Yanzhong Wang， Guoying Su,N， Daoyun Qiao， Weiwei Feng and Yuxia Pei

（1. School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China；2. Inner Mongolia First Machinery Group Co., Ltd, Baotou 014000, Inner Mongolia, China）

Abstract: To shorten the process of face gears, the grinding?hardening effect experiment of face gears under minimum quantity lubrication(MQL) was carried out. Firstly, the grinding method of face gears was analyzed based on the envelope principle, and the control equation of grinding move?ment was constructed. Secondly, the distribution ratio equation of heat flux density was estab?lished, and the theoretical calculation formula of triangle heat source was derived. Thirdly, since a MATLAB calculation program was compiled, the temperature change law under MQL grinding was analyzed. In the end, the influence of grinding parameters on the grinding?hardening layer depth was analyzed. The results demonstrate that MQL grinding achieves the grinding?hardening effect.

Key words: face gear；grinding；heat treatment；tooth hardening

Face gear drive is a new kind of transmis?sion, which has been applied widely in heli?copters[1?2]since its huge advantages such as small volume, excellent torque splitting, big drive ratio and so on. In the traditional face gear pro?cessing, heat treatment and grinding are two sep?arate processes. Grinding?hardening is a new pro?cess technology that uses the heat generated by grinding to heat treat the processed surface. It ef?fectively integrates the surface quenching and mechanical cold processing technology[3]. Thus, it is of great practical significance to carry out re?search on face?gear grinding?hardening.

In terms of grinding?hardening mechanism,the concept of grinding?hardening can be traced back to Wagner[4], but no further research on the hardness of the surface layer has been carried out. Brinksmeier and Brockhoff[5?6]carried out many grinding strengthening tests on the an?nealed AISIE5120 steel, ISI414 steel, SAFA?140 steel and tempered SAE52100 steel, and ob?tained a 0.25 mm thick martensite hardened lay?er. Jin[7]carried out the grinding?hardening test of 40Cr steel based on the double pass grinding method, and analyzed the structure morphology and hardness distribution of the hardened layer. Jiang[8]revealed the distribution law of the lubrication liquid sprayed into the grinding area,and carried out the grinding strengthening test under dry grinding and minimum quantity lub?rication(MQL) conditions, and simulated the MQL distribution of grinding temperature field.Zhang[9]carried out the active control of the grinding?hardening process strategy based on dif?ferent grinding amounts, and revealed the distri?bution of residual stress under different grinding amounts. Liu[10]carried out the grinding?quench?ing test on 42CrMo steel by means of liquid ni?trogen cooling. The changes of the structure and thickness of the hardened layer of steel under dif?ferent conditions were analyzed. Zhang[11]carried out the grinding test of GCr15 hardened bearing steel with low?temperature nanoparticle micro?lubrication. The result shows that low?temperat?ure nanoparticle micro?grinding grinding can ef?fectively reduce the normal grinding force in the grinding process.

In terms of face gear grinding, He[12]studied the influence of gear tooth surface error after worm grinding on its meshing performance. The result shows that the meshing performance of face gear after grinding is superior to the face gear after shaping in 2014. Zhao[13]established the grinding temperature field based on a disc wheel and used an infrared method to measure the grinding temperature field. Ming[14]obtained the basic parameters based on the instant ellipse contact theory, and established an infinite ele?ment model of grinding. Zhao[15]established a fi?nite element model of the face gear grinding tem?perature field and studied the temperature distri?bution law of tooth surface under different grind?ing process parameters.

In summary, grinding?hardening research mainly focuses on the grinding?hardening experi?mental research of steel without specific applica?tion scenarios. The research of face gear grinding technology mainly focuses on the research of tooth surface error, roughness and temperature field.

The first section of the paper includes the grinding mechanism and the control equation of face gears grinding based on disc wheels. The second section includes building the heat flux density distribution model and the theoretical calculation formula of triangle heat source. The third section includes writing a MATLAB pro?gram and the temperature law under MQL grind?ing. The fourth section is the analysis of the in?fluence of grinding amount on the hardening depth by adjusting the grinding parameters.

1 Face Gear Grinding Method

1.1 Gear forming mechanism

The principle of face gear grinding is shown in Fig. 1. The cross?sectional shape of the disc wheel and the virtual spur gear are both invol?ute profiles. When face gears are ground, in addi?tion to high?speed rotational movement about its axis, the disc wheel also needs to swing along the axis of the virtual spur gear to simulate the meshing movement between the virtual spur gear and the face gear. By adding feed motion in the direction of tooth height and tooth width, the formation of a single tooth is realized. Through the additional indexing movement, all the teeth of the face gear are achieved.

Fig. 1 Schematic diagram of face gear grinding envelope

1.2 Grinding control methods

The layout of face gear computer numerical control(CNC) grinder is shown in Fig. 2. “1” is the axial feed axis X, “2” is the radial feed axis Y, “3” is the accessory feed axis Z, “4” is the ro?tation axis A, “5” is the workpiece axis B, and“6” is the grinding wheel spindle C.

Fig. 2 Structure drawing of face gear CNC grinder

According to the principle of face gear grind?ing and the layout of face gear CNC grinder, the above required motion is equivalently and geo?metrically transformed(Fig.3a). The trajectory of the swing center O of the machine tool spindle is a line OO′, the center O1of the profile of the grinding wheel is an arc O1O′1, the workpiece of face gear is a line MM′, θ1is the swing angle of the tool holder, R is the length of the tool holder.The specific information is shown in Fig.3b.

