## 1 Introduction  
Drilling a structurally complex well, irrespective of whether it is a horizontal well, a directional well, an extended reach well, or a multilateral well, has become commonplace in the oil and natural gas industry, as companies seek to drill deeper and further optimize the oil and gas production in the target field [1; 2; 3]. As a result, the high frictional resistance of a drill-string against the borehole rock has become a concern in the drilling process [4; 5; 6]. This source of additional torque and drag will lead to a low rate of penetration (ROP), the wear of drilling tools, short runs, wellbore instability, and complex stress of the drill string, etc. [1]. In particular, wellbore instability sometimes leads to the pipe becoming stuck, which may require plugging and side tracking, significantly driving up the cost of reservoir development [7]. Moreover, the driller's ability to maintain tool face control and to transfer weight to the bit can be severely limited because of the excessive friction, which limits the depth and accuracy of the drilled boreholes [1,8]. There are a series of methods and tools used for torque and drag reduction, and which ultimately allow the drill-string to drill to the total depth. Axial oscillation tools (AOTs) and lateral vibration tools (LVTs) are the two most common tools used to generate benign vibrations within the drill-string and/or bottom-hole assembly (BHA) to reduce friction [9]. AOTs usually employ sliding or rotating valves driven by mud to generate pressure pulses, and the pressure pulses can be converted into an axial oscillating motion by a shock tool that is run above or incorporated into the AOT [10]. LVTs usually employ eccentric rotating masses driven by mud to create a vibration between the borehole wall and the tool, thereby reducing friction. Both of these tools have been previously demonstrated to be effective, although AOTs exhibit a better performance than LVTs [9,11]. One of the most popular AOTs currently on the market is the Drilling Agitator System (DAS), which was developed by National Oilwell Varco(r) and was introduced into the market in 2002 [6,12,13]. It has been used for drilling practices in thousands of runs globally and has shown a clear improvement in drilling performance by reducing the drag and torque at the drill-string. The Friction Drag Reducer (FDR) tool is another AOT on the market which has been widely used for coiled tubing (CT) [14]. This tool is a double acting hydraulic cylinder, generating axial oscillation in the BHA by mechanical valves, causing a minor reciprocating movement. A representative LVT is the drag reduction tool based on a rotary-eccentric mass [15]. It can generate lateral vibration by the internal periodic rotation of an eccentric shaft driven by a screw motor. There are still some less common friction reduction tools on the market, such as the LoTAD(tm) drilling system of Weatherford(r), which is neither an AOT nor an LVT, using innovative rollers to minimize torque, drag, and tool-joint wear while drilling [16]. The Surface Acoustic Pulse Generator (SAPG) is another friction reduction tool, generating an intense pressure pulse by creating a water hammer in flowing mud at a location at the surface to vibrate the drill-string, resulting in a reduced torque requirement [17]. All of the friction reduction tools motioned above have been successfully used in numerous drilling engineering projects. However, due to the complicated structure with deformable or movable parts and the subsequent maintenance, technical difficulties associated with erosion, wear, and failures have slowed down the improvement of these tools and made it challenging to use them within practical applications.