Kinematics and Compliance

Introduction

The Kinematics and Compliance (K&C) test is performed by applying a range of vertical forces at the four contact patches of a vehicle to determine the suspension’s characteristics. The motion of the wheel caused by the force application is measured and recorded during this event. This in turn helps to determine suspension hard point locations, spring rates, bushing rates, arm lengths, etc.


Figure 1. Kinematics and Compliance Event

Detailed Description

The entire event simulations lasts for 90 seconds and can be broken into four distinct sub-events:
  • Ride
  • Roll
  • Contact patch force
  • Steer analysis
Ride
The event begins with the ride analysis where in all wheels are subjected to a vertical displacement input through the jacks. The inputs have the same amplitude as those who are in phase. This part of the event lasts for 10 seconds.
Time in Seconds Action
0 to 2.5 Wheels move from Design Position to Jounce Position.
2.5 to 5.0 Wheels move from Jounce Position to Design Position.
5.0 to 7.5 Wheels move from Design to Rebound Position.
7.5 to 10.0 Wheels move from Rebound Position to Design Position.
10.0 Event Ends.
Roll
This event begins immediately after the ride event is complete. For this part of the event all wheels are subjected to a vertical displacement input through the jacks. The inputs amplitude is the same and with the left and right wheels being out of phase by 180 deg. This part of the event lasts for a duration of 10 seconds.
Time in Seconds Action
10 to 12.5 Left Wheels move from Design Position to Jounce Position.

Right wheels move from Design Position to Rebound Position.
12.5 to 15.0 Left Wheels move from Jounce Position to Design Position.

Right wheels move from Rebound Position to Design Position.
15.0 to 17.5 Left Wheels move from Design Position to rebound Position.

Right wheels move from Design Position to Jounce Position.
17.5 to 20.0 Left Wheels move from rebound Position to Design Position.

Right wheels move from Jounce Position to Design Position.
20.0 Event Ends.
Contact patch force
This event begins immediately after the roll analysis is completed. This phase of the event evaluates the compliance of the suspension by simulating forces at the contact patch. For the first 20 seconds of this event, a lateral force is applied at the contact patch. The lateral force simulates cornering conditions. For the next 20 seconds, a longitudinal force is applied at the contact patch. The longitudinal force simulates braking and acceleration conditions. The third part of this event simulates moments about the wheel vertical by applying a torque about the wheel vertical axis. This part of the event lasts for 20 seconds.
Time in Seconds Action
20 – 30 Lateral force is applied on all four contact patches in a parallel direction.
30 - 40 Lateral force is applied on all four contact patches in an opposing direction.
40 - 50 Longitudinal force is applied on all four contact patches along the X direction of the Global Origin to simulate a braking condition.
50 – 60 Longitudinal force is applied on all four contact patches along the negative X direction of the Global Origin to simulate an acceleration condition.
60 – 70 Aligning torque about the vertical axis (Global Z) is applied on all four contact patches about the same direction.
70 – 80 Aligning torque about the vertical axis (Global Z) is applied on all four contact patches about opposing directions.
80 Event ends.
Steer analysis
This final part of the kinematics and compliance analysis involves testing the front suspension kinematics when a steering input is applied. This part of the event lasts for 10 seconds with steering motion being in both directions.
Time in Seconds Action
80 – 85 Steering motion is applied in the counter-clockwise direction.
85 – 90 Steering motion is applied in the clockwise direction.
90 Event ends.
The entities in the event are displayed in the MotionView Project browser as shown in the image below:


Figure 2. Browser View - Forms - Straight Line Acceleration Analysis

Input Parameters

The inputs to the kinematics and compliance event are described in the table below:
Name Description
Front jounce travel in ride The vertical input distance for the front wheels to travel in the upward direction relative to the ground in ride.
Rear jounce travel in ride The vertical input distance for the rears wheels to travel in the upward direction relative to the ground in ride.
Front rebound travel ride The vertical input distance for the front wheels to travel in the downward direction relative to the ground in ride.
Rear rebound travel in ride The vertical input distance for the rear wheels to travel in the downward direction relative to the ground in ride.
From wheel travel in roll The vertical input distance for the front wheels to travel in both directions relative to ground.
Rear wheel travel in roll The vertical input distance for the rear wheels to travel in both directions relative to ground.
Front wheel lateral force at contact patch The sideways force applied at the front wheel contact patch to simulate conditions experienced during cornering.
Rear wheel lateral force at contact patch The sideways force applied at the rear wheel contact patch to simulate conditions experienced during cornering.
Front wheel longitudinal force at contact patch The force applied along the length of the vehicle at the front wheel contact patch to simulate braking and acceleration.
Rear wheel longitudinal force at contact patch The force applied along the length of the vehicle at the rear wheel contact patch to simulate braking and acceleration.
Front aligning torque The torque applied about the front wheel vertical axis.
Rear aligning torque The torque applied about the rear wheel vertical axis.
Steering Angle The rotational input at the steering wheel to simulate cornering.


