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The Half - Shaft and Wheel Hub of Formula One racing car was designed taking into consideration one of the popular model of Redbull racing car. The various dimension of shaft and hub were altered to attain maximum factor of safety.
Design of half shaft and wheel hub assembly for racing car
DESIGN OF HALF – SHAFT AND REAR WHEEL HUB ASSEMBLY OF A RACE CARFaculty co-ordinator: Prof. Gokul KumarDesign project guide: Prof. B . K Jha Manvendra Singh Inaniya(08BME126) 9047288146 Ravi Shekhar (08BME181) 9566810725
Project Objective• It was required to design a hub assembly and half–shafts for the Formula 1 car of mass about 640 kg, maximum speed of 300 km/hr and average speed of 150km/hr.• The assembly must give stability during rotation of the wheels. The weight and the dimension of the hub must be as small as possible because of the unsprung weight which further reduces the rotational mass. The half-shafts should not fail under stress.
Red Bull RB7 Formula 1 CarRB7 F1 is the official car from World Champions Red Bull for the 2011 season ofFormula 1. We have considered this vehicle as a reference for this Design Projectas it is one of the fastest and most technologically matured vehicle in the racingscenario.
Half - Shafts• A half - shaft is an axle on a front wheel drive vehicle connecting the transmission to the driven wheels.• The rear wheel driven Formula 1 vehicle being observed for the project uses half shafts in rear, as the differential is rigidly mounted and an independent rear suspension is used.
Design ConsiderationHalf shafts are designed as – a hollow metal tube to reduce weight. – CV joint at either end, allowing the driven wheels to maintain constant velocity . – Splines to transmit power between differential, CV joints, shaft and wheel hub. – the suspension travels during driving. – fatigues due to high speed rotation.
Wheel-Hub• A hub assembly contains the wheel bearing, and the hub to mount the wheel to vehicle.• It is located between the brake rotors and axle.
Design Consideration• The bolt pattern is determined by the number of bolts on the wheel hub.• Selection of material strong enough to take the weight of the car.• Wheel bearings in the hub depending on ID and OD of spindle coming out of hub.• Type of lug nuts or bolts.
DESIGN CRITERIA AND DURABILITY APPROVAL OF WHEEL HUBSAE international,USA 11-16-1998 technical paper authors : Gerhard fischer , Vatroslov V. grubisic The author says that the design of wheel hub must be based on stress generated under customer usage through operational loads acting on wheels. Wheel hub are highly steered safety components which must not fail under the applied loading conditions. The main parameters for design of wheel hub assembly are loading conditions , manufacturing process and material behavior. The influence of these parameters are interactive so material fatigue behaviour will be changed depending upon the wheel hub design and loading conditions.
FRACTURE ANALYSIS OF WHEEL HUB FABRICATED FROM PRESSURE DIE ALUMINIUM ASSEMBLYtheoretical and applied fracture mechanics ,vol 9 feb 1988 authors : S . Dhar The author says that a catastrophic failure of wheel hub occurred during service. The nature of crack was a corner crack. An analytical investigation was carried out using tool of linear elastic fracture mechanics to establish the cause of failure. The non – linear behavior is due to the presence of material inhomogeneties and discontinuities. An analytical estimation was carried out in order to calculate the minimum no. of cycles carried by wheel hub in service. The initiation of crack growth is complex because the heterogeneity and morphology of fracture surface. Fractographic and metallographic studies are carried out to assist the understanding of corner cracking problem.
Finite element modeling of dynamic impact and cornering fatigue of cast aluminum and forged magnesium road wheels. Proquest dissertation and thesis 2006 authors : Shang, Shixian (Robert)The author says that numerical investigation of wheel dynamics impact and cornering fatigue performance is essential to shorten design time , enhance mechanism performance and lower development costs. The desertion focused on two objectives: i) Finite element models of a dynamic impact test on wheel and tire assembly were developed which considered the material in homogeneity of wheels. Comparison of numerical predictions with experimental measurements of wheel impact indicated 20% reduction of initial striker kinetic energy provide an effective method for simplifying modeling.ii) numerical prediction of wheel cornering fatigue testing was considered.It proceeded in two methods, first was static stress analysis with bending direction applied to the hub. Second was dynamic stress analysis with application of a rotating bending moment applied to hub.
Prototype CAD Model Half - Shaft Isometric View
Parameters for Half-shaft• L – Length of shaft• Do – Outer diameter of shaft• Di – Internal diameter of shaft• T – Maximum Torque applied by differential on shaft• σ – Maximum Normal Stress on shaft• τ – Maximum Sheer Stress on shaft• J – Polar Moment of Inertia of shaft• G – Modulus of Rigidity
Parameters of Wheel Hub• n - Number of Bolts• b - Bolt Circle Diameter or Pitch Circle Diameter• d - Flange diameter is measured between opposite holes• S - Spoke hole diameter• W - Width centre to flange• P - Load capacity is the amount of weight a wheel will carry
Half - ShaftGIVEN :• Maximum Torque of engine at 14000 rpm = 280 N-m• Gear ratio for 1st gear = 1.833• Final Drive ratio = 2.15Material selection:• The material chosen for the design of Half – shaft is ion nitrided titanium alloy.• The titanium and titanium alloys have unique corrosion, nonmagnetic and strength – to-weight ratio properties.• Mechanical properties of nitride titanium alloys are as follows: Yield stress = 1.24105631 × 109 Pascal Maximum Sheer Stress = 0.62052815 × 109 Pascal
Calculation of Torque at half-shafts:Shock torque = factor of safety x first gear ratio x final drive x maximum engine torque = 2.5 x 1.833 x 2.15 x 280 = 2758.665 N-m. Internal to external diameter ratio, k = 5As T = 6246.765 N-m , τ = 0.62052815 × 109 Pascal , k = 5The Axial Force acting upon the half-shafts has been countered by adding plunge to theC.V. joints at the end of the half-shaftsThe Gyroscopic couple acting due to rotational masses likes tyres, camshafts andcrankshafts is negligible as the rims, camshafts and crankshafts are made of light weighttitanium alloys which contribute insignificantly to gyroscopic couple.No bending moment is observed as no additional weight, except self-weight of half-shafts, is loaded on the half-shafts. Thus our calculations would be based upon thestrength required from shaft under torsional loading only.
