Device and method for reducing noise of a gear pump by non-uniform spacing simulation control

Abstract

The present invention relates to a device for reducing noise of a gear pump by non-uniform pitch simulation control and a method thereof. The device includes a calculation unit for calculating a different control current value of a tooth of each tooth number by applying a number of teeth, a tooth number, and a tooth angle of a gear pump in which a plurality of teeth are uniformly formed, a storage unit for mapping and storing the tooth number and the different control current value corresponding to the tooth number for each tooth, and a current controller for variably generating a control current value corresponding to the tooth number mapping when each tooth reaches a reference position while the gear pump is rotated by a motor, wherein the control current value is added to a reference current value of a motor control signal and applied to the motor.

Description

[0001] Cross-references to related applications

[0002] This application claims the benefit of Korean Patent Application No. 10-2020-0100525, filed on August 11, 2020, which is incorporated herein by reference. Technical Field

[0003] This invention relates to a device for reducing gear pump noise through non-uniform spacing simulation control. Background Technology

[0004] Typically, if multiple blades are evenly arranged and installed on the outer periphery of an impeller, there is a problem of noise being generated in the frequency band corresponding to the number of blades when the impeller is running.

[0005] To address the aforementioned issues, a traditional approach has been proposed in which the blades are arranged with a non-uniform spacing to reduce sound pressure and minimize pulsating sound (e.g., low-frequency peaks) generated by the non-uniform arrangement of the blades.

[0006] However, in the case of electro-hydraulic pumps, the teeth of the two meshing gears must be evenly spaced. Therefore, non-uniformly spaced gears cannot be used in electro-hydraulic pumps. Furthermore, when an electro-hydraulic pump is running, there is a problem of noise generation in the frequency band corresponding to the number of teeth.

[0007] The information disclosed in this background section is only intended to enhance the understanding of the background technology of this invention, and therefore may include information that does not constitute prior art known to those skilled in the art.

[0008] The conventional technology is disclosed in Korean Patent Publication No. 10-0872294 (December 5, 2008) and the corresponding U.S. Patent Application Publication No. 2010 / 0054949. Summary of the Invention

[0009] This invention relates to an apparatus for reducing gear pump noise through non-uniform pitch simulation control. A specific embodiment relates to an apparatus for reducing gear pump noise, which can reduce the drive noise of the gear pump through non-uniform pitch simulation control.

[0010] An embodiment of the present invention provides a device for reducing gear pump noise by simulating non-uniform pitch control. In this device, when the gear pump is running, the current value of the drive motor is controlled to simulate non-uniform pitch gears, thereby effectively reducing drive noise.

[0011] In an apparatus for reducing noise of a gear pump by non-uniform pitch simulation control, the apparatus can include a calculation unit calculating a different control current value for each tooth of a tooth number by applying a tooth number, a tooth sequence number, and a tooth angle of a gear pump to a predetermined function, in which a plurality of teeth are uniformly formed in the gear pump; a storage unit mapping and storing the tooth sequence number and the different control current value corresponding to the tooth sequence number for each tooth; and a current controller variably generating a control current value corresponding to the tooth sequence number mapped when each tooth reaches a reference position, in which the control current value is added to a reference current value of a motor control signal and thus applied to a motor, when the gear pump is rotated by the motor.

[0012] The current controller can instantaneously generate the control current value mapped by the tooth corresponding to the tooth sequence number when the tooth corresponding to the tooth sequence number reaches the reference position, and apply only the reference current value to the motor for the remaining time in which the control current value is not generated.

[0013] The current controller can variably generate the control current values corresponding to all teeth sequentially reaching the reference position according to time, and a pattern of the control current according to time can have a form of a sine function.

[0014] An nth control current value corresponding to an nth tooth sequence number is calculated from the following equation:

[0015]

[0016] where N can represent a tooth number, n can represent a tooth sequence number (n=1, 2, …, N), 2π / N can represent a tooth angle, I Δθn may represent a basic current value applied to the nth tooth, e(·) can represent an exponential function for adjusting I Δθn , and B m may represent a variable determined by a type of the gear pump and has a value between 10 and 90.

[0017] I Δθn is calculated from a non-uniform pitch generation function:

[0018]

[0019] where A m may represent a current reference value and has a range of 5A±20%, 0<P1<N and 0<P2<N.