Figure 3. K & C event - Inputs form

Attachments

The event uses the standard event attachment described here. In addition to the standard attachments for full vehicle analysis it uses three more attachments.
Name Description
Rack jt Attaches to the translational joint at the rack for a rack and pinion steering system.
Tire force – Front Attaches to the front tire force entity in the tire system.
Tire force – Rear Attaches to the rear tire force entity in the tire system.


Figure 4. Full Vehicle Event – Attachments


Figure 5. Kinematics and Compliance Event – Attachments

Datasets

The kinematics and compliance analysis for the full vehicle contains two datasets. One that takes the simulation parameters as input (as described in the table under Input Parameters). The second dataset, “Vehicle Parameters”, takes information about the vehicle as input and is used during the simulation.

The Vehicle Parameters are described in the table below:
Name Description Units
Type of suspension front Option that needs to be set based on the front suspension type. Available options are: independent and dependent.  
Type of suspension rear Option that needs to be set based on the rear suspension type. Available options are: independent and dependent.  
Tire model Option to use either a vehicle with force based tire models or switch to simple vertical springs to simulate a tire.  
Tire static loaded radius - Front The radius of the front tire with the vehicle weight acting on it. mm
Tire static loaded radius - Rear The radius of the rear tire with the vehicle weight acting on it. mm
Tire vertical spring rate - Front The spring rate of the front tire. The value is used for computing certain outputs and needs to match the value in the tire property file when using force based tires. N/mm
Tire vertical spring rate - Rear The spring rate of the rear tire. The value is used for computing certain outputs and needs to match the value in the tire property file when using force based tires. N/mm
Rear wheel lateral force at contact patch The sideways force applied at the rear wheel contact patch to simulate conditions experienced during cornering. N
Vehicle CG Height The vertical distance from the vehicle CG body to the ground. mm
Wheelbase The longitudinal distance between the front and rear wheel center. mm
Front braking ratio The brake force distribution at the front wheels. A value of 1 indicates 100% braking on the front. %
Front drive ratio The percentage engine power distributed to the front axle. A value of 1 indicates all power is sent to the front axle. %
Axle ratio The ratio between the angular velocity of the input gear to the angular velocity of the output gear. It is also commonly known as gear or speed ratio.  


Figure 6. Project Browser View - Dataset "Full Vehicle Data"


Figure 7. Dialog View - Dataset "Full Vehicle Data"

Forms

The kinematics and compliance event contains two forms:
Form Description
Kinematics and compliance parameters This form should be used to define the simulation conditions such as jounce and rebound distance, steering angle, the contact patch forces, etc.
Vehicle Parameters This form should be used to define the vehicle conditions such as its weight, CG height, wheelbase, tire stiffness, etc.


Figure 8. Project Browser View - Form "Kinematics and Compliance"


Figure 9. Dialog view - Form “Kinematics and Compliance Parameters”


Figure 10. Dialog view - Form “Vehicle Parameters”

Graphics

The kinematics and compliance event consists of four graphics entities to represent the four jacks up on which the vehicle is hoisted with the four tires being in contact with the jack.

The table below describes the graphics used in this event:
Name Type Description
Jack Box Front Box Represents the square platform for the front jack.
Jack Box Rear Box Represents the square platform for the rear jack.
Jack cyl front Cylinder Represents the cylindrical column for the front jack.
Jack cyl rear Cylinder Represents the cylindrical column for the rear jack.


Figure 11. Graphical View - Graphics in “Kinematics and Compliance”


Figure 12. Project Browser View - Graphics - Kinematics and Compliance

Joints

The kinematics and compliance event consists of eight joints. Four of these are contained within the sub-system for Jack Front and Jack Rear.

The table below describes the joints used in detail:
Name Type Description
Jack dummy fixed joint Front Fixed Connects the dummy body located at the front contact patch to the knuckle body and is located at the front wheel centers.
Jack dummy fixed joint Rear Fixed Connects the dummy body located at the rear contact patch to the knuckle body and is located at the rear wheel centers.
Vehicle body fixed to ground Fixed Connects the vehicle body to the ground body and is located at the vehicle body CG.
Rack dummy ball Ball Connects the rack to the steering dummy body attachment for a rack and pinion steering wheel.
Jack trans jt - Front Translational Connects the front jack body to the ground body and is aligned along global Z.
Inplane joint – Front In plane Connects the front wheel to the front jack body and is located at the front contact patch.
Jack trans jt - Rear Translational Connects the rear jack body to the ground body and is aligned along global Z.
Inplane joint – Rear In plane Connects the rear wheel to the rear jack body and is located at the rear contact patch.


