Integrated Multi-Physics Design of a GGG40 Agricultural Trailer Wheel Hub: Concurrent Topology Optimisation and CFD-Based Lubrication Enhancement

Abstract

Wheel hubs in heavy-duty agricultural trailers operate under demanding conditions comprising rough terrain, impact loads, and highly variable load spectra. Current design practice relies predominantly on experience-based sizing rather than systematic multi-physics analysis. This study presents an integrated design methodology combining finite element analysis (FEA), density-based topology optimisation, and computational fluid dynamics (CFD) to concurrently improve the structural and tribological performance of a GGG40 spheroidal graphite cast iron agricultural trailer wheel hub. A reference commercial hub geometry was modelled and analysed under multiple load conditions with a safety factor of 5. Critical stress regions were identified, and the free design volume was optimised while preserving all functional surfaces. The optimised design achieved 35% mass reduction (14.9 to 9.6 kg), 30% lower maximum von Mises stress (235 to 165 MPa), and up to 40% stress reduction in the bearing seat region. Oil-circulation channels integrated into the bearing housing raised mean lubrication flow velocity by 28% and eliminated stagnation zones, yielding a more homogeneous oil-film distribution and directly benefiting bearing tribological performance. The proposed framework provides a manufacturable engineering methodology that concurrently addresses structural integrity and lubrication performance in agricultural wheel hub design.

1. Introduction

Wheel hubs serve as the primary load-transfer interface between axles, bearings, and wheel assemblies, and they are therefore central to the structural reliability of rotating mechanical systems. In agricultural trailer applications, these components are subjected to high stress levels and complex multi-axial loading, as they operate over uneven terrain, withstand impact forces, and carry highly variable load spectra. Accordingly, the reliable design and structural assessment of hub systems constitute an important area of research in machine design [1,2,3].

A considerable body of work has examined the structural behaviour of wheel hubs in automotive and heavy-machinery contexts. Mohite [4] performed stress analysis and optimisation of a front wheel hub and identified the flange root as the dominant stress-concentration site under cornering loads. Yuvaraja and Kumar [5] used finite element analysis to optimise an automotive wheel hub and reported that targeted geometric refinement at load-transfer regions reduces peak stress without compromising stiffness. Li and Zhou [6] evaluated wheel hub performance under complex multi-axial loading and showed that out-of-plane bending substantially elevates stress at the flange–body junction. Liu et al. [7] coupled bionic optimisation with fatigue life prediction for a honeycomb-structured wheel hub and demonstrated that biologically inspired stiffening patterns extend service life under cyclic loading. Shin and Jin [8] conducted numerical impact stress prediction for a wheel and showed that transient terrain-induced peaks can exceed static design values by a factor of three. Taken together, these contributions indicate that stress concentrations consistently arise in the flange region [4,6], at bearing-seating surfaces [6,7], and in body transition zones [7,8], all of which are critical from a fatigue damage standpoint.

In recent years, weight reduction strategies have become an increasingly prominent topic in engineering design. In this context, topology optimisation has emerged as a powerful method for rearranging material distribution within load-bearing structures so as to achieve a high performance-to-mass ratio. The theoretical foundations were established by Bendsøe and Sigmund [9], whose monograph formalises the SIMP density-based formulation, and were subsequently consolidated by Sigmund and Maute [10] in a comparative review of topology optimisation approaches. Zhu et al. [11] documented the extension of these methods to aerospace structural design, while Mirzendehdel and Behandish [12] addressed manufacturing accessibility constraints, a key requirement for casting and machining workflows. Mantovani and Leali [13] further demonstrated the synergy between topology optimisation and additive manufacturing for structural components. In the automotive and manufacturing domains, Erdoğan [14] applied topology optimisation to drive plate components under mechanical loading and reported substantial mass savings while preserving structural stiffness; Costa and Vieira [15] developed an integrated CFD–FEA optimisation framework for rotating mechanical components; Flores and Silva [16] analysed agricultural trailer axles subjected to impact loads; and Kashid and Mane [17] performed finite element analysis and optimisation of a tractor trolley axle. More recently, SIMP-based topology optimisation has been extended to tribological and fluid–structure applications. Kong et al. [18] applied topology optimisation to textured journal bearings and showed that distributed micro-texture patterns can be obtained as optimisation outputs; Shi et al. [19] reported experimental and numerical results for topology-optimised liquid-cooled heat sinks; and Zhou et al. [20] proposed a novel mini-channel heat sink design with an arc-type design domain obtained by topology optimisation.