[0020] A method of reducing noise of a gear pump through non-uniform pitch simulation control can include calculating different control current values for each tooth number of teeth by applying the number of teeth, tooth numbers, and tooth angles of the gear pump to a predetermined function; mapping and storing the tooth numbers and the control current values corresponding to the tooth numbers for each tooth; and variably generating the control current values mapped with the tooth numbers whenever the teeth sequentially reach a reference position, wherein the control current values are added to a reference current value of a motor control signal and thus applied to a motor.

[0021] In variably generating the control current values, the control current values mapped with the tooth numbers corresponding to the teeth can be instantaneously generated at the time when the teeth corresponding to the tooth numbers reach the reference position, and the reference current value can be applied only to the motor for the remaining time when the control current values are not generated.

[0022] In variably generating the control current values, the control current values corresponding to all the teeth sequentially reaching the reference position can be variably generated according to time, and a pattern of the control current according to time can have a form of a sine function.

[0023] According to one embodiment of the present application, by controlling a current value of a motor operating a gear pump according to time, an effect of non-uniform pitch for noise reduction can be realized in software without applying a structural change to the gear pump. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 FIG. 1 is a diagram illustrating an apparatus for reducing noise of a gear pump through non-uniform pitch simulation control according to an embodiment of the present application.

[0025] Figure 2 FIG. 2 is a graph illustrating a predetermined function according to a change of a variable B m .

[0026] Figure 3 FIG. 3 is a graph illustrating control currents generated corresponding to each tooth number according to an embodiment of the present application.

[0027] Figure 4 FIG. 4 is a diagram illustrating a pump control system applied to an apparatus for reducing noise of a gear pump through non-uniform pitch simulation control according to an embodiment of the present application.

[0028] Figure 5 FIG. 5 is a flowchart illustrating a method of reducing noise of a gear pump through non-uniform pitch simulation control according to an embodiment of the present application.

[0029] Figure 6is a graph showing noise measurement results when the non-uniform pitch simulation control according to the embodiment of the present application is applied to an electric hydraulic pump and noise measurement results of a conventional technology when the non-uniform pitch simulation control is not applied to the electric hydraulic pump.

[0030] Figure 7 is a spectrogram when the non-uniform pitch simulation control according to the embodiment of the present application is applied to an electric hydraulic pump and a spectrogram of a conventional technology when the non-uniform pitch simulation control is not applied to the electric hydraulic pump.

[0031] Embodiments of the present application can be described with the following elements in conjunction with the accompanying drawings.

[0032] 10: gear pump

[0033] 20: motor

[0034] 100: apparatus for reducing noise of gear pump

[0035] 110: calculation unit

[0036] 120: storage unit

[0037] 130: current controller. DETAILED DESCRIPTION

[0038] The present application will be described more fully hereinafter with reference to the accompanying drawings, in which embodiments of the application are shown. As this described embodiments can be modified in various different ways, all of which do not depart from the spirit or scope of the application, the application should not be construed as limited to the embodiments set forth herein. The drawings and description are to be regarded as illustrative in nature, and not as restrictive. Like reference numbers are denoted throughout the drawings.

[0039] In the present specification and in the following claims, when describing that one element is "coupled" to another element, the element can be "directly coupled" to the other element or "electrically coupled" to the other element through a third element. In the present specification and in the following claims, unless explicitly described to the contrary, the word "comprise" or variations such as "comprises" will be understood to imply the inclusion of the stated elements but not the exclusion of any other elements.

[0040] Figure 1 is a graph showing noise measurement results when the non-uniform pitch simulation control according to the embodiment of the present application is applied to an electric hydraulic pump and noise measurement results of a conventional technology when the non-uniform pitch simulation control is not applied to the electric hydraulic pump.

[0041] As Figure 1 shown, the apparatus 100 for reducing noise of a gear pump by non-uniform pitch simulation control according to the embodiment of the present application can include a calculation unit 110, a storage unit 120, and a current controller 130.

[0042] The device 100 applies a control current that has an effect of simulating a non-uniform pitch to a motor 20 that drives a gear pump 10 (e.g., an electric hydraulic pump), so that noise generated when the gear pump 10 operates is minimized.

[0043] In the case of a conventional impeller, driving noise is minimized by applying a non-uniform pitch that makes the gap between the blades different. However, in the case of the gear pump 10, since two gears externally engage each other and the gap between the teeth must be constant, it is not possible to adopt a structure of a non-uniform pitch.

