending upon the direction of rotation. The multiplier 25 multiplies the outputs of the sine-cosine generator 24 with the output of a weighting unit 26, which derives the cosine of the output signal of the third arithmetic unit 9. The multiplier 25 therefore obtains the products Bo.cos θ /2.cos ##EQU7## with Co.cos θ /2.sin ##EQU8## which are applied to an eccentricity computer 27. The eccentricity computer 27 obtains Bo.cos θ/2.cos ##EQU9## + Co.cos θ/2.sin ##EQU10## which in turn is applied to a second converter 16 in response to each pulse transmitted from the first pulse generator 3 (based upon the output K of the first counter 5) so that the analog signal may be derived. The analog signal is transmitted to an adder amplifier 14 in a reduction control circuit or a circuit for controlling the gap between the working rolls. To this amplifier 14 are also applied the feedback signal derived from a sensor 15 for detecting the position of the roll and the output signal from a roll position setting unit 17 so that a servo valve 12 controls the flow rate of working oil under pressure discharged from a hydraulic pump 13 into a cylinder 11, thereby making the difference between the two signals zero.

In case of a two-high mill, the work rolls are controlled in a manner substantially similar to that described hereinabove.

As described above, according to the present invention a sensor for detecting the eccentricity is not located around a roll, but the rolling pressure is set in response to a rolling pressure detector or sensor, and the rotation of the rolls is measured by the first pulse generator and the first counter. The measured rolling pressure is sampled at a predetermined time interval by the first arithmetic unit so that the values required for the computation of the roll eccentricity and phase may be obtained. The second arithmetic unit converts these values into the optimum values, and from these optimum values the correction signal is computed from the eccentricity computer. Therefore the eccentricity and phase of the backup rolls may be immediately measured with a higher degree of accuracy so that the correction signal for correcting the variation in thickness due to the roll eccentricity may be transmitted to the roll gap control unit. As a result the variation in thickness due to the roll eccentricity may be minimized so that the materials may be rolled with a higher degree of accuracy in thickness.

According to the present invention, the gate is interposed between the first and second arithmetic units and controlled in response to the control signal from the rolling pressure sensor so that the gate is automatically controlled depending upon whether the rolling pressure exists or not. That is, only when the rolling pressure exists the output signal of the first arithmetic unit is transferred into the second arithmetic unit which makes the intermittent outputs of the first arithmetic into the continuous data. Furthermore the sensor for sensing the direction of rotation is incorporated so that the signal representing the direction of rotation may be transmitted to the sign controller and other suitable units so that the data processed or to be processed by the second arithmetic unit are given a sign depending upon the direction of rotation and transmitted to the roll gap control unit. Therefore the variation in thickness may be accurately corrected depending upon the direction of rotation. Moreover the pulses are generated depending upon the angular portion of the other backup or work roll and applied to the second counter. Based upon the output signals from the first and second counters, one half of the angular deviation is computed by the third arithmetic unit in the circuit for correcting the relative roll slip angle, and is applied to the sine-cosine generator and to the weighing unit. Therefore even when the relative slip angle occurs between the upper and lower rolls, the correcting signal is applied to the roll gap correcting unit from the correcting circuit so that the adverse effect of the eccentricity of the rolls may be completely eliminated.

Thus the present invention can eliminate the variation in thickness of the materials due to the eccentricity of the backup or work rolls. The present invention is applied not only to the strip mills but also the plate mills which roll the materials intermittently in the opposite directions.

The accuracy in thickness of the materials rolled by the metal rolling mills has been recently much improved, but the problem of the eccentricity of the roll or rolls of the rolling mills which adversely affects the accuracy in thickness has not been solved yet. The eccentricity of the rolls presents the serious problem not only in the two-high mills but also the four-high mills having backup rolls. When the work rolls in the two-high mills and the backup rolls in the four-high mills have any eccentricity, the roll gap varies as the rolls make one rotation, resulting in the variation in the thickness of materials rolled.

Recently the reduction response speed of the rolling mills have been much improved so that if the eccentricity of the roll is detected, the variation in thickness due to the roll eccentricity may be substantially eliminated.

SUMMARY OF THE INVENTION

Briefly stated, according to the present invention the eccentricity of the work or backup roll is detected by measuring the rolling pressure, not by directly sensing the eccentricity of the roll by a sensor disposed around the roll so that the signal for correcting the variation in thickness may be applied to a roll gap control unit of the rolling mills.

