Some Comments Concerning the Preparation of and Fatigue Testing of the Aircraft’s Cable-Control System

Cable-control systems of GA¹ aircraft and gliders will remain in use, owing to the use of the electrical or hydraulic systems being irrational due to the inappropriate costs and complex services involved. Currently, symmetrical loads and bending are used in the fatigue tests of airplane cable-control systems, just like in the tests of elevator ropes². The cable and ropes tests are commonly conducted by bending them in the range of ±90° with a constant load. The mentioned tests are adequate for assessing the operational loads of cable transport systems such as cranes, lifts, vertical and horizontal cable transport, and so on (Brzęczek, 2020; Kubryn et al., 2018; Tytko, 2021). For the ropes and pulleys of transport systems, the described methods are used to assess the wear and for damage evaluation (Hankus & Hankus, 2006; Kubryn et al., 2018; Tytko, 1998, 2021). Typical cables test results are given in Figure 1. Kubryn et al. (2018) and Tytko (1998) could only partially point out to the real wear as a function of the operational measure and fatigue life of the aviation-control systems, and these do not correlate with the real deflections and loads.

Figure 1.

The forces transferred by the control system should ensuring stability and control are limited by admissible control are results from surfaces deflections ϴ_w and values of forces P_F and flying controls as well, Figure 6. (Brzęczek, 2019; Certification Specifications for CS-23, 2003). The flight stability and the aircraft’s control are carried out by changing the moments relative to the CG³ of the aircraft (Figure 2). Values of the hinge moments are not linear functions of control surface deflection, and it is difficult to precisely determine their actual values as well.

Figure 2.

The given dependencies indicate the complexity of the issue with random loads and deformations (see Figures 8 and 9). The characteristics of variability are typical and similar for defined airplane categories, operation profiles, and the in-flight mass and CG position. Real loads of the control systems are modified by the required pretensioning (Certification Specifications for CS-23, 2003). The sum of the pretensioning and the real loads cannot reach a negative value for any permissible flight configuration, including loads generated by doubled control systems (Brzęczek, 2019; Certification Specifications for CS-23, 2003). Specifications (Certification Specifications for CS-23, 2003) also require that the designed systems ensure the positive gradients of the flying controls forces P_F (steering wheel, control stick, pedals) as a function of their range of displacement ϴ_w (Figure 6).

Transmission of hinge moments, M_zaw, (Figure 4) causes the difference in tension between the active and passive cables (Figure 6). The random loads of cables caused a complex state of stresses of the wires: stretching, twisting, and contact pressure loads related to the wrap angles of the cable sheaves ϴ_L (Figures 6 and 13). Variations of the deflections, β_H and δ_H, (Figures 4 and 6) are the results of the required configurations of moments: M, L, and N in flights related to the aircraft’s CG (Figures 2 and 8). Results of tests (Kubryn et al., 2018; Figure 1) of aviation cables based on the symmetrical variable loads and bending cycles cannot be used for predicting the service life and unequivocal guidelines for the planning, inspection, and intervals of dianosis. Due to the lack of reliable test results, it is recommended to mandatorily inspect defined areas of cable-control systems, especially for the most-loaded element with relatively short inspection intervals, for example, 25 hr of flight. The regulations (Certification Specifications for CS-23, 2003) also require the visual ongoing inspection of critical elements of cable-control systems.

In the present article, only the longitudinal control of the aircraft was analyzed (Figure 2). The resultant value of the force on the tail, P_H, (Figure 3) ensures longitudinal balance, stability, and flight control. Values of forces in the reference coordinate system of the airplanes are dependent on the flight speed v, aircraft CG, and their position l_h, tail angle of attack angle α_H, deflections β_H, and trimming tab δ_H (Figures 3 and 4). The components of the resultant forces on the horizontal tail unit, P_H, are described using simplified formulas (1–4).

Figure 3.

Figure 4.

Required values of forces and moments depend on the current aircraft configuration (CG position, l_h α_h), control surface deflections (β_h, δ_h) and their aerodynamic parameters (dC_zh, dC_xh) Figures 2 and 3).

Generalized aerodynamic data can be used for the estimation of β_H and α_H (Eqs (3) and (4)), but the hinge moments, M_zaw (Figure 4) cannot be easily estimated. The mandatory requirements (Certification Specifications for CS-23, 2003) determine the maximum values of the forces (Eq. (3)), but the actual value M_mz and its variability are necessary for the determination of the load spectrum and for programming the fatigue test of the aircraft’s cable systems. Measurements of the strain gauge of the cable forces in connection with the α_H angle inclination, deflections β_H, and the trim tab δ_H (Figure 4) are disturbed by the specificity of the analyzed airplane’s system and the real measurement conditions of the preload changes (Brzęczek, 2019).

