An optimization study of polishing efficiency of blisk and its technological parameters

Abstract

When applied to blisk blade profile polishing of aero-engines, “five-axis NC + flexible grinding head + elastic grindstone” polishing technological equipment has advantages of high precision, minor interference, favorable adaptivity, etc. In order to improve the polishing quality and polishing efficiency, a mathematical calculation formula of polishing efficiency was established according to the polishing principles of elastic grindstone (sanding wheel). The optimized combination of technological parameters (ω = 6000 r/min, a_p = 0.9 mm, v_f = 320 mm/min) was obtained through the range method of orthogonal test results with double optimization objectives—surface roughness and polishing efficiency. Based on the relationship between number of polishing times and surface roughness, a technological program was put forward, that is, polishing is firstly conducted using 320^# sanding wheel for 6 times and then 400^# sanding wheel for 9 times (totally 15 times) under the optimized combination of technological parameters, then surface roughness less 0.4 μm can be achieved. Blade polishing test results indicate that: efficiency-optimized technological parameters can not only significantly shorten polishing time but also acquire qualified blade surface roughness less 0.4 μm, thus verifying reliability of the optimization method and results.

Introduction

As a critical component of aero-engines, blisk has been extensively applied to military and civil aero-engines in various countries. As obvious scallop height and crest & trough ¹ exist on the blisk after milling, ² surface roughness is large, fatigue failure and, deformation or fracture can easily occur under high-temperature and high-pressure conditions, ³ and the consequence is severe. Therefore, polishing technology should be adopted to acquire surface roughness satisfying technical requirements ⁴ in order to improve fatigue durability and surface friction performance ⁵ of the blisk and improve performance and lengthen service life of aero-engines.

Kuo et al. ⁶ developed an Ace-Tone gaseous polishing system to polish acrylonitrile-butadiene-styrene complex geometric structural part, which was prepared by fused deposition model, using acetone vapor, thus reducing the surface roughness with favorable process stability. Xiao et al. ⁷ put forward a longitudinal micro-scratch measurement method for rounded corner at blisk root based on anti-fatigue machining principle, used point-to-point method to optimize the polishing path, conducted denoizing and smoothing of grinding vectors, formed small uniform longitudinal micro-scratches and improved surface quality uniformity. For Ti-6Al-4V grinding, Liu et al. ⁸ implemented preliminary optimization of grinding parameters through orthogonal test and signal-to-noise ratio (SNR) analysis, and obtained the optimal combination of grinding process parameters by taking material removal rate and specific grinding energy as optimization objectives, and on this basis, they improved grinding efficiency and surface quality. Following gray relational analysis of orthogonal test results, Zhang et al. ⁹ acquired the optimal combination of abrasive belt polishing process parameters and effectively reduced the roughness of polished surface. In order to improve the quality of laser polished surface, Zhao and Guo ¹⁰ proposed nonuniform rational B-Splines (NURBS) to optimize the polishing path and improve the track precision. Gerhard and Stappenbeck ¹¹ elevated the damage threshold of laser polishing by optimizing the process conditions for glass preparation, and thus the quality of laser polished surface was remarkably improved. For blade polishing of aeroengine, Xiao et al. ¹² studied grinding cutting mechanism of single abrasive particle, constructed a multi-particle parametric mathematical model and raised abrasive belt grinding method for micro-bionic zigzag surface, so as to improve the integrity of the polished surface. In order to improve polishing quality of workpiece surface, Chen et al. ¹³ developed a magnetic and elastic grinding material to polish the inner surface of workpiece under attraction of ring magnet and driving of turning pole, which reduced polishing force and avoided deep scratches on workpiece surface. Liu et al. ¹⁴ conducted a numerical simulation in order to improve polishing quality of abrasive particle flow in micropore canal, acquired the optimal combination of process parameters via an orthogonal test and improved the polishing quality for abrasive particle flow in micropore canal. Qi et al. ¹⁵ constructed a prediction model for material removal depth through abrasive belt polishing, and improved the model precision in full consideration of the influence of abrasive particle characteristics on removal depth.

In order to realize automatic blisk polishing of aero-engines, Shi YY, Lin XJ et al., from Northwestern Polytechnical University independently developed “five-axis NC + flexible grinding head + elastic grindstone (sanding wheel)” polishing technological equipment;^1,16 this equipment has high trajectory accuracy, good adaptivity and other advantages, and elastic grindstone—sanding wheel—featured small volume and good elasticity, so it’s applicable to blisk blade polishing.^17,18 In order to improve polishing efficiency and save cost, an optimization study of polishing efficiency was carried out in this paper; the concept and calculation model of flexible polishing efficiency of the elastic grindstone—sanding wheel—were proposed; the optimal efficiency-based combination of technological parameters was obtained through the range analysis of orthogonal test results, and number of polishing times was optimized based on the study of the relationship between number of polishing times and surface roughness; reliability of the proposed method and its result was verified through blade polishing test results in the end.