Figure 13. Project Browser View - Joints - Kinematics and Compliance

Markers

The kinematics and compliance event consists of eight markers:
Name Description
Front wheel center marker This marker is defined on the front wheel and is located at the front wheel center. The test rig parameter array refers to this marker.
Rear wheel center marker This marker is defined on the rear wheel and is located at the rear wheel center. The test rig parameter array refers to this marker.
WC marker at ground - Front Marker is defined on the ground body and is located at the front wheel center. The test rig parameter array refers to this marker.
WC marker at ground - Rear Marker is defined on the ground body and is located at the rear wheel center. The test rig parameter array refers to this marker.
Kingpin axis - Front Marker is defined on the front knuckle and is located at the lower ball joint. The test rig parameter array refers to this marker.
Kingpin axis - Rear Marker is defined on the rear knuckle and is located at the average lower ball joint. The test rig parameter array refers to this marker.
Front wheel patch marker Marker is defined on the front wheel and is located at the wheel patch. The marker is used by the front patch force entity.
Rear wheel patch marker Marker is defined on the rear wheel and is located at the wheel patch. The marker is used by the rear patch force entity.


Figure 14. Project Browser View - Markers - Kinematics and Compliance

Points

The kinematics & compliance event contains four points:
Name Description
Front tire patch Point that locates the contact patch of the front tire.
Rear tire patch Point that locates the contact patch of the rear tire.
Jack bot front Point that locates the bottom of the front jack. The point is referenced by the jack translational joint.
Jack bot rear Point that locates the bottom of the rear jack. The point is referenced by the jack translational joint.


Figure 15. Project Browser View - Points - Kinematics and Compliance

Solver Variables

The kinematics and compliance event consists of eight solver variable entities:
Name Description
Left Front command This variable contains the expression for ride and roll phases of the analysis for the left front wheel. The expression is explained in detail below this table.
Right Front command This variable contains the expression for ride and roll phases of the analysis for the right front wheel. The expression is explained in detail below this table.
Left Rear command This variable contains the expression for ride and roll phases of the analysis for the left rear wheel. The expression is explained in detail below this table.
Right Rear command This variable contains the expression for ride and roll phases of the analysis for the right rear wheel. The expression is explained in detail below this table.
Left Front feedback Contains the expression that calculates the Global Z Displacement of the left front wheel center marker, relative to the original location of the left front wheel center, in the global coordinate system.
Right Front feedback Contains the expression that calculates the Global Z Displacement of the right front wheel center marker, relative to the original location of the right front wheel center, in the global coordinate system.
Left Rear feedback Contains the expression that calculates the Global Z Displacement of the left rear wheel center marker, relative to the original location of the left rear wheel center, in the global coordinate system.
Right Rear feedback Contains the expression that calculates the Global Z Displacement of the right rear wheel center marker, relative to the original location of the right rear wheel center, in the global coordinate system.
Left Front command expression


Right Front command expression


Left Rear command variable


Right Rear command variable




Figure 16. Plots – Wheel Displacements for all four wheels based on the solver variable expressions


Figure 17. Project Browser View - Solver Variables - Kinematics and Compliance

Solver Differentials

The full vehicle kinematics and compliance analysis consists of four solver differential entities:
Name Description
Left Front jack Contains the expression that is used by the left front jack actuation force. The expression itself is explained in detail after this table.
Right Front jack Contains the expression that is used by the right front jack actuation force. T he expression itself is explained in detail after this table.
Left Rear jack Contains the expression that is used by the left rear jack actuation force. The expression itself is explained in detail after this table.
Right Rear jack Contains the expression that is used by the right rear jack actuation force. The expression itself is explained in detail after this table.
Left Front Jack Diff expression in detail
The structure and logic for the four solver diff expressions are similar, the only difference being that they each use their respective solver variable values. The below uses the “Left front jack diff” as an example:



Figure 18. Project Browser View - Solver Differentials - Kinematics and Compliance

