## 1 Introduction  
In order to improve the fuel efficiency of eco-friendly vehicles, components that were previously driven by engine power or hydraulics are being converted to electric equivalents [1]. Among them, mechanical oil pumps that are directly connected to the engine and transmission are being replaced with electric oil pumps driven by permanent magnet synchronous motors and controllers [2, 3].  
Compared to mechanical oil pumps, which operate in proportion to the engine rotation speed, electric oil pumps operate independently of the engine and require relatively high hydraulic pressure and flow rates even when the vehicle is stopped or driving at low speeds. These stopped or low-speed driving conditions make acoustic noise and vibration reduction design of electrical oil pumps even more important than for mechanical pumps.  
The sources and composition of oil pump noise are known, and the design technology to reduce them is typically unique to the pump manufacturer, requiring much design experience and knowledge [4]. The main design factors for noise and vibration reduction are the pump blade and tooth shape, clearance, and port shape; by adjusting these shape variables, the internal flow can be improved, and the noise reduction effect can be obtained.  
As the technology used to reduce noise by changing these shape variables is closely related to pump performance, there is a limit to reducing noise while maintaining hydraulic performance; in other words, while increasing the clearance between the pump rotor and housing and the clearance between the pump teeth can reduce noise, it can also lower the pump's volumetric efficiency, which will lower its hydraulic performance.  
Design technology has been introduced for vane pumps, which involves distributing the frequency band of generated noise by arranging pump vanes with asymmetric pitches to reduce noise in a specific frequency band and avoid resonant frequency bands [5; 6; 7]. Vane pumps feature a rotor with vanes that slide into and out of it as the rotor turns. This sliding motion creates chambers into which the liquid flows, and as the rotor turns, the liquid is moved to the outlet, where it is discharged as the pumping chamber is squeezed down [8; 9]. Gear pumps create flow by pushing liquid through a mesh of teeth between two rotating gears. A drive shaft moves one gear, and this motion moves the other gear. The rotating gears form a liquid seal inside the casing, creating a vacuum at the inlet as the gear teeth separate [10; 11]. Gear pumps are extensively used in the automotive industry due to advantages such as small size, light weight, reliable operation, and low production costs [12; 13; 14]; however, a significant disadvantage is their relatively high noise emission [15].  
As each vane of the vane pump independently creates hydraulic pressure, the pitch angle between vanes can be asymmetrically arranged mechanically [16]. In contrast to the vane pump, the gear pump generates hydraulic pressure by the meshing of two rotating gears, which are dependent on each other with the same clearance [17]. Therefore, the pitch angle between each tooth should be symmetrically arranged mechanically.  
Compared to mechanical oil pumps, asymmetric pitch control can be applied to drive electric oil pumps under conditions similar to those when applying asymmetric pitch by actively varying the rotation speed and torque of the motor to the gear-type pump, for which mechanical asymmetric pitch cannot be applied.  
This article applies the asymmetric pitch control technique to electric oil pumps, based on internal and external gear pumps for which asymmetric pitches cannot be mechanically applied. It also analyzes the noise characteristics through experiments using an electric oil pump with an external gear pump for a transmission, in order to confirm its effectiveness.