Loads and strain of the cable should be presented in conjunction with the changes in wrap angles ϴ_L and the aircraft’s operation profiles. To avoid disturbances generated in the specific aircraft being tested, the results of the hinge moments of the rudders (Krzysiak, 1983) data have been used in the study. The proposed solution will allow to generalize the preparation of the spectrum of loads and test results as well, for the analyzed category of airplanes according to the implemented exploitation profiles.

This approach with respect to the geometric configuration as given in Figure 2 and the required values of deflection for profiles of exploitation (Figures 4, 7, and 8), CG position, and mass changes in the flight should be used for analyses and tests and for programing the service life of aviation control-cable systems.

The values of the control systems forces with respect to surface deflection, β_H, (Figure 4) and the variability of the hinge moments can be estimated by two ways: (a)

From the measurements of the actual values of the forces on the passive and active cables of the aircraft operated in a specific operating profile, related to angle β_H of deflection (Figure 4). The actual reliable values are not obtainable due to the frictional forces and the actual pre-tension values and other disturbances. Additionally, the collected data are related to the specific tested airplane.

Method (a) is closely related to the configuration of the aircraft (see Figure 1), the specific CG, and the profile of its operation. In this study, the second method (b) was analyzed. Data prepared in this way can be further generalized by taking into account the actual values of air speed, mass in flight, and the actual CG position. When converting data into the test loads spectrum, the maximum pre-tension values should be used as a conservative approach (Figure 13).

The sources and methods of the loads of the aircraft and the aircraft’s control system acquisition are presented in Figures 5 and 7.

Figure 5.

Figure 6.

Figure 7.

All real or postulated missions of the selected airplane category allow to define a typical operating profile. The spectrum of the real loads of the aircraft’s control systems are divided into:

– controlled loads (depending on the pilot and his training, but determined by the category of the aircraft and their operational profile) are resulting from performed missions;

Actual load values of control system elements (Figure 6) during the flight mission (Figures 7 and 8) should be collected as the result of the operating load spectrum based on the operation aircraft’s profile.

Figure 8.

The loads of cables are combined with deformations on the pulleys or sliders, and real forces cause a complex state of stress in the strands and wires of the cables (Brzęczek, 2019).

The requirement is for a positive cable tension for each extreme load (Certification Specifications for CS-23, 2003); hence, the need to introduce the P_W cable pre-tension (Brzęczek, 2019; Certification Specifications for CS-23, 2003) (Eq. (5)).

From analyzing the stability and maneuverability of airplanes related to the geometrics and kinematics of cable control systems, we conclude: the deflections of the control surfaces are ±10° for >90% of the total surface deflection (see Figure 9).

Figure 9.

The above-mentioned control-cable deformations and displacements indicate that their fatigue lives are much more than those obtained in the tests (Kubryn et al., 2018; Pieróg, 2011).

The factor significantly influencing the fatigue life of the cables is a relatively low-value cable load. The method described below and the results of the related tests can be useful for predicting the fatigue life of the cables and defining the diagnostic and adjustment intervals.

The force values of the cable-control system can be presented in formulas (5) and (6): 5 P(αH,βH,υ,n,t)=PW±PM≥0 \[P\left( {{\alpha }_{H}},{{\beta }_{H}},\upsilon ,n,t \right)={{P}_{W}}\pm {{P}_{M}}\ge 0\]

Note: Positive tension of the passive cable of control systems means that P_W should always be greater than P_M for any permissible flight maneuver (Certification Specifications for CS-23, 2003; Figure 5). 6 PM=kCmz(αH,βH,δH,υ,τ) \[{{P}_{M}}=k{{C}_{mz}}\left( {{\alpha }_{H}},{{\beta }_{H}},{{\delta }_{H}},\upsilon ,\tau \right)\] where:

P (α_H, β_H, υ, n, t) – total forces in the active and passive cables as a function of flight parameters (Figures 6 and 13);

Figure 10.

