Optimum end milling tool path and machining parameters for micro Laval nozzle manufacturing

Abstract

Cutting tool path has significant effects on the performance of micro nozzles manufactured by micro machining. Different tool paths induced different directions of surface roughness. As for it, the manufacturers need to obtain optimal cutting tool path and cutting parameters. In this article, optimum machining parameters for the fabrication of micro Laval nozzle with two different end milling tool paths are presented. First, surface roughness models for different types of cutting tool paths are proposed. A case of machined nozzle surface is then given to verify the applicability of the developed roughness model. Second, theoretical profile geometries for the Laval nozzle to be manufactured are designed. Third, the influences of surface roughness on the nozzle performance parameters including total pressure, average outlet velocity and thrust are investigated through computational fluid dynamic analysis. Simulated performance parameters are contrasted with their theoretical values. It is found that for different tool paths, the nozzle of axial tool path has larger total pressure and average outlet velocity than that of circular tool path. Moreover, with surface roughness increasing, thrust decreases obviously when surface roughness R_z is larger than 4.8 μm. Micro end milling experiments based on axial tool path are then performed, and the optimum cutting parameters are obtained. Finally, a nozzle was manufactured with the axial tool path as well as the optimized cutting parameters.

Keywords

Micro Laval nozzle cutting tool path micro end milling optimum cutting parameters

Introduction

The rapid development of micro/nano-technologies has led to the development of an increasing number of extremely small devices.^1,2 Mini-spacecraft is a typical small device, which has become an important branch in the field of aerospace.^3,4 To obtain a high degree of maneuverability and capability, mini-spacecraft requires significant propulsion performance, such as velocity and thrust.⁵

Micro-scale propulsion system with tiny thrust is the power plant of mini-spacecraft. With the aid of micro-scale propulsion system, mini-spacecraft can achieve its orbit adjustment, station keeping and attitude controlling.^6–8 Micro Laval nozzle plays a significant role in micro-scale propulsion system and laser cutting system as well.^9,10 There are several different manufacturing processes for nozzle, such as etching,^11–13 electrochemical machining,¹⁴ ultrasonic machining,¹⁵ drilling and micro milling.^16,17

La Torre et al.³ analyzed that thrust changes with nozzle throat size varying from 0.01 to 1 mm. The nozzle rough surface was matched by the sinusoidal curve. Performance difference was analyzed with different orientations and amplitudes of the sinusoidal curve. It showed that sinusoidal curves with an orientation perpendicular to the main flow direction were found to lead to the formation of multiple weak shocks along the divergent part of the nozzle and performance reduction up to 18%. Ding et al.¹⁸ studied the effects of surface roughness in micro channels and took into account a roughness–viscosity function. Also, the compressible two-dimensional (2D) and three-dimensional (3D) models were proposed to interpret the experimental results. Better agreements between calculation results and experimental data were found using the models. Darbandi and Roohi² studied the effects of gas/surface interactions on the flow field in micro/nano-scale nozzles and showed that a high viscous force creation in the wall boundary layer prevents any supersonic flow formation in the divergent part of the nozzle. Thakre and Vigor¹⁹ found that the nozzle erosion rate follows the trend exhibited by the heat-flux variation, and most severe at the nozzle throat. Moreover, the erosion rate has notable increase at the throat when surface roughness is considered. Krishnamurty and Shyy²⁰ computed the effect of roughness height on the performance of 2D Laval nozzles. However, the total thrust decreases as the wall roughness increases. There is a tradeoff between the losses associated with the shock system and those associated with the skin friction. The normalized skin-friction coefficient is seen to be virtually independent of the Mach number variation.

There are many studies on the roughness effect on nozzle flow. However, few studies have shown what kind of roughness values nozzle should have. Moreover, few studies focus on the optimal cutting tool path and cutting parameters for micro Laval nozzle. Optimization of cutting tool path and cutting parameters in micro nozzle fabrication process under high speed and accuracy condition is a crucial problem.

