help PROBLEM $4[20$ MARKS$]$

A critical design challenge has emerged at Proton's powertrain manufacturing facility in Shah Alam, where engineers are developing a new transmission assembly for their next$-$generation compact SUV. The system features an outer hub rotating around a fixed shaft, supported by two tapered roller bearings in a specific configuration. This design is particularly crucial as it needs to withstand Malaysia's tropical climate conditions, including high humidity and temperatures ranging from $\backslash (24^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ to $\backslash (35^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ while meeting the stringent quality standards of the ASEAN automotive market. The design specifications, aligned with Proton$-$Geely's quality benchmarks, require continuous operation at $275$ rpm $,$ with a defined usage pattern of $8$ hours daily, $5$ days per week. The bearings must maintain their functional integrity for $7$ years before replacement, with a reliability requirement of $\backslash (98\mathrm{.}5\backslash \%\backslash )-$ a standard that aligns with Malaysia's National Automotive Policy $($NAP$)2020$ goals for enhancing local automotive manufacturing capabilities. This operating schedule and reliability target are critical given the growing demand for Malaysian$-$made vehicles in Southeast Asian markets. The force analysis at MIROS $($Malaysian Institute of Road Safety Research$)$ testing facilities reveals complex loading conditions on both bearings. Bearing A experiences a combination of forces: a tangential force of $7\mathrm{.}5$ kN and a radial force of $10\mathrm{.}5$ kN $.$ The loading on Bearing B is more severe, with tangential and radial forces of $10\mathrm{.}5$ kN and $12\mathrm{.}5$ kN $,$ respectively. Additionally, the system must accommodate a downward thrust force of $6\mathrm{.}5$ kN applied by the outer hub, which is critical for maintaining stability during Malaysia's diverse driving conditions, from urban highways to rural roads. The bearing selection process must utilize specifications from DRB$-$HICOM's approved supplier catalogue $($Manufacturer $1),$ which provides a K factor $1\mathrm{.}5$ for their tapered roller bearings. The design calculations must incorporate an application factor $1\mathrm{.}05$ to account for Malaysian road conditions and climate variables. These factors are crucial for meeting the Malaysia Automotive, Robotics and IoT Institute $($MARii$)$ standards for component durability and reliability. The engineering challenge, undertaken by local Malaysian automotive engineers, is selecting appropriately sized tapered roller bearings that can handle the combined loads while adhering to the government's localization requirements under the NAP $2020.$ The solution must consider the technical specifications and factors such as local maintenance capabilities, thermal performance in tropical conditions, and costeffectiveness for the ASEAN market segment.