Research on agricultural machinery components consistently indicates that terrain-induced dynamic loads can reach several times the corresponding static values. Andersson [21] redesigned a wheel hub to reduce unsprung mass for a rallycross car and reported peak loads markedly above quasi-static estimates. The commercial design data published in the ADR Group catalogue [22] and in the Çayırova Makina catalogue [23] confirm that heavy-duty agricultural axle hubs are routinely sized with conservative safety factors to accommodate such transient peaks, while Totten [24] documents that bearing systems in heavy off-road machinery must withstand repeated impact-induced load amplification. For this reason, realistic load scenarios must be considered when designing trailer axles and suspension systems. Nonetheless, the majority of existing studies focus on automotive applications, and investigations directed specifically at the structural optimisation of heavy-duty agricultural axle hubs remain limited.

Multi-disciplinary numerical analysis methods have gained widespread use in engineering design processes. The finite element method (FEM) has become a fundamental tool for structural evaluation, while computational fluid dynamics (CFD) methods afford notable advantages for analysing lubrication behaviour and internal flow in rotating systems. Spikes [25] reviewed the role of friction-modifier additives in lubricant performance; Versteeg and Malalasekera [26] established the finite volume formulation that underpins modern CFD codes; Ferziger and Perić [27] consolidated the corresponding numerical methods for fluid dynamics; and Menter [28] reported best-practice guidelines for scale-resolving simulations in engineering flows. Furthermore, studies in manufacturing engineering have demonstrated that integrated design approaches, combining structural analysis with optimisation, can materially improve the performance of mechanical systems. Costa and Cunha [29] developed a topology-optimised milling cutter head with integrated internal cooling channels; Costa et al. [30] subsequently extended this concept to additive manufacturing and reported that manufacturing-constraint-compliant designs preserve cost competitiveness.

Despite these advances, the concurrent application of SIMP-based topology optimisation and CFD-based lubrication analysis to a single rotating machine component has received limited attention in the open literature. Topology optimisation studies on rotating components have predominantly addressed structural compliance and mass reduction in isolation [9,10,11,12,13,18], while CFD investigations of bearing lubrication have focused on flow field characterisation without coupling to structural redesign [19,20,23,24,25]. The few integrated FEA–CFD studies that exist for mechanical components [15,26,30,31,32] demonstrate that joint optimisation of structural and fluid performance yields outcomes that cannot be achieved by sequential, discipline-specific design. Specifically, material redistribution through topology optimisation alters the internal geometry of the bearing housing, which in turn modifies the oil-flow boundary conditions and channel cross-sections, creating a direct coupling between structural and tribological performance. This coupling is particularly significant in heavy-duty agricultural wheel hubs, where the simultaneous demands of structural reliability under high dynamic loads and continuous bearing lubrication under contaminated operating conditions cannot be addressed adequately by single-discipline design methods [21,22,23,24].

In this study, we develop an integrated design optimisation approach for a heavy-duty agricultural wheel hub manufactured from GGG40 spheroidal graphite cast iron. In the proposed methodology, structural behaviour is evaluated through finite element analysis, material distribution is rearranged via density-based topology optimisation, and the oil-circulation performance within the hub is examined by means of CFD analysis. The overarching objective is to reduce the hub mass while simultaneously improving stress distribution and lubrication performance.

Although numerous studies have addressed the structural strength, fatigue behaviour, and lightweighting strategies of wheel hubs, the overwhelming majority focus on automotive applications. Integrated design approaches that simultaneously consider multiple load scenarios, parametric design analysis, and topology optimisation for heavy-duty agricultural wheel hubs made of GGG40 spheroidal graphite cast iron remain scarce; indeed, most commercial hub designs still rely on experience-based sizing methods. The synergy between SIMP-based topology optimisation and CFD-based lubrication analysis has not been systematically explored for agricultural wheel hub components, representing a clear research gap.

The present study addresses this gap by developing an integrated engineering approach that concurrently evaluates structural strength, mass optimisation, and lubrication performance for a heavy-duty agricultural wheel hub manufactured from GGG40. To this end, parametric analyses were conducted under multiple load conditions based on a reference commercial bearing geometry, density-based topology optimisation was applied subject to casting manufacturability constraints, and the performance of internally designed lubrication channels was assessed through CFD analysis.

The principal contributions of this work are: (1) the development of a parametric design approach incorporating multiple load scenarios for agricultural wheel hubs; (2) the application of a topology-optimisation-based lightweighting strategy compatible with casting manufacturing constraints; (3) the formulation of an integrated design methodology in which FEA and CFD analyses are employed jointly; and (4) the proposal of a general hub design approach applicable to different bearing configurations and bolt arrangements.

2. Materials and Methods

2.1. Reference Hub Geometry and Material Properties

The reference geometry analysed in this study was modelled on the basis of a commercial heavy-duty wheel hub that is widely used in agricultural trailer applications and features a six-bolt, eight-to-ten bearing configuration. The hub body is manufactured from GGG40 spheroidal graphite cast iron, a material selected for its high strength, impact resistance, and fatigue performance; the corresponding material properties are defined in accordance with EN 1563 [33]. For the CFD analyses, ISO VG 68 grade oil, which is commonly employed in bearing systems, was adopted as the working fluid; the oil properties used in the flow simulations were determined on the basis of tribological data reported in the literature [24]. The mechanical and physical properties of GGG40 cast iron and ISO VG 68 oil are listed in

Table 1. Material properties of GGG40 cast iron and ISO VG 68 lubricant used in the numerical simulations.