As shown in Figure 1, the research direction and technology courses were indicated. In this article, surface roughness model based on different tool paths and cutting parameters is built first. Then, the roughness model should be validated. Second, surface roughness effect on nozzle average outlet velocity, thrust and total pressure is investigated, which is simulated through computational fluid dynamics (CFD). Based on simulation results, the type of cutting tool path and the roughness values can be confirmed, which play a guiding role for machining process of nozzle in practice. Moreover, the machining parameters can be obtained through experiments, which can satisfy the CFD calculation requirements. Finally, the qualified nozzle was produced successfully.

Figure 1.

Research technical road map.

Surface roughness modeling and validation of micro nozzle

Three sections including convergent, throat and divergent regions for a micro Laval nozzle are distinguished in Figure 2. In the convergent section, the flow is accelerated from the initial subsonic velocity to the sonic condition when arriving at the throat. The flow supersonically expands to the outlet in the divergent section. As shown in Figure 2, the throat diameter for the studied nozzle in this article is determined as 1 mm. The outlet diameter of the nozzle is 3.28 mm and the inlet diameter is 4.06 mm.

Figure 2.

Experimental geometry of the nozzle.

In micro nozzle machining process, two different types of cutting tool paths based on nozzle circular direction and nozzle axial direction are proposed as shown in Figure 3.

Figure 3.

Two different types of cutting tool paths: (a) cutting tool path of nozzle circular direction and (b) cutting tool path of nozzle axial direction.

Different tool path has different surface residual direction. In other words, it leads to different roughness direction. To investigate the cutting tool path effects on nozzle performance of velocity, pressure and thrust, surface roughness model based on different tool path should be built.

Micro-ball end milling is the finishing process for the nozzle machining as shown in Figure 3. In this study, the surface roughness model is proposed on different tool path for the micro nozzle using ball end milling cutter. As shown in Figure 4, the surface roughness model based on machining residual for different tool path was built, where the solid lines and dashed lines indicate different position of ball end mill. The shaded area CDE is the residual area, and h is the residual height.

Figure 4.

Micro-ball end milling of the nozzle on different tool path: (a) axial tool path model and its top view and (b) circular tool path model and its front view.

The residual height computation equation can be obtained based on geometry relationship. Equation (1) is for axial tool path, and equation (2) is for radial tool path. From Figure 4, the maximum residual height (h) is supposed to be equal to the height of irregularities which are regarded as the surface roughness parameter R_z. Thus, different surface roughness model based on equations (1) and (2) can be built

h = r_{i n} - \sqrt{{(r_{i n} - R)}^{2} - \frac{a_{p}^{2}}{4}} - \sqrt{R^{2} - \frac{a_{p}^{2}}{4}}

(1)

h = R [1 - \cos (\arcsin \frac{a_{p}}{2 R \cos α})]

(2)

To study the relationship between the nozzle performance and the tool path, it is imperative to establish the 3D models for the nozzle profile on different tool paths. 3D models of nozzle with R_z increasing from 0.6 to 19.2 μm are built. Two models on different tool path with the same surface roughness R_z 1.2 μm are shown in Figure 5. The outside surface of 3D model amounts to inner surface of nozzle, and the entire model is defined as the fluid field in the CFD simulation.

Figure 5.

Nozzle 3D model for different tool path with the same surface roughness: (a) cutting tool path of nozzle circular direction and (b) cutting tool path of nozzle axial direction.

It is necessary to confirm its applicability after building 3D model. However, the current existing measuring equipment is hard to be applied in measuring nozzle inner surface roughness. A novel convenient method to measure nozzle inner surface roughness is developed in this research. The nozzle inner surface is simplified into slopes with the same angle (20.6°) as shown in Figure 6. Five slope arrays are arranged in one workpiece, for reducing tool setting errors.

Figure 6.

Slopes with angle 20.6°.

After machining experiments, white light interferometer is used in the measurement of the slope surface roughness. And extracting contour of the measured results, whose direction is perpendicular to the tool path, contrasted with predicted contour of the nozzle is shown in Figure 7. The predicted contour is drawn based on residual model. X axial indicates direction perpendicular to tool path, and coordinate y represents residual contour amplitude of nozzle surface.