[0044] In an embodiment of the present application, by controlling the current value of the motor 20 that operates the gear pump 10 according to time, without applying a structural change to the gear pump 10, the effect of a non-uniform pitch for noise reduction can be implemented in software.

[0045] Herein, a device for reducing noise of a gear pump according to an embodiment of the present application will be described with reference to the accompanying drawings. Figure 1 A detailed description of a device for reducing noise of a gear pump according to an embodiment of the present application will be described.

[0046] The calculation unit 110 calculates a different control value for each tooth by applying the number of teeth (N) of the gear pump 10, the tooth number (n = 1, 2, …, N), and the tooth angle (2π / N) to a predetermined function, in which a plurality of teeth are uniformly formed in the gear pump 10.

[0047] In the case of Figure 1 , it is an example in which the number of teeth (N) is 11. In this case, the tooth angle (2π / N) is 32.7 degrees (360 / 11), and the tooth number exists from 1 to 11.

[0048] The predetermined function can be defined as Equation 1 below.

[0049] Equation 1

[0050] Equation 1 represents a function for calculating an n-th control current corresponding to a tooth of an n-th tooth number, N represents the number of teeth, n represents the tooth number, and 2π / N represents the tooth angle.

[0051] I Δθn is a basic current value applied to the n-th tooth, and is calculated based on a non-uniform pitch generation function. e(·) represents an exponential function for adjusting I Δθn .

[0052] B m is a variable determined by the type of the gear pump, and its value is between 10 and 90. B m may vary according to the type of the gear pump 10.

[0053] mod(A, B) is a known function that calculates the remainder of A divided by B.

[0054] Figure 2 is a graph showing a predetermined function according to the change of variable B m .

[0055] Referring to Figure 2 , Equation 1 can be simply expressed as At this time, considering the mod function, x is set to the range of −1 ≤ x ≤ 1

[0056] Referring to Figure 2 , it can be seen that the pattern of the predetermined function changes according to the adjustment of B m (for example, B m = 10, 30, 90). As the value of B m increases from 10 to 90, the bell-shaped pattern becomes narrower m . Therefore, when different B

[0057] values are applied based on the type of gear pump, the pattern of the predetermined function can be adjusted Δθn .

[0058] Equation 2

[0059] In Equation 2, A m represents a current reference value with a range of 5A ± 20%, and P1 and P2 are factors affecting the period, where 0 < P1 < n and 0 < P2 < n

[0060] Since the tooth number (n) is between 1 and 11, I of Equation Δθn 2 is calculated for each tooth, and I Δθn is used to calculate of Equation 1. That is, a total of 11 Equation 1s are derived corresponding to the number of teeth

[0061] The storage unit 120 receives the calculation result from the calculation unit and stores the calculation result. At this time, the storage unit 120 maps and stores the control current value derived for each tooth with the tooth number. The current controller 130 changes the control current value based on the position of each tooth when the motor 20 is driven and the information stored in the storage unit 120

[0062] Specifically, when the gear pump 10 rotates through the motor 20, each time each tooth reaches the reference position, the current controller 130 variably generates the mapped control current value corresponding to the tooth of the tooth number

[0063] Each tooth reaches the reference position whenever the gear pump 10 rotates 32.7 degrees. Here, the reference position can correspond to, for example, the dotted line (- · -) point. The position of each tooth can be easily checked by the rotation angle of the shaft of the motor 20.

[0064] Referring to Figure 1 , the control current value generated by the current controller 130 is added to the reference current value (I s_ref ) that is the motor control signal and is thereby applied to the motor 20.

[0065] The gear pump 10 is engaged with the shaft of the motor 20 and is rotated by the motor 20, and as the gear pump 10 rotates, the teeth of the gear pump 10 sequentially reach a predetermined reference position.

[0066] Each time the first through eleventh teeth sequentially reach the reference position, the current controller 130 generates a control current value corresponding to the tooth of the tooth sequence number by referring to the information mapped in the storage unit 120. Accordingly, the current controller 130 generates a control current value corresponding to the tooth of the tooth sequence number at the appropriate time.

[0067] Herein, the timing at which the tooth corresponding to the tooth sequence number reaches the reference position can be easily determined from the angle of the rotating shaft of the motor. For example, every time the rotating shaft of the motor rotates 32.7 degrees, the tooth sequence number reaching the reference position sequentially changes.