Material	Property	Symbol	Value	Unit
GGG40 Cast Iron	Density	ρ	7100	kg/m3
GGG40 Cast Iron	Elastic modulus	E	170	GPa
GGG40 Cast Iron	Poisson’s ratio	ν	0.28	–
GGG40 Cast Iron	Yield strength	σy	275	MPa
ISO VG 68 Oil	Density	ρ	870	kg/m3
ISO VG 68 Oil	Dynamic viscosity	μ	0.068	Pa·s

.

Figure 1 shows the assembly view, engineering drawings, and internal structural features of the conventional heavy-duty wheel hub used as the reference geometry in the numerical computations. The isometric assembly view in the upper portion illustrates the shaft-connection geometry and the six-bolt fastening arrangement at the flange, while the front and rear engineering drawing views reveal the bolt-hole layout, flange diameter, and symmetric disposition of the bearing axes [22,23].

The three-dimensional CAD model and cross-sectional engineering drawing presented in the lower portion of Figure 1 identify the critical structural areas through which load transfer occurs. In particular, the fixed wheel-seating surface, the fixed bolt-hole surface, and the fixed bearing-seating surfaces were designated as critical functional zones with regard to high load transfer and stress concentrations. These surfaces were defined as non-design regions during the optimisation process, and topology optimisation was applied exclusively to the non-load-bearing free design volume.

2.2. Numerical Modelling Strategy

The numerical analysis procedure comprises three main stages: (i) identification of the free design volume and the application of density-based topology optimisation, (ii) structural analysis of the wheel hub by the finite element method (FEM), and (iii) evaluation of the oil-circulation performance by the finite volume method (FVM). During topology optimisation, the wheel-seating surface, bolt-holes, and bearing seats were designated as non-design domains, and material distribution was optimised solely within the free design volume. The topology results were subsequently remodelled in compliance with casting manufacturability constraints to obtain the final hub geometry.

Structural and flow analyses were carried out using the Dassault Systèmes 3DEXPERIENCE platform (Dassault Systèmes, Vélizy-Villacoublay, France). The geometry model was discretised with a tetrahedral volume-element mesh so as to accurately represent the flange and transition regions. The resulting mesh comprised approximately 1.1–1.3 million elements, with local mesh refinement applied in regions where stress accumulation was anticipated. Mesh-independence studies confirmed that, upon further refinement, the maximum von Mises stress and total displacement values varied by less than 2%. In the numerical model, the global coordinate system was defined along the x, y, and z axes, and three translational degrees of freedom (Ux, Uy, Uz) together with three rotational degrees of freedom (Rx, Ry, Rz) were considered at each node. The rotational axis of the hub was defined by a single-degree-of-freedom boundary condition; the relevant boundary conditions are depicted in Figure 2.

In the structural analyses, a 2.5-ton static load was imposed as a boundary condition that reflects the operating conditions of the hub. The axle-connection surfaces were modelled with a single-degree-of-freedom (Rx) boundary condition to represent bearing behaviour, and loads were applied axially to the bolt regions on the wheel-mounting flange. Given that the hub is a rotating machine element and taking into account the dynamic effects and impact loads that may arise under agricultural terrain conditions, the analyses were performed with a safety factor of 5 [2,7]. Maximum equivalent (von Mises) stress and total displacement were adopted as the principal structural performance criteria.

The principal simulation parameters employed in the FEA, CFD, and topology optimisation analyses are consolidated in

Table 2. FEA boundary conditions and structural analysis parameters.

Parameter	Value	Notes
Applied static load	2.5 ton	Agricultural trailer service load
Axle BC (rotational DOF)	1-DOF (Rx)	Bearing behaviour representation
Load application point	Bolt-hole regions	Axial load on wheel-mounting flange
Design safety factor	5	Accounts for dynamic/impact terrain loads [2,7]
Structural performance criteria	σeq (von Mises), Utotal	Max. equivalent stress and total displacement
Symmetry condition	1/6 periodic	Six-bolt geometric periodicity

,

Table 3. CFD analysis operating conditions and modelling parameters.

Parameter	Value	Notes
Rotational speed	2500 rpm	Maximum operating condition
Turbulence model	k–ω SST	Rotating flow and boundary-layer accuracy
Fluid treatment	Incompressible Newtonian	ISO VG 68 oil
Pressure–velocity coupling	Iterative algorithm	SIMPLE-type algorithm
Convergence criterion	Residuals < 10−4	All governing equations
CFD mesh (control volumes)	∼0.8 million	Cartesian-based control-volume mesh
Boundary condition type	Rotational motion	Centrifugal force effects included

,

Table 4. SIMP topology optimisation parameters.

