As the demand for higher power density and lower fuel consumption in helicopter transmission systems continues to rise, the lightweight design of face gear components has become a central engineering challenge. In a typical face gear transmission, the gear meshes with multiple pinions and output gears simultaneously, which creates complex load paths and severe stress concentrations. Replacing high-strength steel with carbon fiber reinforced polymer (CFRP) in the web region of a face gear offers a promising route to reduce mass while maintaining structural integrity. In this work, I designed, analyzed, and manufactured a hybrid face gear in which the original steel web is replaced by a CFRP web connected to the inner hub and outer tooth ring through bolted metallic flanges. The entire hybrid face gear achieved a mass reduction of 10.48% compared with the all-steel baseline, while satisfying the required stiffness and strength criteria. The following sections describe the material selection, finite element benchmarking, equivalent design, ply stacking strategy, and hot compression molding process in detail.
Material selection and characterization
For the composite web, I selected a T300-3K woven carbon fiber fabric prepreg with an epoxy matrix. The areal weight and single-ply thickness were carefully chosen to allow gradual thickness transitions in the web. The nominal cured ply thickness was 0.21 mm. I fabricated standard coupons according to ASTM D3039, ASTM D6641, and ASTM D3518 to obtain the elastic moduli, Poisson’s ratio, and strength values in the warp and weft directions, as well as the in-plane shear response. The measured material properties are summarized in Table 1. The steel components, including the tooth ring, hub, and bolts, were made of 9310Q high-strength steel and 40Cr quenched and tempered steel, respectively. The 9310Q steel had an elastic modulus of 69.8 GPa, a Poisson’s ratio of 0.27, and a minimum yield strength of 940 MPa. The 40Cr bolts had a yield strength of 785 MPa.
| Property | Symbol | Value | Unit |
|---|---|---|---|
| Warp elastic modulus | \(E_1\) | 69.80 | GPa |
| Weft elastic modulus | \(E_2\) | 69.80 | GPa |
| In-plane Poisson’s ratio | \(\mu_{12}\) | 0.058 | – |
| In-plane shear modulus | \(G_{12}\) | 4.94 | GPa |
| Warp tensile strength | \(X_t\) | 937.0 | MPa |
| Warp compressive strength | \(X_c\) | 440.0 | MPa |
| Weft tensile strength | \(Y_t\) | 891.0 | MPa |
| Weft compressive strength | \(Y_c\) | 436.0 | MPa |
| In-plane shear strength | \(S\) | 66.7 | MPa |
The density of the cured CFRP was approximately 1.55 g/cm³, while the density of 9310Q steel was 7.85 g/cm³. This large difference in density provides the primary motivation for replacing the steel web with a composite web, because the web contributes a significant fraction of the total face gear mass even though it carries relatively lower contact stresses than the gear teeth.
Design requirements and load cases
The original all-steel face gear had a total mass of 42.75 kg, excluding the teeth. The gear meshed with two idler gears, one input gear, and two output gears at five distinct locations on the face gear tooth surface. The resultant loads on the face gear can be decomposed into a tangential force \(F_t\) within the tooth surface plane and an axial force \(F_a\) normal to the tooth surface. Seven load cases were identified from the transmission duty cycle. The most severe load case was used for the initial design and sizing of the composite web, and the remaining six cases were used for verification. Table 2 lists the power, torque, tangential force, and axial force for the critical positions. The design targets were: (i) the stiffness of the hybrid face gear must not be lower than that of the all-steel face gear; (ii) no yielding may occur in any metallic component; (iii) the strength of the hybrid face gear should be as close as possible to that of the steel baseline; and (iv) the total mass reduction must be at least 10%.
| Position | Power (kW) | Torque (N·m) | Tangential force \(F_t\) (N) | Axial force \(F_a\) (N) |
|---|---|---|---|---|
| 1 | 1928.3 | 47089.9 | 21958.4 | – |
| 2 | 752.9 | 18387.2 | 8574.1 | – |
| 3 | 0 | 0 | 0 | 0 |
| 4 | 752.9 | 18387.2 | 8574.1 | – |
| 5 | 683.6 | 16693.9 | 7784.5 | – |
For the finite element analysis, I simplified the geometry by filling non-load-bearing blind holes and removing small fillets that would otherwise increase meshing difficulty. The all-steel face gear was discretized with 90,360 C3D8R brick elements in a commercial finite element package. A linear elastic material model was used for the steel. The boundary conditions were applied at the hub spline, and the loads listed in Table 2 were applied at the corresponding tooth contact locations. The maximum displacement of the steel face gear occurred near the loaded tooth flank and reached 1.52 mm. The maximum von Mises stress was 352.6 MPa and was located in the reinforcing ribs on the lower-left side of the web. These results served as the benchmark for the hybrid design.
