Influence of Available Rear Wheel Travel and Target Sag on Suspension Performance of a Cruiser Motorcycle

Type of the Paper: Conference Paper

Influence of Available Rear Wheel Travel and Target Sag on Suspension Performance of a Cruiser Motorcycle

K. Peck^1,*, and J. Sadauckas²

¹ Vehicle Dynamics Group, Harley-Davidson Motor Company, Milwaukee, WI, 53222, USA; kasey.peck@harley-davidson.com; ORCID 0009-0004-8497-7691

² Trek Performance Research, Trek Bicycle Corporation, Waterloo, WI, 53594, USA; jim_sadauckas@trekbikes.com; ORCID 0000-0002-6055-9047

*corresponding author

Name of Editor: Jason Moore

Submitted: 28/03/2024
Revised: 29/03/2024

Accepted: 02/04/2024

Published: 02/04/2024

Citation: Peck, K. & Sadauckas, J. (2023). Influence of Available Rear Wheel Travel and Target Sag on Suspension Performance of a Cruiser Motorcycle. The Evolving Scholar - BMD 2023, 5th Edition.
This work is licensed under a Creative Commons Attribution License (CC-BY).


Abstract:

The design and optimization of two-wheel vehicle suspension provides an exciting design challenge due to the multitude of potential layouts and interrelated variables to consider. Balancing these design factors to achieve the desired comfort and road holding performance while also ensuring the vehicle achieves the desired trim state under the various operating conditions, termed chassis control for the purposes of this paper, requires a deep level of technical understanding to execute successfully. Consequently, a specific area of two-wheel vehicle suspension development that has received little attention is defining the nominal vehicle trim state in terms of target sag and the associated proportion of vertical wheel travel to be used in compression versus that available for extension. For closed course racing vehicles, both on-road and off-road, the suspension travel and target sag are determined experimentally based on simulation or testing to obtain the primary objective of minimum lap time. However, for commercial on-road vehicles, suspension travel and target sag are often constrained by numerous vehicle design requirements such as aesthetics, seat height, and packaging limitations. These design constraints require production-intent suspension travel and target sag to be selected early in the product development cycle. Until now, limited literature has been published regarding nominal target sag and how best to proportion suspension travel between compression and extension, though a general guideline proposes ~33% target sag as the starting point. The intention of this paper is to provide a deeper technical understanding of suspension performance trade-offs between available suspension travel and target sag using physical vehicle testing and multibody simulations.

Keywords: Motorcycle, Two-wheeler, Sag, Rebound, Ride Quality, Road Holding, Chassis Control, Suspension, Preload

Introduction

Suspension travel, i.e., the available suspension displacement from a fully extended to fully compressed condition, is known to be a critical factor in overall suspension performance. However, suspension sag, defined here as the suspension displacement at ride height under steady-state operating conditions, is an important setup and tuning parameter, largely neglected in the available motorcycle research literature. This paper aims to provide foundational knowledge regarding the influence of suspension sag on vehicle comfort, roadholding, and chassis control.

Within the motorcycle industry, optimal suspension sag is dependent on the specific performance the suspension must deliver but within scientific literature this topic has received very little attention. As a general guideline ~33% target sag has been proposed (Thede, 2010). Most motorcycle owner’s manuals specify a preload adjuster setting to achieve a desired sag state depending on rider weight and vehicle load. For closed course racing vehicles, both on-road and off-road, the sole objective of the vehicle is to achieve the fastest possible lap time. As a result, optimal suspension sag is determined experimentally to achieve the desired vehicle trim state at specific areas on the racecourse to maximize traction, drive, cornering, or braking. Conversely, for commercially available road-going motorcycles, suspension travel and target sag are constrained by numerous vehicle-level design requirements including aesthetics, seat height, and packaging limitations. These design constraints require production-intent suspension ride-height, thus travel and target sag, to be selected early in the product development cycle. Fixing two of the key suspension variables prior to physical suspension tuning limits the engineer’s ability to fully optimize the suspension performance of the vehicle. Additional foreknowledge regarding the relationship between suspension travel and target sag on the resultant suspension performance can better inform the production suspension layouts and offer the potential of improved suspension performance with no additional investment in part cost or damper technology.

