BAO Youlin，LI Lixin，CAO Peng，LI Ciying，HUANG Xinglong

AECC Hunan Aviation Powerplant Research Institute，Zhuzhou 412002，P.R.China

Abstract: The rotor initial unbalance of an aeroengine gas generator of turboshaft engine seriously affects rotor assembly process. To reasonably optimize rotor assembly process，the effect analyses of rotor initial unbalance of single disc and combined discs on rotor dynamic characteristics are firstly implemented in respect of the dispersity of rotor initial unbalance. It is found that the most important factors contributing to rotor vibration are the unbalances of the first stage compressor disc and the second stage turbine disc. However，reducing the mass of two discs conflicts with the control of the whole gas generator rotor balance resulting from the unbalance increase of single components.Thus，we further analyze the key control factors of affecting rotor initial unbalance，and give the strict control measures of centrifugal impeller runout in the assembly process by adjusting the angle of central tie rod axis. The purpose of this measures to make the assembly process simpler and more effective for timely controlling rotor initial unbalance. The efforts of this study validate that the proposed method is workable for the rotor tightened by a central tie rod and possesses the significant meaning of practical application in engineering.

Key words：turboshaft engine；initial unbalance；assembly process；gas generator rotor；control technique

0 Introduction

Typical gas generator rotor system of turbo?shaft engine comprises three stages of axial compres?sors，one stage of centrifugal impeller and two stag?es of axial gas turbine rotor. The gas generator rotor is supported by 1-0-1 structure，assembled by curvic couplings centering and central tie rod with segment?ed retightening measure. For the central tie rod，the ratio of length to radius is to 15. In this case，the bearing before compressor is ball bearing and the bearing after gas turbine is rolling bearing. The structural diagram of gas generator rotor is shown in Fig.1. The datum plane of rotor balance locates on the convex platform before blade-root of the first stage bladed disc and the fixed bolt of second stage gas turbine baffle. The allowable unbalance levels of each rotor component and sub-rotor system are ap?proximately in［2 g·mm，4 g·mm］as well as 12 g·mm（front）and 16 g·mm（back），respectively. Un?der the effect of numerous parts，the unbalance of rotor system is so excessive in quantity and dispersi?ty that 50 test values distribute in the range［180 g·mm，500 g·mm］. It is very easy to induce the ex?cessive unbalance of single part and the vibration of whole-body aeroengine due to excessive material elimination of rotor parts and too large balance weight，catering for the requirement of repeatedly disassembling for faulty aeroengine［1］. What is more，the scrap of aeroengine parts emerges due to the reduction of materials and induces the efficiency decrease of aeroengine dynamic balance［2］. There?fore，it is urgent to reasonably control the initial un?balance of rotor system.

Fig.1 Schematic diagram of an aeroengine rotor

The objective of this paper is to find the critical controlling points of rotor initial unbalance in assem?bly process，and to optimize the assembly tech?nique and design quantitative standards，by analyz?ing main factors which affect the rotor initial unbal?ance.

1 Affecting Factors of Initial Un?balance

Initial unbalance of one component is often in?duced by manufacturing error and uneven material.It is impractical to further improve the allowable un?balance level of a single rotor part from technology and economy perspectives. The initial unbalance of rotor system is the vector sum of allowable unbal?ance values for many stages and additional unbal?ance values induced by eccentric assembly.

To reduce the initial unbalance of rotor，rota?tion angle method is commonly adopted to adjust the angular position of all stages of discs，with the assist of optimization algorithms such as genetic al?gorithm（GA），particle swarm optimization（PSO），and so on. In fact，the eccentric distance of all as?sembled discs has large deviation comparing to the theoretical zero values，so that the adaption of the existing optimization algorithms［3-5］is too low to control initial unbalance. In other words，it is im?possible to reduce the initial unbalance of rotor as only considering the unbalance angle degree of each component in assembling rotor system without re?gard to the control of jump after assembly［6-7］. In this case，it is necessary to precisely measure the jump of all components and accurately orient the an?gle direction of initial unbalance of single part［6-7］.The requirement leads to the improvement of manu?facture and checkout for factory and the difficulty of production cost control. Therefore，this study is to reduce the rotor initial unbalance by controlling the assembly quality（featured by jump value）of one component or some components in respect of test data.

The influencing factors of rotor initial unbal?ance in assemble process［8-9］include as follows：

（1）Unbalance of single component

The vector sum of single components’unbal?ance seriously influences rotor initial unbalance［3］.