Fig. 3 Schematic diagram of motion control of face gear grinding

The moving distance of the swing center O of the tool handle in the Z direction of the ma?chine tool, that is, the Z axis displacement is

The swing angle of the tool holder θ1is the rotation angle along the B direction of machine tool, Rwis the radius of disc wheel, Rpis the ra?dius of the addendum circle of pinion.

2 Calculation Model of Temperature Field in Grinding Zone

During the process of MQL grinding, grind?ing heat is mainly transferred to the workpiece,grinding wheel, grinding fluid, and grinding debris through heat conduction and convection.The calculation of the grinding heat energy dis?tribution ratio should include the grinding para?meters, the thermophysical properties of the ma?terial and the grinding wheel parameters. The calculation model of incoming face gear tooth blank after MQL grinding is[16]

Kohli[17]proposed a model of triangular mov?ing heat source in the grinding zone. The test shows that the triangular model is closer to the actual temperature field in comparison with the rectangular heat source proposed by Jager in 1942. When grinding face gear, the grinding thickness of the abrasive particles is inconsistent in the contact arc between the grinding wheel and the face gear tooth blank. Therefore, the heating power of the heat source in the grinding contact area cannot be evenly distributed, and the triangular distribution is more reasonable.The thermal model calculation of the triangular heat source distribution is shown in Fig. 4.

Fig. 4 Calculation diagram of triangle heat source distribution

The heat flux density of face gear in the grinding contact area is

3 Example Analysis

3.1 Input parameters

Based on the above formula, a MATLAB calculation program was compiled. The input parameters are listed as follows. The material of face gear is 20Cr2Ni4A. The grinding paramet?ers of face gear based on disc wheel are that the material of disc wheel is CBN, the speed of disc wheel is 50 m/s, the feed speed is 5 000 mm/min,the grinding depth is 0.1 mm, the MQL grinding fluid flow is 240 mL/h. In the actual grinding process, Rwtcan also be determined according to previous experiences. When grinding workpieces with CBN wheels, Rwtis 52% during dry grinding,13% during traditional wet grinding and 46%during MQL grinding[18].

3.2 Output results

The regularity of temperature change under different periods of time is shown in Fig. 5. The maximum temperature of grinding is 906 ℃ and the cooling rate is 240 ℃/s. According to the Heat Treatment Manual, when the maximum temperature of 20Cr2Ni4A material is higher than the austenite transformation temperature Ac3 (780 ℃) and the cooling rate exceeds the critical value of martensite transformation 60 ℃/s,it is believed that the surface layer forms a hardening layer after cooling.

Fig. 5 Regularity of temperature change under MQL grinding

4 Influence of Grinding Amount on Grinding Hardened Layer Depth

4.1 Grinding depth

Fig. 6 shows the curves of grinding hardened layer with the grinding depth when the feed rate is constant. The grinding parameters of disc wheel are that the material is CBN, the speed is 50 m/s, the feed rate is 5 000 mm/min, the grind?ing depth are 0.1, 0.2, 0.3, 0.4, 0.5 mm and the grinding fluid flow is 240 mL/h. As can be seen from Fig. 6, as the grinding distance increases ho?rizontally, the depth of the hardened layer is pos?itively correlated; as the grinding depth in?creases longitudinally, the depth of the hardened layer is positively correlated; the greater the grinding depth overall, the more uniform the depth of the hardened layer.

Fig. 6 Influence curves of grinding depth on the depth of hardened layer

It can be seen from Eqs. (4)–(6)(12), as the grinding depth increases, the cutting area in?creases, the tangential grinding force also in?creases, the heat flux density also increases, and the surface temperature of the grinding area also increases, thereby the depth of the hardened lay?er formed after the face gear is cooled also in?creases accordingly. It suggests that the uniform?ity of the hardened layer on the grinding surface is better and the unhardened area is smaller when a larger grinding depth is selected.

4.2 Feed rate

Fig. 7 shows the influence curves of feed rate on the depth of hardened layer when the grind?ing depth is constant. The grinding parameters of disc wheel are that the material is CBN, the speed is 50 m/s, the feed rate is 0.2, 0.4, 0.6, 0.8,1.0 mm/min, the grinding depth are 0.1 mm and the grinding fluid flow is 240 mL/h. As can be seen from Fig. 7, as the grinding distance in?creases horizontally, the depth of the hardened layer is positively correlated; as the feed rate in?creases longitudinally, the depth of the hardened layer is negatively correlated; the greater the feed rate overall, the more uniform the depth of the hardened layer.

From Eqs. (4)–(6)(12), as the feed rate in?creases, the tangential grinding force also in?creases, the heat flux density also increases, and the surface temperature of the grinding area also increases, however, the time of the heat flow acts on the face gear becomes less. The results show that the length of heat action time is more signi?ficant than the change of grinding force on the tooth surface temperature. It suggests that select?ing the feed rate, the depth, uniformity and un?hardened area of the hardened layer should be weighed according to the requirements.

Fig. 7 Influence curves of feed rate on the depth of hardened layer

5 Conclusions

① The heat distribution ratio equation un?der the MQL grinding conditions and the trian?gular moving heat source model are established,the calculation formula of the surface temperat?ure of the grinding contact area is derived.

② With the compiled MATLAB calculation program, the regularity of temperature change at a certain point under MQL grinding is analyzed.The highest temperature of grinding is 906 ℃,and the cooling rate (240 ℃/s) exceeds the crit?ical value of martensite transformation (60 ℃/s).Therefore, the surface layer of the material can form a hardening layer after cooling.

③ When the feed rate is fixed, the uniform?ity of the hardened layer on the grinding surface is better and the unhardened area is smaller as the grinding depth becomes larger. When the grinding depth is fixed, the choice of feed rate must consider the hardened layer depth, uniform?ity and unhardened area and other factors.