This paper presents the results of physical testing of a cruiser motorcycle with three unique rear suspension layouts with variations in suspension travel, sag, and rebound damping. For each layout, qualitative suspension performance ratings were captured on selected closed-course suspension events by a professional motorcycle test rider, trained to articulate perceptible differences in suspension performance. At the same time, quantitative suspension data was collected on the vehicle including front fork and rear shock displacement and velocity, accelerations at the steer head and mid-frame, and the chassis pitch rate, as well as vehicle speed. Correlation analysis between the qualitative and quantitative data was conducted to identify suspension performance indices useful in the development of predictive multibody simulations.

After multibody model correlation was assessed, simulations were conducted to further understand the vehicle performance trends observed during physical testing. The simulation model closely represented the actual test vehicle and was fitted with the three unique rear suspension layouts as characterized on a suspension dynamometer. Simulation of the specific closed-course suspension events enabled calculation of tire normal load, and thereby the determination of road holding, which is difficult to measure during physical testing. Simulation further supplemented the physical test by examining additional variations in damper settings, vehicle speeds, and maneuver constraints.

Physical Testing

Test Setup

The test vehicle used for this research was a heavyweight cruiser motorcycle with front and rear suspension subsystems. The front suspension uses conventional telescopic forks with linear springs and bilinear damping characteristics (Lot, 2021). The rear suspension uses a direct acting hydraulic “mono-shock” shock absorber with linear springs and bilinear damping in both compression and rebound.

Three different rear suspension shock absorber setups, referred to as layouts, were tested. Each layout is a unique combination of travel, sag, and rebound damping. For each layout, the vehicle ride height and resultant seat height, remain unchanged. Layout #1 represents the production vehicle, with a moderate 86 mm of rear wheel travel and rear spring preload set to achieve 30% sag. Layout #2 increases the rear shock travel by 13 mm (a 26 mm increase in rear wheel displacement due to the kinematics of the swingarm) while maintaining the same rear shock damper characteristics and vehicle ride height as Layout #1. This is achieved by sagging the suspension deeper into its travel. Layout #3 is the same as Layout #2 with rebound damping reduced by 40% via changes to the piston architecture and hydraulic rebound damper shim stack. Table 1 outlines the rear suspension layouts tested.

Table 1. Detailed description of the rear suspension layouts tested.

Figure 1 shows overlays of both force versus velocity, at left, and shock spring force versus displacement information, at right, for the three rear suspension layouts tested as measured on a suspension dynamometer. The force versus velocity data shows the damping force between Layout #1 and Layout #2 are nearly identical, while Layout #3 achieves the desired 40% reduction in rebound damping. For Layout #3, changes to the hydraulic damping circuit required to achieve the reduced rebound damping resulted in slightly lower compression damping. The force versus displacement spring curves show all three rear suspension layouts use the same spring rate and jounce bumper, with the differences in available compression and extension displacement clearly labelled.

Figure 1. Force versus Velocity and Force versus Displacement comparisons for the rear suspension layouts tested.

The test vehicle was instrumented to quantify suspension performance differences between the three layouts as follows: vehicle speed via a GPS receiver, front fork and rear shock displacement via linear potentiometers, rear frame acceleration via a DC tri-axial accelerometer mounted under the rider’s seat, and pitch rate via a pitch rate gyrometer also mounted under the rider’s seat. The front fork and rear shock linear potentiometers were zeroed at full extension with positive suspension displacement and velocity indicating a compression event. The DC tri-axial accelerometer and pitch rate sensor were mounted under the rider’s seat in the global orientation following the SAE sign convention (x-axis forward, y-axis to the right, and z-axis to the down) per SAE J670. The pitch rate sensor follows the right-hand rule with positive values indicating the front of the vehicle rotating upward while the rear of the vehicle tilts toward the ground.

Each rear suspension layout was tested over three specific suspension events: Pothole, Camel, and Threshold braking. The Pothole is a negative/downward event of roughly trapezoidal cross section with depth 0.10 m, length 0.91 m and 70-degree vertical slope, used in this paper to evaluate suspension comfort. The Pothole was tested at 24, 32, 40, and 48 kph. The Camel is a positive half-sinusoidal event with length 5.35 m and height 0.15 m and was used to evaluate both chassis control and road holding. Results from the Camel at 32 kph are described. The final event was a front-only threshold braking event from 100 kph to a full stop executed at the limit of front tire grip without skidding or ABS activation. This threshold braking maneuver was used as an initial attempt to further quantify chassis control.