（2）Runout of curvic couplings（end-tooths）

The runout of a well-balanced component has little effect on the initial unbalance. However，the runout of component’s curvic couplings mating surface has a great influence on the initial unbal?ance of the rotor［10］. When the eccentricity of com?ponents resulting from the curvic coupling runout is 0.005 mm，the amount of induced unbalance is 3.5 kg×0.005 mm=17.5 g·mm which is much larger than the residual unbalance 2 g·mm of sin?gle component.

（3）Processing quality of screw-thread in cen?tral tie rod

The central tie rod is an elongated shaft，and contains three screw-threads which distribute on the front，middle and back of the central tie rod. It is re?quired that the runout of the middle diameter of each thread relative to the rotating center of the part is no more than 0.05 mm. But the measurement of the re?al runout value is indeed difficult. When the coaxiali?ty of the threads of central tie rod is poor and is not parallel to the axial line of the curvic couplings of ro?tor part，the central tie rod will sways，and the back end of the central tie rod exists structural interfer?ence which is presented by the increased tightness of parts assembly that is illustrated in Fig.2. This inter?ference reversely affects the centering accuracy of curvic couplings and significantly influences rotor initial unbalance.

Fig.2 Schematic diagram of interference after the center tie rod swaying

（4）Influence of rotor pre-tightening

The type of rotor is segmental pre-tightening and its preload control has specific requirement that the preload of rotor dynamic balance is consistent with that of assembly［9，11］. The automatic curvic cou?plings are not fully utilized by once pre-tightening.Besides，strong randomness of components’con?centricity easily causes large rotor eccentricity.

2 Effect Analysis of Discs’Unbal?ances on Rotor Dynamic Charac?teristics

To control rotor initial unbalance，the rotation angle method［3］is usually used to adjust the relative position of two components unbalance. In respect of 50 times assemblies and dynamic balance checks，however，the approach is found to hold strong ran?domness and cannot obtain obvious effect since the concentricity influence of components’assembly.To find the key factors of controlling rotor initial un?balance，the effect degree is discussed using vibra?tion response when the rotor system has only one unbalanced disk.

2.1 Effect analysis of single component initial unbalance

Assuming the residual unbalance value of all the assembled disks is less than 2 g·mm and the ro?tor assembly is completely concentric without any additional unbalance，the displacement responses of the combined rotor are calculated and the results are shown in Figs.3—4. The amplitude variation of ro?tational speeds for different points under many stag?es of discs are described in Figs.5—8. Herein，the distributions of 10 points along the rotor are shown in Fig.1.

Fig.3 Displacement responses of rotor at the speed that is higher than the first order critical speed

Fig.4 Displacement responses of rotor at the speed that is higher than the second order critical speed

As revealed in Figs.3—8，the displacement re?sponses of the first stage rotor of the turbine are the highest and those of the first stage disk of the axial flow are the lowest at the speed that is higher than the first order critical speed；the displacement re?sponses of the first stage disk of the axial flow are the highest，and those of the centrifugal impeller are the lowest at the speed that is higher than the sec?ond order critical speed.

Fig.5 Displacement responses with rotational speed of 10 points along the rotor (Unbalance in the first bladed disc)

Fig.6 Displacement responses with rotational speed of 10 points along the rotor(Unbalance in the second blad?ed disc)

Fig.8 Displacement responses with rotational speed of 10 points along the rotor (Unbalance in the first turbo disc)

2.2 Effect analysis of single component unbal?ance variation

We assume that the mass of the six disks in ro?tor system are 0.5，1.0，1.0，3.5，1.5，and 0.5 kg，and the allowable unbalance is 0，and the existing eccentricity e between the geometric center of the as?sembled single component and the rotating center of the rotor is shown in Fig.9. Herein，the eccentricity is defined by the runout difference of components be?fore and after assembly. If the eccentricity is 0.005 mm，the additional unbalances（m×e）are 2.5，5，5，17.5，7.5，and 2.5 g·mm，respectively. In this case，the displacement responses of the combined rotor are obtained as shown in Figs.10—11.