Parameter	Value	Notes
Optimisation method	SIMP	Solid isotropic material with penalisation [9]
Objective function	Min. compliance C	C = Fᵀ u (Equation (4)); max. global stiffness
Volume fraction target (f)	f = 0.65	V ≤ 0.65⋅V0; consistent with 35% mass reduction (Equation (5))
Penalisation factor (p)	p = 3	Standard value for 0/1 convergence; penalises intermediate densities [9,10]
Sensitivity filter radius (rmin)	rmin = 4 mm	Prevents chequerboard; ≈1/2 minimum casting wall thickness (8 mm)
Filter type	Sensitivity	Linear density-weighted averaging of sensitivities [9]
Convergence criterion	ΔC/C < 1%	Relative change in compliance between successive iterations
Non-design domains	Fixed	Wheel seat, bolt-holes, bearing seats
Manufacturing constraint	Casting	Min. wall thickness and draft angle enforced

and

Table 5. FEA mesh statistics and independence study results.

Mesh Level	No. of Elements	Element Type	Δσmax (%)
Coarse	~0.7 million	Tetrahedral	—
Medium (adopted)	1.1–1.3 million	Tetrahedral (local refinement)	<2%
Fine	~2.1 million	Tetrahedral	<2%

for clarity of presentation.

For the flow analyses, a rotational-motion boundary condition was defined to examine the oil-circulation performance within the bearing, and a rotational speed of 2500 rpm was applied as the maximum operating condition. In the CFD analyses carried out with the finite volume method, centrifugal force effects were taken into account, and the velocity distribution, pressure variation, and flow continuity within the oil channels were investigated. The convergence criterion was based on the stabilisation of residuals. The k–ω SST turbulence model was employed to represent turbulence effects in the flow field; this model was selected because it provides reliable results in rotating flow fields and in engineering problems where boundary-layer behaviour is significant.

The discrete system equilibrium equation used in the FEM-based structural analysis is expressed as follows:

K u = F

(1)

where K denotes the global stiffness matrix, u the nodal displacement vector, and F the load vector. Stress distributions were calculated using the linear elasticity relation:

σ = D ε

(2)

where σ is the stress vector, D the elasticity matrix, and ε is the strain vector.

The oil-circulation performance within the hub was analysed using the finite volume method. The flow domain was modelled with a Cartesian-based control-volume mesh comprising approximately 0.8 million control volumes. The fluid was treated as an incompressible Newtonian oil. The general conservation equation is expressed as

∂(ρφ)/∂t + ∇·(ρvφ) = ∇·(Γ∇φ) + Sφ

(3)

where φ is the transported quantity (velocity, energy, etc.), v is the velocity vector (m/s), Γ is the diffusion coefficient, Sφ is the source term.Pressure–velocity coupling was achieved by means of an iterative solution algorithm, and the convergence criterion was based on residuals falling below the 10⁻⁴ level. From the flow analyses, the velocity distribution, pressure drop, and circulation efficiency within the oil channels were evaluated.

Following the parametric design improvement, density-based topology optimisation was applied to the identified free design volume. The objective function was defined as the minimisation of structural compliance:

C = Fᵀ u

(4)

where C is the structural compliance, F is the load vector, and u is the displacement vector. The volume constraint in the optimisation is defined as

V ≤ f · V₀

(5)

where V is the optimised volume, V₀ is the initial volume, and f is the permissible volume fraction.

The final optimised hub geometry was generated by remodelling the obtained material distribution in consideration of the minimum wall thickness, symmetry conditions, and casting manufacturability. The topology optimisation procedure is illustrated in Figure 3.

3. Design Process and Development Stages

This section describes the design process for the optimised hub, the logic of the stepwise geometric evolution, and the structural improvements applied in the final design. The stepwise development of the design is shown in Figure 4, while the optimised regions, the preserved functional surfaces, and additional structural features are detailed in Figure 5.

3.1. Stepwise Design Evolution

Figure 4 illustrates the evolution of the optimised hub geometry from the conventional reference design to the final CAD model by means of front views, dimetric views, and cross-sectional views. Throughout the design process, not only the external geometry but also the internal structure, which governs load transfer, was progressively redesigned.

As shown in Figure 4, the hub design was carried out in four principal steps. In Step 1, the reference geometry was established and an initial CAD model was obtained by preserving critical functional areas such as the bearing housings, the flange mounting surface, and the central hub. In Step 2, the internal volume of the body was reorganised: controlled material removal was applied in low-stress regions while maintaining the continuity of the load-transfer paths. In Step 3, on the basis of the topology optimisation results, a rib structure was defined between the flange and the hub to support load transfer, thereby improving the stiffness distribution and reducing localised stress concentrations. In Step 4, the geometry was refined in compliance with casting manufacturing constraints; sharp corners and abrupt cross-sectional transitions were mitigated, and flow channels to facilitate oil circulation within the hub were integrated. At the conclusion of this process, the final optimised CAD hub design, supported by structural verification analyses, was obtained.

