## 4 Conclusions  
This study's aim was to understand the mechanisms contributing to self-rotating water jet bit rock breaking that had not been studied previously. The water jet parameters bit rotation speed, jet pressure, and impact angle were studied. Our conclusions are:  
1. The volume of crushed pit by rotary jet erosion increases as the jet pressure increases. The erosion from a rotating bit increases quadratically with pump pressure but the increase is consistent with the results from fixed jet erosion. The depth to which the rock is broken is the dominant factor that defines the volume of broken rock; the diameter or the area broken is of secondary importance.
2. There is an optimum jet bit rotation speed for rock-breaking erosion, and this speed correlates positively with pump pressure. The reason there is an optimum speed is that it is difficult for pressurized water to collect at the bottom of the cutting groove when the jet rotates and erodes the rock, and this lack of water in the groove reduces the water cushioning effect and enhances the breaking ability of the water jet. However, excessive rotation speed causes the jet to deflect and atomize, and the effective erosion range becomes shorter, leading to the weakening of the jet's rock-breaking ability.
3. An optimum rock-breaking impact angle (10\({}^{\circ}\)) exists for the jet to break the rock. The reason for this is that the water cushion effect and reflection of the jet are reduced when the jet impacts at an oblique angle, but the angle must not be too large. If the jet impact angle is increased too much, the large impact angle causes the jet's impact force to decrease, resulting in a weakening of the jet's erosion ability. However, when the jet is rotated to erode the rock, the rock eroded in an area radially around the jet increases because of the tensile forces on the rock surface. This leads to an exponential increase in the volume of rock broken by the jet.
4. Concerning self-rotating water jet drill bit design, it can be concluded that: (1) the higher the pump pressure is, the greater the rock-breaking ability of the self-rotating bit will be. However, in this case the water consumption is higher, and the bit should be designed to match the performance of the other equipment in the drilling system (like the high-pressure pump). (2) The self-rotating bit has an optimum rock-breaking rotation speed, and this speed is positively correlated with the jet pressure. Hence, when designing the bit, it is necessary to add a speed-limiting mechanism to the bit to prevent bit rotation speeds that are too high. (3) The optimum rock-breaking angle for the self-rotating bit is about 10\({}^{\circ}\). When a large volume of broken rock is to be obtained, the nozzle angle can be increased appropriately.  
[PERSON], [PERSON], [PERSON], and [PERSON] contributed to conceiving and designing the experiments, analyzing the data, and writing the paper. [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] performed the experiments.  
This research was funded by Open Research Fund of State Key Laboratory of Coking Coal Exploitation and Comprehensive Utilization, China Pingneri Shennma Group (Grant No. 41010220171106-1), National Natural Science Foundation of China (grant numbers 51625401, 51774055), Fundamental Research Funds for the Central Universities (grant number 2018 CDQYZH0030, cqu2018 CDHB1B10) and the China Postdoctoral Science Foundation (2017M620415).  
We thank [PERSON] from Liwen Bianji, Edanz Editing, China (www.liwenbianji.cn/ac) for editing the English text of a draft of this manuscript.