# RD-E: 1200 Jumping Bicycle

After a quasi-static pre-loading using gravity, a dummy cyclist rides along a plane, then jumps down onto a lower plane. Sensors are used to simulate the scenario in terms of time.

The purpose of this example is to illustrate how to use the Radioss description when resolving a demonstration example. The particularities of the example can be summarized using dynamic loading during a four-step scenario where a dummy is first put on a bike, then it rides on a plane to subsequently jump back down onto the ground. The scenario described is created using sensors.

## Options and Keywords Used

Two types of rigid walls are set up:
• A fixed infinite plane (floor)
• A fixed parallelogram (springboard)

The characteristics of the parallelogram plane are: 2013 mm x 1200 mm. Both rigid walls are tied to allow the wheels to turn.

The infinite plane is defined by the normal vector ($\stackrel{\to }{M{M}_{1}}$) and the parallelogram by the coordinates of three corners ($M$, ${M}_{1}$, and ${M}_{2}$). For both rigid walls, the secondary nodes are obtained from the tire and rim parts (displayed in green in Figure 3).

Several rigid bodies are created (/RBODY) and activated by sensors for use at the appropriate time and in a chronological manner (sens_ID not equal to 0). Thus, every rigid body is not active at the same time. The activation order is described in the paragraph dedicated to /SENSOR. According to their activation time, the rigid bodies are classified in groups which are:

The inertias of rigid bodies are set in local skew frames for groups A, C and D.

Rigid body activation/deactivation
Groups A and B
The rigid bodies are activated during pre-loading up to equilibrium then applied to the initial velocity start. They are activated again just before the impact of the bike on the inferior plane.
During the free fly phase, both the cyclist and the bike undergo a rigid body motion. In order to save the computation time, the motion can be simulated by putting the whole structure into a global rigid body (Group D). The rigid body is deactivated just before landing.
Group C
Three rigid bodies include the dummy, the frame and both wheels (not including the tires). This configuration allows just the wheels to turn, taking into account the active tires action on the plane. This rigid body is activated while the bike is running on the springboard.
Group D
This global rigid body, including all nodes of model is activated as long as the bike is in the free fly phase and is deactivated just before impact on the floor.
Group E
This rigid body is activated before impact ensures the stiffness level of the lower fork.

A 8333 mms-1(30 km/h) initial velocity (/INIVEL) is applied to all nodes of the model (bicycle and cyclist) in a parallel direction to the high plane at time t = 0.004 s. This initial condition is defined in the Engine file *_0002.rad (start time: 0.004 s) which is run after the quasi-static equilibrium with gravity loading.

Options in Engine file (*_0002.rad):
/INIV/TRA/X/1
initial translational velocities in direction x
8333
of 8333 mm/s
1 338000
on node 1 to 338000
Gravity is applied to all nodes of the model. A constant function defines the gravity acceleration in the Z direction versus time. Gravity is activated by /GRAV.
The explicit time integration scheme starts with the nodal acceleration computation. It is efficient for the simulation of dynamic loadings. Nevertheless, quasi-static simulations via a dynamic resolution method need to minimize the dynamic effects to converge towards the static equilibrium. Among the methods usually employed, the kinetic relaxation method is quite effective and is activated in the Engine file (*_0001.rad) with /KEREL (Figure 7). All velocities are set to zero each time the kinetic energy reaches a maximum value.
Rigid bodies are activated and deactivated with sensors (/SENSOR). A sens_ID flag characterizes the sensors and it is required in the rigid bodies' definition. The five types of sensors used are:
TIME
Activated with time
DIST
Activated with nodal distance
INTER
Activated after impact on rigid wall
SENSOR
Activated with sensor IS1 and deactivated with sensor IS2
NOT
ON as long as sensor IS1 is OFF

At the beginning of the simulation (time=0), the rigid bodies are automatically set to ON, as long as the sensors are not active. Thus, in order to deactivate the rigid bodies at the first cycle, active sensors at time t=0 should be used. Consequently, the rigid bodies are active when the sensors are not active.

Added masses and inertia, as well as the flag for the gravity center, are ignored when a rigid body is managed by sensors. By default, the gravity center is only computed by taking into account the secondary nodes mass (ICoG set at 2). The main node is moved to the computed center of gravity where added mass and inertia are placed. In order to distribute the mass to the dummy over the rigid bodies, option /ADMAS is used.
Table 1. Sensors Used for Simulation
Name Type Definition Rigid Body's Group using Sensor
S1 TIME Time 0s. -
S2 DIST Distance between rear hubs and extremity of springboard equal to 1810 mm. -
S3 DIST Distance between rear hubs and extremity of springboard equal to 345 mm. -
S4 RWALL When the infinite rigid wall is impacted. -
SEN(S2,S3) SEN Activated with S2 and deactivated with S3 -
SEN(S3,S4) SEN Activated with S3 and deactivated with S4 -
SEN(S2,S4) SEN Activated with S2 and deactivated with S4 Group A/B
NOT(SEN(S2,S3)) NOT Deactivated with S2 and activated with S3 Group C
NOT(SEN(S3,S4)) NOT Deactivated with S3 and activated with S4 Group D
Sensor (S4) is also used for deactivating both the beam type springs modeling links between the feet and pedals (Ishear set to 1). A case could be considered without this sensor to study the risks of automatic pedals.