Polishing efficiency of sanding wheel

Metal resection efficiency refers to the material removal volume per unit time. ¹⁹ The purpose of polishing is to reduce surface roughness by removing a small residual height of the surface. From the view of efficiency, the aim of polishing is not only to obtain a smaller surface roughness but also to improve the polishing speed as much as possible, that is, to get a larger polishing area and a smaller surface roughness in a given amount of time. Therefore, the material removal volume in polishing can be approximately expressed as the product of the roughness reduction ΔR_a and the polished area S.

Therefore, polishing efficiency of sanding wheel is defined as product of polishing area within unit time and surface roughness reduction, which can be expressed by equation (1).

As shown in Figure 1, on the plane with polishing length of l and width of h, polishing path interval is p, then polishing area is S = lh and feed velocity is v_f, and polishing time is T=S/(v_f*p).

Figure 1.

Polishing principle of sanding wheel.

Polishing efficiency can be expressed by equation (1). ²⁰ according to the definition of metal resection efficiency.

$$E_f=\frac{S\mathrm{\Delta }{R}_a}{T}=\frac{\mathrm{lh}\mathrm{\Delta }{R}_a}{\frac{lh}{v_{f}p}}=\mathrm{\Delta }{R}_a{v}_{f}p$$

(1)

Where E_f is polishing efficiency, μm cm²/min; ΔR_a is variable quantity of surface roughness, μm; v_f is feed velocity, mm/min.

Polishing path interval is known as p = L/N, and then equation (1) can be expressed as equation (2).

$$E_f=\frac{\mathrm{\Delta }{R}_a{v}_{f}L}{N}\times {10}^{-2}$$

(2)

Where L is contact length between grinding tool perpendicular to feed direction and workpiece polishing area, mm; N is number of polishing times.

If polishing is carried out on a hook face, polishing path interval p and contact length $L$ will change with the shape change of the hook face, but their linear relations with polishing efficiency will not. Therefore, equation (2) is also suitable for measurement of hook face polishing efficiency of blisk blade in aero-engines.

Polishing test and results

Hereunder the optimized combination of technological parameters with dual optimization objectives—roughness and polishing efficiency—is obtained through the analysis of orthogonal polishing test results.

Test conditions BBD

The polishing equipment is a self-developed five-axis NC polishing machine as shown in Figure 2. The polishing machine consists of three rectilinear coordinate axes and three rotational coordinate axes. These axes of motion include rectilinear axes (X, Y, and Z), rotational axis of blade(U), swing axis of blade(C), and swing axis of flexible grinding head(A). The principal axis A allows for real-time adjustment of the grinding head pose involving three micro-displacement cylinders in radial uniform distribution and one axial micro-displacement cylinder according to the changes in blade geometric profile in the CNC program, which protects effective contact between the abrasive cloth wheel and the blade geometric profile, thus realizing flexible adaptive polishing. Machine tool structure and its working principles are introduced in References 1, 16∼18 in details.

Figure 2.

Five-axis NC polishing machine.

Ten TC11 blade specimens were totally used in the test and numbered as A∼J as shown in Figure 3. Blade backs were divided into three test areas which are marked as 1, 2 and 3 successively from blade root to blade tip in order to save the cost of the test. In the polishing test, a group of polishing technological parameters were used in each polishing area. The surface roughness on the polished surface vary slightly from place to place. In order to improve the measurement accuracy and objectively reflect the whole surface roughness, before and after polishing, five roughness measuring points were randomly selected in each polishing area, Mar Surf XR 20 surface roughness measuring instrument was used to measure surface roughness (sampling length: 0.8 mm, evaluation length 4 mm) in the direction perpendicular to polishing trajectory, and average value was taken as the final measuring result. Blade surface roughness before polishing is 0.86 μm.

Figure 3.

TC11 blade specimens.

Grinding wheel with dimensions of 8.5 mm×14 mm×P (initial radius r₀× thickness L×granularity P; P = 60^#, 320^#, 600^#), abrasive material of green silicon carbide (GC) and base material of cloth were used as the grinding tools in the test.