As the Pothole and Camel are discrete transient bump events, road roughness and the corresponding comfort frequency analysis were of limited applicability (De Luca, 2007). Past research also showed that test rider comfort correlates to the highest peaks of acceleration (Strandemar, 2005). As a result, peak vertical acceleration at the mid-frame of the vehicle was the primary metric used to quantify suspension comfort for this study. Further examination of chassis control considered the rear suspension extension rate over the Camel and during threshold braking, whereas road holding was gleaned from rear suspension displacement trends and further examined by considering simulated rear tire normal load.

Qualitative Evaluations

For each layout, qualitative suspension performance was evaluated on closed-course suspension events by a single professional motorcycle test rider. The test rider used for this research has been trained to articulate minute differences in suspension performance through years of motorcycle suspension testing and tuning experience. A single test rider was purposely used for this research to provide a direct performance comparison between the tested layouts. Multiple test rides would have provided a wider range of qualitative suspension performance feedback given differences in skill level and ride feel but would have provided less resolution on the performance differences between layouts. For this research, the test rider’s suspension performance feedback was limited to the three events being studied. The specific suspension performance attributes that were evaluated for each event are outlined in Table 2.

Table 2. Suspension event and corresponding attribute for rider qualitative feedback.

For each suspension layout, the rider took detailed notes on the subjective performance across the three events and speeds being studied and provided a subjective score of 1 through 7 for each performance attribute, with a rating of 1 indicating poor performance, 4 indicating acceptable performance and 7 being excellent performance. A subjective score change of 0.5 was defined as perceptible to a trained rider, while a subjective score change of 1 was defined as being perceptible to an average rider. After the three layouts were tested, rider qualitative feedback and subjective scores for all three layouts were compiled. Figure 2 outlines the subjective scores for each performance attribute.

Figure 2. Summary of subjective ratings (from 1 = Poor to 7 = Good) of suspension performance for a cruiser motorcycle by trained test rider for three rear suspension layouts across five performance attributes over three test events (Pothole, Camel, Braking). Maximal enclosed area suggests best overall performance.

Over the Pothole, the rider noted discernable differences in the abruptness that resulted in differences in perceived comfort. Both Layout #2 and Layout #3 reduced the perceived impact and, thus, increased comfort at 40 kph and 48 kph specifically, with the increase in comfort from Layout #3 greater than Layout #2. At 24 kph and 32 kph, the level of perceived comfort was similar between the three rear suspension layouts.

The Camel at 32 kph also showed discernable performance differences between the three rear suspension layouts. Layout #1 provided adequate control of the stored spring energy during the initial rebound phase after cresting the Camel. However, the rear suspension reached full extension quickly with an audible noise during topping, defined here as full extension of the suspension, and the rider was momentarily separated from the seat. Layout #2 provided similar control of the stored spring energy during the initial rebound phase, but the rear shock did not reach full extension or separate the rider from the seat. The rebound control of Layout #3 was found to be insufficient and extended faster than the rider desired. Additionally, Layout #3 reached full extension with an audible topping noise and a very subtle separation of rider from the seat, the magnitude of both were smaller than Layout #1.

Threshold Braking events showed small differences in performance between the three rear suspension layouts. Layout #1 had an acceptable reaction to the initial brake input, providing the necessary chassis control to enable the rider to apply the brakes aggressively and achieve the desired brake dive (fork compression) rate and vehicle geometry. Additionally, the maximum pitch rate for Layout #1 was perceived to be acceptable. Layout #2 exhibited similar performance during initial brake application as Layout #1 but achieved higher maximum pitch angle at threshold. However, the increased pitch angle did not impact braking performance or chassis control and was not found to be objectionable by the rider. Layout #3 was found to be more sensitive to the initial brake application, with the rear suspension extending noticeably faster than Layouts #1 and #2. This increased pitch rate and rear suspension extension velocity during the initial brake application required more precise input from the rider to control the dive rate (of the front forks), hence load transfer, and was perceived as a degradation in chassis control. The maximum pitch rate perceived for Layout #3 was unchanged from Layout #2 and was not found to be objectionable.

Quantitative Data Analysis

The data collected from all three suspension layouts for the three test events was analyzed. Data analysis for each event was tailored to identify key system response parameters best correlated to the subjective rider feedback for each suspension performance attribute.

Figure 3. Pothole suspension test event for cruiser motorcycle with three rear suspension layouts, showing A) shock displacement, B) shock velocity and C) mid-frame vertical acceleration of the chassis.