Fig.9 Schematic diagram of the eccentricity of six disks rel?ative to rotational center

Fig.10 Displacement responses of rotor with additional un?balance at the speed that is higher than the first or?der critical speed

Fig.11 Displacement responses of rotor with additional un?balance at the speed that is higher than the second order critical speed

As shown in Figs.10—11，the displacement re?sponses of the first stage rotor of the gas turbine are the highest，and those of the first stage disc of the axial flow are the lowest，at the speed that is higher than the first order critical speed. The displacement responses of the first stage disk of the axial flow are the highest and those of the centrifugal impeller are the lowest at the speed that is higher than the sec?ond order critical speed. Besides，the displacement responses of the gas turbine rotor are the highest at the speed that is higher than the first and second or?der critical speeds.

3 Key Parameter Analysis of Initial Unbalance Control

To reasonably control the initial unbalance of gas generator rotor，it is necessary to analyze and verify the influence of various factors on the rotor initial unbalance，and then to determine the most in?fluential component as the key control factor in as?sembly.

3.1 Effect of single component initial unbal?ance

As illustrated in Section 2，the unbalances of both the first-stage bladed disk of the axial flow and the second-stage disk of the gas turbine should be controlled，to ensure the minimal assembly influ?ence of gas generator rotor on the rotor dynamic characteristics. Moreover，the unloading position of the combined rotor balance is located at the two disks. It should be noted that the unloading and weighting are strictly controlled in engineering be?cause they can reduce the unbalance of the whole ro?tor and increase the unbalance of single component.Obviously，unloading and weighting are one irrecon?cilable contradiction and need to be reasonably weighted.

To satisfy the requirement of the combined ro?tor dynamic balance，the weight of the counter?weight of turbine disk exceeds the allowable value due to the unloading limitation of the first-stage compressor disk. Although the dynamic balance val?ue of the rotor system meets the requirement of de?sign，the unbalances of the compressor first-stage axial flow disk and the gas turbine second-stage disk are more than 10 times the allowable value of single component，so that the gas turbine rear fulcrum largely vibrates in whole-body aeroengine test.Therefore，it is impractical that the initial unbalanc?es of both the first-stage bladed disk of the axial flow and the second-stage disk of the gas turbine are regarded as key control factors in assembly.

3.2 Effect of curvic couplings runout

In this section，the high and low points of mea?suring curvic couplings runout are taken as the objec?tive of study. Assembling test with the high point dislocated 180° and 0° are carried out to verify the high and low points of measuring curvic couplings runout. We find that the eccentricity of the rotor can be effectively controlled when high point dislocates 180°. The initial unbalance distribution range of the rotor is significantly reduced by reducing the assem?bly eccentricity of components with large mass，for example centrifugal impeller. Based on the test，10 testing values distribute in the range［140 g·mm，300 g·mm］. Therefore，it is suitable to take the matching of the high and low points of curvic cou?plings as control factor in assembly.

3.3 Effect of thread processing quality of cen?tral tie rod

Typical gas generator rotor of turboshaft en?gine is assembled by the central tie rod pre-tighten?ing in stages. On the central tie rod，there are three threads and three lug-bosses. The coaxiality be?tween two threads or two bumps or threads and bumps directly affect rotor curvic couplings，and the assembled coaxiality of rotor components，so that the eccentricity emerges. When the central tie rod is completely screwed in the first stage of compressor disc，especially，the verticality of the end face to the diameter for the front thread of the central tie rod greatly influences rotor initial unbalance so that it is difficult to further improve the verticality in the man?ufacture.

To reduce the influence of thread processing quality，the corresponding adjustment procedures should be added in the assembly process in term of the analysis of comparison. The adjustment proce?dure is that the eccentricity effect of the central tie rod caused by the top dead of front end（such as re?treating at least 30°—60°）can be eliminated by ad?justing the axial distance between the central tie rod and the inner hole of the first disk. Meanwhile，cen?trifugal impeller runout is ensured to meet the de?sign requirements by adjusting the relative position of the central tie rod relative to the centrifugal impel?ler（through the retreat range of 30°—360°）.

Through the monitoring results of outer circle runout of rotor curvic couplings of many gas genera?tor assemblies，it is found that the outer circle run?out of the front and rear curvic couplings of the hub axle least affects the initial unbalance，while the out?er circle runout of the curvic couplings between pri?mary and secondary and tertiary disks has the great?est effect.