According to Literatures,^1,16–18 polishing technological parameters of grinding wheel include rotation speed ω, amount of compression a_p, feed velocity v_f, granularity P and polishing path interval p. Isoline method ¹⁶ was used for programming of polishing trajectory in the test and polishing was conducted through transverse trajectory method. ¹⁸

Sequence of influence factors

Polishing test results are shown in Table 1, where polishing efficiency in each test group was calculated through equation (2), the test level of technological parameters were selected in the optimum range of process parameters in which the ideal surface roughness and test results can be obtained according to the reference 1.

Table 1.

Test results using central composite design.

Number	ω/(r/min)	p/mm	a p/mm	v f (mm/min)	P	Polished area	R a/μm	ΔR a/μm	Ef (μm cm2/min)
1	4500	0.7	0.6	320	60	D3	0.697	0.163	0.36512
2	4500	1.2	0.9	220	600	C2	0.349	0.511	1.34904
3	4500	1.7	1.2	120	320	G1	0.315	0.545	1.1118
4	6000	0.7	0.6	220	600	B3	0.332	0.528	0.81312
5	6000	1.2	0.9	120	320	G2	0.196	0.664	0.95616
6	6000	1.7	1.2	320	60	A1	0.604	0.256	1.39264
7	7500	0.7	0.9	320	320	E3	0.230	0.63	1.4112
8	7500	1.2	1.2	220	60	D2	0.493	0.367	0.96888
9	7500	1.7	0.6	120	600	C1	0.417	0.443	0.90372
10	4500	0.7	1.2	120	600	C3	0.271	0.589	0.49476
11	4500	1.2	0.6	320	320	E2	0.332	0.528	2.02752
12	4500	1.7	0.9	220	60	D1	0.570	0.29	1.0846
13	6000	0.7	0.9	120	60	A3	0.485	0.375	0.315
14	6000	1.2	1.2	320	600	B2	0.357	0.503	1.93152
15	6000	1.7	0.6	220	320	E1	0.323	0.537	2.00838
16	7500	0.7	1.2	220	320	G3	0.281	0.579	0.89166
17	7500	1.2	0.6	120	60	A2	0.519	0.341	0.49104
18	7500	1.7	0.9	320	600	B1	0.383	0.477	2.59488

K _i in Table 2, is the sum of the test results for a factor column in Table 1 where its level is i; range is R = max (K₁, K₂, K₃) – min (K₁, K₂, K₃). The greater the range, the greater the numerical change of test results due to change of factor values in this column within the test range, so the column (factor) with the maximum range is the primary factor. Range values of polishing technological parameters on change value ΔR_a of roughness and polishing efficiency E_f and their sequence are shown in Table 2. Range values were used to draw impact trend of factor level change on ΔR_a and E_f as shown in Figures 4 and 5.

Table 2.

Range analysis of test results.

optimization objectives	Range	ω/(r/min)	p/mm	a p/mm	v f (mm/min)	P
ΔR a / μm	K 1	2.626	2.864	2.54	2.957	1.792
	K 2	2.863	2.914	2.947	2.812	3.483
	K 3	2.837	2.548	2.839	2.557	3.051
	R	0.237	0.366	0.407	0.4	1.691
	Sequence of influence factors	P, a p, vf, p, ω
Ef (μm cm2/min)	K 1	6.43284	4.29086	6.6089	4.27248	4.61728
	K 2	7.41682	7.72416	7.71088	7.11568	8.40672
	K 3	7.26138	9.09602	6.79126	9.72288	8.08704
	R	0.98398	4.80516	1.10198	5.4504	3.78944
	Sequence of influence factors	v f, p, P, ω, ap

Figure 4.

Impact trend of technological parameters on variable quantity of roughness.

Figure 5.

Impact trend of technological parameters on polishing efficiency.

According to range values in Table 2, influence factors of roughness, from primary to secondary, are P, a_p, v_f, p and ω; influence factors of polishing efficiency, from primary to secondary, are v_f, p, P, ω and a_p.

Optimization levels of technological parameters will be determined by taking variable quantity ΔR_a of roughness and polishing efficiency E_f as dual optimization objectives to obtain the optimized combination of technological parameters.

Dual-objective optimization of technological parameters

Range analysis of technological parameters

Rotation speed ω, which has identical impact trend on dual objectives, is a secondary influence factor of dual objectives and its impact on dual objects is minor. From Figures 4 and 5, its intermediate level 6000 r/min has a major influence on dual objectives, so 6000 r/min is determined as the optimal level of rotation speed.