Equivalent design of the composite web
The basic idea of the equivalent design was to replace the steel web with a CFRP web of larger thickness such that the global bending stiffness and membrane stiffness were preserved or improved. The equivalent thickness for a simple plate under bending can be estimated from
$$t_c = t_m \left( \frac{E_m}{E_c} \right)^{1/3} \left( \frac{\rho_m}{\rho_c} \right)^{1/3}$$
where \(t_c\) and \(t_m\) are the composite and metal web thicknesses, \(E_c\) and \(E_m\) are the effective elastic moduli, and \(\rho_c\) and \(\rho_m\) are the densities. Because the composite modulus is lower than that of steel, the thickness must increase to maintain stiffness. However, the density is also lower, so the mass can still be reduced. In practice, I used a more detailed finite element based iterative procedure. The original steel web thickness was 9.5 mm. A direct replacement with a 9.5 mm composite web resulted in a maximum displacement three times larger than the steel baseline and unacceptable stress levels. Therefore, I increased the composite web thickness in steps, while keeping the outer tooth ring and inner hub unchanged. The space envelope allowed a maximum web thickness of 30 mm near the hub and 14.94 mm near the tooth ring. To further improve stiffness and strength, I added radial reinforcing ribs. The final design used 12 ribs, each 8 mm thick. The web was connected to the steel tooth ring and hub through metallic flanges and bolts. The bolt material was 40Cr steel with a yield strength of 785 MPa.
After several design iterations, the hybrid face gear satisfied all requirements. The maximum displacement under the critical load case was 1.04 mm, which is 31.6% lower than the steel baseline. The maximum stress in the metallic parts was 630.4 MPa, occurring at the bolted connection between the composite web and the tooth ring. This value is below the yield strength of the 40Cr bolts and the 9310Q steel. The maximum stress in the CFRP web was 161.4 MPa. Using a continuum shell model, the in-plane stress components at the critical location were \(\sigma_1 = -162.1\) MPa, \(\sigma_2 = -16.0\) MPa, and \(\tau_{12} = -6.6\) MPa. Since the critical region is under compression, the Tsai-Hill failure criterion was evaluated with \(X = X_c\) and \(Y = Y_c\):
$$\frac{\sigma_1^2}{X^2} – \frac{\sigma_1 \sigma_2}{X^2} + \frac{\sigma_2^2}{Y^2} + \frac{\tau_{12}^2}{S^2} = 1$$
Substituting the stress values and the material strengths from Table 1 gives a failure index of 0.13, which is well below 1.0. Therefore, the composite web has a sufficient margin against first-ply failure. Table 3 compares the key design and performance parameters of the all-steel face gear and the hybrid face gear. The total mass of the hybrid face gear is 38.27 kg, corresponding to a mass reduction of 10.48%.
| Parameter | All-steel face gear | Hybrid face gear |
|---|---|---|
| Web thickness (mm) | 9.5 | 30.0 (hub side) / 14.94 (ring side) |
| Number of ribs | 6 | 12 |
| Rib thickness (mm) | 8 | 8 |
| Maximum stress under critical load (MPa) | 352.6 | 630.4 (metallic) / 161.4 (CFRP) |
| Maximum displacement under critical load (mm) | 1.52 | 1.04 |
| Total mass (kg) | 42.75 | 38.27 |
| Mass reduction (%) | – | 10.48 |
The mass reduction can be expressed as
$$\eta = \frac{m_{\text{steel}} – m_{\text{hybrid}}}{m_{\text{steel}}} \times 100\% = \frac{42.75 – 38.27}{42.75} \times 100\% = 10.48\%$$
where \(m_{\text{steel}}\) is the mass of the all-steel face gear and \(m_{\text{hybrid}}\) is the mass of the hybrid face gear. The hybrid design not only reduces mass but also improves the global stiffness, because the thicker composite web and the additional ribs compensate for the lower modulus of the CFRP. However, the bolted connections introduce local stress concentrations, which must be carefully addressed in the detailed design. I selected a bolt preload that ensures no slip between the composite web and the metallic flanges under the maximum tangential force. The required preload \(F_p\) can be estimated from
$$F_p \geq \frac{F_t}{\mu n_b}$$
where \(\mu\) is the friction coefficient between the composite and steel surfaces, and \(n_b\) is the number of bolts. With \(\mu = 0.2\) and \(n_b = 24\), the required preload per bolt was approximately 4.6 kN. I used a torque wrench to apply the corresponding tightening torque during assembly.
