Suspension System Design

Good day everyone,

I have designed the suspension system of an 240 kg (without driver), 80 kW electric race car. The vehicle has been developed with a focus on maximizing maneuverability in tight spaces.

I started the design process by determining the placement of the vehicle’s components. By positioning the motor, battery, controllers, wiring, differential, pedals, and finally the driver(s), I calculated the approximate center of gravity (which was later refined through adjustments).

Next, using sketch work and a suspension analysis program, I determined the suspension hardpoints by testing various parameters such as static camber, camber gain, toe, bump steer, Ackermann, caster, caster trail, kingpin inclination, scrub radius, and the instant centers of the wishbones in front/side/top views, as well as anti-dive/lift/squat geometries. These were analyzed under roll/pitch/heave motions with different ride height, camber, and toe settings.

Although placing the steering rack in front of the wheel axis increased the vehicle’s moment of inertia, it subjected the outer wheel’s tierod to tensile loading during cornering, which helps prevent bending and improves steering feel. Moreover, compared to a rear-mounted steering rack, this layout reduces the angular deflection of the double universal joint on the steering shaft, lowering friction and making steering smoother.

Due to accessibility and budget constraints, I had to use gas-charged bicycle shock absorbers. Therefore, I aimed to maximize the effective use of the shock’s stroke range. To achieve this, I designed a bell crank system that compresses the shock from both sides, ensuring a linear motion ratio across different ride heights. This system also lowers the center of gravity compared to conventional pushrod systems with top-mounted shocks, and the gas shocks are lighter than coil springs. Since the vehicle does not have aerodynamic wings, an anti-roll bar was deemed unnecessary. Nitrogen will be charged into the shocks to prevent changes in stiffness and height caused by temperature rise.

After determining the hardpoints, I proceeded to design the control arms, tierods, pushrods, brackets, bell crank, upright, and hub. Throughout the design phase, manufacturability, lightness, rigidity, adjustability, and ease of maintenance were prioritized. The loads on each component were calculated and optimized through FEA analysis.

While designing the upright, I ensured it could be manufactured on a 3-axis CNC milling machine and allow camber adjustment. I maximized suspension performance by efficiently utilizing the space inside the wheel.

When designing the hubs, I decided to use a floatless brake disc system. The reason was the disc’s ability to self-center with the caliper and its easy removability. Since a 4 mm thick disc was sufficient, any misalignment could cause uneven pad pressure and disc warping, posing a safety risk. The disc’s floater was fixed to the hub via wheel studs, meaning the studs secured both the wheel and the brake disc simultaneously. This design eliminated the need for additional mounting interfaces on the hub, simplifying manufacturing and reducing wheel offset. Consequently, a smaller KPI angle could be used while maintaining the same scrub radius. This allowed for the same camber gain during cornering with reduced caster, softening the steering. Additionally, since the in-wheel carrier system’s center of gravity moved closer to the KPI axis, moment forces due to inertia were reduced.

Wishing everyone productive work and success.