First the underlying principle of the present invention for sensing the eccentricity and phase of the work or backup roll in a rolling mill will be described. The correlation between the eccentricity of a roll and the variation in load (i.e. rolling pressure) is given by ##EQU1## where ΔP = variation in rolling pressure;

ΔS = eccentricity of roll,

K = mill modulus; and

M = plasticity modulus depending upon rolling conditions.

Since ΔS is the roll eccentricity, it corresponds to the period of a backup roll in the case of a four-high mill.

That is,

where

A = eccentricity of a backup roll;

ω = angular velocity of the backup roll;

t = time; and

β = phase angle, that is an angle between a predetermined angular position of the backup roll to a point at which the roll eccentricity is maximum.

Substituting Eq. 2 into Eq. 1, we have ##EQU2## Therefore, A and β may be measured from the value ΔP measured during one rotation of the backup roll.

The rolling pressure and the rotation of the backup roll are measured. The measured rolling pressure is sampled at a predetermined time interval so as to be converted into the digital signals. Based upon the digital signals the eccentricity and phase are obtained by an arithmetic unit and held by a holding circuit. The eccentricity or both eccentricity and phase are converted into the analog signals again which are used as the signals for correcting the variation in thickness due to the eccentricity of the roll.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph illustrating the variation in rolling pressure;

FIG. 2 is a graph illustrating that the rolling pressure shown in FIG. 1 is sampled;

FIG. 3 is a graph illustrating that the deviations of the sampled signals shown in FIG. 2 are obtained and the averages of these deviations are obtained; and

FIG. 4 is a block diagram of one preferred embodiment of the present invention.

DETAILED DESCRIPTION

The present invention will be described hereinafter with reference to a four-high rolling mill. According to the present invention, first the rolling pressure and the rotation of a backup roll are measured. FIG. 1 shows the rolling pressure curve a, the rolling pressure P being plotted along the ordinate while the time, along the abscissa. The rolling pressure P is sampled as shown in FIG. 2 at a time interval in which is equal to T/n, where T is a time required for the back roll to make one rotation and n, an integer. The sampled digital quantities or signals are stored. In general, the rolling pressure P

The present invention will be described in more detail hereinafter with reference to FIG. 4. A first pulse generator 3 is coupled to an upper backup roll 1 while a second pulse generator 4, to a lower backup roll 2. A discriminator or sensor 8 is coupled to the rotary shaft of a motor 7, which drives an upper work roll 28 and a lower work roll 29, so as to sense the reverse in direction of the rotary shaft and hence the work rolls. The rolling pressure P is picked up as the analog signal by a load cell 10, and the analog signal is transmitted to a first converter 19 to be converted into the digital signal which in turn is transmitted to a first arithmetic unit 20. Thus, the deviation ΔPk is obtained. Meanwhile the pulses generated by the first pulse generator 3 are counted by a first counter 5, and the output signal of the counter 5 is transmitted to the first arithmetic unit 20 as the value K used in Eq. 3. Consequently, the first arithmetic unit 20 obtains B and C in Eq. 3 based upon Pk and K. A comparator 18 detects whether the rolling pressure signal exists or not so as to control a gate 21.

The angle of the upper backup roll 1 is detected by a third arithmetic unit 9. That is, the output K of the counter 5 is applied to the third arithmetic unit 9 so that 2π/n . K in Eq. 3 is obtained. In like manner, the angle of the lower backup roll 2 is detected by the third arithmetic unit 9. That is, the pulses generated by the second pulse generator 4 are counted by a second counter 6, and the output K' of the counter 6 is applied to the third arithmetic unit 9, so that 2π/n . K' may be derived. Furthermore the third arithmetic unit 9 derives one half of the angular deviation, i.e. ##EQU4## in order to correct the relative slip angle between the backup rolls. The output of the third arithmetic unit 9 is applied to a sine-cosine generator 24 which produces sin ##EQU5## and cos ##EQU6##

In addition to transmitting the output K to the first arithmetic unit 20, the counter 5 has a function to transmit to a second arithmetic unit 22 the signal representing one rotation of the upper back roll 1.

The output of the first arithmetic unit 20 is controlled by the gate 21. That is, when there is no rolling pressure P, the gate 21 is closed in response to the output of the comparator 18 so that no output signal is transmitted from the first arithmetic unit 20 to the second arithmetic unit 22, but when there exists the rolling pressure P, the gate 21 is opened so that the output signal of the first arithmetic unit 20 is transmitted to the second arithmetic unit 22.