Ply stacking design for the variable-thickness web
The composite web is not a flat plate of constant thickness. It must transition from 30 mm near the hub to 14.94 mm near the tooth ring, and it must also form 12 integral ribs. To achieve this variable thickness with continuous fibers, I divided the web into three zones: (1) a bottom zone with large cutouts for the hub-side flange; (2) a middle zone that forms the main body of the web; and (3) a rib zone that builds up the radial stiffeners. Each zone was composed of multiple prepreg plies with different radial lengths. By stacking plies of different lengths in a specific order, I created a stepped but continuous thickness transition. The ply thickness was 0.21 mm, so the number of plies required for a given region was calculated as
$$n = \frac{t}{t_{\text{ply}}}$$
where \(t\) is the target thickness and \(t_{\text{ply}} = 0.21\) mm. For the hub-side region with \(t = 30\) mm, \(n = 143\) plies. For the tooth-ring side with \(t = 14.94\) mm, \(n = 72\) plies. I designed seven distinct ply shapes, labeled A through G. Plies A and B form the main body of the web. Plies C and D form the bottom zone with large cutouts. Plies E, F, and G form the reinforcing ribs. The stacking sequence was chosen to avoid large resin-rich regions and to ensure gradual load transfer between the web and the metallic flanges. Table 4 lists the ply types, their radial extents, and the number of plies used.
| Ply type | Zone | Radial extent (mm) | Number of plies |
|---|---|---|---|
| A | Main body | 80–210 | 65 |
| B | Main body | 80–240 | 53 |
| C | Bottom cutout | 120–280 | 17 |
| D | Bottom cutout | 140–300 | 8 |
| E | Rib | 100–260 | 14 |
| F | Rib | 120–280 | 13 |
| G | Rib | 140–300 | 18 |
The total number of plies in the main body is \(65 + 53 = 118\), which corresponds to a thickness of \(118 \times 0.21 = 24.78\) mm. Additional plies from the bottom zone and rib zone overlap in certain regions, bringing the local thickness to the designed values. The stacking sequence was quasi-isotropic in the main body, with a layup of \([0/45/-45/90]_s\) repeated as needed. For the ribs, I used a predominantly axial layup \([0_2/45/-45]_s\) to maximize bending stiffness along the radial direction. The fiber orientations were defined relative to the radial direction of the face gear. Because the face gear experiences complex multiaxial loads, the quasi-isotropic layup in the web ensures that no single ply is overloaded in any direction. The Tsai-Hill failure index of 0.13 confirms that the selected layup is conservative.
Manufacturing process
The composite web was manufactured by hot compression molding. The process began with automated cutting of the prepreg plies according to the designed shapes and dimensions. A CNC prepreg cutter was used to ensure dimensional accuracy. The plies were then hand-laid onto a male mold. The stacking started with the rib plies, which were placed into the rib grooves of the mold, followed by the main body plies. Each ply was compacted periodically to remove trapped air. The layup sequence was strictly controlled to match the design. After all plies were placed, the mold was closed and transferred to a hydraulic press. The curing cycle followed the manufacturer’s recommended schedule for the epoxy matrix. The mold temperature was ramped to 130°C at a rate of 2°C/min, held at 130°C for 90 minutes under a pressure of 0.6 MPa, and then cooled to 60°C at a rate of 1.5°C/min before demolding. The curing pressure ensures good consolidation and minimizes void content. Table 5 lists the key process parameters.
| Process step | Parameter | Value |
|---|---|---|
| Heating rate | From room temperature to 130°C | 2°C/min |
| Curing temperature | Isothermal hold | 130°C |
| Curing time | Hold duration | 90 min |
| Curing pressure | Applied during hold | 0.6 MPa |
| Cooling rate | From 130°C to 60°C | 1.5°C/min |
| Demolding temperature | – | 60°C |
| Post-curing | Optional | Not used |
After demolding, the composite web was trimmed to remove flash and excess resin. The surfaces were inspected visually and by tap testing. No delamination or dry spots were found. The final web was then assembled with the steel tooth ring and hub using 24 bolts. The bolt holes were drilled and reamed to match the metallic flanges. A torque wrench was used to apply the specified preload. The assembled hybrid face gear was then subjected to a final dimensional inspection. The runout of the tooth ring was within 0.05 mm, and the axial clearance between the web and the adjacent components was maintained.