3.2. Optimisation Details and Final Design Concept

The one-sixth symmetry scheme shown on the left side of Figure 5 represents the numerical modelling approach employed to capture the geometric repeatability. The rib and clearance angles likewise defined therein are critical design parameters determined so as to reduce potential stress concentrations at channel corners and to ensure structural balance.

The rib placement in the optimised flange geometry was defined by a parametric design rule based on the number of bolts, with the objective of ensuring a balanced load-transfer distribution and achieving symmetric stiffness in the flange region. In this approach, the number of ribs was set equal to twice the number of bolts on the flange, that is

Nr = 2 Nb

(6)

where Nr denotes the number of ribs and Nb the number of bolts. This arrangement ensures that each bolt load path is supported by two separate ribs, resulting in a more homogeneous load transfer. The circumferential placement of the ribs was defined according to the equal-angular-distribution principle, such that the angular spacing between two consecutive ribs is expressed as

θr = 2π/Nr

(7)

where θr is the angular clearance (rad) between two ribs and Nr is the total number of ribs. By virtue of this geometric relationship, the ribs are positioned so as to provide equal load sharing between bolt connection areas. The one-sixth symmetric schematic view given in Figure 5 illustrates the rib angle and the relationship among the rib clearances.

The front and rear views of the optimised hub, shown in the central portion of Figure 5, display the principal design areas affected by the topology optimisation. Critical load-transfer areas around the flange and hub were preserved, whereas non-load-bearing volumes were reorganised for mass reduction and designated as the “optimised topology region.” Functionally critical mounting surfaces, including the wheel-seating surface, bearing-seating surfaces, and bolt-holes, were excluded from the design domain to maintain geometric compatibility with the assembly. The “optimised internal region” indicated in the cross-sectional view, together with the multi-channel bearing support structure, provides a more balanced load distribution, increases local stiffness, and reduces deformation tendencies in the bearing region. In addition, oil-circulation channels integrated into the design support continuous bearing lubrication, thereby affording additional functional improvement. As a result of this integrated approach, the developed hub design constitutes an optimised engineering solution that simultaneously delivers structural weight reduction and functional performance improvement and is adaptable to different bolt counts and bearing configurations.

4. Results and Discussion

In this section, the structural and flow performances of the conventional and optimised hub designs are evaluated comparatively under identical boundary and loading conditions. The analysis results are examined numerically in terms of maximum stress levels, stress distribution, flow-velocity fields, and axial velocity profiles.

4.1. Linear Static FEA Results

The linear static analysis results shown in Figure 6 indicate that the maximum von Mises stress in the conventional hub design reached approximately 230–240 MPa and was concentrated primarily at the flange–body transition zones and bearing shoulders. In the optimised design, the maximum stress values decreased to the 160–170 MPa range, representing an approximately 30% stress reduction.

The underlying mechanism governing this stress reduction can be attributed to three concurrent structural effects introduced by the topology-optimised geometry. First, the addition of radial ribs between the flange and the hub body creates supplementary load-transfer paths that distribute the applied axial bolt loads over a wider cross-sectional area, thereby lowering the local stress intensity at the flange–body junction. This mechanism is analogous to the load-spreading effect reported for rib-reinforced rotating components, where increasing the number of load paths reduces peak stress concentrations at geometric transitions [6,7]. Second, the controlled removal of material from low-stress interior regions eliminates abrupt stiffness discontinuities that would otherwise generate stress concentrations at volume boundaries; the resulting smoother stiffness gradient across the hub cross-section promotes more gradual load redistribution. Third, the elimination of sharp internal corners and the mitigation of abrupt cross-sectional transitions during the CAD remodelling stage further reduce stress-concentration factors at the bearing-seat shoulders, where the notch sensitivity of GGG40 cast iron is a critical design parameter. Collectively, these three mechanisms shift the stress distribution from a localised, high-gradient pattern in the conventional design towards a more homogeneous field in the optimised design, as evidenced by the von Mises contour maps in Figure 6.

The stress distribution maps reveal that, in the conventional design, high-stress regions are localised and steep stress gradients are present. In the optimised design, by contrast, the stress is spread over a wider area, and the redistribution of load-transfer paths results in a more homogeneous distribution.

4.2. Flange and Bearing Region Stress Comparison

Stress comparisons along the flange path show that the mean stress in the conventional design ranges between 225 and 235 MPa. In the optimised design, stress levels in the same region decreased to the 155–165 MPa range, corresponding to an approximately 30% reduction. This result indicates that load transfer in the flange region has become more balanced (Figure 7).

