IN FIELD MEASUREMENT OF FORCES AND DEFORMATIONS AT
THE REAR PART OF A MOTORCYCLE AND STRUCTURAL
OPTIMIZATION
G. Olmi, A. Freddi and D. Croccolo
DIEM Department, Engineering Faculty
University of Bologna
Viale del Risorgimento, 2, 40136 Bologna, Italy
ABSTRACT
The present work is about the analysis of the asymmetric displacement behaviour of the rear part of a motorcycle. Stylistic
reasons led to the design of a vehicle with only one suspension located at the left side. Experimental tests performed on a
circuit with seven obstacles along a straight line confirmed that bending displacement is higher on the right side than on the left
one. This work aims to perform a structural optimization of the components involved in the rear side of the motorcycle, in order
to find a solution to the problem. A hybrid approach is applied: the force acting on the suspension and bending displacements
at the rear side were simultaneously measured in working conditions, then a FEM model was set up, validated and applied for
design optimization purposes. Both methodological aspects and applicative results are presented and discussed. Finally a
solution in accordance with design specifics is proposed.
Introduction
Nowadays in the sector of sport motorcycles, designers aim to the development of products with better characteristics than
competitors’ not only from the mechanical point of view, but which can be attractive also for other features. Stylistic design is
becoming more and more important. Aiming to more original designs, motorbike models with only one suspension were
developed. In this case mechanical connection between the frame and the fork is performed on just one side (usually the left
one), which implies an asymmetric design for the fork itself and for the whole rear part of the motorbike. Experimental tests
performed on a prototype led to the result that, due to the asymmetric layout at the rear side, also the structural response was
different on two sides. Displacement sensors (resistance potentiometers) measured the relative movement between the frame
and the fork on both sides. In particular work conditions it resulted some millimetres higher on the right side than on the left
one (where the suspension is applied). This unacceptable behaviour was observed during an in field experimental campaign:
the motorbike was driven at constant speed (50 km/h) on a straight line with seven obstacles: asymmetric behaviour was quite
evident when overcoming each obstacle. This behaviour is graphically explained in Fig. 1: the difference between relative
approaching on left and right sides, sum of the two contributions ∆t (related to the frame) and ∆f (related to the fork) is later
indicated by ∆.
The aim of this work is to perform a structural optimization of the motorbike rear side, in order to reduce asymmetry effects. A
hybrid approach was applied: firstly the force acting on the suspension was measured during in field tests. Such load is
transmitted between the frame and the fork by the suspension. The force R (Fig. 1), is the result of the superposition of several
effects due to suspension mechanical response. Under a compressive load the reaction is to the sum of elastic, oleo dynamic
and pneumatic contributions and is not easy to estimate by a theoretical or numerical approach, especially in real conditions.
On the basis of references [1-4] it can be argued that performing in field tests, mainly with the application of strain gage
sensors on the most loaded locations is often the only way to obtain a rigorous measurement of forces. For example Petrone
et al. [5-9] used strain gage devices to measure load spectra on the wheels of a scooter or on main components of a
motorbike. Strain gages were directly applied on components or on particularly shaped transducers. In all the papers the
numerical results always need an experimental validation, because it is very difficult to simulate real working conditions with
numerical analysis [10]. Experimental results were the first step for a further analysis conducted by finite element modelling of
the fork and the frame. Such models, validated by comparing simulated deformations at the rear part to experimental results
concerning displacements, were then used for structural optimization purposes.
Left side
Right side
Left side
Right side
FRAME
∆t
R
R
∆f
FORK
Figure 1. Scheme of the motorbike rear side
Figure 2. Suspension at the left side of the motorbike
Experimental tests and results
For the force measurement strain gages rosettes were applied on a location where strain intensity was sufficiently high and
acceptable with reference to the gage sensitivity.
In order to measure the force acting on the suspension, two-grid (0°/90°) strain gage rosettes were used. They were applied
closely to the hinge hole. A little extension of the threaded bar near the hole was machined so that a cylindrical shape was
made available for rosettes application and strain were adjusted to increase measurement sensitivity. In Fig. 3 a detail of
rosettes collocation and of Wheatstone bridge connection are shown.