Figure 3 shows the rear shock displacement, rear shock velocity, and mid-frame vertical acceleration through the Pothole at 32 kph. The plot is divided into three phases: In Phase I the rear shock extends into the pothole, during Phase II the rear shock compresses as the tire exits the Pothole, during Phase III the rear shock returns to sag. Phase II, containing the largest mid-frame vertical acceleration, was chosen to inform the analysis of suspension comfort. However, Phase I and Phase III also offer insights into rear suspension performance. In Phase I, differences in available extension travel from sag are prevalent between Layout #1 and Layouts #2 and #3. The extra extension travel (plot A) in Layout #2 and #3 provides more topping resistance than Layout #1, though none of the Layouts reach full extension in this specific example. In Phase 1, Layout #3 extends at a higher velocity (plot B) and achieves a greater total extension displacement than Layout #1 and #2 due to its reduced rebound damping. As the rear wheel enters Phase II, the magnitudes of peak shock compression velocity (plot B) for each of the three layouts remains similar. However, Layout #1, which has 43 mm of total shock travel, and Layout #2, which has 56 mm of shock travel, both reach full compression abruptly as indicated by the dwell at the peak in the shock displacement overlay (plot A). These abrupt bottoming events result in a similar peak amplitude of mid-frame vertical acceleration (plot C). Conversely, Layout #3, which started Phase II with more remaining compression travel due to its faster and greater extension in Phase 1, also reaches full compression (blue peak) but less abruptly. This reduction in bottoming abruptness yielded a 1.2 g reduction in peak mid-frame vertical acceleration for Layout #3 with respect to the other layout for this Pothole event at 32 kph, thus providing more comfort.

Figure 4. Peak mid-frame vertical acceleration during Pothole impact for three motorcycle cruiser rear suspension layouts plotted for four different test speed. Negative acceleration of the chassis is upward with respect to ground per SAE J670

Figure 4 shows the peak mid-frame vertical acceleration during Pothole impact for all three rear suspension layouts across all test speeds. For all three layouts, the peak mid-frame vertical accelerations at 24 kph are similar, and small in magnitude. The peak mid-frame vertical acceleration of Layouts #1 and #2 increase proportionally to the vehicle speed, reaching a peak mid-frame vertical acceleration of −9.0 g at 48 kph. Conversely, Layout #3 has a peak mid-frame vertical acceleration of −4.0 g at 32 kph and maintains a similar magnitude at both 40 and 48 kph. At 48 kph, Layout #3 achieves a 5 g (44%) reduction in magnitude of peak acceleration, and an associated improvement in comfort over Layout #1 and #2. This reduction in peak mid-frame vertical acceleration for Layout #3 is the result of an increase in the available compression travel due to Layout #3’s faster rebound during Phase 1 of the Pothole. Performance of Layout #3 may also benefit from reduced seal friction within the damper since the setting generates less rebound force [Doria, 2009]

Figure 5. Camel (half-sinusoid) suspension test event for cruiser motorcycle with three rear suspension layouts, showing A) shock displacement, B) shock velocity, C) mid-frame vertical acceleration of the chassis, and D) pitch rate of the chassis.

Figure 5 shows rear shock displacement, rear shock velocity, mid-frame vertical acceleration, and pitch rate over the Camel at 32 kph. The plot is divided into four phases: In Phase I the rear suspension compresses as it encounters the Camel, in Phase II the rear suspension extends over the backside of the Camel, in Phase III the landing on the backside of the Camel occurs, and in Phase IV the rear suspension returns to sag. Early in Phase I the difference in target sag as well as the resulting difference in available extension travel between Layout #1 and Layouts #2/#3 is evident (plot A). During Phase II, Layout #1 reaches full extension quickly (plot A) and has an abrupt and prolonged topping event before eventually transitioning to Phase III where its compression is delayed with respect to the other layouts. The Layout #1 topping event corresponds to a spike in the mid-frame vertical acceleration (plot C) and a sharp reduction in the negative pitch rate (plot D) that is not present for Layouts #2 and #3. Conversely, Layout #2 during Phase II does not reach full extension which removes the abrupt topping event (plot A), subsequent mid-frame acceleration spike (plot C) or pitch rate change (plot D). Layout #3 through Phase II reaches full extension sooner than Layout #2, while its subtle topping corresponds to a similar magnitude mid-frame vertical acceleration (plot C). The reduction in topping abruptness for Layouts #2 and #3 is attributed to the increase in available extension travel and also to the reduced spring force near full extension (i.e., the lower installed spring preload force afforded by the deeper target sag state). Although suspension topping indicates reduced tire normal load, measuring normal load on a moving vehicle, especially over bump events, is difficult. As such, in a later section of this paper, simulation will be utilized to quantify rear tire normal load variation across the three rear suspension layouts as it relates to road holding performance.