Stress analyses along the bearing-seating surface indicate that the stress levels in the conventional design range between 165 and 200 MPa. In the optimised hub design, these values decreased to 110–120 MPa, yielding an approximately 35–40% stress reduction in the bearing region. This outcome suggests that load transfer has become more homogeneous and that the service life and operational reliability in the bearing region have been improved (Figure 8).

Overall, the optimised design reduces maximum stress levels in both the flange and bearing regions and provides a more balanced structural response along the critical load paths.

4.3. CFD Analysis Results

The CFD analysis results presented in Figure 9 show that the velocity distribution in the optimised hub design has become more homogeneous as a consequence of the improved internal flow geometry. In the conventional design, the flow velocity drops to 6–8 m/s in certain regions and localised stagnation zones are observed, whereas in the optimised design the minimum velocity values rise to 9–10 m/s. This result indicates that flow continuity has increased and internal flow resistance has decreased.

4.4. Velocity Profile Comparison

Velocity profiles obtained along the flow path show that the average flow velocity in the conventional hub design remains at approximately 12–13 m/s and that significant velocity drops occur along the flow path. In the optimised design, the average velocity rises to 15–17 m/s and the velocity profile becomes more stable along the axis. These results indicate an approximately 20–30% increase in average flow velocity (Figure 10).

The observed increase in flow velocity contributes to improved bearing lubrication performance; however, it is acknowledged that higher flow velocities also imply elevated shear rates within the oil film, which may in turn raise the local oil temperature and reduce dynamic viscosity. For ISO VG 68 oil at the operating speed of 2500 rpm, the shear-rate increase associated with the 28% velocity improvement remains within the hydrodynamic regime, and the resulting viscosity reduction is expected to be moderate and self-limiting owing to the thermal mass of the GGG40 housing. Nonetheless, a full thermohydrodynamic analysis coupling the CFD flow field with a heat-transfer model is warranted as part of future work to quantify the thermal impact precisely. It is also worth noting that flow-velocity enhancement is one of several strategies available for improving lubrication performance. Texture-based approaches, in which surface micro-features guide and retain lubricant in the contact zone, represent a particularly effective complementary method for addressing starved-lubrication conditions; recent work by Dai et al. [34] demonstrated that bulk-cusp microstructures can achieve controllable multi-directional liquid spreading; the thermal implications of flow-velocity enhancement have similarly been quantified for topology-optimised cooling channels by Tong et al. [31], offering a passive and geometry-driven route to improved lubricant distribution. The integration of such surface-texture strategies with the internal channel geometry developed in the present study constitutes a promising direction for further performance enhancement. As such, the optimised design exhibits superior performance relative to the conventional design not only from the standpoint of structural stress but also with regard to tribological operating conditions.

The overall performance improvements achieved in this study compare favourably with findings reported in the recent literature on topology-optimised structural components. Mass reductions of 20–40% have been reported for topology-optimised automotive and rotating machine components [9,10,11,14], placing the present 35% reduction within the expected performance envelope for SIMP-based approaches applied to cast-iron hub geometries. The 30% reduction in maximum von Mises stress observed here is consistent with the stress-redistribution benefits documented for rib-reinforced hub designs [6,7], and is particularly significant given that the optimisation was performed subject to conservative casting manufacturability constraints. The 40% stress reduction in the bearing-seat region is noteworthy from a tribological standpoint, as reduced contact stress at the bearing interface directly mitigates fretting fatigue initiation, a dominant failure mode in agricultural hub applications [2,8]. With respect to CFD performance, the 28% increase in mean lubrication flow velocity achieved through the optimised internal channel geometry is consistent with flow-improvement rates reported for redesigned oil-circulation paths in rotating bearing housings and topology-optimised internal flow geometries [18,19,35,36]. The elimination of stagnation zones further reduces the risk of local oil-film breakdown, which is a critical concern at the 2500 rpm operating speed considered. The key performance metrics for both designs are compared graphically in Figure 11 and summarised in

Table 6. Performance comparison between the conventional and optimised wheel hub designs.

Performance Parameter	Conventional Hub	Optimised Hub	Improvement
Total mass (kg)	14.9	9.6	35% reduction
Max. von Mises stress (MPa)	235	165	30% reduction
Mean flange stress (MPa)	230	160	30% reduction
Max. bearing-seat stress (MPa)	200	120	40% reduction
Mean flow velocity (m/s)	12.5	16.0	28% increase

.

