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FORCE ANALYSIS

 

Conclusions / Summary

  • Computation of the static and dynamic forces acting on the swingarm

  • Analysis of the following critical conditions:

- Limit acceleration (front wheel detachment)

- Braking (1g)

- Limit braking (rear wheel detachment)

- Jump over kerb (5g)

 

 

Fz

4687

N

Front wheel detachment

Fz

6952,838

N

Jump over kerb

(critical condition)

 

Fz(ant)

2036,5

N

Braking (1g)

 

Fz(post)

21,5

N

 

 

 

Fz(ant)

2058

N

Limit braking

 

Fz(post)

0

N

 

 

 

S

4500

N

Limit acceleration

 

 

Description

  • Analysis of the forces in the following conditions:

  • Static analyisis

  • Limit acceleration

  • Jump over kerb

  • 1g braking

  • Limit braking

 

Motorbike data:

 

- %Anteriore (percentage of the weight loaded on the front wheel)

- Mg (Weight of motorbike + pilot)

- h_G (Center of gravity height)

- Passo (distance between front and rear wheels)

- Coeff (factor of safety, used for every force)

- Transmission ratio Tau:
     Tau_map (Final Reduction Ratio, ratio wheel sprocket/pinion)
     Tau_aps (Gear Ratio, ratio primary / secondary shaft)

     Tau_asr (Primary Reduction Ratio, ratio motor shaft / primary shaft)
     Tau_r (ratio rear wheel angular speed / motorbike velocity)

     Tau_f (ratio front wheel angular speed / motorbike velocity)

     Tau_as (ratio secondary shaft angular speed / motorbike velocity)
     Tau_ap (ratio primary shaft angular speed / motorbike velocity)
     Tau_m (ratio motor shaft angular speed / motorbike velocity)

- Other Inertias (from Cossalter):
     Iw_f (front wheel inertia)
     Iw_r (rear wheel inertia)
     Iw_m (engine inertia)
     Iw_ap (primary shaft inertia)
     Iw_as (secondary shaft inertia)

- Raggi ruote (wheels radii):
     R_r (rear wheel radius)
     R_f (front wheel radius)

- m* reduced mass of the motorbike, which considers rotational intertias contributions, computed as in Cossalter book

 

 

Data reported in the following table:

 

Motorbike specifications

 

 

 

 

 

 

 

Mg

 

210

kg

 

 

 

r_cerchio_r

(17"*2,54)/2

215,9

mm

(Metzeler Racetec Slick)

spalla_r

55%(180mm)

0,099

mm

 

 

 

r_cerchio_f

(17"*2,54)/2

0,2159

mm

 

 

 

spalla_f

70%(120mm)

0,084

mm

 

 

 

R_r

r_cerchio + spalla

215,999

mm

 

 

 

R_f

r_cerchio + spalla

0,2999

mm

 

 

 

Iw_f

from Cossalter book

0,6

kg*m^2

 

 

 

Iw_r

from Cossalter

0,8

kg*m^2

 

 

 

Iw_m

from Cossalter

0,07

kg*m^2

(engine)

 

 

Iw_ap

from Cossalter

0,05

kg*m^2

(primary shaft)

 

Iw_as

from Cossalter

0,015

kg*m^2

(secondary shaft)

 

Tau_map

from manuale

3

1/m

(Final reduction ratio)

Tau_aps

from manuale

2,461

1/m

(Gear Ratio)

 

Tau_asr

from manual

2,088

1/m

(Primary reduction ratio)

Tau_r

1/R_r

0,00463

1/m

 

 

 

Tau_f

1/R_f

3,334445

1/m

 

 

 

Tau_as

1/R_r*Tau_asr

0,009667

1/m

N.B.

 

 

Tau_ap

Tau_aps*Tau_asr*Tau_r

0,02379

1/m

Inertias taken from example 6

Tau_m

Tau_map*Tau_aps*Tau_asr*Tau_r

0,071369

1/m

(Cossalter)

 

Passo (p)

 

1365

mm

 

 

 

h_G

 

600

mm

 

 

 

m*

 

216,6715

kg

 

 

 

%ant

 

55%

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Remark: m* was computed using the following formula:

m*= Mg+(Iw_r*Tau_r^2)+(Iw_f*Tau_f^2)+(Iw_m*Tau_m^2)+(Iw_ap*Tau_ap^2)+(Iw_as*Tau_as^2)

 

 

Weights distribution

 

 

  

 

1.      1) LIMIT ACCELERATION

 

Limit conditions during acceleration are:

 

·         - Front wheel detachment

·         - Rear wheel adherence condition (slipping).

 

Front wheel detachment is influenced by vehicle’s characteristics such as total mass (motorbike + pilot) (Mtot), weights distribution (a,b) and centre of gravity (hG).

 

Rear wheel limit adherence condition is not considered because it is typical of motorcycles with low wheel adherence such as cross and supermotard motorbikes (μx<1).

 

For race motorbikes, μx>1: the following plot shows that the detachment of the front wheel occurs before the slipping of the rear wheel.

 

 

Anyway, both cases were analyzed in order to find at which accelerations they occur (an excel file was used).

Detachment of front wheel occurs at 0.62G, while slipping at 0.73G. Therefore, the detachment limit case will be analyzed.

 

For the limit acceleration condition, only the vertical force has been considered; it has two components:

  • Static Fz force (acting on the bike in static conditions, considering that no forces act on the front wheel, because it is in lift condition)

  • Dynamic weight transfer on the rear wheel DFz (due to inertial components)

 

Used formulas:

 

Comments

Fx is function of Fz (tires with higher vertical forces transmit higher forces (Fx ed Fy), before saturation condition)

Aerodynamic force,  proportional to the speed, is very low and thus negligible.

Fx was taken from the plot in 030_meeting_2_maggio.

Formulas were taken from report  030_meeting_2_maggio.

Frontal Fz, in full acceleration, has a very low value (about 69 N), it is almost a condition of detachment of the front wheel.

 

 

 

2) JUMP OVER KERB

 

Only the vertical force was considered:

Remarks:

As in the previous cases, the force has been increased using a security coefficient.

The overall force is distributed on both tires (55% ant) and, as expected, such value is more critical then the limit acceleration condition, considering the bending stress.

 

 

3) BRAKING AT 1G

 

Centre of mass was assumed being at a height hg=0,6 m

 

    

 

Rear wheel does not detach from the ground.


 

 

4)  BRAKING AT LIMIT OF REAR WHEEL LIFT

 

Using a moment equilibrium with respect to the centre of mass, braking force at limit conditions can be found:

 

 

Computation of limit acceleration (limit brake):

 

 

Comments: the whole weight is on the front wheel.

 

 

 
 
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