Figure 6 shows a time series overlay of vehicle speed, front fork displacement, rear shock displacement, and pitch angle for all three rear layouts during a Threshold Braking event from ~100 kph. Layout #1 rear shock reaches full extension quickly (plot C) and sustains full extension for the duration of the braking event. It can also be observed that Layout #1 front fork nearly reaches full compression (plot B) during the Threshold Braking event. Conversely, the rear suspensions for both Layouts #2 and #3 never achieve full extension (plot C) during the Threshold Braking event and the front forks do not quite reach full compression (plot B). This additional margin to front fork full compression provides more suspension travel to absorb small road irregularities during threshold braking and having available rear shock travel before topping theoretically allows more rear brake to be applied, both of which can enable higher deceleration rates [Cossalter, 2004]. It is also hypothesized that for Layouts #2 and #3, the available shock extension displacement (plot C) during the threshold brake event provides a more consistent rear tire load, and thus additional (directional) stability under braking by inhibiting vehicle yaw. Again, multibody simulation will prove useful to quantify rear tire roadholding.

Figure 6. Threshold Braking test event of a cruiser motorcycle with three rear suspension layouts, showing A) vehicle speed, B) fork displacement, C) shock displacement and D) pitch angle of the chassis.

Qualitative vs. Quantitative Comparison

For the qualitative performance metric Exit Abruptness in the Pothole, Layout #3 achieved the best perceived rider comfort performance followed by Layout #2 and the difference in comfort was most noticeable at 40 kph and 48 kph. This qualitative performance directionally aligns with the peak mid-frame vertical acceleration measurement results (Figure 3). That data showed similar peak mid-frame vertical acceleration at the slower 24 kph and 32 kph speeds for all three layouts beyond which measured peak acceleration for Layout #1 and, to a lesser degree, Layout #2 increases linearly with vehicle speed, while Layout #3 maintains a reduced peak acceleration at 32 kph through 48 kph.

For the qualitative performance metric Rear Rebound Rate over the Camel, the rider noted the performance of Layouts #1 and #2 were very similar, while Layout #3 extended faster and was found to lack the desired chassis control by the rider. These perceived differences in rear suspension rebound performance can be observed within the quantitative data (Figure 5), with Layout #3 rear shock rebound velocity faster than both Layouts #1 and #2.

For the qualitative performance metric Rider-Vehicle Separation over the Camel, Layout #1 provided the largest rider-vehicle separation while Layout #2 provided none. Analysis of the Camel time series overlay (Figure 5) indicates that for Layout #1, a positive mid-frame vertical acceleration is generated when the suspension abruptly tops and is followed by a reduction in the negative pitch rate that slows the forward rotation of the vehicle. This change in pitch rate is hypothesized to cause the rider to momentarily separate from the vehicle. The rider, who is not rigidly attached to the rear sprung mass, maintains an initial, higher negative (forward) pitch rate from before the topping event even after the rear sprung mass pitch rate is reduced, thus causing separation through disparate rotational velocities. Conversely, as discussed for Figure 5, the peak mid-frame vertical acceleration for Layouts #2 and #3 does not indicate an abrupt topping event and the pitch rate of the chassis stays consistent (thus matched with that of the rider) during Phase 2 of the Camel.

For the qualitative performance metric Reaction to Brake Input during a Threshold Braking event, Layouts #1 and #2 provide similar perceived sensitivity to the initial brake input and were not found to be objectionable to the rider. However, Layout #3 was found to be more sensitive than desired, with the rear suspension extending quickly during the initial brake input and lacking the desired chassis control. However, after analyzing the Threshold Braking time series data (Figure 6), there is no clear indication in rear suspension displacement or in pitch angle that indicates Layout #3 performed deficiently. The lack of correlation between the Threshold Braking qualitative and quantitative data is attributed to the manner in which the rider executed this specific event. Regardless of the suspension layout, the rider tried to perceptibly load the front tire before reaching maximum brake force. As a result, differences in rear suspension chassis control influence how the rider modulated the application of the front brake under these conditions. The rider was adapting their input and thus affecting measured vehicle response.