Figure 7.

Contour comparison for different tool path:(a) contour comparison for cutting tool path of nozzle circular direction and (b) contour comparison for cutting tool path of nozzle axial direction.

In Figure 7, theoretical prediction and experimental measurement charts agree well with each other, especially for the length between 0.05 and 0.2 mm (Figure 7(a)). There might be several possible reasons for the tiny difference, for example, vibration of the cutter, elastic recovery of workpiece and measurement error. Despite the approximations in the model, it should be emphasized that the experimental and theoretical results agree well with the parameter domains in this study.

Theoretical calculations and CFD simulation of nozzle performance

Theoretical calculations

The nozzle flow model is so complex that reasonable simplification is needed. In this research, a one-dimensional (1D) steady compressible flow model in the divergent section is used as shown in Figure 8. In Figure 8, the region between dashed lines indicates unit volume in the model, and the property parameters of gas flow are listed.

Figure 8.

One-dimensional steady compressible flow model.

In the 1D nozzle flow physics model, the constraints of section changes are taken into consideration. The premise assumption is that flow is an isentropic and adiabatic process. On the basis of mass conservation, the mass flow rate of nozzle is constant. The continuity equation is presented as shown in equation (3), and its differential form is shown in equation (4)

\overset{\cdot}{m} = ρ_{1} S_{1} V_{1} = ρ_{2} S_{2} V_{2}

(3)

\frac{d ρ_{1}}{ρ_{1}} + \frac{{dS}_{1}}{S_{1}} + \frac{{dV}_{1}}{V_{1}} = \frac{d ρ_{2}}{ρ_{2}} + \frac{{dS}_{2}}{S_{2}} + \frac{{dV}_{2}}{V_{2}} = 0

(4)

Isentropic relationship of pipe is shown in equation (5). Energy equation is shown in equation (6)

\frac{P_{1}}{P_{2}} = {(\frac{ρ_{1}}{ρ_{2}})}^{γ} = {(\frac{T_{1}}{T_{2}})}^{\frac{γ}{γ - 1}}

(5)

C_{P} T_{1} + \frac{V_{1}^{2}}{2} = C_{P} T_{2} + \frac{V_{2}^{2}}{2} = C_{P} T^{*}

(6)

where $\overset{\cdot}{m}$ is the mass flow rate of pipe; S₁ and S₂ are the areas of two different sections, respectively; ρ₁ and ρ₂ are the density of flow media; V₁ and V₂ are the flow media velocity; P₁ and P₂ are the static pressure; T₁ and T₂ are the static temperature; γ is the specific heat ratio; T^* is the total temperature and C_p is the isobaric heat capacity of flow media.

Nozzle total pressure, outlet velocity and thrust in equations (7)–(9) can be calculated based on above 1D steady compressible flow model

\frac{P_{e}^{*}}{P_{e}} = {(1 + \frac{γ - 1}{2} M_{e}^{2})}^{\frac{γ}{γ - 1}}

(7)

V_{e} = \sqrt{\frac{2 γ}{γ - 1} {RT}_{e}^{*} [1 - {(\frac{P_{e}}{P_{e}^{*}})}^{\frac{γ - 1}{γ}}]}

(8)

F = \overset{\cdot}{m} V_{e}

(9)

where $P_{e}^{*}$ is the total pressure; P_e is the static pressure and γ is the specific heat ratio of N₂ (nozzle flow gas in this research), its value is 1.4. M_e is the Mach number of nozzle outlet (M_e = 4 in this research); V_e is the outlet velocity of nozzle; R is the gas constant; $T_{e}^{*}$ is the total temperature of nozzle outlet and F is the thrust of nozzle. The calculated theoretical values of nozzle performance are shown in Table 1.

Table 1.

Theoretical value of nozzle performance index.

Index	$P_{e}^{*}$ (MPa)	V_e (m/s)	F (mN)
Theoretical value	1.5184	677.6	1884

The calculated theoretical value of nozzle performance contrast with simulation value, what kind of tool path could bring nozzle better performance and more close to the theoretical value will be shown in the next section.

