Optimized Design and Structural Mechanics of a Single-piece Composite Helicopter Driveshaft

Open Access
Henry, Todd Carl
Graduate Program:
Aerospace Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
June 09, 2014
Committee Members:
  • Charles E Bakis, Dissertation Advisor
  • Edward C Smith, Committee Chair
  • George A Lesieutre, Committee Member
  • Christopher Rahn, Special Member
  • Flexible Matrix Composites
  • Optimization
  • Helicopter Driveshaft
  • Filament Winding
In rotorcraft driveline design, single-piece composite driveshafts have much potential for reducing driveline mass and complexity over multi-segmented metallic driveshafts. The single-piece shaft concept is enabled by the relatively high fatigue strain capacity of fiber reinforced polymer composites over metals. Challenges for single-piece driveshaft design lie in addressing the self-heating behavior of the composite due to the material damping, as well as, whirling stability, torsional buckling stability, and composite strength. Increased composite temperature due to self-heating reduces the composite strength and is accounted for in this research. The laminate longitudinal stiffness (Ex) and strength (Fx) are known to be heavily degraded by fiber undulation, however, both are not well understood in compression. The whirling stability (a function of longitudinal stiffness) and the composite strength are strongly influential in driveshaft optimization, and thus are investigated further through the testing of flat and filament wound composite specimens. The design of single-piece composite driveshafts, however, needs to consider many failure criteria, including hysteresis-induced overheating, whirl stability, torsional buckling stability, and material failure by overstress. The present investigation uses multi-objective optimization to investigate the design space which visually highlights design trades. Design variables included stacking sequence, number of laminas, and number of hanger bearings. The design goals were to minimize weight and maximize the lowest factor of safety by adaptively generating solutions to the multi-objective problem. Several design spaces were investigated by examining the effect of misalignment, ambient temperature, and constant power transmission on the optimized solution. Several materials of interest were modeled using experimentally determined elastic properties and novel temperature-dependent composite strength. Compared to the baseline multi-segmented metallic driveline, weight reductions of 43% and 48% were obtained for single-piece flexible and rigid matrix composite shafts. The rigid matrix weight reduction was slightly lower than that seen in the literature due to consideration of shaft misalignment. In filament wound composites, the existence of fiber undulation introduces unique challenges in the prediction of compressive modulus and strength using traditional laminated composite theories. In the current investigation, novel full field strain measurements of compressively loaded specimens were used to evaluate local strain distributions in the region of a 0-deg. undulated lamina in a [0n/90n]s laminate (n=2,4,6) and a 30-deg. undulated lamina in a [30n/-60n]s laminate (n=2,4). Unique to this research, specimens were fabricated with carbon fibers, various amplitudes of undulation, and matrix materials with three different moduli of elasticity. Full-field strains were measured on the free edge and across the width of the compressively loaded specimens using two-dimensional digital image correlation (DIC). The observed strains were highly influenced by the undulation geometry. The longitudinal modulus of a [0n/90n]s laminate was more sensitive to reinforcement undulation when the matrix was flexible rather than rigid. An undulation with an amplitude/length ratio of 0.1 (low for a filament wound cylinder) reduces the average longitudinal modulus of elasticity in the undulation region by approximately 43% and 3% in laminates with flexible and rigid matrices, respectively, relative to a similar material without undulation. Observations of strain on the free edge revealed that fiber undulation caused elevated out-of-plane shear (εxz) and through-thickness normal (εzz) strains in regions eventually involved in the fiber microbuckling failure process. A new three dimensional method was derived for the homogenization of a heterogeneous composite laminate consisting of individual anisotropic lamina for which structural coupling (Bij) may occur due to in- and out-of-plane (undulation) fiber reinforcement orientation. Three-dimensional elastic constants were calculated by considering a representative volume element taken from the heterogeneous laminate. Three-dimensional elastic constant predictions were validated through comparison with established methods, both two- and three- dimensional. When the new derived three dimensional theory was applied to experimental results, the modulus and strength predictions compared favorably. A series of [±Θ/89/±Θ] cylinders with multiple helical fiber angles, winding patterns, and matrix materials were fabricated and tested in compression. Digital image correlation was used for the first time to measure outside surface displacements and strains. Longitudinal and hoop direction strain fluctuations between the undulated and non-undulated regions were found to be of the order of 20-30% of the mean values throughout the cylinders. Qualitatively, these fluctuations can be related to non-classical elastic couplings (Bij) in the anti-symmetric regions of the filament winding pattern. Failure of the cylinder occurred by fiber microbuckling, which initiated near the crossing of circumferential and helical cross-over bands. Based on a statistical analysis of surface strains in the local fiber coordinate system, it was determined that longitudinal compressive and in-plane longitudinal shear strains at incipient microbuckling were two to four times greater than their respective global counterparts. These results indicate the magnitude of strain concentration existing in the cylinders immediately before final failure (possibly during local failure) and highlight the importance of longitudinal compressive (ε11) and in-plane longitudinal shear strains (ε12) in the failure process. A novel local-global approach was used in predicting the longitudinal modulus and strength of filament wound cylinders. Several representative volume elements were chosen to represent the filament winding rhombus, and were used as a basis for homogenization. Strength predictions were augmented with empirical critical distance factors. The average Ex and nuxy prediction error for Conathane DPRN 30917 was 6.8 % and 21 % and the average error for EPON 862 was 9.7 % and 14 % respectively. The strength prediction error was approximately 7.7 % and 24 % for 30917 and EPON 862 with failure location typically at the circumferential undulation by mode sig6 (tau12). The failure mode prediction was consistent with experimental observations from filament wound cylinders and flat-undulated specimens of similar lamination arrangement. Additional comparison with previous Adiprene LF750 filament wound cylinder testing produced prediction error of 11.8 % and 8.9 % for longitudinal modulus and strength respectively. The average absolute value of the error, considering every material, for modulus, strength, and Poisson’s ratio was 14 %. Application of critical distance factors to flat undulated specimens was deemed unadvisable due to considerably higher strain intensity at failure compared to filament wound cylinders.