For the qualitative performance metric Maximum Pitch Angle during a Threshold Braking event, differences in perceived maximum pitch angle were noted between Layout #1 and Layouts #2 and #3, though none were found objectionable by the rider. Analysis of the Threshold Braking data (Figure 6) clearly shows a difference if maximum pitch angle between Layout #1 and Layouts #2 and #3 that directionally aligns with rider feedback. The differences in front fork compression and rear shock extension between Layout #1 and Layouts #2 and #3 were not mentioned as being perceptible by the rider. This omission is likely due to the smooth test surface, which would diminish the necessity of enhanced bump absorption, and by the usage of the front brake only, which foregoes potential improvements in deceleration from increased rear tire load if the rear brake was also being applied [Cossalter, 2004].

Multibody Simulation

Using FastBike (Cossalter, 2002), three multibody simulation models were developed based on physical measurements of the test vehicle and the measured rear suspension force versus velocity and force versus displacement characterization data (Figure 1). Each simulation model was tested over virtual events developed to match the Camel and Threshold Braking used during physical testing. The primary objective of this simulation was to enable of the calculation of tire normal load, for the determination of road holding, which is difficult to measure during physical testing due to cost and complexity associated with the required instrumentation.

Camel - Road Holding

Figure 7. Test data (black/solid) and the simulation (pink/dotted) for cruiser motorcycle rear suspension Layout #1 (43mm rear shock travel | 30% sag | Nominal rear shock rebound damping) over Camel event, showing A) shock displacement, B) shock velocity and C) mid-frame vertical acceleration of the chassis and D) pitch rate of the chassis.

Figure 7 shows the rear shock displacement, rear shock velocity, mid-frame vertical acceleration, and pitch rate over the Camel at 32 kph for both Layout #1 physical test data (black/solid) and simulation (pink/dotted). The multibody simulation correlates well to the physical test data. In Phase II, both the test and simulation show a similar prolonged topping event (plot A) with corresponding spike in mid-frame vertical acceleration (plot C). Additionally, both test and simulation show a change in pitch rate in conjunction with the topping event (plot D), though the magnitude of pitch rate change for the simulation is less than that of the physical test data. Similar correlation between test and simulation across the three Layouts is deemed sufficient to use their respective models to further study rear tire load, and road holding, for the Camel at 32 kph.

Figure 8. Simulation data for three rear suspension layouts on a cruiser motorcycle over the Camel event, showing A) shock displacement, B) shock velocity and C) rear tire normal load (label highlighted in orange) and D) pitch rate of the chassis.

Figure 8 shows simulated rear shock displacement, rear shock velocity, mid-frame vertical acceleration, and pitch rate over the Camel at 32 kph for each of the three rear suspension layouts. In Phase II, Layout #1 and Layout #3 have prolonged topping events (plot a) that corresponds to the rear tire load going to zero (plot C), indicating the rear tire is unloaded and potentially off the ground. As Layouts #1 and #3 move through Phase III and begin to compress, the rear tire load increases abruptly (plot C) as the tire regains contact with the ground, causing the tire load to oscillate momentarily. Conversely, Layout #2 does not have a prolonged topping event (plot A) and maintains a positive, albeit small, rear tire load. As Layout #2 begins to compress through Phase III, the tire load increases linearly until the Phase III compression event is complete. For Layout #1 and Layout #3, the momentarily null tire load in Phase II and the tire load variations in Phase III are not desired and have a negative impact on road holding.

Threshold Braking - Chassis Control and Road Holding

A virtual Threshold Braking event was simulated using the same three simulation models outlined above. Simulation model correlation across layouts was deemed acceptable, as alluded to in Figure 7. The virtual Threshold Braking event applies a front braking force to achieve a target deceleration rate of -0.72 g based on the track test average. During the physical Threshold Braking test (Figure 6), the rider modulated the front brake while monitoring the chassis pitch rate to achieve the desired load transfer to the front tire before applying maximum braking force. The virtual Threshold Braking maneuver achieves the desired deceleration but achieves it in a more consistent and abrupt manner.

Figure 9. Simulation data for three rear suspension layouts on a cruiser motorcycle during Threshold Braking event, showing A) vehicle speed, B) shock displacement, C) shock velocity and D) rear tire normal load (label highlighted in orange).