Example Definition Symbol Value Unit Example2 Definition2 Symbol2 Value2 Unit2
1) Racing car basics         
1.1Combined massmm310kg1.2(a)LoadW3041,1N
1.1Horizonal distance to combined masslm820mm1.2(a)Front static axle loadWF1462,80759N
1.1Vertical distance to combined masshm285mm1.2(a)Rear static axle loadWR1578,29241N
 WheelbaseL1580mm1.2(b)% to front 48,1012658 
 TrackwidthT1150mm1.2(b)% to rear 51,8987342 
 Rolling radius (Rear)Rr265mm1.2(c)Rear static wheel loadsWRR,WRL789,146203N
     1.2(c)Front static wheel loadsWFR,WFL731,403797N
     1.3(a)Traction forceF2680,29153N
1.3Coefficient of friction (Acceleration)μ1,3 1.3(a)Longitudinal load transferΔWx483,470307N
1.4Coefficient of friction (Braking)μ1,3 1.3(a)Rear wheel loads (Acceleration)WRR,WRL1030,88136N
1.5Coefficient of friction (Cornering)μ1,3 1.3(a)Front wheel loads (Acceleration)WFR,WFL489,668644N
1.6Coefficient of friction (Braking with downforce)μ1,3 1.3(b)Peak torque at rear wheelsTwheels710,277254Nm
1.7Coefficient of friction (Cornering with downforce)μ1,3 1.3(c)Accelerationa8,64610169m/s²
     1.3(c)Accelerationa0,88135593g
 Acceleration    1.4(a)Maximum braking forceF3953,43N
 Braking    1.4(a)Total longitudinal weight transferΔWx713,118703N
 Cornering    1.4(a)Rear wheel loads (Braking)WRR,WRL432,586851N
 Must be calculatet manually    1.4(a)Front wheel loads (Braking)WFR,WFL1087,96315N
 Extra    1.4(a)Rear tires brake % 28,4493671 
 Important    1.4(a)Front tires brake % 71,5506329 
     1.4(b)Decelerationa12,753m/s²
     1.4(b)Decelerationa1,3g
     1.5(a)Maximum cornering forceF3953,43N
     1.5(b)Total lateral weight transferΔWy979,763087N
Example3 Definition3 Symbol3 Value3 Unit3 Example4 Definition4 Symbol4 Value4 Unit4
3) Suspension links         
3.1Slope (for front anti-geometry)θ14,32506degree3.1% of total braking force at the frontFF%71,55063 
3.1Slope (for rear anti geometry)θ22,9degree3.1% of total braking force at the rearFR%28,44937 
From Max. vertical load 3Load  3.1% anti-dive 30 
Table Max. torsion 1,3cases 3.1% anti-lift 7,989715 
2.2 Max. cornering 1,3and 3.1% anti-squat 28,08398 
 Max. braking 1,3dynamic 3.2(a)DownforceD N
 Max. acceleration 1,3factors 3.2(a)Design vertical load/side(max. vertical load) 4561,65N
3.2(a)Factor from aerodynamic downforce 1,3 3.2(a)Front wheel design vertical load (max. vertical load)Wvert2194,211N
     3.2(b)Design load (vertical)Wvert1414,352N
     3.2(b)Design brake force(longitudinal)Wlong1838,658N
     3.2(c)Effective weight of carW3041,1N
     3.2(c)Maximum cornering forceF3953,43N
     3.2(c)Total lateral weight transferΔWy979,7631N
     3.2(c)% amount transferred to individual wheel 62,5 
     3.2(c)Front outer vertical wheel load 1343,756N
     3.2(c)Design load (vertical)Wvert1746,882N
     3.2(c)Front outer design cornering forceWlat2270,947N
     3.2(d)Acceleration design loadWvert1340,146N
     3.2(d)Design acceleration forceWlong1742,189N
Example5 Definition5 Symbol5 Value5 Unit5 Example6 Definition6 Symbol6 Value6 Unit6
4) Springs, dampers and anti-roll         
4.1Corner sprung massms50kg4.1Soft car    
4.1Corner unsprung massmu15kg4.1Wheel centre rateKW10,2N/mm
4.1Tyre stiffnessKT150N/mm4.1Ride rateKR9,550562N/mm
     4.1Natural frequencyfs2,19963Hz
     4.1Unsprung natural frequencyfu16,44772Hz
     4.1Hard car    
     4.1Wheel centre rateKW30N/mm
     4.1Ride rateKR25N/mm
     4.1Natural frequencyfs3,558813Hz
     4.1Unsprung natural frequencyfu17,43455Hz
          
4.2Sprung massms200kg4.2Zero downforce car    
4.2Perp. dist. from ms centre of mass to roll axisha243,5mm4.2Roll coupleC621,0711Nm
4.2Ground clearence 60mm4.2    
4.2%F distrubution of sprung mass  50 4.2Front   
4.2%F distrubution of roll couple 50 4.2Roll couple resisted at frontCf310,5356Nm
4.2Front track widthT1,3m4.2Resulting weight transferCf/T238,8735N
4.2Rear track widthT1,3m4.2Required front ride rateKR9,55494N/mm
4.2Tyre stiffnessKT150N/mm4.2Required front wheel centre rateKW10,20499N/mm
4.2Zero downforce car    4.2Front sprung mass/wheelms50kg
4.2Lateral g forceG1,3g4.2Front sprung natural frequencyfs2,200134Hz
4.2Allocation of ground clearence budget   4.2Vertical displacement from roll 25mm
4.2Dynamic movement of the chasis 15mm4.2Body roll2,21,5degree
4.2Weight transfer from cornering 25mm4.2Roll gradient 1,153846deg/g
4.2High downforce car    4.2Roll rate207,0237Nm/deg
4.2DownforceD N4.2    
4.2Lateral g forceG g4.2Rear   
4.2Allocation of ground clearence budget   4.2Roll couple resisted at rearCr310,5356Nm
4.2Dynamic movement of the chasis  mm4.2Resulting weight transferCr/T238,8735N
4.2Weight transfer from cornering+downforce  mm4.2Required rear ride rateKR9,55494N/mm
     4.2Required rear wheel centre rateKW10,20499N/mm
     4.2Rear sprung mass/wheelms50kg
     4.2Rear sprung natural frequencyfs2,200134Hz
     4.2Vertical displacement from roll 25mm
     4.2Body roll 1,5degree
     4.2Roll gradient 1,153846deg/g
     4.2Roll rate207,0237Nm/deg
Example9 Definition9 Symbol9 Value9 Unit9 Example10 Definition10 Symbol10 Value10 Unit10 Example11 Definition11 Symbol11 Value11 Unit11 Example12 Definition12 Symbol12 Value12 Unit12
6) Front wheel assembly and steering         7) Rear wheel assembly and power transmission        
                    