CFD simulation

As nozzle is an axisymmetric structure, it is reasonable to adopt half of the nozzle model in CFD simulation. ANSYS FLUENT 14.5 is applied for simulation in this article. In CFD simulation, operating media is N₂, whose viscosity is determined by Sutherland’s law. Temperature-dependent viscosity and thermal conductivity are calculated from kinetic theory. The inner surface of nozzle is assumed to be adiabatic. Density-based solver and realizable k–ε viscous model are chosen as the computation model. During the iterations, residual error and inlet–outlet mass flow balance are selected as the convergence criterion. The nozzle inlet gas temperature is 300 K. Pressure boundary conditions are inducted for inlet and outlet of nozzle. Nozzle inlet pressure is 1,518,400 Pa and its outlet pressure is 10,000 Pa.

In this study, the total pressure, the average outlet velocity, the mass flow rate and thrust of the nozzle based on different surface roughness and different tool path are investigated in this section. Surface roughness R_z increases from 0.6 to 19.2 μm for two types of tool paths. The four kinds of parameters of nozzle are selected as its critical evaluating index. Simulation and theoretical values (as shown in Table 1) of total pressure for different tool path and different R_z are shown in Figure 9.

Figure 9.

Total pressure for different tool path and different R_z.

When R_z increased from 0.6 to 19.2 μm, the total pressure tends to decline for the two tool paths. Moreover, theoretical values are larger than the simulated roughness values for the two different tool paths because those theoretical calculations are adiabatic, isentropic and frictionless. However, simulation calculate is viscous, non-isentropic and rough. As shown in Figure 9, the total pressure of nozzle for axial tool path is greater than nozzle for circular tool path obviously.

Fluid flow in the nozzle induced the total pressure drop due to the energy loss, which is to overcome the friction within the fluid flow, and to exchange momentum in turbulent fluid when the particles crash each other. This phenomenon caused difference in pressure before and after the fluid flow. It is called total pressure drop. The nozzle machining by circular tool path, apparently, has larger total pressure drop than that by axial tool path.

Velocity distribution of different tool path and different R_z is shown in Figure 10. In this research, 95% of V_e was selected as a dividing line between core flow region and boundary layer. Thus, boundary layer thickness ratio (h_b/r_e) can be calculated as shown in Table 2, where the boundary layer thickness is h_b and the outlet radius is r_e.

Figure 10.

Distributions of velocity for different tool path and different R_z: (a) velocity distribution of nozzle for circular tool path and (b) velocity distribution of nozzle for axial tool path.

Table 2.

Boundary layer thickness ratio (h_b/r_e).

Tool path	R _z
Tool path	0.6 μm	4.8 μm	9.6 μm	19.2 μm
Circular	6.1%	7.9%	11.6%	18.9%
Axial	5.5%	6.7%	6.5%	7.3%

As shown in Figure 10(a) and Table 2, it can be seen that with R_z increasing, the thickness of boundary layer increases, which increases the energy loss of gas gradually. However, the velocity distribution of nozzle for axial tool path change is not very notable as shown in Figure 10(b) and Table 2. It shows that the velocity has small sensitivity to different roughness nozzle machined by axial tool path.

To illustrate the change in the outlet velocity, average outlet velocity is chosen as the calculate index. The simulation and theoretical values of average outlet velocity for different tool path are shown in Figure 11.

Figure 11.

Average outlet velocity for different tool path and different R_z.

The theoretical value of average outlet velocity is 677.6 m/s. There is no obvious relationship between velocity and surface roughness as the average outlet velocity tends to be unchanged when R_z increases from 0.6 to 19.2 μm for axial tool path. However, the average outlet velocity of circular tool path tends to decline. Furthermore, the velocity of nozzle with axial tool path is apparently larger than the nozzle with circular tool path. The former is much closer to the theoretical value.