[0068] In the embodiment of the present application, when the tooth corresponding to the tooth sequence number reaches the reference position, the current controller 130 instantaneously generates a control current value corresponding to the tooth corresponding to the tooth sequence number. Accordingly, during the remaining time in which the control current value is not generated, only the reference current value is applied to the motor 20.

[0069] Figure 3 is a graph showing the control current generated corresponding to each tooth sequence number according to the embodiment of the present application.

[0070] In Figure 3 , the horizontal axis represents the angle of the gear pump and represents the range of 0 ~ 360 degrees, and the vertical axis represents the control current value generated for each tooth sequence number. Since the angle of the gear pump changes over time, the vertical axis of Figure 3 may correspond to the time axis.

[0071] The current controller 130 variably generates control current values corresponding to all the teeth sequentially reaching the reference position according to time. At this time, each time the tooth reaches the reference position, the current controller 130 instantaneously generates a control current value by Equation 1.

[0072] Herein, it can be seen that the pattern of the control current over time has a sinusoidal function form. That is, the control current value can have a sinusoidal function form with a period of 360 degrees.

[0073] Furthermore, since the control current value is added to the reference current value (I s_ref ) and thereby applied to the motor 20 as an input current (see Figure 1 ), only the reference current (I s_ref ) is applied to the motor 20 when the control current is not generated (when the control current is zero).

[0074] Figure 4 is a diagram showing a pump control system to which the device for reducing noise of a gear pump by non-uniform pitch simulation control according to an embodiment of the present application is applied.

[0075] Figure 4 A motor drive unit for operating the motor 20 is shown. Referring to Figure 4 , the motor drive unit can include a speed controller 21, a current controller 22, and a pulse width modulation (PWM) inverter 23. The motor drive unit can be embedded in the motor 20 or connected to the motor 20.

[0076] The motor drive unit controls the motor 20 by PWM control based on a PWM signal generated corresponding to a control value, and the motor 20 is driven by PWM control and speed-controlled.

[0077] The motor drive unit is electrically connected between the device 100 and the motor 20, adds a control current value generated by the device 100 and a reference current value output from the speed controller 21, and applies them (the control current value and the reference current value) to the current controller 22. When the control current is zero, only the reference current value is applied to the current controller 22.

[0078] The current controller 22 converts the current value into a voltage value, and outputs the voltage value to the PWM inverter 23. The PWM inverter 23 generates a PWM signal based on the voltage value input from the current controller 22, and applies the PWM signal to the motor 20. The operation and speed of the shaft of the motor 20 are controlled according to the PWM signal, and thus the operation and speed of the gear pump 10 connected with the shaft of the motor 20 are controlled.

[0079] The motor can be provided with a position sensor to detect a rotational position or a rotational angle of the shaft of the motor 20. The rotational position or the rotational angle of the shaft detected by the position sensor is transmitted to the speed controller 21, and the speed controller 21 can compensate for an error between a feedback angle (ω m_beedback ) (for example, a rotational angle of the shaft of the motor detected by the position sensor) and a reference angle (ω m_ref ). Furthermore, the PWM signal output from the PWM inverter 23 can be fed back to the reference current value.

[0080] As described above, it can be seen that the control current value generated by the device 100 is used as an input signal to control the motor 20. The device 100 can be electrically connected to the motor 20 as in Figure 4 the related art, but the device 100 can be embedded in a motor driving unit.

[0081] Since the motor driving unit generates a control current value for controlling the speed of the motor 20 by reflecting the rotational angle of the shaft of the motor 20, the motor 20 can be stably controlled.

[0082] Figure 5 is a flowchart illustrating a method of reducing noise of a gear pump by non-uniform pitch simulation control according to an embodiment of the present application.

[0083] As Figure 5 shown in FIG. 5, in step S510, the device 100 for reducing noise of a gear pump calculates a different control current value for each tooth of the tooth number by applying the tooth number, the tooth number, and the tooth angle of the gear pump 10 to a predetermined function. At this time, the device 100 can generate a function based on non-uniform pitch, and calculate a control current value corresponding to the tooth number of the tooth by Equation 1.

[0084] In step S520, the device 100 maps and stores the tooth number and the control current value corresponding to the tooth number for each tooth. Then, the device 100 operates the gear pump 10 based on the mapped information, thereby minimizing the operating noise of the gear pump 10.