Figure 3. Application of (0°/90°) strain gage rosettes on the suspension
The first step regarded the calibration of the sensing system. It was required to determine an equation for the conversion of
Wheatstone bridge output into the measurement of the force acting on the suspension. A testing machine was used for such
operation. The machine (Fig. 3) is a two-column type, with the loading cell at its higher side. On the lower side the lower grip is
connected to the cam device transmitting up & down motion. The suspension is subjected to a compression cyclic load, which
is applied in displacement control conditions (closed loop control on displacements). In order to determine the force-bridge
output relationship on a sufficiently wide load range, several tests were performed for maximum strokes varying between 25
and 80 mm. A null value of the stroke is associated to a null value of force acting on the suspension. During the tests the force
acting on the suspension was measured by a strain gage loading cell, meanwhile the strain signal was acquired by a Leane
MCDR-M-128 device. The load cycle was repeated for ten times. Finally peak values of force distribution, corresponding to
maximum stroke condition, were related to the highest values of strain output (an example is shown in Fig. 5, above, right
2
hand). The result is shown in Fig. 5 (below, left hand), emphasizing the high linearity (R = 0.99) between force and strain.
Both force and strain are considered with negative values due to compression.
Strain output
[microstrain]
Lettura [microepsilo
Adjustable transverse element
Loading cell
Higher grip
0
-200
-400
-600
-800
-1000
-1200
0
10
20
30
40
50
-200
0
Time [s]
Force on the
suspension
[N]
Forza
[N
Suspension
Lower grip
Cam device
0
-1200
-1000
-1000
-800
-600
-400
-2000
-3000
-4000
-5000
Strain output [microstrain]
Figure 5. Calibration tests outputs
Figure 4. Testing machine used during calibration tests
1000
N.L. (spring pre-load)
0
Force
Forza [N]
[N
0
20
40
60
80
-1000
2
R = 0.951
-2000
-3000
-4000
N.L. rubber disk
-5000
Stroke [mm]
Figure 6. Force – Stroke diagram
In the calibration phase the diagram relating the suspension mechanical response vs. its stroke (Fig. 6) was also determined.
At low value non linearity is due to spring pre-load, while at high values it is due to the compression of a rubber disk when the
2
theoretical maximum value of the stroke (80 mm) is overcome. In the central zone the linearity is very high (R = 0.95).
Figure 7. The application of potentiometers on both motorcycle sides
The calibration was essential for further experimental phase aimed to the measurement of the force on the suspension in
working conditions. The suspension, equipped by strain gages was mounted on a motorbike, then potentiometers were
applied both on the left and on the right sides. They measured relative movement between the frame and the fork, to which
they were connected by hinges, as shown in Fig. 7. Also the output signals from potentiometers were acquired by the same
equipment for simultaneous measurement of force and displacements at left and right rear sides.
1
2
3
4
5
6
7
4000
6
3000
4
2000
2
1000
0
-1000362
363
364
365
366
0
368
-2
367
-2000
-4
-3000
-4000
-6
Force [N]
Diff.
∆ [mm]
Time [s]
Force on the Forza
susupension
[N]
[N
Force on the
susupension
[N]
Forza
[N
Figure 8. Circuit for in field tests with seven obstacles
Figure 9 a. Results of in field tests (40 km/h)
1000
500
-1
R2 = 0.9365
0
-500 0
1
2
3
4
5
6
-1000
-1500
-2000
-2500
-3000
-3500
[mm]
∆D[mm]
Figure 9 b. Stiffness diagram for in field tests (40 km/h)
4000
6
3000
4
2000
2
1000
0
-1000445
446
447
448
449
0
451
-2
450
-2000
-4
-3000
-4000
-6
Force [N]
Diff.
