Kinematics March Part 1 : Suspension Kinematics Design
Summary
This video provides a comprehensive overview of vehicle kinematics, focusing on how different geometric aspects of suspension design influence vehicle performance, handling, and driver feedback. It delves into concepts like wheelbase, track width, caster, camber, steering geometry, roll centers, pitch centers, and motion ratios. The presentation emphasizes the importance of understanding tire models and integrating kinematic design with overall vehicle architecture, particularly for racing applications while also drawing parallels to passenger cars. It highlights the interplay between various kinematic parameters and their impact on key performance indicators like lap time, tire wear, and steering effort, concluding with the crucial role of compliance in overall vehicle behavior.
Key Insights
Shorter wheelbases offer advantages in weight and agility, crucial for Formula Student.
A short wheelbase (e.g., Formula Student's 1525mm min) provides benefits in weight reduction (smaller car = lighter) and improved responsiveness, essential for tight, low-speed circuits.
Minimizing unsprung mass is critical for reducing vehicle inertia and improving handling.
The inertia contribution of unsprung masses (like wheels and suspension components) is significantly higher than that of sprung masses (like the engine), emphasizing the need to reduce unsprung weight.
Combining small mechanical trail with large caster angle can offer the best of both worlds.
This configuration can achieve low steering torque while still benefiting from significant camber variation effects, optimizing tire performance across different steering angles.
The distance between the non-suspended mass CG and the kingpin axis is critical for dynamic stability.
During braking or acceleration, inertial forces of the non-suspended mass create significant torque around the kingpin axis, especially when this distance is large. Reducing this distance is crucial.
Maximizing the steering arm length is a fundamental principle for efficient steering.
A longer steering arm provides greater leverage, reducing steering torque for a given force. The steering arm length on the upright dictates the steering rack ratio.
Focusing on application point and direction of forces is often more impactful than their intensity.
Small adjustments in suspension pickup points (location and direction) can yield significant performance improvements, sometimes more so than changes in spring rates or tire pressures.
Sections
Introduction and Course Overview
This is the first session of a four-part series on vehicle kinematics.
The first session focuses on vehicle damage aspects and car performance influenced by kinematics. The subsequent three sessions will be presented by Ariel Avi, covering kinematic software usage, force models, and optimization.
Key kinematic elements to be discussed include wheelbase, track, scrub radius, and mechanical trail.
The session will cover definitions of wheelbase, track, scrub radius, mechanical trail, KPI (Kingpin Inclination), and caster. It will also discuss outboard pickup points on the upright (front view virtual swing axle, instant center, roll center) and inboard wishbone pickup points.
Steering rack inboard and outboard position influences bump steer and Ackerman geometry.
The discussion will cover steering rack inboard and outboard positions, their influence on bump steer and Ackerman geometry, suspension motion ratios, and the integration of kinematics with vehicle design.
Wheelbase and Track Width Considerations
Passenger car dimensions are often dictated by regulations and packaging constraints.
For passenger cars, dimensions like wheelbase and track width are often predetermined due to width restrictions (e.g., not exceeding 3 meters) and class considerations (Class A, B, C).
Racing car design considers inertia, circuit type, driver skill, rules, and weight targets.
In racing, factors like the type of circuit (fast vs. tight), driver skills, tire characteristics, rules, weight targets, downforce, and potential rollover are crucial considerations for design choices like wheelbase.
Downforce is significantly generated by the diffuser and floor, especially in F1 and IndyCar.
In Formula 1, the diffuser contributes about 60% and front/rear wings about 20% of downforce. In IndyCar at Indianapolis, up to 85% of downforce comes from the underbody.
Longer wheelbases increase stability but reduce responsiveness, which is disadvantageous on tight circuits.
A long wheelbase (e.g., F1's 3600mm max) aids stability but increases inertia, hindering responsiveness on tight circuits like Monaco. Reduced downforce makes this difference less critical.
Shorter wheelbases offer advantages in weight and agility, crucial for Formula Student.
A short wheelbase (e.g., Formula Student's 1525mm min) provides benefits in weight reduction (smaller car = lighter) and improved responsiveness, essential for tight, low-speed circuits.
Minimizing unsprung mass is critical for reducing vehicle inertia and improving handling.
The inertia contribution of unsprung masses (like wheels and suspension components) is significantly higher than that of sprung masses (like the engine), emphasizing the need to reduce unsprung weight.
Double wishbone suspension can significantly reduce inertia compared to MacPherson struts.