Below, the two possible methods of C_mz determination are presented (both based on tunnel research): (a)

Using the C_mz = f (α_H, β_H, υ) chart for specific aviation profiles with appropriate values of: K (Eq. (10); Figure 6), R_e, M, similarity number (Figure 10);

The values of the hinge moments coefficients of the control surfaces determined by the data obtained from tunnel tests are given by formula (7): 7 Cmz(Re,Ma,K)=b1αH+b2βH+b0 \[{{C}_{mz}}\left( {{R}_{e}},{{M}_{a}},K \right)={{b}_{1}}{{\alpha }_{H}}+{{b}_{2}}{{\beta }_{H}}+{{b}_{0}}\] where: 8 b1=∂Cmz∂α \[{{b}_{1}}=\frac{\partial {{C}_{mz}}}{\partial \alpha }\]

– see Figure 11

– see Figure 12

b₀ – coefficient related to the shape of the tail profile.

Figure 11.

Figure 12.

Loads of the passive and active cables of the airplane control system should be additionally corrected by the friction forces of the systems (Brzęczek, 2019). The values of the deflections β_H are additionally correlated with the angles of attack α_H and δ_H; the CG position enables completing the operating spectrum of cable loads (Figure 9).

The stochastic deflections of the control surfaces, β_H, δ_H, CG, (Figures 7–9.) measured for the typical exploitation profile of the defined airplane’s category enable determining the loads spectrum of active and passive cables of the control systems (Figure 5). Test spectra (Figure 9) are related to the flight hours and are not the quantity of cable bending (Department of Avionics and Control Systems of Rzeszów University of Technology, 2019) is presented. The test results are described as a function of flight hours for a given aircraft category (Figures 5 and 9) that should be performed on the critical pulley of the system, i.e., on the greatest bending (max ϴ_L) (Figure 13). Test results with additional measurements of the cable elongation and broken wires enable determining the real wear of the cable and pulley (Figure 13) as a function of flight hours. On the basis of the above-mentioned data and the fatigue tests results, formula (11) can be used to determine the fatigue life and diagnostic intervals of the cable system (Tytko, 1998, 2021).

Figure 13.

The main task involved in conducting the tests of airplane cable-control systems (Figures 6 and 13) is the use of stochastic non-linear loads correlated with cable deformation. The strand allows test cables with different wrap angles, but with the same variable (stochastic) load values, for two or more cables at the same time. The cable loads are applied by angular excitation, and the nonlinearity of the forces changes as a function of the deflection angles and is implemented by spring or hydraulic systems.

In addition, as emphasized in this paper, the magnitude of the used loads is in correlation with the cable deformation and displacement (Figure 6). Loads and operational spectrum are related to the specific type of airplane control system (Figures 5 and 7) moreover enables to define a critical point on the cable system by the wrap angle displacement (Figure 13). The critical point and fatigue test results should be used to plan the inspection and diagnostic intervals of the aircraft’s cable-control systems.

A measure of the symptoms of wear of the aviation control-cable systems can be conducted by the cable elongation, reduction of cable diameter, and the broken wires. The measurement test’s results will be used for coefficients a₁, a₂, and a₃ for the elongation estimate (Eq. (11)). The course of the curve lengthening of the operated cable similar to the tribological curve and, in accordance with Hankus and Hankus (2006) and Hankus (2004, 2014), can be well described by formula (11): 11 ε=a0+a1P(+a2P3+a3P3) \[\varepsilon ={{a}_{0}}+{{a}_{1}}P\left( +{{a}_{2}}{{P}^{3}}+{{a}_{3}}{{P}^{3}} \right)\] where:

ε – limit elongation of the cable or rope;

The assessment of the elongation of the cable can be determined by the measurement of the pre-tension (Brzęczek, 2019, 2020) as well. Based on the results of measuring the cable elongation, the term for the diagnostics intervals and the cable replacement can be predicted (Brzęczek, 2019).

The presented method for preparing and performing the fatigue tests of an airplane’s control-cable system is based on the real loads and deformations of the cable under random values of forces. The loads of the control cables with the associated complex stress of the individual wires, in the presented proposal, are determined by the real values of the hinge moment and other related factors such as the aircraft’s operational profile consequence. The proposed solutions are based on flight measurements of α_H, δ_H, related to the CG position and laboratory wind tunnel profiles test results. The advantage of the proposal is the availability of data related to the real surface deflections of the control systems. A drawback of the proposed solution is the necessity to control the cable tension with the appropriate measurement accuracy, which according to Brzęczek (2019, 2020) is a complex task. The results of the measurement of the line elongation as a function of flight hours give reliable information on the service life of the cable-control system, intervals of inspection, fatigue life forecasting, and decisions concerning cable replacement.