The theoretical calculate neglects the boundary layer’s influence on average outlet velocity, which mainly leads to the difference between theoretical value and simulation value. The axial tool path results in roughness element along the direction of the flow. However, the circular tool path leads to roughness element perpendicular to the flow direction. So, the circular tool path induced more energy loss because of overcoming the friction when gas flow collides with surface roughness element. Moreover, the velocity mainly increases along the axial direction in nozzle. Thus, there are no cross section surface area variations for nozzle machined by axial tool path. The simulation and theoretical values of thrust for different tool path are shown in Figure 12.

Figure 12.

Thrust for different tool path and different R_z.

The thrust has small variation when R_z is smaller than 4.8 μm for the two different tool paths, while that of 9.6 and 19.2 μm decrease obviously. Furthermore, the thrust of nozzle with axial tool path is slightly larger than nozzle with circular tool path. When R_z is smaller than 9.6 μm, the former is closer to the theoretical value. The thrust decreases for two kinds of tool path, compared with theoretical value, mainly caused by increase in energy loss that is induced by viscosity effect and roughness effect.

In conclusion, there are significant differences in total pressure, velocity and thrust between theoretical value and simulation value. On one hand, viscosity effect of the gas causes wall boundary layer. On the other hand, the contact area between nozzle wall and the fluid increases with increasing R_z. The viscosity effect enhances significantly. For different tool path, the nozzle of axial tool path has better performance than that of circular tool path.

With the increase in roughness, total pressure and average outlet velocity decrease obviously when R_z is larger than 4.8 μm caused by surface roughness element. To avoid this undesirable feature, nozzle surface roughness should not be greater than 4.8 μm (R_z) after machining process.

In a word, the axial tool path should be chosen with a small depth of cut in nozzle machining process. In order to make the nozzle surface roughness R_z not larger than 4.8 μm, it is essential to optimize processing parameters through experiments. Moreover, the cutting experiment is essential as there are some other parameters, such as feed rate, which influence the surface roughness.

Experiments and nozzle machining

Experimental set-up and procedure

A five-axis micro machining center (KERN-2520) is employed to carry out the micro milling experiments. The maximum rotational speed is 50,000 r/min and axis travels are 250 mm for X, 220 mm for Y and 250 mm for Z, respectively. It is equipped with a laser control NT which is used to measure the micro milling tools.²¹ In this study, aluminum alloy 7050-T7451 is chosen as the nozzle material. It has excellent combination performances, such as high strength, stress-corrosion cracking resistance and toughness, which can satisfy the need of property for the nozzle, preferably.²²

The different finish machining parameters are designed and shown in Table 3, including rough machining parameters as well. Flat end milling cutter with diameter 3 mm is used in rough machining process. Ball end milling cutter with diameter 0.8 mm is used in finish machining process as shown in Figure 13. S is the spindle speed, and f_z is the feed per tooth.

Table 3.

Machining parameters.

No.	S (r/min)	a_p (mm)	f_z (μm/Z)	Process
A	8000	0.1	10	Rough machining
B	20,000	0.02	1	Finish machining
C	20,000	0.02	1.5	Finish machining
D	20,000	0.02	2	Finish machining
E	20,000	0.02	2.5	Finish machining
F	20,000	0.02	3	Finish machining
G	20,000	0.02	3.5	Finish machining
H	20,000	0.04	2	Finish machining
I	20,000	0.04	3	Finish machining
J	20,000	0.08	2	Finish machining
K	20,000	0.08	3	Finish machining

Figure 13.

Ball end mill with diameter 0.8 mm.

In surface finish machining, based on previous research results, micro processing spindle speed 20,000 r/min is optimal. Surface roughness increases with a_p increasing obviously; so, too many groups of a_p are meaningless. Small a_p is reasonable. In micro milling process, there is a reasonable f_z, which can obtain the best surface quality and related with cutting edge radius and machining materials. Thus, six groups of f_z is needed.

Experimental results

A total of 10 micro slopes were machined with micro milling tools using cutting parameters in Table 3. To get the surface roughness results, white light interferometer is used in slope roughness measurement, and R_z is chosen as an evaluation index. It should be noted that each case is measured three times, and each roughness value is the average value of three different positions on the same workpiece. The measurement area of each time is 640 × 480 μm².