## Input Files

The input files used in this example include:
Jumping_bicycle

## Model Description

The purpose of this example is to set up a demonstration in which sensors and restart files are used to allow the change of a problem over time.

Subjected to the gravity field, a dummy cyclist rides on a higher plane, then jumps down onto a lower horizontal plane. The problem can be divided into four phases:
• positioning the cyclist under the gravity effect
• running the bicycle on the high plane
• free fly
• the impact on the ground
The following system is used: Ton, mm, s, N, MPa

### Model Method

The material of the metallic parts use the Johnson-Cook law (/MAT/LAW2) with the following properties:
Steel Spokes Material Properties
Young's modulus
210000 $\left[\mathrm{MPa}\right]$
Poisson's ratio
0.3
Density
7.9x10-9$\left[\frac{Ton}{m{m}^{3}}\right]$
Yield stress
185.4 $\left[\mathrm{MPa}\right]$
Hardening parameter
540 $\left[\mathrm{MPa}\right]$
Hardening exponent
0.32
Aluminum Frame Material Properties
Young's modulus
60400 $\left[\mathrm{MPa}\right]$
Poisson's ratio
0.33
Density
2.7x10-9$\left[\frac{Ton}{m{m}^{3}}\right]$
Yield stress
90.27 $\left[\mathrm{MPa}\right]$
Hardening parameter
223.14 $\left[\mathrm{MPa}\right]$
Hardening exponent
0.375
A QEPH formulation (Ishell= 24) is used for tires in order to prevent hourglass deformations. A Belytschko & Tsay element with a TYPE4 hourglass formulation is used for the other shell parts. A global plasticity model is used.
Table 2. Properties and Materials of Main Parts
Parts Properties Materials
Bike Frame Shell Q4 - 3 mm Aluminum - Law 2
Spokes Truss - 2 mm2 Steel - Law 2
Rim Shell Q4 - 3 mm Aluminum - Law 2
Tires Shell QEPH - 3 mm Rubber - Law 1
Hubs Beam - 900 mm2 Steel - Law 2
Saddle Brick Foam - Law 1
Pedals Beam - 900 mm2 Steel - Law 2
Tube of saddle Shell Q4 - 3 mm Aluminum - Law 2
Dummy Body (limbs) Shell Q4 - 3 mm Law 1
Joints Spring (8) -
Hierarchy organization:
Bike model
6 subsets comprising 23 parts
Dummy model
11 subsets comprising 38 parts

### Monitored Volumes / Perfect Gas

A perfect gas monitored volume with /MONVOL/GAS is defined to model the pressure in the tires. For further details about monitored volumes, refer to GAS Type in the Radioss Theory Manual.

The main properties are:
External pressure Pext
0.1 $\left[\mathrm{MPa}\right]$
Initial internal pressure Pini
Front tire: 0.75 $\left[\mathrm{MPa}\right]$
Rear tire: 0.1 $\left[\mathrm{MPa}\right]$
Gas constant $\gamma$
1.4
All other properties are set to default values.
• Quasi-static loading: gravity effect on initial static equilibrium

The quasi-static solution of gravity loading on structure deformation corresponds to the steady state part of the transient response. It describes the pre-loading case before the dynamic analysis. Therefore, the simulation is divided into two phases: quasi-static response (structure subjected to the gravity) and dynamic behavior (run, jump and landing). The solution is obtained from kinetic relaxation (/KEREL). Gravity is defined by /GRAV.

• Contacts modeling
The TYPE7 interface using the penalty method serves to model contacts between the dummy cyclist and the bike. With contact in /RWALL to treat the landing of the bike. Figure 14 illustrates the description of the interface.
A TYPE11 interface models contact between the pedals (beams) and the feet (shells).
• Links between man and bicycle
The spring TYPE8 (/PROP/SPR_GENE) general spring property model the links between the feet/pedals and the hands/handlebar.
Stiffness (TX, TY and TZ)
50 $\left[\frac{N}{mm}\right]$
Mass
1e-10 $\left[\mathrm{Ton}\right]$
Inertia
1e-5 $\left[{\mathrm{mm}}^{2}\mathrm{Ton}\right]$
A rupture criteria based on displacements is activated by the beams connecting the hands and handlebar in order to simulate the fall of the cyclist after landing.
• Left hand: Z = 20 mm
• Right hand: Z = 20 mm
• Dummy joints

The general TYPE8 springs, characterize a spherical hinge with a stiffness given for each DOF. Directions are local and attached to a moving skew frame. Two coinciding nodes define a spring.

Limbs are linked to the springs via the secondary nodes of the rigid bodies, as shown in Figure 17.
• Wheel rotation
Beam elements are used to attach the wheel to the forks. The rotational DOF is released around the beam axis.

## Results

The elements included in a rigid body are deactivated. Therefore, the element flags saved in /TH/RBODY provide information on the activation and deactivation of rigid bodies during simulation.