In response to the output signal from the counter 5, the first arithmetic unit 20 transmits the signals representing B and C in Eq. 3 to the second arithmetic unit 22 during one rotation of the upper backup roll 1 when and only when the rolling pressure P exists. The first arithmetic unit 20 has a function of adding the minus (-) sign to the signal C in response to the output signal of the sensor 8 when the rotation is reversed as indicated by the dotted line in FIG. 4.

The values B and C required for computing the eccentricity A and the phase angle β are applied to the second arithmetic unit 22 in the manner described above. When these intermittent values are made into the continuous data or values in one direction of rotation, the continuous data may be derived from the second arithmetic unit 22. Therefore, the averages of the values B and C for a predetermined number of rotations are used as the correcting signals for the next rotation as described hereinbefore with reference to a continuous rolling mill. The values B and C obtained in the next rotation are compared with the average values B and C, and the deviations are added to the average values B and C, respectively, so that the correcting signals for the next rotation may be derived. In other words, the optimum values Bo and Co may be derived from the second arithmetic unit 22.

The second arithmetic unit 22 is connected to a multiplier 25 through a sign controller 23 which in response to the output signal from the sensor 8 adds the positive or negative sign to the optimum value Co depending upon the direction of rotation. The multiplier 25 multiplies the outputs of the sine-cosine generator 24 with the output of a weighting unit 26, which derives the cosine of the output signal of the third arithmetic unit 9. The multiplier 25 therefore obtains the products Bo.cos θ /2.cos ##EQU7## with Co.cos θ /2.sin ##EQU8## which are applied to an eccentricity computer 27. The eccentricity computer 27 obtains Bo.cos θ/2.cos ##EQU9## + Co.cos θ/2.sin ##EQU10## which in turn is applied to a second converter 16 in response to each pulse transmitted from the first pulse generator 3 (based upon the output K of the first counter 5) so that the analog signal may be derived. The analog signal is transmitted to an adder amplifier 14 in a reduction control circuit or a circuit for controlling the gap between the working rolls. To this amplifier 14 are also applied the feedback signal derived from a sensor 15 for detecting the position of the roll and the output signal from a roll position setting unit 17 so that a servo valve 12 controls the flow rate of working oil under pressure discharged from a hydraulic pump 13 into a cylinder 11, thereby making the difference between the two signals zero.

In case of a two-high mill, the work rolls are controlled in a manner substantially similar to that described hereinabove.

As described above, according to the present invention a sensor for detecting the eccentricity is not located around a roll, but the rolling pressure is set in response to a rolling pressure detector or sensor, and the rotation of the rolls is measured by the first pulse generator and the first counter. The measured rolling pressure is sampled at a predetermined time interval by the first arithmetic unit so that the values required for the computation of the roll eccentricity and phase may be obtained. The second arithmetic unit converts these values into the optimum values, and from these optimum values the correction signal is computed from the eccentricity computer. Therefore the eccentricity and phase of the backup rolls may be immediately measured with a higher degree of accuracy so that the correction signal for correcting the variation in thickness due to the roll eccentricity may be transmitted to the roll gap control unit. As a result the variation in thickness due to the roll eccentricity may be minimized so that the materials may be rolled with a higher degree of accuracy in thickness.

According to the present invention, the gate is interposed between the first and second arithmetic units and controlled in response to the control signal from the rolling pressure sensor so that the gate is automatically controlled depending upon whether the rolling pressure exists or not. That is, only when the rolling pressure exists the output signal of the first arithmetic unit is transferred into the second arithmetic unit which makes the intermittent outputs of the first arithmetic into the continuous data. Furthermore the sensor for sensing the direction of rotation is incorporated so that the signal representing the direction of rotation may be transmitted to the sign controller and other suitable units so that the data processed or to be processed by the second arithmetic unit are given a sign depending upon the direction of rotation and transmitted to the roll gap control unit. Therefore the variation in thickness may be accurately corrected depending upon the direction of rotation. Moreover the pulses are generated depending upon the angular portion of the other backup or work roll and applied to the second counter. Based upon the output signals from the first and second counters, one half of the angular deviation is computed by the third arithmetic unit in the circuit for correcting the relative roll slip angle, and is applied to the sine-cosine generator and to the weighing unit. Therefore even when the relative slip angle occurs between the upper and lower rolls, the correcting signal is applied to the roll gap correcting unit from the correcting circuit so that the adverse effect of the eccentricity of the rolls may be completely eliminated.

Thus the present invention can eliminate the variation in thickness of the materials due to the eccentricity of the backup or work rolls. The present invention is applied not only to the strip mills but also the plate mills which roll the materials intermittently in the opposite directions.