From the measurement results shown in Figure 14, the roughness parameter R_z of nozzle first decreases and then increases with the increase in f_z. So, the best parameter is group E. Its surface topography measured for different groups using white light interferometer is shown in Figure 15.

Figure 14.

Surface roughness with different f_z.

Figure 15.

Surface topography measured for different groups: (a) group E, a_p = 0.02 mm, f_z = 2.5 μm/Z, (b) group G, a_p = 0.02 mm, f_z = 3.5 μm/Z, (c) group H, a_p = 0.04 mm, f_z = 2 μm/Z and (d) group J, a_p = 0.08 mm, f_z = 2 μm/Z.

Based on white light interferometer measurements, the optimum parameters for nozzle machining process are determined as group E (S = 20,000 r/min, a_p = 0.02 mm, f_z = 2.5 μm/Z).

Nozzle machining process

Nozzle machining process is shown in Figure 16(a) blank, (b) micro-ball end milling, (c) drilling, (d) reverse 180° and micro-ball end milling and (e) cylindrical surface milling. The combined process of micro milling with drilling is adopted in the nozzle machining process. The optimum parameters of group E were used in finishing process, rough machining parameter was used group A in Table 3.

Figure 16.

Machining process of nozzle: (a) blank, (b) milling, (c) drilling, (d) milling and (e) milling.

With the serial machining process above, Micro Laval nozzle with throat radius 500 μm is manufactured. Excellent machining quality is achieved as shown in Figure 17.

Figure 17.

Nozzle machined result: (a) nozzle convergent section, (b) nozzle throat and (c) nozzle divergent section.

The dimension of nozzle is shown in Table 4.

Table 4.

Comparison of nozzle size between designed value and machined results.

	d_in	d_t	d_e
Designed value (μm)	4060	1000	3280
Measured value (μm)	4070.2	983.1	3283.6
Relative error (%)	0.25	1.7	0.11

As shown in Table 4, throat radius r_t has the maximum machining tolerance and reaches 1.7% compared with the designed value. Errors are inevitable in all the measuring process. However, every dimension of nozzle was measured three times and the average was taken.

In this research, roughness model was built. This method can be used for other nozzles based on machining surface residual. CFD simulation results indicated the nozzle machining by axial tool path, which leads to axial direction residual with better velocity performance and smaller total pressure drop. Similar to the results, La Torre et al.’s³ research indicated that surface roughness oriented in the direction parallel to the flow has no significant influence on the flow. Furthermore, tool path chosen principle and proper roughness value can be determined based on simulation results. Machining parameters are optimized based on experiments.

Conclusion

Cutting tool path has significant effects on the performance of micro nozzles which are manufactured by micro machining. Flow characteristics of micro nozzles were investigated based on the theoretical calculation and numerical simulation for micro nozzle machining with different types of cutting tool paths. Micro end milling operations based on axial tool path were performed, and the optimum machining parameters were obtained. The micro Laval nozzle was finally manufactured with the axial tool path and the optimized machining parameters.

The conclusions can be summarized as follows:

The micro nozzle end milled with axial tool path has better performance than that with circular tool path.

Surface roughness generated in axial tool path has no significant influence on the flow total pressure and average outlet velocity. However, surface roughness influence on thrust is obvious.

For both axial and circular tool path, with the increase in surface roughness, thrust decreases obviously when R_z is larger than 4.8 μm. Therefore, the surface roughness should not be greater than 4.8 μm (R_z) after nozzle machining process.

The optimum parameters for nozzle machining process are determined as group E (S = 20,000 r/min, a_p = 0.02 mm, f_z = 2.5 μm/Z).

Micro Laval nozzle with excellent machining quality can be manufactured with optimum cutting parameters. Throat radius r_t has the maximum machining tolerance which could reach 1.7% compared with the designed value.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was financially supported by the National Natural Science Foundation of China (51425503, 51375272, U1201245) and the Major Science and Technology Program of high-end CNC machine tools and basic manufacturing equipment (2014ZX04012014). This work was supported by grants from Taishan Scholar Foundation.

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