Abstract—The motion of main rotor head of helicopter rotor system is complex. Its reliability influences flying qualities and safety of helicopter directly. But, traditional experiments and deterministic simulation have been difficult to measure movement (flapping, lead-laging and pitching angles) and analyze motion reliability of main rotor head quantitatively. The virtual prototype model was built in the integrating simulation environment, which integrated Catia, MSC.Simdesigner and Adams. On the platform of Adams, we used the deformation of torsional spring to fit the moving angles. The kinematic and dynamic properties were simulated and analyzed deterministically. According to the compared result with the test data, it is shown that the virtual prototype is true and the result is feasible. Finally, we implemented reliability software-ARES which has been developed independently to call Adams and computed the flapping reliability quantitatively. The reliability and the sensitive parameters were obtained. Combined with the results and practical engineering, we presented an effective way to improve the flapping reliability from 0.9904 to 0.9993.
Keywords-Helicopter, Main Rotor Head, Flapping Motion, Virtual Prototype, Reliability
I. INTRODUCTION As the primary lifting surface and control surface of
maneuvering flight of helicopter, main rotor system has so many moving parts, manipulate complex and its reliability problem is serious. On one hand, main rotor system has strength reliability which includes static strength reliability, fatigue reliability etc. Presently, the strength reliability has attracted scholar’s attention. Along with the adoption of new material, composites and the technical of fail-safe, the strength reliability has been effectively raised. On the other hand, main rotor system also has the motion reliability which is defined as in appointed time and condition, mechanism or part’s ability of performing the compulsory motion accurately, coordinately and in time. Main rotor system controls the flight status through flapping, lead-laging and pitching motion; its reliability influence the flying qualities and security. For instance, the flapping couldn’t excess the set range. Otherwise, the collision between tip of blade and body or other parts will cause accident. One-tenth accidents of helicopter are because of motion reliability of main rotor system [1].
There are two hard nuts in motion reliability analyses of main rotor system. The first is motion angle is hard to be measured. Photometry, electrical measurement method of strain and laser test method in laboratory all need precision
instruments which may produce error because of the nonlinear character of sensor. Also, flying status that can be simulation in laboratory is limited. The second, quantitative reliability computation is complex. The motion of main rotor system is a typical aero-elastic problem and involves a number of random factors which are hard to be simulated and controlled.
Focusing on the problem of measuring flapping angles, we simulated the motion angle with flexible parts in Adams according to the main rotor head’s characteristic. In this paper, we simulated various flying status by changing loading factors. With quantitative reliability computation, we applied mechanical reliability software ARES, in which main influencing factors were build as random variables, so we can simulate factors’ randomness by sampling. The command file of Adams which called the solver to compute the range of flapping was modified by approach of direct mapping stochastic simulation [2]. Lastly, we got the reliability and sensitivity of parameters by statistic method. Combined with the results and practical engineering, we present an effective way to improve the flapping reliability.
II. MULTI-BODY DYNAMICS MODELING AND SIMULATION
In the process of multi-body dynamic modeling of main rotor head, geometrical model for the key parts were built up and assembled using Catia firstly, and then this model was introduced into Adams seamlessly. In this way, the parameters (mass, rotational inertia) which are introduced into Adams from Catia will not be changed. Constraint of kinematical pairs can be added in MSC.Simdesigner, but they should be modified in Adams to guarantee the success of dynamic simulation [3].
The model should be modified because it is rigid that doesn’t fit the fact, which is introduced into Adams from Catia. The main elastic parts of main rotor head are damper and spherical bearing. According to the experience of project, damper can be simplified with spring. Spherical bearing is the key part of main rotor head which is composed of two joints (one is bigger than the other), layered bowel-shaped spacer and layered rubber by process of sulfuration. Spherical bearing applies flapping, lead-laging and pitching by the deformation of layered rubber [4]. The type for spherical bearing is shown in the Fig. 1.
Focusing on the problem of difficultly to measure the flapping angles, we divided sphere bearing into two parts, connected the two parts with spherical joint to simulate its flapping, lead-laging and pitching function, attached three torsional springs which were orthogonal to each other to fit the resistance movement. We also assigned flapping stiffness, lead-laging stiffness and pitching stiffness which had been obtained from experiment to the torsional springs. So we can simulate the motion angle with the deformation of the corresponding torsional spring. Details are shown in Fig.2.
Figure 2. simplification of the spherical bearing
According to the connection of main rotor head, we added constraint of kinematical pairs and loaded the laboratory dates which had started from static status to autorotation limit status. These dates included stiffness of spherical bearing, torque from the spindle, static and dynamic force and torque from blade etc (as in table I). And then we set solver parameters, obtained flapping angle in the process. (Fig.3).According to the compared result with the test data [5], it is shown that the virtual prototype is true and the result is feasible.
TABLE I. .SITFFNESS OF ELASTIC BEARING
Performance indicators Test result Computation value Item Design requirement Test value Error%
The minimum flapping value in flapping angle curve closely to lower flapping stops in early transient regime. But owning to the limitation of the deterministic simulation, we are hard to estimate the influence of factors’ randomicity, and we can’t get the flapping reliability. Therefore, quantitative reliability simulation should be taken on in the next stage.