∆ [mm]
Time [s]
[N
Force on theForza
susupension
[N]
Force on the
susupension
[N]
Forza
[N
The in field tests were performed on a circuit with seven obstacles on a straight line, as shown in Fig. 8. Four obstacles out of
seven (referenced with numbers 4, 5, 6, 7) were larger sized than the others. The obstacles were overcome at three different
speeds (40, 50, 60 km/h), with three replications: passages through each obstacle were totally nine. The acquiring system is
particularly designed for in field tests. The forces and the differential displacement ∆ were related and compared by plotting
diagrams as shown in Figg. 9 a ÷ 11 a. See also [11].
6
4000
3000
4
2000
2
1000
0
-1000631
631.5
632
632.5
633
633.5
634
634.5
0
635
-2
-2000
-4
-3000
-4000
-6
Time [s]
Figure 11 a. Results of in field tests (60 km/h)
500
-1
R2 = 0.9346
0
-500 0
1
2
3
4
5
6
-1000
-1500
-2000
-2500
-3000
-3500
∆D[mm]
[mm]
Figure 10 b. Stiffness diagram for in field tests (50 km/h)
Force [N]
Diff.
∆ [mm]
Force on theForza
susupension
[N]
[N
Force on the
susupension
[N]
Forza
[N
Figure 10 a. Results of in field tests (50 km/h)
1000
500
-2
R2 = 0.9202
-1
0
-500 0
1
2
3
4
5
-1000
-1500
-2000
-2500
-3000
-3500
-4000
[mm]
∆D[mm]
Figure 11 b. Stiffness diagram for in field tests (60 km/h)
6
Discussion
The force in Figg. 9 a ÷ 11 a is indicated with negative values, due to suspension compression: at the first impact with the
obstacle, force module rapidly increases up to a maximum. At the same time the differential displacement ∆ increases, and the
asymmetric behaviour of the rear side is particularly evident: the frame and the fork tend to approach more at the right side
than at the left one (Fig. 12 a). Then, after a drop-kick, the load on the suspension suddenly decreases. Positive values in the
force diagram indicate that the suspension becomes slightly in tension. When the force sign changes, ∆ becomes negative,
meaning that the distance between the frame and the fork is higher at the right side than at the left one (Fig. 12 b). Then the
force trend is inverted and the suspension is again subjected to compression, with maximum positive value for ∆. The
described trend is repeated for seven times, as seven are the obstacles. Plotting results together shows that ∆ distribution
appears to be qualitatively mirrored with respect to force’s. When load module has a maximum value, also ∆ becomes
maximum, with the same trend also for minimum values. The sign changes of ∆ and of the force take place at the same times.
Such observations suggest that the relationship between the force acting on the suspension and ∆ is linear: to verify this
hypothesis, stiffness diagrams were plotted in Figg. 9 b ÷ 11 b with reference to results shown on the left side. For sake of
clearness only data points were plotted: in all the cases response can be well interpolated by linear regression lines with high
2
values of R (greater than 0.9). Some non linearity effects can be observed when force and ∆ assume high values with
impulsive increase and following decrease. Such effects appear to be more evident at higher speeds, at 50 and 60 km/h: when
the suspension stroke is very high, the rubber disk is compressed and the structural response becomes non linear as shown in
Fig. 6.
On circuit straight line with no obstacles, the measured force on the suspension is about 1,700 N with no strong variation. This
value is due to the pilot and motorbike weights transmitted to the rear part of the vehicle. Experimental results emphasize that
such value is highly increased by dynamic effects due to the impacts against obstacles. The highest value for the compressive
force is 3,600 N, i.e. more than 100% incremented with respect to load in static condition. As previously observed, as the
motorcycle overcomes obstacles, the force has two peak values, with in-between decrease. Such values are summarized in
histograms below (Figg. 13 ÷ 15) for tests at different speeds. Values of force peaks [N] were processed in an ANOVA test [12]
(Table 1): two factors were considered: the mean speed during the test and the type of the obstacle indicated by progressive
number (see Fig. 8). Two close peaks were interpreted as two replications for each treatment combination. The result of the
statistical analysis was that no significant differences exist among force peaks at the 5% significance level. It implies that force
peaks are not influenced by the speed, ranging from 40 and 60 km/h, and by the obstacle size (obstacles 4, 5, 6, 7 were larger
sized). Consequently the grand mean value for the increased force due to dynamic effects could be calculated: such value is
2,850 N, corresponding to a 60% increase.