6.1Lateral forceWlat2270,95N6.1Maximum bending moment in the axleMaxle572191,3Nmm6.1Lateral forceWlat2161,56N6.1Maximum bending moment in the axleMaxle549617Nmm
6.1Vertical forceWvert1746,88N6.1Elastic modulusZ4087,081mm³6.1Vertical forceWvert1662,74N6.1Elastic modulusZ3925,84mm³
6.1Bearing spacingl124mm6.1Minimum diameter of axleϕ34,65808mm 6.1Bearing spacingl137mm6.1Minimum diameter of axleϕ34,1962mm 
6.1Distancel216,95mm     6.1Distancel213,95mm     
6.1Rolling radiusRr265mm     6.1Rolling radiusRr265mm     
6.1Yield strengthσy210N/mm²     6.1Yield strengthσy210N/mm²     
                    
6.2Longitudinal forceWlong1838,66N6.2Effective bearing spacing 79mm6.2Longitudinal forceWlong731,072N6.2Effective bearing spacing 37mm
6.2Vertical forceWvert1414,35N6.2Case 1 - cornering    6.2Vertical forceWvert562,363N6.2Case 1 - cornering    
6.2Axle diameterϕ45mm6.2Raidal load on inner bearingP1i7,85102kN6.2Axle diameterϕ85mm6.2Raidal load on inner bearingP1i14,8545kN
6.2From manufacturer's data sheet:   6.2Raidal load on outer bearingP1o6,104138kN6.2From manufacturer's data sheet:   6.2Raidal load on outer bearingP1o13,1918kN
6.2Dimension α 37mm6.2Case 2 - braking    6.2Dimension α 0mm6.2Case 2 - braking    
6.2WidthB19mm6.2Inner bearing vertical load -0,18888kN6.2WidthB13mm6.2Inner bearing vertical load 0,21203kN
6.2Basic static loadC026kN6.2Inner bearing longitudinal load -0,24554kN6.2Basic static loadC043kN6.2Inner bearing longitudinal load 0,27563kN
6.2Basic dynamic loadCr35kN6.2Inner bearing resultant radial loadP2i0,309784kN6.2Basic dynamic loadCr52kN6.2Inner bearing resultant radial loadP2i0,34775kN
6.2    6.2Outer bearing vertical load 1,225473kN     6.2Outer bearing vertical load 0,77439kN
6.2    6.2Outer bearing longitudinal load 1,593115kN     6.2Outer bearing longitudinal load 1,00671kN
6.2    6.2Outer bearing resultant radial loadP2o2,009926kN3.2(b)Design load (vertical)Wvert562,363N6.2Outer bearing resultant radial loadP2o1,27009kN
6.2    6.2Check static loads    3.2(b)Design brake force(longitudinal)Wlong731,072N Case 3 - accelerating    
6.2    6.2Maximum radial load from aboveP07,85102kN3.2(c)Effective weight of carW3041,1N Raidal load on inner bearingP2i0,65685kN
6.2    6.2Static safety factors03,311671 3.2(c)Maximum cornering forceF0N Raidal load on outer bearingP2o2,39904kN
6.2Dynamic load profile   6.2Check dynamic loads    3.2(c)Total lateral weight transferΔWy979,763N6.2Check static loads    
6.2Turning right    6.2Inner bearingPmi5,559999kN3.2(c)% amount transferred to individual wheel 50 6.2Maximum radial load from aboveP014,8545kN
6.2Assumed % time 30 6.2Outer bearingPmo4,941518kN3.2(c)Rear outer vertical wheel load 1279,03N6.2Static safety factors02,89474 
6.2Inner bearing load 7,85102kN6.2Estimated fatigue life (choose bigger [Pmi,Pmo])2,49E+08cycles3.2(c)Design load (vertical)Wvert1662,74N     
6.2Outer bearing load 6,10414kN6.2Max range 415342km3.2(c)Rear outer design cornering forceWlat2161,56N     
6.2Turning left                   
6.2Assumed % time 20                
6.2Inner bearing load 5,11087kN               
6.2Outer bearing load 6,3199kN               
6.2Braking                   
6.2Assumed % time 15                
6.2Inner bearing load 0,30978kN               
6.2Outer bearing load 2,00993kN               
6.2Accelerating                   
6.2Assumed % time 25                
6.2Inner bearing load -0,085kN               
6.2Outer bearing load 0,55156kN               
6.2Cruising                   
6.2Assumed % time 10                
6.2Inner bearing load -0,293kN               
6.2Outer bearing load 1,90119kN               
                    
     6.3 Fouter22094,42     6.3 Fouter13191,8
     6.3 Finner23841,31     6.3 Finner14854,5
6.3 l379,55mm6.3 Vouter2413,2386.3 l379,55mm6.3 Vouter774,389
6.3 l423,2mm6.3 Houter3137,216.3 l423,2mm6.3 Houter1006,71
6.3 l588,9mm6.3 Vinner998,88626.3 l588,9mm6.3 Vinner212,026
     6.3 Hinner1298,552     6.3 Hinner275,634
       Fbrake4742,037       Fbrake1885,49
       Vbrake2371,018       Vbrake942,745
       Hbrake1237,517       Hbrake492,051