The effect of the topology-optimised geometry on structural stiffness and dynamic behaviour warrants explicit consideration. In the present study, the compliance-minimisation objective function (Equation (4)) ensures that global structural stiffness is maintained or improved relative to the reference design for the applied load cases; the 30% reduction in maximum stress under identical loading directly reflects this stiffness retention. At the component level, the introduction of circumferential ribs and the redistribution of wall thickness increase the local flexural rigidity of the flange region, counteracting the stiffness reduction that would otherwise accompany the 35% mass removal. With respect to dynamic behaviour, the rib-reinforced topology is expected to raise the fundamental natural frequency of the hub relative to the thin-walled conventional geometry, since both mass reduction and stiffness increase shift resonant frequencies upward according to ωn = √(k/m). This is a beneficial outcome for a rotating component operating at up to 2500 rpm, as it reduces the likelihood of resonance excitation by terrain-induced harmonic loads. A modal analysis quantifying the natural frequencies and mode shapes of both designs was subsequently performed; the results are presented in Section 4.5 and fully confirm this prediction. Precedent for this type of coupled CFD–structural–modal analysis exists in the wind turbine blade literature, where Song et al. [32] demonstrated that CFD-derived aerodynamic loads, topology-optimised internal structure, and modal analysis can be integrated within a single design workflow.

The practical viability of the optimised design also depends on manufacturing cost, which is a critical factor in agricultural equipment markets where cost sensitivity is high. The optimised hub was designed from the outset subject to sand-casting manufacturability constraints, including minimum wall thickness, draft-angle compliance, and avoidance of undercut features. These constraints ensure that the optimised geometry can be produced using the same casting process as the conventional hub without requiring investment in new tooling categories. The integration of oil-circulation channels can be implemented via standard sand-core inserts in GGG40 foundry practice, without recourse to additive manufacturing or precision machining of internal features. A unit-level manufacturing cost estimate was performed considering three cost drivers: raw-material cost, machining cost, and casting operation cost. Material cost was calculated using the current GGG40 spheroidal graphite cast iron price of 60 TRY/kg (approximately $1.33/kg at USD/TRY = 45.07, April 2026). The 35% mass reduction from 14.9 to 9.6 kg yields a direct material saving of $7.06 per unit. Machining cost was estimated at $35/h (representative of mid-scale CNC operations in Türkiye), with a reference machining time of 2.5 h for the conventional hub; the reduction in the number of machined surfaces in the optimised design, combined with fewer internal recesses, reduces the machining cycle time by 30%, yielding a saving of $26.25 per unit. Casting operation cost, covering pattern preparation, pouring, shakeout, and cleaning, was estimated at $25.00 per unit for the conventional design; the simpler internal geometry of the optimised hub, which releases more readily from the sand mould and requires fewer cores, reduces this cost by an estimated 15%, saving $3.75 per unit. The resulting total unit manufacturing cost decreases from $132.34 for the conventional hub to $95.28 for the optimised hub, representing a 28% reduction and savings of $37.06 (approximately 1670 TRY) per unit. The cost breakdown and category savings are illustrated in Figure 12 and summarised in

Table 7. Unit manufacturing cost breakdown for the conventional and optimised wheel hub designs (GGG40 at 60 TRY/kg; USD/TRY = 45.07; April 2026).

Cost Driver	Conventional (USD)	Optimised (USD)	Saving (USD)	Reduction (%)
Material (GGG40, 60 TRY/kg)	19.84	12.78	7.06	35.6
Machining ($35/h; −30% cycle time)	87.50	61.25	26.25	30.0
Casting operation (−15% mould release)	25.00	21.25	3.75	15.0
Total unit cost	132.34	95.28	37.06	28.0

. These findings are consistent with the observations of Costa et al. [30], who reported that manufacturing-constraint-compliant topology-optimised components retain cost competitiveness relative to conventional geometries, primarily through material and machining savings.

4.5. Modal Analysis Results

A free-vibration modal analysis was performed for both the conventional and optimised hub designs, with rigid-body modes (Modes 1–6, f = 0 Hz) excluded from the comparison. The first 24 structural modes were extracted for each design; the corresponding natural frequencies are listed in

Table 8. Natural frequency comparison of the optimised and conventional wheel hub designs (Modes 1–24; rigid-body modes excluded).

Mode	Optimised (Hz)	Conventional (Hz)	Δf (Hz)	Δf (%)
1	3029.84	2192.87	+836.97	+38.2
2	3268.49	2252.10	+1016.39	+45.1
3	3772.10	3548.21	+223.89	+6.3
4	4182.60	3617.35	+565.25	+15.6
5	4671.63	3776.99	+894.64	+23.7
6	5006.33	4235.92	+770.41	+18.2
7	5322.21	4369.96	+952.25	+21.8
8	5339.56	4392.45	+947.11	+21.6
9	6012.20	4396.06	+1616.14	+36.8
10	6110.95	5101.09	+1009.86	+19.8
11	7129.92	5119.31	+2010.61	+39.3
12	7279.66	6013.16	+1266.50	+21.1
13	7451.45	6016.21	+1435.24	+23.9
14	7608.60	6885.62	+722.98	+10.5
15	8507.12	6887.23	+1619.89	+23.5
16	8657.14	7483.46	+1173.68	+15.7
17	8781.92	7492.42	+1289.50	+17.2
18	8935.92	8337.94	+597.98	+7.2
19	8956.29	8361.91	+594.38	+7.1
20	9205.99	8458.05	+747.94	+8.8
21	9420.53	8704.19	+716.34	+8.2
22	9500.21	8722.65	+777.56	+8.9
23	9629.44	8869.21	+760.23	+8.6
24	9825.50	8900.27	+925.23	+10.4

, and the mode shapes are illustrated in Figure 13 and Figure 14.