Left side
Right side
Left side
Right side
FRAME
3500
FRAME
∆>0
Force peak [N]
3000
∆<0
a)
b)
FORK
2500
2000
1500
1000
FORK
500
0
1
3500
Force peak [N]
Force peak [N]
4000
3000
1500
1000
500
0
1
2
3
4
5
6
7
Obstacle
Figure 14. Force peaks for in field test at 50 km/h
4
5
6
7
Figure 13. Force peaks for in field test at 40 km/h
3500
2000
3
Obstacle
Obstacle
Figure 12. Deformation at the rear side (cases for ∆ > 0 and ∆ < 0)
2500
2
3000
2500
2000
1500
1000
500
0
1
2
3
4
5
6
Obstacle
Figure 15. Force peaks for in field test at 60 km/h
7
SPEED
40
km/h
50
km/h
60
km/h
1
2831
2895
2501
2914
2377
2792
Table 1. Factorial plan and two-factor ANOVA statistical analysis (Force peaks in N)
OBSTACLE NUMBER
2
3
4
5
6
7
2600 2903 3042 3118 3058 2851
SSQ
DOF
MSQ
2819 3011 2792 2823 2764 2768 Speed
64,910
2
32,455
2485 2585 2660 2788 2792 3106 Obstacle
865,371
6 144,229
2823 2995 3082 2887 2935 2684 Interaction
671,883
12
55,990
2214 2389 3365 3194 3019 3636 Error
1,296,757
21
61,750
2716 2847 3238 3027 2923 2764 Total
2,898,920
41
Fcalc.
0.526
2.336
0.907
p-v.
59.9
6.94
55.6
Frame and fork FEM modelling with the use of shell elements
During experimental tests the force on the suspension and relative displacements between the fork and the frame were
simultaneously measured. FEM structural analysis both of the frame and of the fork was then performed considering a mean
value of the measured force peaks. Frame and fork were modelled by the software I-DEAS (release 11) in the elastic field, due
to the linear relationship between force and displacement (Figg. 9 b ÷ 11 b). 3D CAD models with shell elements [13] were
adopted. The algorithm assumes a linear variation for stress along the thickness.
FEM models were validated by experimental results, concerning the elements choice, models meshing, constraining and
loading systems in order to use them for structural optimization.
In the frame model the engine, usually supposed to have infinite stiffness, was modelled by the application of beam elements,
having square sections with finite stiffness value. The cavities of holes for connections to the engine were modelled by radial
elements with infinite stiffness: central points were connected to the engine by “couple degree of freedom” constraints [13] .
Only the rotation along the horizontal axis is left free. Hinges for connections between the fork and the anterior wheel were
meshed by beam elements with the real circular section. The ∆t (Fig. 1) was evaluated for the nodes located where
potentiometers had been mounted. Suspension reactive force was applied to the node at the centre of radial elements with
infinite stiffness located at the hinge hole.
In Fig. 16 a sketch of the structure is shown: “beam elements” are indicated by lines with related transverse sections. Arrows
represent constraints preventing a translational motion, and double arrows are located on the hinge linking the frame to the
fork. In this case just one rotation, around the hinge axis, is permitted, while constraints prevent rotating motions around other
perpendicular axes.
A negative displacement for the right side and a simultaneous positive one for the left one can be observed. Such a behaviour
is quite reasonable because the reactive force, transmitted by the suspension, is applied at the left side. By supposing the
mean value of 2,850 N for the force, the difference between two sides displacements ∆t assumed the value of 0.93 mm.
Sspension
connection
Bearings for
connection to
the frame
Backward
wheel hinge
Suspension
connection
Hinge for
connection
to the fork
"beam"
elements
Forward
wheel hinge
Figure 16. Constraining and loading system of the frame.