T = (π/16) x τ x (do)3 x [ 1 – (di / do)4] We have, k = di / do = 5 So, 2758.665 = (3.14/16) x 0.62x 109 x (do)3 [ 1 – (1/5)4] do3 = 22882.115 do = 28.39 mm Or, do = 29 mm. Therefore, di = 29/5 di = 5.66 mm.From the design calculation we find that the required external and internaldiameter of the half – shaft as per the specified engine parameters and givenconditions is 29 mm and 5.6 mm.
Wheel-Hub AssemblyTires and rims selection:The tires selected were of 13” diameter. The diameter was selected assuch that floor of the formula car does not touch the ground. At the sametime a low ride height would give an aerodynamic as well as low Center-of-gravity advantage.Number of bolts is taken 4 as it is a standard for 13” wheels.Pitch Circle Diameter(P.C.D.) is fixed at 100 mm as it is a standard for13” wheels.Spoke Hole Diameter(S) is taken as M12 as it is a standard for 13”wheels.Material : Ti6Al4V - titanium alloy is the most widely used .
Brake Force Calculation• Brake force is required to estimate the load on the wheel hub.• As almost all the design parameters of a wheel hub are fixed by the size of wheel, the thickness of the wheel hub is the defining parameter.• The thickness of wheel hub is determined by maximum force acting on a wheel.
Brake Calculation :-Velocity of Vehicle = voFrictional force will be acting on it = FStopping distance = dFriction force of the road must do enough work on the car to reduce its kineticenergy to zero .To reduce the kinetic energy to zeroWorkfriction = µmgd = 0.5mv02 d= vo2/2µgVelocity of our vehicle = 150 km/hrFriction of road = 0.90 d = 98.31 m
Acceleration of the vehicle:-vo2 = u2 + 2adWhere a is the acceleration of the vehiclea = vo2/2da = 8.8m/sTotal force acting on the vehicleFtotal = mv* aWhere mv is the mass of the vehicle = 640kgFtotal = 640 * 8.8 = 5632NForce on each wheel:-F1 = Ftotal/4 = 3953.43/4 =1408 NF1 = 1408 N
Torque on the tire:-Tr = F1 * rtireRim is taken to be 13”rtire = 20.43 * 0.0254/2 = 0.2595 mTr = 1408 * 0.2595 = 365.35 N-mTorque on disc:-Tdisc = Ffriction*reffectivedisc is assumed to be 200mm , therefore reffective should be 9cmwe know that Tdisc = TtireFfriction = 25647.012 / 9Ffriction = 2849.67NForce on the clamp:-Fclamp = Ffriction/µ = 2849.67/0.5 = 5699.34 N
Wheel Hub Assembly• In design stage, we estimated all the forces acting on hub and disc• The wheel hub was modeled in CAD with given parameters• The forces were applied on model using Finite Element Analysis in..COSMOS• The thickness of hub was varied in increments of 2 mm till a Factor..of Safety value of 2 was attained• Thus the final design of wheel hub is complete
Finite Element AnalysisNo external force External force applied Factor of Safety = 2
Half - ShaftMaterial = ion nitride titanium alloy Yield stress = 1.241 x 109 Pascal Max. Shear stress = 0.62 x 109 Pascal Engine characteristics N = 1400 rpm T = 280 N-m. First gear ratio = 2.833 Final drive ratio = 2.15 Shock torque = 2758.665 N-m. K, d0/di =5 External dia. = 29 mm. Internal dia. = 5.6 mm
Wheel hubTyre dia. = 13”No. of bolts =4Pitch circle dia. = 100mm.Spoke hole dia . = M12Material = Ti6Al4V – titanium alloyStopping distance = 98.31 m.Velocity of vehicle = 150 Km/hr.Acceleration of vehicle = 8.8 m/s2.Force on each wheel = 1408 N.Torque on tyre (R-13) = 388.75 N-m.Diameter of disc = 200 mm.Effective radius = 90 mm.Clamping force = 8638.86 N.Width of flange = 10 mm.
conclusion• Wheel Hub has been designed for a formula 1 car of mass about 640 kg, maximum speed of 300 km/hr and average speed of 150 km/hr.• The designed assembly gives stability during rotation of the wheels.• The weight and dimension of the hub is such that it reduces the rotational mass.• The design project enabled us to understand the various forces that act on a half – shaft and wheel hub, while the Formula 1 race car is in running condition.• The calculated parameters help us to design half - shaft and wheel hub such.• The design project helped to better under the uses of software in real scenario.
GANTT CHART(Design Project) "DESIGN OF HALF - SHAFT OF A PROTOTYPE RACE CAR"Sl Time in WeeksNo. CATEGORY 1 2 3 4 5 6 7 8 9 10 11 12 Topic and guide selection A for projectB Literature review Develop preliminaryC product designD Theoretical DesignE CAD modellingF Software analysisG Optimization of design Develop detailed productH design Final PresentationI Compilation ***Please note that the weeks mentioned above doesnot contain the CAT weeks.