By strategically placing dampers behind the front axle and forward of the rear axle, a double wishbone setup can reduce vehicle inertia by up to 35% compared to a MacPherson strut setup.
Outboard Kinematic Points: Caster, KPI, Trail, and Scrub Radius
Outboard pickup point geometry (caster, KPI, trail) affects steering feel and dynamics.
The choice of KPI, caster angle, and mechanical trail on the upright influences steering torque, camber variation while steering, aerodynamic behavior, and cross-weight.
Target steering wheel torque should be below 10 Nm for driver comfort and control.
Excessive steering torque (e.g., 20 Nm) can lead to driver fatigue. Aim for a maximum of 10 Nm, significantly lower than passenger cars which typically have power steering.
The kingpin axis should ideally intersect the tire's contact patch center for optimal steering.
Aligning the kingpin axis with the center of the tire contact patch minimizes unwanted torques. Offsets can create significant loads on the steering system and chassis.
Large mechanical trail generates significant steering torque and camber variation.
A large mechanical trail leads to high steering torque but also considerable camber variation. A small mechanical trail reduces steering torque but offers less camber variation.
Combining small mechanical trail with large caster angle can offer the best of both worlds.
This configuration can achieve low steering torque while still benefiting from significant camber variation effects, optimizing tire performance across different steering angles.
Steering torque is generated by lateral forces offset from the kingpin axis and tire characteristics.
Various forces, including lateral force (Fy), longitudinal force (Fx), vertical load (Fz), and tire moments (Mz), contribute to steering torque, especially when offset from the kingpin axis.
Tire vertical load distribution changes significantly during cornering, impacting grip.
During a left turn, the vertical load increases on the left front and right rear tires, while decreasing on the right front and left rear. This diagonal weight transfer affects tire performance.
Camber variation is also observed on the non-steered wheels due to load transfer and roll.
Load transfer and suspension compliance (roll angle, tire deflection) cause minor camber changes even on the rear wheels during cornering, influenced by the load distribution across the axles.
Achieving consistent tire temperature across the contact patch requires careful camber management.
Infrared temperature readings reveal issues like excessive camber causing high inner tire temperatures. Adjusting static camber alone may worsen other areas, necessitating a kinematic solution like increased caster.
Caster angle significantly influences camber variation during steering, especially in tight corners.
In tight turns, greater steering angles amplify the effect of caster on camber variation. The connection point of the pushrod (on wishbone vs. upright) also impacts this.
Downforce generation is heavily influenced by the interaction of kinematic parameters with aerodynamics.
Changes in steering angle can lead to significant variations in aerodynamic downforce. Understanding this relationship is crucial for optimizing car balance during cornering.
High downforce often necessitates power steering due to increased steering torque.
The significant vertical loads generated by high downforce can create excessive steering torque, making power steering a necessity for driver control, even if not explicitly mandated by rules.
Suspension Geometry and Packaging
Packaging the suspension components around the upright presents significant challenges.
Fitting components like the tire, rim, hub, brake caliper, disc, and potentially cooling ducts or outboard electric motors requires careful design consideration around the upright.
The distance between the non-suspended mass CG and the kingpin axis is critical for dynamic stability.
During braking or acceleration, inertial forces of the non-suspended mass create significant torque around the kingpin axis, especially when this distance is large. Reducing this distance is crucial.
Incorrect placement of suspension pickup points can lead to mechanical failure.
Locating pickup points too far outboard or improperly aligning linkage can overstress components, as seen with inboard electric motors causing buckling during braking.
Maximizing the steering arm length is a fundamental principle for efficient steering.
A longer steering arm provides greater leverage, reducing steering torque for a given force. The steering arm length on the upright dictates the steering rack ratio.
Steering rack ratio should be determined after defining steering arm length and tire forces.
The optimal steering rack ratio is a consequence of the upright's steering arm length and the forces acting on the tire, not a starting point for design.
Front View Kinematics: Virtual Swing Axle and Roll Center
The front view virtual swing axle relates instant center to tire contact patch.
The distance between the instant center and the contact patch is the front view virtual swing axle, which influences camber variation during roll and heave.
Long virtual swing axles cause significant camber variation during roll.
A long virtual swing axle leads to substantial camber changes when the car rolls, while a very short one results in considerable camber variation during heave (vertical movement).
Instant center position affects scrub and tire wear.
A high instant center position can lead to increased scrub, causing higher tire temperatures and potentially accelerated wear, though this is less of a concern in racing than in road cars.