"Couple degree of
freedom" element
Figure 17. Constraining and loading system of the fork
Triangular parabolic shell elements were used for fork modelling, while elements named “constraints” [13] were applied for the
welding connections between rods. The hinge for connection to the wheel was meshed by “beam” elements. An annular
section reproducing the real one was considered. Radial elements with infinite stiffness were created at the slotted hole
internal cavity. The central node was then connected to the hinge terminal nodes by “couple degree of freedom” constraints.
The only rotation around backward wheel axis was left. Suspension reaction was applied at the centre of radial elements,
considering the mean peak value of the force.
Fig. 17 shows a loading and constraints systems . The “couple degree of freedom” constraint is indicated by a blue circle at the
centre of radial elements. Only vertical displacements are considered for data processing: for force value of 2,850 N the
difference in displacements at the two fork sides (term ∆f, Fig. 1) was estimated as 3.05 mm.
On the basis of results in Figg. 9 b ÷ 11 b, a linear model was adopted in structural analysis. Estimated displacements under
the action of 2850 N force were 3.05 mm for the fork (∆f) and 0.93 for the frame (∆t), which implies a total value ∆ of 3.98 mm.
By assuming a linear relationship between the force and differential displacement ∆, each of the measured force values was
processed for the calculation of the corresponding value of ∆. Values of ∆, simultaneously measured with forces and
numerically simulated, were compared in diagrams for all the performed tests. Some of the results, related to tests at 40, 50
and 60 km/h, are shown on the left in Figg. 18 ÷ 20. “Truth Diagrams” (Figg. 18 ÷ 20 on the right) show a direct comparison
between experimental and numerical results. Mean absolute error is about 0.3 mm, while mean relative errors range between
12 and 16%.
6
6
5
5
∆ [mm]
4
4
∆ [mm] (simulated)
3
Experimental
3
Simulated
2
2
1
1
0
362
-1
363
364
365
366
367
368
0
-1
Time [s]
0
1
-1
2
3
4
5
6
(experimental)
D [mm]
(experimental)
∆ [mm]
Figure 18. Validation of the FEM model for the test at 40 km/h
6
6
5
5
∆ [mm]
∆ [mm] (simulated)
4
4
3
Experimental
3
Simulated
2
2
1
1
0
445
-1
446
447
448
449
450
451
0
-1
Time [s]
0
1
2
3
4
5
6
5
6
-1
D [mm] (experimental)
∆ [mm]
(experimental)
Figure 19. Validation of the FEM model for the test at 50 km/h
6
6
5
5
∆ [mm]
∆ [mm] (simulated)
4
4
3
3
Experimental
2
Simulated
2
1
0
631
-1
631.5
632
632.5
633
633.5
634
634.5
1
635
0
-2
-1
Time [s]
0
-1
Figure 20. Validation of the FEM model for the test at 60 km/h
1
2
3
4
D [mm](experimental)
(experimental)
∆ [mm]
Structural optimization
After validation, the FEM model was applied even to modified versions of the fork and the frame for several simulation tasks.
The aim was to determine the best structural solution with low values for the differential displacement ∆. A key issue in design
improvement was not to modify the aesthetics and the stylistic line of the motorbike. Consequently strong modifications
involving the structural layouts of the frame and the fork could not be acceptable, and the main feature of the motorbike, i.e.
the adoption of just one suspension at the left side had to be maintained.
By comparing the values of ∆t and ∆f, it can be guessed that the greatest contribution is due to fork deformations: term ∆
depends on fork displacements for the 80% of its total value. Such a result, with the term ∆f strongly higher than ∆t, suggested
that any modification of the frame would imply just a little improvement in displacement reduction with the risk of altering the
stylistic line. Consequently further simulating tasks involved the fork, with the aim of optimizing its design and to reduce ∆f.
Beams of the fork structure are tubes with annular section (external diameter: 60 mm, internal diameter: 56mm). According to
specifics, proposed modifications did not involve the external shape or dimensions, but only the thickness. Modified versions of
the fork, with tubes having different internal diameters were simulated with two goals: firstly to investigate the sensitivity of ∆f to
thickness variations, then to optimize the value of thickness to reduce ∆, without strongly modifying the original project.