III. QUANTIATIVE MOTION RELIABILITY SIMULATION
A. The Direct Mapping Stochastic Simulation Scheme Based on Adams Direct mapping stochastic simulation based on the Adams,
is mainly about the reliability software ARES which is developed independently to invoke input and output files of adams. Next, ARES revise variables in input files and feedback to Adams solver to compute dynamic response. We can get plenty of minimum value of flapping angle by
sampling a lot of times. Lastly, under the reliability model we selected an appropriate reliability algorithm to compute the flapping reliability [6]. The main processes are shown in Fig.4.
Figure 4. Direct mapping simulation based on Adams
B. The Reliability Simulation of Flapping Motion I) Random Variables and Their Statistic Characteristics
Based on the characteristic of flapping motion of main rotor head, we defined 8 variables; these were static and dynamic load inputted by blade pin, flexural rigidity and
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damping coefficient of spherical bearing, rotating speed of main rotor etc, which were shown in table II.
TABLE II. RANDOM VARIABLES AND THEIR STATISTIC CHARACTERISTICS
Number random variable Mean value Coefficient of variation Distribution 1 Minimum value of flapping(r) 06−
0.01 Normal distribution
2 flexural rigidity of spherical bearing(f) 1053Nm/d 0.1 Normal distribution 3 damping coefficient of spherical bearing (p) 0.1 0.1 Normal distribution 4 rotating speed of main rotor (w) 35rad/s 0.01 Normal distribution 5 Static bending moment of blade pin I (t1) 263.1Nm 0.05 Lognormal distribution 6 Dynamic bending moment of blade pin I (t2) 320Nm 0.1 Exponent distribution 7 Static bending moment of blade pin II(t3) 263.1Nm 0.05 Lognormal distribution 8 Dynamic bending moment of blade pin II(t4) 320Nm 0.1 Exponent distribution
II) Define the limit state equation of Flapping Motion Based on the stress strength model, we defined the problem
statement of flapping motion as follows:
(1) ( , , , 1, 2, 3, 4)y r g f p w t t t t= −
In the equation, r is the designed minimum value of
flapping, is the minimum value which is outputted from Adams.
( , , ,w t1, 2, 3, 4)g f p t t t
As the flapping motion of main rotor head is a typical aero-elastic problem, its dynamic response is a nonlinear function, so choose the Monte Carlo Radius-Outside Adaptive Importance Sampling (MCROIS) algorithm to compute the reliability [7], obtained the results shown in table III and parameters insensitivity in Fig.5.
TABLE III. THE RESULTS OF RELIABILITY
Reliability Algorithm Simulation times Failure probability Reliability Simulation time/h MCROIS 10000 0.0096 0.9904 5.2h
Figure 5. sensitivity of parameters
III) Analysis of Reliability Simulation Result According to the parameters’ sensitivity, we know that
flexural rigidity of spherical bearing influent the reliability mostly. Raising the mean value and reducing the coefficient of variation of flexural rigidity can enhance the reliability. Raising the mean value to 1100Nm/deg, reducing the coefficient of variation to 0.05, we get the reliability is 0.9993.
Furthermore, the calculating formula for flexural rigidity of spherical bearing is as follows, according to the bearing’s types.
Flexural rigidity for one layer:
2 4
0(cos cos )90
ii
GRKt
π β β= − (2)
Flexural rigidity for elastic bearing:
1
1
1( )n
i i
Kk
−
=
= ∑ (3)
G is shear modulus for one layer of spherical bearing, iR is radius for one layer of spherical bearing, t is thickness for
one layer of spherical bearing, 0β is original bending angle, β is bending angle.
Therefore, raising radius, raising shear modulus, reducing thickness for one layer and reducing original bending angle of spherical bearing can raise the flexural rigidity and improve the flapping reliability. Besides, raising the technique level to reduce the coefficient of variation also can achieve the same purpose.
IV. CONCLUSIONS This paper has proposed an approach for the analysis of
motion reliability of main rotor head which integrated Catia, MSC.Simdesigner, Adams and ARES. Key technologies have been settled, cost has been reduced and the design cycle has been shortened.
According to the flapping reliability simulation, the practicability of the simulation scheme was approved. Combined with practical engineering, we improved the reliability from 0.9904 to 0.9993.The scheme is also suitable for computing the lead-laging and pitching reliability.
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Therefore, we apply an effective way to solve the difficult problem of motion reliability of main rotor head.
Besides, the direct mapping stochastic simulation scheme in the environment of ARES which based on Adams is suitable for motion reliability simulation.
ACKNOWLEDGMENT The authors wish to thank the Chinese Helicopter
Research and Development Institute for its continued support. This work has also been supported by Dept. of Project System Engineering of Beihang University.
A special thanks goes to Zhang Jianguo for his valuable supports and comments on the preparation of this paper.
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[4] Ji lianyuan, Application research of rotor system spherical thrust bearing, Helicopter technologh,2003,131(3):3-11
[5] Eurocopter, Main Rotor Dynamic Characteristics of EC× × ,2006 [6] Raizer V.theory of reliability in structural
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