Amount of compression a_p, which has identical impact trend on dual objectives, is the main influence factor of roughness and secondary influence factor of polishing efficiency, namely its change has a major influence on roughness but minor influence on polishing efficiency; according to Figure 4, its intermediate level 0.9 mm has a great bearing on roughness, so 0.9 mm is confirmed as the optimal level of amount of compression.

Feed velocity v_f is a general influence factor of variable quantity ΔR_a of roughness and its change exerts a general influence on roughness. As the main influence factor of polishing efficiency E_f, its change can exert a great impact on polishing efficiency and it presents approximately linear relation with polishing efficiency. As shown in Figure 5, 320 mm/min is its optimal level, which can significantly improve polishing efficiency.

Granularity P is the primary influence factor of roughness but a general influence factor of polishing efficiency; path interval p is the primary influence factor of efficiency and secondary influence factor of roughness and it is used to characterize number (N = L/p) of polishing times. As the surface roughness gradually declines in the polishing process, selecting proper granularity for polishing based on surface roughness can not only significantly reduce surface roughness but also effectively reduce number of polishing times. Therefore, the coupling effect of granularity P and polishing path interval p on polishing efficiency should be considered in the optimization process.

Optimization of granularity and path interval

Path interval p, which is the primary influence factor of efficiency and secondary factor of roughness, decides number (N = L/p) of polishing times on the polished surface. The study indicates that as the number of polishing times increases, roughness presents an exponential declining trend as shown in equation (3). ²⁰

$$R_a=(R_{a0}-R_{\mathrm{ae}})e^{-\lambda N}+R_{\mathrm{ae}}$$

(3)

Where λ is polishing index of sanding wheel, which is related to specifications of sanding wheel and the selected polishing technological parameters; R_a is surface roughness after polishing; R_a0 is surface roughness before polishing; R_ae is limiting surface roughness, and as number of polishing times increases, surface roughness declines and approaches R_ae.

Therefore, a proper granularity P should be selected to obtain large path interval (or small number N of polishing times) according to roughness change.

In order to study the relationship between number of polishing times and roughness, combination of technological parameters optimized using the range method specified in section 3.1 (ω = 6000 r/min, a_p = 0.9 mm and v_f = 320 mm/min) is adopted, sanding wheels of different granularities are used for polishing test, roughness is measured every once polishing is conducted for 5 times, and the relation curve chart between number of polishing times and roughness is obtained as shown in Figure 6.

Figure 6.

Influence laws of different granularities on surface roughness.

As shown in Figure 6, after sanding wheel of each granularity operates polishing for a certain number of times, surface roughness handsomely declines, but if polishing is continued, declining amplitude of roughness becomes very small and polishing efficiency is reduced. Granularities leading to large declining amplitudes are 400^# and 320^#; other granularities can give rise to minor change of surface roughness. Therefore, in order to guarantee polishing quality and improve polishing efficiency, sanding wheels of granularities 400^# and 320^# are optimally selected for polishing.

Based on data in Figure 6, limiting surface roughness values $R_{a\epsilon }$ under granularities 320^# and 400^# are 0.3 μm and 0.25 μm respectively; solving is implemented using the least square method, polishing index of 320^# sanding wheel can be obtained as $\lambda =0.133$ , and that of 400^# sanding wheel is $\lambda =0.119$ , equations (4) and (5) can be obtained by substituting them into equation (3).

$$R_a=0.95e^{-0.133N_L}+0.3$$

(4)

$$R_a=0.95e^{-0.119N_L}+0.25$$

(5)

The relationship between number of polishing times and surface roughness can be described according to equations (4) and (5) as shown in Figure 7.

Figure 7.

Number of polishing times and surface roughness.

The slope of curve in Figure 7(a) expresses the variable quantity caused by number of polishing times to roughness. Number of polishing times when slopes of two slopes are equal can be solved through equation (6) as N = 6.

$$\frac{\partial {R_a}^{320\mathrm{\#}}}{N}=\frac{\partial {R_a}^{400\mathrm{\#}}}{N}$$

(6)

After N = 6 is substituted into equation (4), surface roughness after 320# sanding wheel operates polishing for 6 times is solved as 0.72 μm; according to equation (5), number of polishing times needed by 400# sanding wheel to polish from 0.72 μm to 0.4 μm can be solved as nine as shown in Figure 7(b).

According to equations (4) and (5), if initial surface roughness changes from 1.2 μm to 0.4 μm through polishing, 320# sanding wheel needs to polish for 17 times while 400# sanding wheel needs to polish for at least 19 times.