Simulations were conducted, by supposing to modify the thickness of just one tube: the tube at the left side, or the tube at the
right side or the central one (Fig. 21). The diagram in Fig. 22 shows the percentage variation of ∆: sensitivity is doubled when
the variation involves the central beam. This result suggests the best design strategy to reduce displacements ∆f and ∆.
Values of ∆ are plotted vs. thickness: it can be observed that the relationship is non linear: the improvement on displacement
reduction becomes smaller as the thickness is increased. Such a trend is well interpolated by a quadratic curve which has a
plateau for a thickness value of 4.5 mm: for this value the reduction on ∆ is a bit greater than 20%. On the basis of this result, it
seems to be not convenient to increase the thickness any more, because no further appreciable reductions could be achieved.
The only way to obtain a stronger reduction would be to change the whole project, by increasing the thickness not only of the
central tube, but also of the lateral ones. However this solution would not be acceptable because it would imply a strong
increase in the fork weight, which would be doubled. The performed numerical analysis shows that acceptable improvements
can be obtained by adopting a quite easy modification of the original design. Reduction of ∆ to very low values would require
more strong modifications, which would alter the stylistic solution and imply a too high increase in weight.
Central tube
30
Right side tube
25
20
2
∆ reduction [%]
R = 0.9979
Central tube
Left or right tube
15
10
Interpolation
5
Left side tube
0
2
Figure 21. FEM simulations on modified versions of the fork
2.5
3
3.5
4
4.5
Thickness [mm]
Figure 22. Sensitivity analysis and design optimization
Conclusions
Some in field tests performed on a motorbike prototype with only one suspension on just left side had shown an asymmetric
mechanical response of the vehicle rear part. Relative bending displacements between the frame and the fork were quite
different at the left and the right side. The object of this research was to develop a modified version of original design, with a
reduction of the effect and by maintaining the original stylistic line.
A hybrid approach was applied aiming to structural optimization of the rear part, by integration of experimental testing and
numerical FEM analysis. Main steps of the work and related results can be so summarized:
•
•
•
•
Two (0°/90°) strain gage rosettes were applied on the suspension for measuring force in working conditions.
The whole device for force measurement was calibrated in lab. The linear relationship between the force on the
2
2
suspension and Wheatstone bridge output reading was determined with a high value of R (R = 0.99).
In field tests were performed on a circuit with seven obstacles at different speeds ranging from 40 to 60 km/h. Both
force on the suspension (by strain gage rosettes) and differential displacement ∆ (by potentiometers) were
simultaneously measured.
Experimental results show a good repeatability: force is about 2 kN in normal driving conditions and is strongly
increased when overcoming obstacles. An ANOVA test confirmed that differences among force peaks are non
•
•
•
•
•
significant for speed variation and obstacle size: mean value is about 2850 N (60% more with respect to static
conditions).
A further analysis was conducted to investigate the linearity of the relationship between measured force and ∆.
2
Linearity hypothesis was acceptable, as confirmed by high values of R of interpolating lines (greater than 0.9%)
FEM models with shell meshing elements were developed to investigate displacements ∆t and ∆f due to the frame
and the fork deformations.
Numerical models were validated by comparing simulated displacements to experimental measured ones. A good
agreement was observed, with mean relative error of about 13 %.
One of main results was that ∆ (=∆t+∆f) strongly (80%) depends on fork deformations, which led to the determination
of the component which mostly needed modifications. Consequently further analysis was focused to optimize its
design.
Validated fork model was finally simulated to investigate the sensitivity of the differential displacement to tubes
thickness variations. Different design versions were considered and finally a solution was proposed with a reduction
of ∆ up to 20%. An optimization was performed on the thickness variation to be applied to the original design. This
solution does not require a radical modification of the original project, does not imply strong weight variation and
maintains the same stylistic line.
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I-DEAS V11 On Line Tutorial