[0085] To this end, when the gear pump 10 is operated by the motor 20, the device 100 generates a control current value based on the position of each tooth. Specifically, in step S530, the device 100 generates a control current value mapped by the tooth number by synchronizing the timing at which each tooth of the gear pump 10 sequentially reaches a reference position.

[0086] In step S540, the control current value is added to the reference current value and applied to the motor 20 as a control signal.

[0087] In an embodiment of the present application, the gear pump 10 can be an electro-hydraulic pump. When the method according to the embodiment of the present application is applied to the electro-hydraulic pump, the motor speed and torque are instantaneously changed to activate simulation control similar to that applied under non-uniform pitch.

[0088] That is, by changing the current (or torque) applied to each position of the teeth of the external gear to which non-uniform pitch cannot be mechanically applied, control simulating non-uniform pitch can be achieved.

[0089] Figure 6is a graph showing noise measurement results when the non-uniform pitch simulation control according to the embodiment of the present application is applied to an electric hydraulic pump and noise measurement results of a conventional technique when the non-uniform pitch simulation control is not applied to the electric hydraulic pump.

[0090] At this time, as a test condition for reducing noise, the number of teeth of the external gear was set to 11, the gear rotational speed was set to 1500 RPM, and the hydraulic pressure in the gear pump was set to 1 bar.

[0091] Referring to Figure 6 , the entire noise value of the present application is almost the same as that of the conventional technique, but it can be seen that the peak value of the noise value is reduced and the frequency band around the peak value is dispersed at a plurality of frequencies (e.g., 550 Hz, 825 Hz) of a mixed frequency (e.g., 275 Hz = 25 Hz x 11) of the rotational speed and the number of teeth. In particular, the maximum peak value of the embodiment of the present application is reduced by about 4-5 dB compared to the conventional technique.

[0092] Figure 7 is a spectrogram when the non-uniform pitch simulation control according to the embodiment of the present application is applied to an electric hydraulic pump, and a spectrogram of a conventional technique when the non-uniform pitch simulation control is not applied to the electric hydraulic pump. Figure 7 is a spectrogram showing a color noise level in a frequency-time domain. In Figure 7 , the closer to the dark color, the greater the noise.

[0093] Referring to Figure 7 , it can be seen that the noise of the embodiment of the present application is reduced in the 550 Hz and 825 Hz bands and the noise frequency band is dispersed compared to the conventional technique. If the embodiment of the present application is applied to a specific rotational speed to avoid a resonance frequency, the noise reduction effect can be maximized.

[0094] According to the embodiment of the present application as described above, when the gear pump in which the teeth are uniformly arranged is operated, since the non-uniform pitch simulation control is performed by software based on the current value applied to the motor, the driving noise of the gear pump can be effectively reduced.

[0095] While the present application has been described in connection with the embodiments considered to be practical by the inventors, it is to be understood that the application is not limited to the disclosed embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims

1. An apparatus for reducing gear pump noise by non-uniform pitch analog control, the apparatus comprising: a computing unit configured to calculate different control current values for each tooth of a tooth number by applying a tooth number, a tooth sequence number, and a tooth angle of a gear pump to a predetermined function, in which a plurality of teeth are uniformly formed in the gear pump; a storage unit configured to map and store, for each tooth, a tooth sequence number and a different control current value corresponding to the tooth sequence number; and a current controller configured to variably generate, at each tooth reaching a reference position, a control current value corresponding to the tooth sequence number mapped when the gear pump is rotated by a motor, in which the control current value is added to a reference current value of a motor control signal and thus applied to the motor; In the predetermined function, the nth control current value corresponding to the nth tooth number is an exponential function of where N represents the number of teeth, n represents the tooth number, n = 1, 2,..., N, θ is the rotation angle of the shaft of the motor, 2π / N represents the tooth angle, and B m is a variable determined according to the type of the gear pump and has a value between 10 and 90.

2. The apparatus of claim 1, wherein, the current controller is configured to: instantaneously generate the control current value mapped by the tooth corresponding to the tooth sequence number when the tooth corresponding to the tooth sequence number reaches the reference position; and only apply the reference current value to the motor for the rest of the time in which the control current value is not generated.

3. The apparatus of claim 1, wherein, the current controller is configured to variably generate the control current values corresponding to all teeth sequentially reaching the reference position according to time.