Figure 9 shows the simulated time series results overlay of vehicle speed, front fork displacement, rear shock displacement, and rear tire normal load for all three rear suspension layouts during a Threshold Braking event from ~100 kph. Similar to test data shown in Figure 6, Layout #1 shock displacement (plot B) reaches full extension quickly after the Threshold Braking event begins. When the rear shock reaches full extension there is an abrupt reduction in rear tire load (plot D), though the rear tire load does not drop to zero likely because some normal load, due to the substantial unsprung mass, is still present. Additionally, the rear tire load (plot D) on Layout #1 oscillates through the remainder of the Threshold Braking simulated event, likely due to the stiffness and damping of the rear tire as the rear suspension remains at full extension. Conversely, Layouts #2 and #3 maintain a consistent rear tire normal load (plot D) at threshold, providing better road holding than Layout #1.

Figure 9 also shows a degradation in chassis control associated with Layout #3. During the initial virtual brake application, the shock velocity (plot C) for Layout #3 is higher than Layouts #1 or #2. This performance difference between layouts aligns with the qualitative feedback from the rider regarding Reaction to Brake Input, shown in Figure 2. Moreover, the fact that the simulation applies braking force in a consistent manner to achieve the prescribed deceleration allows the simulation to highlight differences in shock velocity that were masked in the instrumented test by the rider adapting their brake application to each layout. Thus, the simulation is better able to capture the degradation in chassis control of Layout#3 during Threshold Braking.

Conclusions

This research investigated the trade-offs of available suspension travel, target sag, and rebound damping on suspension performance in terms of comfort, roadholding, and chassis control for a cruiser motorcycle. Qualitative suspension performance ratings over specific on-road events were evaluated by a professional motorcycle test rider and correlated to quantitative data collected on the vehicle via instrumentation. All of the qualitative attributes noted by the rider were able to be extracted from the quantitative data through detailed analysis of the suspension displacement, stroking velocity, pitch rate, and pitch angle. These sensors and a commensurate data acquisition package are relatively common in industry and easily installed and removed from a test vehicle.

For a cruiser motorcycle with relatively limited rear suspension travel, improved comfort and road holding can be achieved by increasing the suspension travel and also increasing the target sag to maintain the original seat height, i.e., chassis trim. These suspension layout changes provide additional suspension travel from sag to full extension, resulting in an increase in topping resistance. Over the Camel event, the increased topping resistance of Layout #2 reduced both the measured and simulated peak mid-frame vertical acceleration and better maintained rear tire normal load (per simulation),thus providing improved comfort and road holding over the more conventional Layout #1. During Threshold Braking, the increased topping resistance of Layout #2 provided more consistent rear tire load further improving road holding over Layout #1, while also enabling a higher peak deceleration rate if combined front and rear braking were utilized.

As exemplified by Layout #3, increasing the suspension travel and target sag also enabled an improvement in comfort, achieved through a reduction in rebound damping. The reduction in rebound damping is feasible due to the increase in available extension travel between sag and full extension, which enables the suspension to extend faster and further without additional topping. For a negative event, such as the Pothole, where the road surface undulates downward, away from the vehicle, a rear suspension with reduced rebound damping is able better follow the road surface thereby extending further into the event. This additional extension allows for greater subsequent compression displacement over which to absorb the Pothole impact resulting in lower peak vertical acceleration. However, too much of a reduction in rear suspension rebound damping can adversely affect chassis control, allowing the suspension to extend faster than desired during certain large events and/or aggressive braking maneuvers. As demonstrated, the balance between comfort, roadholding, and chassis control is complex. Thankfully, through an appropriate combination of analysis, physical test, and multibody simulation, these tradeoffs can be understood and used to inform design.

Future research comparing qualitative versus quantitative suspension performance could focus on additional events, additional performance attributes, other motorcycle genres, alternate suspension parameter variants, and other test rider populations. Simulation model fidelity that includes bilinear spring and damping characteristics along with appropriately-adjusted spring preloads for setting sag, is crucial to obtaining realistic suspension behavior. Introduction of certain nonlinearities related to internal shock absorber friction and the verification of suspension parameters via subsystem identification and modelling has been shown to hold promise (Schoeneck, 2023). Finally, while directional indications of suspension response can be achieved by simulating generic bump events, correlation to test data requires a fairly accurate bump input profile.

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