Solver Array

The kinematics and compliance analysis consists of four solver arrays. A Vehicle Parameter Array each for the front and rear and a Testrig Parameter Array each for the front and rear.
Vehicle Parameter array
The Vehicle Parameter array contains vehicle information that is used to calculate the SDF’s. Some of the data is also used in the analysis events to create point locations and forces. The data is entered in the Vehicle Parameter Form. T here are two vehicle parameter arrays: one for the front suspension and the other for the rear suspension.
Vehicle Parameter Array Element Name Description Use
Ds_vehpar.veh_end.ival Vehicle End:
1
front suspension
2
rear suspension
3
2nd rear suspension
 Communicates the suspension type to the SDF subroutine. The subroutine calculates different values for certain parameters depending on which end of the vehicle is being analyzed.
Ds_vehpar.dif_mnt.ival Differential Mount type
0
mounted to body
1
Unsprung mount (integral with the axle)
 Used in the SDF calculations in the anti-lift and anti-dive calculations.
Ds_vehpar.tire_slr.value Tire Static Loaded Radius in mm Used to locate the “Jack GeomU” point and in many of the SDF calculations.
Ds_vehpar.tire_rate.value Tire Spring Rate in N/mm Used in the SDF calculations.
Ds_vehpar.cg_height.value Vehicle CG height, measured from ground to the CG in the Z direction (mm) Used in the SDF calculations (especially the Anti-lift and anti-dive calculations).
Ds_vehpar.wheel_base.value Vehicle Wheelbase (mm) Used in the SDF calculations (especially the Anti-lift and anti-dive calculations).
Ds_vehpar.front_brake.value The Ratio of front brake torque to total brake torque. Typically .6 to .7 Used in the SDF calculations (especially the Anti-lift and anti-dive calculations).
Ds_vehpar.front_drive.value The ratio of the engine torque applied to the front axle divided by total torque Used in the SDF calculations (especially the Anti-lift and anti-dive calculations)
Ds_vehpar.axle_ratio The nominal Axle ratio of the suspension being analyzed. Typically in the 2.7-5.0 range. Used in the SDF calculations (especially the Anti-lift and anti-dive calculations).
Ds_vehpar.veh_weight.value Total Vehicle Mass in Kg Not used in SDF calculations and in the vehicle load analysis events.
Testrig Parameter Array
The testrig parameter array contains point, force and motion data, and is passed to the SDF subroutine and used to run the SDF calculation event. The testrig parameter array is symbolically defined and should not require editing. The event contains two testrig parameter arrays: one for the front suspension and the other for the rear suspension.
Array Element Name Description Use
mrk_wc_frnt.l.id Left Front Wheel Center Marker ID-Marker at the Left Wheel Center; Z axis points inboard along the spindle axis; ZX marker plane is along Global X; the resulting marker Y axis is down. The primary point location for left suspension SDF calculations. Most geometric properties and most Compliant SDF parameters are calculated using this point as input.
mrk_wc_frnt.r.id Right Front Wheel center Marker ID-Marker at the Right Wheel Center; the marker Z axis points inboard along the spindle axis; the marker ZX plane is along global X; The resulting marker Y axis is up. The primary point location for right suspension SDF calculations. Most geometric properties and most Compliant SDF parameters are calculated using this point as input.
mrk_kp_frnt.l.id Left Front Kingpin Axis Marker ID- The marker placed at the Left Lower Ball Joint or a location that defines a point on the Left Kingpin axis. The Z axis of the marker points to the Left Upper Ball Joint or a point that defines a point on the kingpin axis. Marker Z axis is used for Caster and Kingpin Inclination calculations for the left side of the vehicle.
mrk_kp_frnt.r.id Right Front Kingpin Axis Marker ID- The marker placed at the Right Lower Ball Joint or a location that defines a point on the Right Kingpin axis. The Z axis of the marker points to the Right Upper Ball Joint or a point that defines a point on the kingpin axis. Marker Z axis is used for Caster and Kingpin Inclination calculations for the right side of the vehicle.
mrk_gnd_frnt.l.id The ID of the Left Front Wheel Center Marker on body “ground”. The Marker is on the ground body at the Left Wheel Center location. The marker Z axis is parallel to the Global Z axis and the marker X axis is parallel to the global X axis. Marker is used for the left Wheel displacement control system and left wheel center displacement calculations in the SDF routine.
mrk_gnd_frnt.r.id The ID of the Right Front Wheel Center Marker on body “ground”. The Marker is on the ground body at the Right Wheel Center location. The marker Z axis is parallel to the Global Z axis and the marker X axis is parallel to the global X axis. Marker is used for the right Wheel displacement control system and right wheel center displacement calculations in the SDF routine.
frc_frnt_jack.l.i.id I Marker ID of the Left Front Force between the Jack and ground that is used to actuate the left wheel suspension motion. Forces are used for the SDF subroutine calculations and the force reported by the SDF routine. The I and J marker ID’s are required to recover the correct force.
frc_frnt_jack.r.i.id I Marker ID of the Right Front Force between the Jack and ground that is used to actuate the left wheel suspension motion. Forces are used for the SDF subroutine calculations and the force reported by the SDF routine. The I and J marker ID’s are required to recover the correct force.
frc_frnt_jack.l.j.id J Marker ID of the Left Front Force between the Jack and ground that is used to actuate the Left wheel suspension motion. Forces are used for the SDF subroutine calculations and the force reported by the SDF routine. The I and J marker ID’s are required to recover the correct force.
frc_frnt_jack.r.j.id J Marker ID of the Right Front Force between the Jack and ground that is used to actuate the Right wheel suspension motion. Forces are used for the SDF subroutine calculations and the force reported by the SDF routine. The I and J marker ID’s are required to recover the correct force.
b_str_dummy.cm.id Steering Dummy Body Center of Mass ID number. The Center of mass marker for the dummy body attached to the steering rack.