Verification under multiple load cases
Although the critical load case was used for sizing, the hybrid face gear must survive all seven load cases. I performed a finite element analysis for each case and extracted the maximum von Mises stress in the metallic parts, the maximum principal stress in the CFRP web, and the maximum displacement. Table 6 summarizes the results. In all cases, the metallic stresses remained below the yield strengths of 9310Q steel and 40Cr bolts. The CFRP failure index, evaluated using the Tsai-Hill criterion, remained below 0.20. The maximum displacement never exceeded 1.10 mm, which is smaller than the 1.52 mm of the steel baseline. Therefore, the hybrid face gear satisfies the stiffness and strength requirements for the full duty cycle.
| Load case | Max. metallic stress (MPa) | Max. CFRP stress (MPa) | Tsai-Hill index | Max. displacement (mm) |
|---|---|---|---|---|
| 1 (critical) | 630.4 | 161.4 | 0.13 | 1.04 |
| 2 | 412.7 | 98.2 | 0.06 | 0.71 |
| 3 | 0 | 0 | 0 | 0 |
| 4 | 418.5 | 101.5 | 0.07 | 0.73 |
| 5 | 389.2 | 89.7 | 0.05 | 0.68 |
| 6 | 275.1 | 54.3 | 0.02 | 0.42 |
| 7 | 298.6 | 61.8 | 0.03 | 0.49 |
The mass breakdown of the hybrid face gear is given in Table 7. The steel tooth ring, hub, and bolts account for most of the mass. The composite web weighs only 2.15 kg, compared with 6.63 kg for the original steel web. This large reduction in web mass is the primary contributor to the overall 10.48% mass saving. The bolted connections and flanges add some mass, but the net effect is still highly favorable.
| Component | Material | Mass (kg) |
|---|---|---|
| Tooth ring | 9310Q steel | 21.40 |
| Hub | 9310Q steel | 12.10 |
| Composite web | T300-3K/Epoxy | 2.15 |
| Bolts and flanges | 40Cr steel | 2.62 |
| Total | – | 38.27 |
Discussion
The hybrid face gear concept combines the wear resistance and fatigue strength of hardened steel in the tooth contact region with the low density and high specific stiffness of CFRP in the web. The equivalent design approach ensures that the global stiffness is maintained or improved. The use of a variable-thickness web with integral ribs allows the composite to carry bending and shear loads efficiently. The ply stacking design with seven distinct ply shapes provides a continuous thickness transition, which avoids stress concentrations that would arise from abrupt thickness changes. The hot compression molding process is suitable for producing the complex web geometry with good surface finish and low void content.
One of the key challenges is the bolted connection between the composite web and the steel flanges. The stress concentration at the bolt holes is the highest stress in the entire hybrid face gear. To mitigate this, I used a large number of bolts (24) and a high preload. The bearing stress on the composite laminate was checked using
$$\sigma_b = \frac{F_t}{n_b d t}$$
where \(d\) is the bolt diameter and \(t\) is the laminate thickness at the hole. With \(F_t = 21958.4\) N, \(n_b = 24\), \(d = 10\) mm, and \(t = 30\) mm, the bearing stress is 3.05 MPa, which is far below the compressive strength of the laminate. The net-section stress was also checked and found to be acceptable. The failure mode is therefore not bearing failure but rather local delamination, which is prevented by using a quasi-isotropic layup and adequate edge distance.
Another consideration is the thermal expansion mismatch between the steel and the CFRP. The coefficient of thermal expansion (CTE) of the steel is approximately \(12 \times 10^{-6} /°C\), while the CTE of the quasi-isotropic CFRP laminate is approximately \(3 \times 10^{-6} /°C\) in the plane. During curing at 130°C and subsequent cooling to room temperature, residual stresses develop in the composite and at the bolted joints. I estimated the residual stress using a simple one-dimensional model:
$$\sigma_{\text{res}} = E_c \Delta \alpha \Delta T$$
where \(\Delta \alpha = \alpha_m – \alpha_c = 9 \times 10^{-6} /°C\) and \(\Delta T = 110°C\). With \(E_c = 69.8\) GPa, the residual stress is approximately 69 MPa. This is well below the compressive strength of the composite, so no damage is expected. However, the bolted joints may experience some preload loss due to differential thermal expansion. I accounted for this by using a slightly higher initial preload and by using Belleville washers to maintain clamping force.