Hence，the angle adjusting process method of the central tie rod can be used as the key control fac?tor in assembly by quantitatively checking whether outer circle runout of curvic couplings between pri?mary disk and secondary and tertiary disks is con?trolled within［0，0.01 mm］. This measure can rap?idly control the runout of centrifugal impeller more which is consistent with the requirement of single pattern runout，and then control the dispersion de?gree of initial unbalance of gas generator rotor. The initial unbalance is controlled within the range［80 g·mm，170 g·mm］through 10 tests.

3.4 Effect of rotor pre?tightening

To fully utilize the self-centering function of curvic couplings，we adjust rotor pre-tightening mode，besides increasing the clearance of the front end of the central tie rod. Conducting the steps of tension—loosening—tension—loosening—tension can eliminate the match randomness of curvic cou?plings and thread，and well guarantee the assembly consistency of all rotor components and improve the stability of connection，so that the maximum value and dispersion of rotor unbalance can be further re?duced by 80%—90%. Therefore，rotor pre-tighten?ing can be considered as one control factor in assem?bling process.

4 Optimization of Rotor Assembly Process

To make rotor initial unbalance meet design re?quirements and minimize the eccentricity between the mass center of centrifugal impeller and rotor ro?tating axis，as illustrated in Fig.5. Through ten dy?namic balance checks and four whole-body aeroen?gine tests，we summarize the main measures of con?trolling rotor runout and initial unbalance as follows：

（1） Single component dynamic balance and flange runout meet the requirements of pattern.

（2）Install curvic couplings according to 180°dislocation of high runout point.

（3）Adjust the distance between the central tie rod and the inner hole of the first stage of disc to eliminate the eccentricity effect of central tie rod caused by the top dead of front end.

（4）Adjust the relative position of the central tie rod relative to the centrifugal impeller（the re?treat range 30°—360°）to ensure centrifugal impeller runout and meet the design requirements.

（5）Adjust rotor pre-tightening form with the steps of tension—loosening—tension—loosening—tension to eliminate the match randomness of curvic couplings and thread，and well keep the assembly consistency of all rotor components and improve connection stability.

（6）Select the reasonable pre-tightening pro?cess to ensure the stability and consistency of pretightening force［8］.

（7）Give the strict quantitative criteria of the runouts of curvic couplings circular and centrifugal impeller at specific locations，which are in accor?dance with the design requirements.

5 Conclusions

To gain the optimal rotor assembly process，this paper firstly analyses the influences of rotor ini?tial unbalance of single disc and combined discs on rotor dynamic characteristics in respect of the disper?sity of rotor initial unbalance and then discuss the key control factors of affecting rotor initial unbal?ance. Through these investigations，some conclu?sions are summarized as follows：

As illustrated in the effect analysis of discs’un?balances on rotor dynamic characteristics，（i）the displacement responses of the first stage rotor of gas turbine are the highest and those of the first stage disk of axial flow are the lowest at the speed that is higher than the first order critical speed；（ii）the dis?placement responses of the first stage disk of the axi?al flow is the highest and those of the centrifugal im?peller are the lowest at the speed that is higher than the second order critical speed；（iii）the displace?ment responses of the first stage rotor of the gas tur?bine are the highest and those of the first stage disc of the axial flow are the lowest at the speed that is higher than the first order critical speed；（iv）the displacement responses of the first stage disk of the axial flow are the highest and those of the centrifu?gal impeller are the lowest at the speed that is higher than the second order critical speed. Besides，the displacement responses of the gas turbine rotor are the highest at the speed that is higher than the first and second order critical speeds. Therefore，the most important factors contributing to rotor vibra?tion are the unbalances of first stage compressor disc and the second stage turbine disc.

From the key factor analysis of initial unbal?ance control，we find that：（i）it is impractical that the initial unbalances both the first-stage bladed disk of the axial flow and the second-stage disk of the gas turbine are regarded as key control factors in assem?bly；（ii）it is suitable that the matching of the high and low points of curvic couplings is regarded as the control factor in assembly；（iii）the angle adjusting process method of the central tie rod can be used as the key control factor in assembly to quantitatively check whether outer circle runout of curvic cou?plings between primary disk and secondary and the tertiary disks is controlled within［0，0.01 mm］；（iv）rotor pre-tightening can be considered as one control factor in assembling process.

The main measures of controlling rotor runout and initial unbalance are given to make the assembly process simpler and more effective as well as timely control the rotor initial unbalance.

The efforts of this study validate that the pro?posed method is workable for the rotor tightened by a central tie rod and possesses the significant mean?ing of practical application in engineering.