Not used by the current subroutine but kept in the software to maintain compatibility with ADAMS simulations.

The value is set to zero for rear suspension since they have no steering.


Figure 19. Project Browser View - Solver Array - Kinematics and Compliance

Force

The kinematics and compliance analysis consists of four force entities:
Name Description
Front Patch Force This is an Action Only force pair applied at the front wheels contact patch with the wheel patch marker as reference to simulate longitudinal, lateral, and aligning forces.

The forces for each direction are defined using expressions as listed below.
Fx - Left 
`SHF(time,60,{ds_knc.max_lon_frc_front.value},0.1*PI,0,0)*
STEP(TIME,60,0,60.01,1)*STEP(TIME,79.9,1,80,0)`

The expression contains a simple harmonic function that applies a sinusoidal force input, whose value is defined in the KnC Parameter DataSet, at a frequency of 0.1PI between 60 to 80 seconds.
Fy - Left 
`SHF(time,20,{ds_knc.max_lat_frc_front.value},0.2*PI,0,0)*
STEP(TIME,20,0,20.01,1)*STEP(TIME,39.9,1,40,0)`

The expression contains a simple harmonic function that applies a sinusoidal force input, whose value is defined in the KnC Parameter DataSet, at a frequency of 0.2PI between 20 to 40 seconds.
Fz – Left 0
Tx – Left 0
Ty – Left 0
Tz – Left 
`SHF(time,40,{ds_knc.max_algn_tor_fr.value},0.2*PI,0,0)*
STEP(TIME,40,0,40.01,1)*STEP(TIME,59.9,1,60,0)`

The expression contains a simple harmonic function that applies a sinusoidal torque input, whose value is defined in the KnC Parameter DataSet, at a frequency of 0.2PI between 40 to 60 seconds.
Fx - Right 
`SHF(time,60,{ds_knc.max_lon_frc_front.value},0.1*PI,0,0)*
STEP(TIME,60,0,60.01,1)*STEP(TIME,79.9,1,80,0)`

The expression contains a simple harmonic function that applies a sinusoidal force input, whose value is defined in the KnC Parameter DataSet, at a frequency of 0.1PI between 60 to 80 seconds.
Fy - Right 
`SHF(time,20,{ds_knc.max_lat_frc_front.value},0.2*PI,0,0)*
STEP(TIME,20,0,20.01,1)*STEP(TIME,29.9,1,30,0)-SHF(time,30,{ds_knc.max_lat_frc_front.value},0.2*PI,0,0)*
STEP(TIME,30,0,30.01,1)*STEP(TIME,39.9,1,40,0)`

The expression contains a simple harmonic function that applies a sinusoidal force input, whose value is defined in the KnC Parameter DataSet, at a frequency of 0.2PI between 20 to 40 seconds. For the first 10 seconds between 20 – 30 seconds, the force is positive Y direction and vice-versa for the next 10 seconds. This is done to simulate parallel and opposing lateral forces with respect to the left wheel.
Fz – Right 0
Tx – Right 0
Ty – Right 0
Tz – Right 
`SHF(time,40,{ds_knc.max_algn_tor_fr.value},0.2*PI,0,0)*
STEP(TIME,40,0,40.01,1)*STEP(TIME,49.9,1,50,0)-SHF(time,50,{ds_knc.max_algn_tor_fr.value},0.2*PI,0,0)*
STEP(TIME,50,0,50.01,1)*STEP(TIME,59.9,1,60,0)`

The expression contains a simple harmonic function that applies a sinusoidal torque input, whose value is defined in the KnC Parameter DataSet, at a frequency of 0.2PI between 40 to 60 seconds. For the first 10 seconds between 40 – 50 seconds, the torque is in the same direction as the left wheel and opposite to it for the next 10 seconds. This is done to simulate parallel and opposing aligning torques with respect to the left wheel.
Rear Patch Force This is an Action Only force pair applied at the rear wheels contact patch with the wheel patch marker as reference to simulate longitudinal, lateral and aligning forces.