Low roll centers may lead to increased elastic load transfer.
A lower roll center generally results in less geometric load transfer and more elastic load transfer (via springs, dampers, anti-roll bars).
Roll center position influences jacking forces and vehicle ride height during cornering.
The lateral and vertical position of the roll center dictates whether cornering forces lift or lower the vehicle chassis, affecting aerodynamic downforce and center of gravity height.
Movement of the roll center is not inherently bad and can be beneficial.
Contrary to some expert opinions, a moving roll center, particularly towards the inside of the corner, can provide advantages. Similarly, bump steer can be a desirable characteristic.
Geometric load transfer dominates at the entry of a corner with a high roll center.
With a high roll center, geometric weight transfer plays a larger role initially. With a low roll center, elastic components, especially dampers, contribute more significantly to early load transfer.
High roll centers promote quicker transient response, beneficial for responsive handling.
A high roll center results in less inertia, leading to a more responsive car. Conversely, a low roll center increases inertia, providing more stability, which might suit amateur drivers or fast circuits.
Roll center altitude and stiffness of the tires influence desired handling characteristics.
A high roll center with stiff tires might require a lower roll center to compensate, and vice-versa, to achieve a balanced and predictable feel.
Roll center crossing the wheel center inverts damper action from compression to rebound.
If the roll center moves such that it passes the wheel center, the outboard dampers switch from compressing to rebounding relative to the chassis, impacting cornering dynamics.
Non-parallel roll centers (front vs. rear) lead to undesirable chassis roll behavior.
A stable roll axis is crucial; if the front and rear roll centers move independently or at different rates, it can cause unpredictable and detrimental chassis roll.
Side View Kinematics: Virtual Swing Axle and Pitch Center
Side view virtual swing axle impacts wheelbase and caster variations.
The length of the side view virtual swing axle influences how caster angle changes with suspension travel.
A high pitch center improves responsiveness and potentially tire temperatures.
A high pitch center leads to lower inertia, quicker response, more anti-dive/anti-squat effect, and potentially higher tire temperatures due to increased load transfer.
Low pitch centers result in higher inertia and slower response.
Conversely, a low pitch center increases inertia, leading to slower response and potentially lower tire temperatures.
Anti-dive and anti-squat definitions are often oversimplified and view-dependent.
Traditional definitions of anti-dive/anti-squat focus on single-plane views (front or side) and can be misleading as they don't account for the entire vehicle's dynamics.
Brake distribution significantly affects anti-dive characteristics.
The ratio of front to rear braking force directly influences the calculation of anti-dive, as it changes the load transfer distribution and resulting suspension geometry angles.
Inboard brakes require different calculations for anti-dive compared to outboard brakes.
The location of the brake system (inboard or outboard) affects the geometry and forces involved, necessitating adjustments in the calculation of parameters like angle 'a' and 'b' for anti-dive.
Hybrid vehicles with both inboard and outboard brakes require dual anti-dive calculations.
Cars employing both types of braking systems need separate anti-dive calculations for each system to accurately assess their dynamic behavior.
Steering Geometry: Ackerman, Bump Steer, and Steering Torque
Proper steering rack position is crucial for balancing responsiveness and stability.
Mounting the steering rack forward or rearward of the front axle, and selecting the Ackerman geometry (pro, parallel, or anti-Ackerman) are critical design choices.
Ackerman geometry should be determined based on tire model data.
The optimal Ackerman setting (how much more the inside wheel turns than the outside) depends on the tire's slip angle characteristics under different loads.
Tire load dictates the required slip angle for optimal grip.
Heavier loaded tires require more slip angle to reach their peak grip. The inside tire is less loaded and thus needs less slip angle than the outside tire in a turn.
Turn-in response is influenced by slip angle, steering angle, and vehicle velocity.
The slip angle experienced by the tires is a combination of the driver's steering input, the car's yaw rate, and the resulting lateral accelerations.
Achieving targeted slip angles requires precise steering angle inputs.
By understanding tire behavior at different speeds, loads, and slip angles, one can calculate the necessary steering angle to achieve desired tire slip.
Balance is as important as front slip angle performance; the rear must follow.
Optimizing front tire grip is essential, but the car's overall balance relies on the rear tires also performing effectively. Overly grippy front tires can lead to understeer.
Suspension compliance significantly alters kinematic predictions.
Real-world components are not rigid; compliance in bushings, arms, and uprights will modify the actual kinematic behavior, often negating precise design intentions.