4. The apparatus of claim 3, wherein, a pattern of the control current according to time has a sinusoidal function form.

5. The apparatus of claim 1, wherein, an nth control current value corresponding to an nth tooth sequence number is calculated from the following equation: where I Δθn represents the base current value applied to the nth tooth, e(·) represents an exponential function for adjusting I Δθn .

6. The apparatus of claim 5, wherein, The I Δθn According to the following non-uniform spacing generation function calculation: where A m represents a current reference value and ranges from 5 A ± 20%, 0 < P1 < N and 0 < P2 < N.

7. A method for reducing gear pump noise by non-uniform pitch analog control, the method comprising: calculating different control current values for each tooth of a tooth number by applying a tooth number, a tooth sequence number, and a tooth angle of a gear pump to a predetermined function, in which a plurality of teeth are uniformly formed in the gear pump; mapping and storing, for each tooth, a tooth sequence number and a control current value corresponding to the tooth sequence number; and variably generating, at each tooth reaching a reference position, a control current value corresponding to the tooth sequence number mapped when the tooth reaches the reference position, in which the control current value is added to a reference current value of a motor control signal and thus applied to a motor. In the predetermined function, the nth control current value corresponding to the nth tooth number is an exponential function of where N represents the number of teeth, n represents the tooth number, n = 1, 2,..., N, θ is the rotation angle of the shaft of the motor, 2π / N represents the tooth angle, and B m is a variable determined according to the type of the gear pump and has a value between 10 and 90.

8. The method according to claim 7, wherein: instantaneously generating the control current value mapped by the tooth corresponding to the tooth sequence number when the tooth corresponding to the tooth sequence number reaches the reference position; and only applying the reference current value to the motor for the rest of the time in which the control current value is not generated.

9. The method of claim 7, wherein, the control current values are variably generated according to time corresponding to all teeth sequentially reaching the reference position.

10. The method of claim 9, wherein, a pattern of the control current according to time has a sinusoidal function form.

11. The method of claim 7, wherein, an nth control current value corresponding to an nth tooth sequence number is calculated from the following equation: where I Δθn represents the base current value applied to the nth tooth, e(·) represents an exponential function for adjusting I Δθn .

12. The method of claim 11, wherein, The I Δθn According to the following non-uniform spacing generation function calculation, where A m represents a current reference value and ranges from 5 A ± 20%, 0 < P1 < N and 0 < P2 < N.

13. A gear pump apparatus comprising: a gear pump including a gear having a plurality of teeth uniformly formed; a motor coupled to drive the gear pump; a processor configured to calculate different control current values for each tooth of a tooth number by applying a tooth number, a tooth sequence number, and a tooth angle of the gear pump to a predetermined function; a memory configured to map and store, for each tooth, a tooth sequence number and a different control current value corresponding to the tooth sequence number; a current generator configured to variably generate, as each tooth reaches a reference position, a control current value corresponding to the tooth number mapping when the gear pump is rotated by the motor; and a current adder having inputs coupled to receive the generated control current values and a reference current value, and an output coupled to the motor; Wherein, in the predetermined function, the nth control current value corresponding to the nth tooth number is The exponential function, where N represents the number of teeth, n represents the tooth number, n = 1, 2,..., N, θ is the rotation angle of the shaft of the motor, 2π / N represents the tooth angle, and B m is a variable determined according to the type of the gear pump and has a value between 10 and 90.

14. The gear pump apparatus of claim 13, wherein, the current generator is configured to: instantaneously generate the control current value mapped by the tooth corresponding to the tooth number as the tooth corresponding to the tooth number reaches the reference position; and for the rest of the time when the control current value is not generated, only the reference current value is applied to the motor.

15. The gear pump apparatus of claim 13, wherein, the current generator is configured to variably generate the control current values corresponding to all teeth that sequentially reach the reference position as a function of time.

16. The gear pump apparatus of claim 15, wherein, the pattern of control current as a function of time has a sinusoidal function form.

17. The gear pump apparatus of claim 13, wherein, the nth control current value corresponding to the nth tooth number is computed from the following equation: where I Δθn represents the base current value applied to the nth tooth, e(·) represents an exponential function for adjusting I Δθn .

18. The gear pump apparatus of claim 17, wherein, The I Δθn According to the following non-uniform spacing generation function calculation, where A m represents a current reference value and ranges from 5 A ± 20%, 0 < P1 < N and 0 < P2 < N.

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