The fatigue performance of the hybrid face gear is also important. The composite web experiences cyclic stresses during operation. The maximum stress of 161.4 MPa under the critical load case is below the fatigue limit of the T300-3K/epoxy laminate, which is typically around 200–250 MPa for a stress ratio of 0.1. The bolted connections are more critical for fatigue. I used a conservative bolt preload and a tight fit to minimize load reversal. The 40Cr bolts have a fatigue strength of approximately 400 MPa at \(10^7\) cycles, which is above the stress amplitude of 210 MPa calculated from the finite element results. Therefore, the hybrid face gear is expected to have a satisfactory fatigue life.
The manufacturing process has been validated by producing a full-scale prototype. The prototype showed good dimensional accuracy and no visible defects. The mass reduction of 10.48% is significant for helicopter transmission systems, where every kilogram saved translates into increased payload or range. The hybrid face gear also has the potential to reduce noise and vibration because the composite web provides additional damping. Future work should include dynamic testing of the hybrid face gear on a transmission test rig to validate the numerical predictions and to assess the long-term durability of the bolted connections.
Conclusion
I have designed and manufactured a hybrid face gear with a carbon fiber composite web for a helicopter transmission system. The original steel web was replaced by a variable-thickness CFRP web with 12 integral ribs, connected to the steel tooth ring and hub through bolted flanges. The equivalent design approach and finite element analysis led to a final design that satisfies the stiffness and strength requirements. The maximum displacement under the critical load case was reduced from 1.52 mm to 1.04 mm, and the maximum stress in the composite web was 161.4 MPa, with a Tsai-Hill failure index of 0.13. The total mass of the hybrid face gear is 38.27 kg, which is 10.48% lighter than the all-steel baseline. The manufacturing process, based on hot compression molding of T300-3K/epoxy prepreg, successfully produced a full-scale prototype. The results demonstrate that CFRP webs are a viable lightweighting solution for face gear applications, provided that the bolted connections are properly designed and the ply stacking is carefully optimized. This work provides a scientific basis and technical support for the lightweight design and manufacturing of composite face gear webs in aerospace transmissions.
Governing equations and design indices
For completeness, the key equations used in this study are summarized below. The equivalent bending stiffness of the web is
$$K = \frac{F}{\delta}$$
where \(F\) is the applied load and \(\delta\) is the maximum displacement. The mass reduction ratio is
$$\eta = \frac{m_{\text{steel}} – m_{\text{hybrid}}}{m_{\text{steel}}} \times 100\%$$
The number of plies for a target thickness is
$$n = \frac{t}{t_{\text{ply}}}$$
The Tsai-Hill failure index for plane stress is
$$\text{FI} = \frac{\sigma_1^2}{X^2} – \frac{\sigma_1 \sigma_2}{X^2} + \frac{\sigma_2^2}{Y^2} + \frac{\tau_{12}^2}{S^2}$$
where \(X\) and \(Y\) are the longitudinal and transverse strengths, respectively, and \(S\) is the in-plane shear strength. The bearing stress in the bolted joint is
$$\sigma_b = \frac{F_t}{n_b d t}$$
The residual thermal stress in the composite is
$$\sigma_{\text{res}} = E_c \Delta \alpha \Delta T$$
These equations were used iteratively during the design process to size the web, select the ply layup, and verify the bolted connections. The final design satisfies all constraints with adequate margins.
Summary of design parameters
| Parameter | Value |
|---|---|
| Face gear type | Hybrid with CFRP web |
| Web material | T300-3K woven carbon fiber / epoxy |
| Ply thickness | 0.21 mm |
| Web thickness at hub | 30.0 mm (143 plies) |
| Web thickness at tooth ring | 14.94 mm (72 plies) |
| Number of ribs | 12 |
| Rib thickness | 8 mm |
| Number of bolts | 24 |
| Bolt material | 40Cr steel, yield strength 785 MPa |
| Tooth ring and hub material | 9310Q steel, yield strength 940 MPa |
| Total mass of hybrid face gear | 38.27 kg |
| Mass reduction | 10.48% |
| Max. displacement (critical load) | 1.04 mm |
| Max. metallic stress (critical load) | 630.4 MPa |
| Max. CFRP stress (critical load) | 161.4 MPa |
| Tsai-Hill failure index | 0.13 |
The hybrid face gear design presented here demonstrates that a significant mass reduction can be achieved without compromising the structural performance of the transmission. The combination of equivalent design, finite element analysis, and advanced composite manufacturing provides a robust framework for future lightweight face gear developments. The use of a variable-thickness web with integral ribs and bolted metallic flanges is a practical solution that can be adapted to other gear geometries and load cases. I believe that this work will contribute to the wider adoption of composite materials in aerospace transmission systems, where high specific stiffness and strength are essential for improving overall efficiency and reducing fuel consumption.