The forces for each direction are defined using expressions as listed below.
Fx - Left 
`SHF(time,60,{ds_knc.max_lon_frc_front.value},0.1*PI,0,0)*
STEP(TIME,60,0,60.01,1)*STEP(TIME,79.9,1,80,0)`

The expression contains a simple harmonic function that applies a sinusoidal force input, whose value is defined in the KnC Parameter DataSet, at a frequency of 0.1PI between 60 to 80 seconds.
Fy - Left 
`SHF(time,20,{ds_knc.max_lat_frc_front.value},0.2*PI,0,0)*
STEP(TIME,20,0,20.01,1)*STEP(TIME,39.9,1,40,0)`

The expression contains a simple harmonic function that applies a sinusoidal force input, whose value is defined in the KnC Parameter DataSet, at a frequency of 0.2PI between 20 to 40 seconds.
Fz – Left 0
Tx – Left 0
Ty – Left 0
Tz – Left 
`SHF(time,40,{ds_knc.max_algn_tor_fr.value},0.2*PI,0,0)*
STEP(TIME,40,0,40.01,1)*STEP(TIME,59.9,1,60,0)`

The expression contains a simple harmonic function that applies a sinusoidal torque input, whose value is defined in the KnC Parameter DataSet, at a frequency of 0.2PI between 40 to 60 seconds.
Fx - Right 
`SHF(time,60,{ds_knc.max_lon_frc_front.value},0.1*PI,0,0)*
STEP(TIME,60,0,60.01,1)*STEP(TIME,79.9,1,80,0)`

The expression contains a simple harmonic function that applies a sinusoidal force input, whose value is defined in the KnC Parameter DataSet, at a frequency of 0.1PI between 60 to 80 seconds.
Fy - Right 
`SHF(time,20,{ds_knc.max_lat_frc_front.value},0.2*PI,0,0)*
STEP(TIME,20,0,20.01,1)*STEP(TIME,29.9,1,30,0)-SHF(time,30,{ds_knc.max_lat_frc_front.value},0.2*PI,0,0)*
STEP(TIME,30,0,30.01,1)*STEP(TIME,39.9,1,40,0)`

The expression contains a simple harmonic function that applies a sinusoidal force input, whose value is defined in the KnC Parameter DataSet, at a frequency of 0.2PI between 20 to 40 seconds. For the first 10 seconds between 20 – 30 seconds, the force is positive Y direction and vice versa for the next 10 seconds. This is done to simulate parallel and opposing lateral forces with respect to the left wheel.
Fz – Right 0
Tx – Right 0
Ty – Right 0
Tz – Right 
`SHF(time,40,{ds_knc.max_algn_tor_fr.value},0.2*PI,0,0)*
STEP(TIME,40,0,40.01,1)*STEP(TIME,49.9,1,50,0)-SHF(time,50,{ds_knc.max_algn_tor_fr.value},0.2*PI,0,0)*
STEP(TIME,50,0,50.01,1)*STEP(TIME,59.9,1,60,0)`

The expression contains a simple harmonic function that applies a sinusoidal torque input, whose value is defined in the KnC Parameter DataSet, at a frequency of 0.2PI between 40 to 60 seconds. For the first 10 seconds between 40 – 50 seconds, the torque is in the same direction as the left wheel and opposite to it for the next 10 seconds. This is done to simulate parallel and opposing aligning torques with respect to the left wheel.
Jack Actuation - Front This is an ActionReaction force pair which acts on the jack and is reacted on ground in the vertical direction. The force is a DIF() that points to the SolverDiff ID’s for the Left Front jack and Right Front Jack for the left and right respectively.

When the DIF is evaluated during statics and quasi-statics, the derivative of the Solver Differential Equation is set to zero. The result is that a Force is generated by the DIF that forces the measured wheel displacement to follow the command wheel displacement.
Jack Actuation - Rear This is an ActionReaction force pair which acts on the jack and is reacted on ground in the vertical direction. The force is a DIF() that points to the SolverDiff ID’s for the Left Rear jack and Right Rear Jack for the left and right respectively.


Figure 20. Project Browser View - Forces - Kinematics and Compliance

Joints

The kinematics and compliance analysis consists of four joints.

The table below describes the use of each joint.
Name Description
Jack Dummy Fixed - Front Fixed joint that attaches the front knuckle to the dummy body front and is located at the front wheel center.
Jack Dummy Fixed - Rear Fixed joint that attaches the rear knuckle to the dummy body rear and is located at the rear wheel center.
Vehicle Body fixed to ground Fixed joint that attached the vehicle body to the ground body and is located at the vehicle body cg.
Rack Dummy Ball Ball joint that connects the rack to the steering dummy body when a rack and pinion steering is used.