Number N of polishing times can be converted into polishing path interval p through equation (7).

$$p=\frac{L}{N}$$

(7)

Therefore, the technological program with dual optimization objectives is: polishing is firstly conducted using 320# sanding wheel for 6 times and then 400# sanding wheel for 9 times (totally 15 times) under the optimized combination of technological parameters (ω = 6000 r/min, a_p = 0.9 mm and v_f = 320 mm/min), surface roughness can decline to 0.4 μm, and optimization results are shown in Table 3.

Table 3.

Optimization results of technological parameters.

Optimization methods	Optimization results
	ω (r/min)	p/mm (N)	a p (mm)	v f (mm/min)	p
Dual-objective	6000	2.3 (6)	0.9	320	320
	6000	1.5 (9)	0.9	320	400
Roughness	6000	0.8 (17)	0.9	120	320
Efficiency	6000	1.4 (10)	0.9	320	320

In addition, in order to compare reliability of technological parameters optimized for two objectives, roughness and efficiency are taken as single optimization objectives. The optimal levels of technological parameters corresponding to each objective are selected using the range method as optimization results of technological parameters for this objective as shown in Table 3.

Experimental verification

Optimized technological parameters in Table 3 were applied to the dedicated NC polishing machine for the sake of polishing test of 3 TC11 blades (blade backs) numbered as A, B and C on the aero-engine blisk as shown in Figure 8. Cloth-based GC abrasive sanding wheel with specification of 8.5 mm × 14 mm/320^# is used as grinding tool. According to technical requirements, post-polishing surface roughness should be smaller than 0.4 μm.

Figure 8.

Blisk polishing test.

Before and after polishing, roughness values of three blades—A, B and C—were measured at five random points in the direction perpendicular to polishing trajectory using a portable roughness measuring instrument, and the maximum value was taken as the measuring result; polishing results and efficiency were shown in Table 4. The surface roughness plot shown in Figure 9 shows that the residual height of the blade surface was cut off after polishing, and the surface roughness is significantly lower than before polishing.

Table 4.

Blisk polishing test results.

Blades		R a (µm)	Polishing time (min)	Ef /(μm cm2/min)
A	Before polishing	1.211	32	1.322
	After polishing	0.381
B	Before polishing	1.186	56	0.756
	After polishing	0.349
C	Before polishing	1.231	17	2.507
	After polishing	0.422

Figure 9.

Surface roughness plot before and after polishing.

According to the polishing results listed in Table 4, post-polishing roughness values of blades A and B satisfy R_a < 0.4 µm, thus meeting the technical requirement; although post-polishing surface roughness (0.381 µm) of blade A is greater than that (0.349 µm) of blade B, the consumed polishing time is short (32 min) and polishing efficiency is high, thus realizing dual optimization objectives—high polishing efficiency and low roughness; blade B obtains the minimum surface roughness by spending long polishing time (56 min) with the lowest polishing efficiency and high cost. Post-polishing efficiency of blade C satisfies R_a > 0.4 µm. Even though polishing time is the shortest (17 min), qualified polishing quality can’t be guaranteed. The comparison of blade surfaces before and after polishing was shown in Figure 10. The test results indicate that the efficiency calculation model and optimization results of technological parameters are reliable.

Figure 10.

Comparison of blade profiles before and after polishing.

Conclusions

Based on the “five-axis NC + flexible grinding head + elastic grindstone” polishing technological equipment, polishing efficiency of the elastic grindstone—sanding wheel—was investigated in this paper, and main research work and results are as follows:

1. Polishing efficiency of sanding wheel was defined as product of polishing area within unit time and surface roughness reduction and it’s calculation method were proposed.

2. After sanding wheel of each granularity operates polishing for a certain number of times, surface roughness handsomely declines, but if polishing is continued, declining amplitude of roughness becomes very small and polishing efficiency is reduced. Granularities leading to large declining amplitudes are 400^# and 320^#; As the number of polishing times increases at the same granularities, roughness presents an exponential declining trend.

3. The technological program with dual optimization objectives is: polishing is firstly conducted using 320^# sanding wheel for 6 times and then 400^# sanding wheel for 9 times (totally 15 times) under the optimized combination of technological parameters (ω = 6000 r/min, a_p = 0.9 mm and v_f = 320 mm/min), surface roughness can decline to 0.4 μm.

4. Blade polishing test results show that roughness less than 0.4 can be obtained after 15 times polishing under the process parameters optimized by the two-objective method. The polishing time was reduced and the qualified surface roughness can be obtained compared with other optimization methods in this paper. This certify that the efficiency optimization method and optimization result are reliable.