Non-linear steering ratios require careful phasing and consideration of intermediate shafts.
Variations in steering ratio necessitate precise alignment of steering column components and intermediate shafts to ensure consistent and predictable steering feel.
Chassis stiffness affects steering precision and driver feedback.
A significantly twisting chassis under steering load can lead to a disconnect between steering input and wheel response, negatively impacting driver confidence.
Steering system compliance can introduce unwanted toe variations.
Even without chassis flex, compliance within the steering rack, linkages, and uprights can cause significant toe angle changes under steering torque.
Motion Ratios and Suspension Components
Motion ratio defines the relationship between wheel movement and spring/damper movement.
The motion ratio is crucial for calculating the effective wheel rate, which is the spring's effect at the wheel, in series with the tire's rate.
Decreasing spring stiffness can paradoxically increase wheel rate due to motion ratio squared.
If the motion ratio decreases (e.g., from 0.9 to 0.8), the wheel rate increases significantly (by the square of the motion ratio), making the suspension stiffer despite a softer spring.
Variable rate motion ratios can create a rising rate suspension characteristic.
Rocker designs can be engineered to provide a changing motion ratio, offering a softer initial rate for mechanical grip and a stiffer rate as the suspension compresses to resist downforce.
Anti-roll bar motion ratio can be defined by displacement or roll angle.
While some define it by wheel movement vs. anti-roll bar end movement, defining it by roll angle vs. anti-roll bar twist angle is preferred for clarity.
Anti-roll bar stiffness characterization requires consistent units (force vs. angle).
Ensure consistency when comparing anti-roll bar stiffness, whether expressed in force per displacement or torque per degree of twist.
Kinematic component alignment is vital to avoid parasitic compliance.
All suspension linkages, including pushrods, rockers, dampers, and anti-roll bars, should ideally lie in the same plane to prevent bending or twisting forces caused by misalignment.
Proper inboard pickup point design prevents premature component failure.
Ensuring pushrods are aligned with the center of ball joints and using appropriate shear strength (double shear for upright components) are critical for durability.
Integration and Advanced Kinematic Concepts
Chassis and upright design teams must collaborate closely on pickup point definition.
The inboard pickup points on the chassis and outboard points on the upright are intrinsically linked. Their meeting point defines force paths and impacts chassis loading.
Rear caster and KPI influence steering torque and suspension forces.
While not always necessary, rear caster and KPI angles affect the torque generated around the kingpin axis, impacting toe-link loads and chassis forces.
Shifting outboard toe points affects steering rotation and ratio.
Maximizing steering arm leverage by placing outboard points as far as possible from the wheel center is desirable for reducing steering effort.
Jacking forces can have unintended consequences beyond aerodynamics.
Upward jacking forces lift the roll center, altering load distribution and potentially impacting suspension behavior, especially with soft springs.
Suspension linkage alignment (vertical vs. horizontal) impacts misalignment angles.
The orientation of suspension rods (e.g., tie rods) influences the potential for bending forces if misalignment angles exceed the spherical joints' capacity.
Bump steer can be a beneficial characteristic, particularly on smooth tracks.
Bump steer, the change in toe angle with vertical wheel travel, can help maintain desired slip angles during cornering but can be detrimental on bumpy surfaces.
Kinematic calculations must account for all suspension components and their interactions.
Motion ratio calculation involves all elements from the wheel to the spring/damper, including wishbones, rockers, and even KPI angle, not just simple rocker ratios.
Kingpin inclination (KPI) is necessary to manage steering torque and self-centering.
KPI is essential for creating a self-aligning torque, providing steering feedback and allowing recovery from steering inputs without excessive driver effort.
Adjusting pickup points can dynamically alter camber and KPI while maintaining static values.
Moving pickup points or adjusting shims can change KPI angle and motion ratios, influencing steering torque and wheel rate without necessarily altering static camber.
Compliance and Conclusion
Compliance is a critical factor that can undermine kinematic design.
Flexibility and compliance in suspension components, bushings, and chassis can significantly alter the intended kinematic behavior, often acting against design goals.
Kinematics and compliance are not easily compensated for by each other.
Poor compliance cannot be fixed with clever kinematics; they are independent factors, and poor compliance will generally worsen the effects of bad kinematics.
Focusing on application point and direction of forces is often more impactful than their intensity.
Small adjustments in suspension pickup points (location and direction) can yield significant performance improvements, sometimes more so than changes in spring rates or tire pressures.
Ask a Question
*Uses 1 Wisdom coin from your coin balance