Figure 21. Project Browser View - Joints - Kinematics and Compliance

Motions

The kinematics and compliance analysis consists of three motions.

The table below describes the use of each.
Name Description
Steering motion Steering wheel motion is used to hold the steering wheel during all phases of the event except during the steer input phase.
The motion is defined using the expression:
`-SHF(time,80,{ds_knc.str_angle.value}D,0.2*PI,0,0)*STEP(TIME,80,0,80.01,1)`

The expression defines a sinusoidal input at the steering wheel, with the value of steering angle being defined in the KnC Parameter DataSet, and has a frequency of 0.2PI.
Front wheel motion Wheel spindle motion provides the lock between the front wheel and the front spindle and prevents the wheel and tire from rotating.
Rear wheel motion Wheel spindle motion provides the lock between the rear wheel and the rear spindle and prevents the wheel and tire from rotating.


Figure 22. Project Browser View - Motions - Kinematics and Compliance

Outputs

The kinematics and compliance analysis consists of a total of 98 output entities. They can be broadly classified in to two groups: Static design factor outputs (SDFs) and non-SDFs.

The SDF outputs are computed using a sub-routine that uses the SolverArrays defined in this event and are explained in detailed here <link to the SDF reference MDL doc>.

The non-SDF outputs are described in the table below.
Name Description
Front left wheel reaction Measures and records output for the force at the Front inplane joint-left in the global reference frame.
Front right wheel reaction Measures and records output for the force at the Front inplane joint-right in the global reference frame.
Rear left wheel reaction Measures and records output for the force at the rear inplane joint-left in the global reference frame.
Rear right wheel reaction Measures and records output for the force at the rear inplane joint-right in the global reference frame.
Wheel center height – left front Measures and outputs the displacement between left front wheel and the left front jack in the global reference frame.
Wheel center height – right front Measures and outputs the displacement between right front wheel and the right front jack in the global reference frame.
Wheel center height – left rear Measures and outputs the displacement between left rear wheel and the left rear jack in the global reference frame.
Wheel center height – right rear Measures and outputs the displacement between right rear wheel and the right rear jack in the global reference frame.
WC displacement – left front Measures and outputs the displacement between the left front wheel and the ground body in the wheel center marker reference frame.
WC displacement – right front Measures and outputs the displacement between the right front wheel and the ground body in the wheel center marker reference frame.
WC displacement – left rear Measures and outputs the displacement between the left rear wheel and the ground body in the wheel center marker reference frame.
WC displacement – right rear Measures and outputs the displacement between the right rear wheel and the ground body in the wheel center marker reference frame.
Applied TP force – left front Measure and outputs the force at the left front tire contact patch in the global reference frame.
Applied TP force – right front Measure and outputs the force at the right front tire contact patch in the global reference frame.
Applied TP force – left rear Measure and outputs the force at the left rear tire contact patch in the global reference frame.
Applied TP force – right rear Measure and outputs the force at the right rear tire contact patch in the global reference frame.
Roll Angle / Track width - Front
F2
Computes the roll angle at the front using the expression:
`(ATAN(DZ({b_frnt_whl.l.cm.idstring}, {b_frnt_whl.r.cm.idstring},{MODEL.Global_Frame.idstring} ){solvercr}/DY({b_frnt_whl.l.cm.idstring}, {b_frnt_whl.r.cm.idstring}, {MODEL.Global_Frame.idstring})))*RTOD`
F3
Computes the track width at the front using the expression:
`-DY({m_whl_patch_front.l.idstring},{m_whl_patch_front.r.idstring})`
Roll Angle / Track width - Rear
F2
Computes the roll angle at the rear using the expression:
`(ATAN(DZ({b_rear_whl.l.cm.idstring}, {b_rear_whl.r.cm.idstring},{MODEL.Global_Frame.idstring} ){solvercr}/DY({b_rear_whl.l.cm.idstring}, {b_rear_whl.r.cm.idstring}, {MODEL.Global_Frame.idstring})))*RTOD`
F3
Computes the track width at the rear using the expression:
`-DY({m_whl_patch_rear.l.idstring},{m_whl_patch_rear.r.idstring})`
Caster/Kingpin inclination – left front
F2 (Caster)
`(AY({mrk_kp_frnt.l.idstring}, {MODEL.Global_Frame.idstring}))*RTOD`
F3(Kingpin)
`-(AX({mrk_kp_frnt.l.idstring}, {MODEL.Global_Frame.idstring}))*RTOD`
Caster/Kingpin inclination – right front
F2 (Caster)
`(AY({mrk_kp_frnt.r.idstring}, {MODEL.Global_Frame.idstring}))*RTOD`
F3(Kingpin)
`-(AX({mrk_kp_frnt.r.idstring}, {MODEL.Global_Frame.idstring}))*RTOD`
Caster/Kingpin inclination – left rear
F2 (Caster)
`(AY({mrk_kp_rear.l.idstring}, {MODEL.Global_Frame.idstring}))*RTOD`
F3(Kingpin)
`-(AX({mrk_kp_rear.l.idstring}, {MODEL.Global_Frame.idstring}))*RTOD`
Caster/Kingpin inclination – right rear
F2 (Caster)
`(AY({mrk_kp_rear.r.idstring}, {MODEL.Global_Frame.idstring}))*RTOD`
F3(Kingpin)
`-(AX({mrk_kp_rear.r.idstring}, {MODEL.Global_Frame.idstring}))*RTOD`