The results demonstrate that the natural frequencies of the optimised hub exceed those of the conventional design across all 24 extracted modes, confirming the qualitative prediction made on the basis of the compliance-minimisation objective (Section 4.4). The fundamental natural frequency (Mode 1) increases from 2192.87 Hz in the conventional hub to 3029.84 Hz in the optimised design, representing a 38.2% improvement. The mean frequency increase across all 24 modes is +19.1%, with individual mode improvements ranging from +6.3% (Mode 3) to +45.1% (Mode 2). The maximum absolute frequency deviation occurs at Mode 11, where the optimised hub achieves 7129.92 Hz compared with 5119.31 Hz for the conventional design (+39.3%). These results are presented graphically in Figure 13 and tabulated in Table 8.

The consistent upward shift in natural frequencies is a direct consequence of the simultaneous mass reduction (14.9 to 9.6 kg, a 35.6% decrease) and the increase in local structural stiffness conferred by the circumferential rib network introduced during topology optimisation. For a single-degree-of-freedom analogy, the natural frequency scales as ω_n = √(k/m); the increase in k and decrease in m act synergistically to raise all modal frequencies. From an operational standpoint, the maximum rotational speed of 2500 rpm corresponds to a fundamental excitation frequency of 41.7 Hz, which is more than two orders of magnitude below the lowest natural frequency of either design (2192.87 Hz for the conventional hub). Consequently, neither design is susceptible to resonance excitation under normal operating conditions; however, the substantially higher frequency spectrum of the optimised hub provides a significantly wider safety margin against resonance induced by higher-order terrain harmonics and transient impact loads, which is particularly important in off-road agricultural service.

The mode shapes illustrated in Figure 14 reveal that the conventional hub exhibits pronounced large-amplitude deformation concentrated at the flange and bearing-seat regions in lower modes, consistent with the localised stiffness deficiencies identified in the static FEA. The optimised hub, by contrast, displays a more distributed deformation pattern across all modes, reflecting the more homogeneous stiffness distribution achieved through material redistribution. This modal behaviour is consistent with findings reported by Song et al. [32] for topology-optimised structural components, where improved material distribution results in higher and more evenly distributed natural frequencies.

5. Conclusions

This study presented an integrated multi-physics design methodology for a GGG40 spheroidal graphite cast iron agricultural trailer wheel hub, combining FEA, density-based topology optimisation (SIMP), and CFD within a unified framework. The methodology demonstrates that structural weight reduction and tribological performance enhancement can be pursued concurrently within a single, manufacturing-compatible design process.

The principal quantitative findings, summarised in Table 6, demonstrate that the optimised hub achieves a 35% mass reduction (14.9 to 9.6 kg), a 30% reduction in maximum von Mises stress (235 to 165 MPa), and up to 40% stress reduction in the bearing-seat region. The integration of internal oil-circulation channels increased mean lubrication flow velocity by 28% (12.5 to 16.0 m/s) and eliminated stagnation zones, directly improving tribological operating conditions in the bearing region.

From an industrial perspective, the proposed integrated design approach addresses a recognised gap in heavy-duty agricultural equipment design, where component sizing has traditionally relied on empirical methods rather than systematic multi-physics analysis. The framework, validated numerically under a safety factor of 5, is directly transferable to industrial applications targeting mass reduction, improved energy efficiency, and extended service life and is equally applicable to hub systems with different bearing configurations and bolt arrangements [37].

From a dynamic standpoint, the modal analysis presented in Section 4.5 confirms that all 24 extracted natural frequencies of the optimised hub exceed those of the conventional design, with a mean frequency increase of +19.1%, reducing the risk of resonance excitation by terrain-induced loads. The optimised geometry was constrained throughout to comply with GGG40 sand-casting practice, ensuring that no new tooling categories are required, and the unit-level cost analysis indicates a 28% reduction in total manufacturing cost.

The present study is subject to certain limitations. The numerical framework lacks physical prototype testing; experimental validation through strain-gauge measurements and bearing-housing flow measurements is recommended as a priority for future work. Additionally, nonlinear impact analyses and the integration of field-measured load histories are warranted to capture fatigue accumulation under variable terrain-induced load spectra.

6. Patents

The optimised wheel hub design developed within the scope of this study has been filed as a national patent application in the Republic of Türkiye under application number 2026/001681.