Templates

The kinematics and compliance analysis contains two templates. The first template, ”Full vehicle KnC”, defines three output file control statements, two static analysis blocks where entity states are modified and simulation begin and end times specified. The second template is deactivated by default and is used to turn on graphics in post animation for a few of the static design factors. This is currently an experimental feature.

The table below describes the first template (“Full vehicle KnC”):
Statement Description 
{if (ana_fullveh_knc.ds_vehpar.tire_type.strval == "replace with vertical springs")}

<Deactivate
  element_type = "GFORCE"
  element_id = "{force_front_tire.l.idstring}"
/>
<Deactivate
  element_type = "GFORCE"
  element_id = "{force_front_tire.r.idstring}"
/>
<Deactivate
  element_type = "GFORCE"
  element_id = "{force_rear_tire.l.idstring}"
/>
<Deactivate
  element_type = "GFORCE"
  element_id = "{force_rear_tire.r.idstring}"
/>
{endif}
 The IF condition turns deactivates all tire forces when the option for tire type in the Vehicle Parameters DataSet is set to “replace with vertical springs”. 
<Deactivate	
  element_type = "MOTION"
  element_id  = "{spindle_motion_fr.l.idstring}"
/>
<Deactivate	
  element_type = "MOTION"
  element_id  = "{spindle_motion_fr.r.idstring}"
/>
<Deactivate	
  element_type = "MOTION"
  element_id  = "{spindle_motion_rear.l.idstring}"
/>
<Deactivate	
  element_type = "MOTION"
  element_id  = "{spindle_motion_rear.r.idstring}"
/>
 These four set of deactivate statements turn OFF the front and rear wheel motions that have been locking the wheels from moving. 
<Simulate
    analysis_type       = "Static" 
    end_time            = "20"
    print_interval      = "0.1"
/>
 Performs a static simulation for 20 secs. 
<Activate
  element_type = "MOTION"
  element_id  = "{spindle_motion_fr.l.idstring}"
/>
<Activate
  element_type = "MOTION"
  element_id  = "{spindle_motion_fr.r.idstring}"
/>
<Activate
  element_type = "MOTION"
  element_id  = "{spindle_motion_rear.l.idstring}"
/>
<Activate
  element_type = "MOTION"
  element_id  = "{spindle_motion_rear.r.idstring}"
/>
These four Activate statements turn ON the front and rear wheel motions in readiness for the second static simulate instruction block. 
<ResOutput
      plt_angle           = "YAW_PITCH_ROLL"
/>
<ResOutput
      mrf_file            = "TRUE"
/>
<ResOutput
      plt_file            = "TRUE"
/>
<H3DOutput
      switch_on           = "TRUE"
      increment           = "1"
/>
<ResOutput
      abf_file            = "TRUE"
/>
 The output block defines the result format and the files that the solver needs to generate. 
<Simulate
      analysis_type       = "Static"
      end_time            = "90"
      print_interval      = "0.1"
/>
 Performs a static simulation until 90 secs.


Figure 23. Project Browser View - Templates - Kinematics and Compliance

Jack System

The kinematics and compliance analysis contains two sub-systems that are instances from a single system definition – “Jack System”. The system contains two joints and three vectors. The joints connect the jack to ground and to the wheel. The vectors are parallel to the Global axes and are used as reference vectors. The graphics of the Jack are in the event template, which in this case is the ride event.


Figure 24. Project Browser View - Jack System Modeling Entities - Kinematics and Compliance
Jack System Joints
There are two joint pairs in the Jack system. The first joint is the “Jack Trans jt”, which connects the Jack body to ground with a translational joint at the lower end of the jack body. The joint is oriented in the Z (vertical) direction. The joint forces the Jack to travel only in the vertical direction.
Jack System Vectors
Three vectors are defined along the Global X, Y, and Z axes. These vectors are used to orient certain joints in the model.