Suspension Systems
Contents
Overview (1)
Suspension Screens with Tabular Data (2)
Screens for Measured Nonlinear Stiffness Properties (3)
The VehicleSim Hysteretic Spring Model (3)
Suspension: Spring (5)
Suspension: Ride Rate (Spring + Tire) (7)
Suspension: Measured Total Roll Stiffness (9)
Non-linear Compliances and Mechanical Ratios (11)
Independent Suspension Systems (12)
Independent Suspension Kinematics (12)
Independent Suspension Compliance (15)
Suspension: Independent System (Simplified, Symmetric) (20)
Solid Axle Suspension Systems (26)
Solid Axle Suspension Kinematics (26)
Solid Axle Suspension Compliance (29)
Suspension: Solid Axle System (Simplified, Symmetric) (34)
Twist Beam Rear Suspensions (39)
Twist Beam Suspension Kinematics (40)
Twist Beam Suspension Compliance (43)
Overview
An independent suspension is one in which vertical movement of one wheel does not cause noticeable movement of the other wheel if the anti-roll bar is disconnected. In contrast, a solid axle suspension has an actual axle or linkage system that causes both wheels to roll together. Stated in another way, the kinematical motions of each wheel in an independent suspension are related to a single coordinate—the vertical deflection, commonly called jounce, of an individual wheel. On the other hand, the motions of each wheel in a solid-axle suspension system are related to two coordinates—axle jounce and axle roll. In both cases, lateral forces are transmitted to the sprung mass along lines of action perpendicular to the path of constrained motion, to determine load transfer due to suspension kinematical properties.
A twist beam or twist axle suspension has a torsionally flexible structure linking the two sides. Lateral forces are transmitted to the sprung mass through lateral reactions at bushings attaching the structure to the chassis, and through vertical reactions at the same bushings caused by the twist (structural deformation) of the beam. Twist beams are available only at the rear suspension on vehicles in CarSim with independent front suspension, and are never steered. Twist beams are not available in TruckSim.
The type of suspension used for a simulation is indicated in the vehicle code that appears on the Run Control screen in vehicle dataset link. In CarSim, SA indicates a solid-axle suspension, Ind is an independent suspension, and Twist is a twist beam. For example, the code Ind_Ind indicates independent suspensions on the front and rear; the code Ind_SA indicates a front independent suspension and a solid-axle rear suspension. In TruckSim, where vehicles can have more axles, S indicates solid-axle and I indicates independent. Drop-down lists on the Vehicle: Assembly screen (CarSim) or vehicle lead units (TruckSim) are used to choose the suspension type for each axle. All trailer suspensions in CarSim and TruckSim have the solid-axle type.
This document has five main sections after this overview. The following section lists the screens that contain tabular data for nonlinear properties of the suspension systems. The next section describes the spring model used in CarSim and TruckSim, along with suspension screens used for handling suspension ride and roll stiffness as commonly measured in kinematics and compliance test rigs. The remaining three sections cover independent, solid-axle, and twist-beam suspensions. Suspension Screens with Tabular Data
Table 1 lists the library screens provided to describe nonlinear properties of suspension systems and components, such as springs, shock absorbers, and kinematical properties. Each screen has a table with standard editing and viewing controls that are described in detail in the VehicleSim Browser Reference Manual.The tabular datasets are identified for the solver programs by keywords based on the root names listed in the table.
Table 1. Summary of suspension table libraries.
Library Screen Root Keyword(s) Description
Suspension: Spring FS_COMP
FS_EXT
Spring force versus deflection
Suspension: Ride Rate (Spring + Tire) RIDE_COMP_TABLE
RIDE_EXT_TABLE Fz at ground versus Z deflection at ground
Suspension: Shock Absorber FD Damper force versus
compressive speed Suspension: Auxiliary Roll Moment MX_AUX Auxiliary roll moment versus
roll angle
Suspension: Measured Total Roll Stiffness MX_TOTAL_TABLE Roll moment at ground versus
roll angle at ground
Suspension: Camber Angle CAMBER Camber angle versus jounce Suspension: Dive Angle (Caster Change) SUSP_DIVE Suspension pitch angle Suspension: Lateral Position SUSP_LAT Lateral movement vs. jounce Suspension: Longitudinal Position SUSP_X Wheelbase change vs. jounce Suspension: Toe Angle TOE Toe change versus jounce Suspension: Lateral Position with Roll SUSP_LAT_ROLL Lateral movement vs roll angle Suspension: Solid Axle Roll Steer SUSP_AXLE_ROLL_STEER Axle steer vs roll angle
Suspension: Jounce and Rebound Stops F_JNC_STOP
F_REB_STOP Jounce or rebound force vs. deflection
Screens for Measured Nonlinear Stiffness Properties
This section describes three screens with tabular data and additional settings beyond those on a screen with standard tabular data. All use a hysteretic spring model based on concepts proposed in the 1980’s at the University of Michigan Transportation Research Institute (UMTRI). The VehicleSim Hysteretic Spring Model
Figure 1 shows spring force vs. deflection obtained during a maneuver in TruckSim. Similar behavior is typically observed in laboratory measurements of leaf springs, and of suspension
systems in general.
3b mm )
Increasing load
Figure 1. Simulation results showing spring force vs. deflection.
The figure shows two force vs. deflection limit curves: one when the load is increasing (during compression), and one when the load is decreasing (extension). Forces are higher during compression. For example, in the figure, a vertical red line is drawn for a deflection of 96.5 mm. During compression, the spring force is 52,600 N; during extension, the force is 42,400 N. The difference (1,200 N) is due to friction.
Friction is a significant factor in heavy truck suspensions, and is present to a lesser extent in nearly all vehicle suspensions.
VehicleSim spring models are typically described with two force/deflection curves: one, which applies during loading, and another one, which applies during unloading.
When a reversal occurs, such as the one between the two vertical red lines in Figure 1, the force does not jump instantly from one limit to the other. A certain amount of deflection must occur for the force to approach the other limit. The math models use a spatial equivalent of a time constant called b to characterize the transition. The deflection needed to cover 95% of the force difference between the two limits is defined in the math model as 3b. For example, the TruckSim spring used to generate the example in Figure 1 has a model parameter of b = 2 mm, so the two vertical red lines are spaced horizontally by 3b (6 mm).
The equations for this model require that the upper force curve (increasing load) never drop below the lower force curve (decreasing load), for any possible deflection.
Bump stops can be incorporated into the spring table or defined using the separate Suspension: Jounce and Rebound Stops tables. If you include the force due to suspension stops in the spring table, any tandem axle load sharing effects (TruckSim or CarSim with Trailers) also distribute the suspension stop forces. In most tandem suspensions, the load sharing mechanism does not distribute the bump stop forces, so using the Suspension: Jounce and Rebound Stops tables is preferred.
When using the Suspension: Jounce and Rebound Stops tables, imagine a spring at the location of the stop. The spring produces zero force for some deflection, until the stop is contacted. Then the spring produces force according to the stiffness of the stop. The deflection over which the force is zero is sometimes called “engagement travel” or “engagement length”.
Some springs (air springs in particular) have rate curves that change with the static load on the spring. These multiple spring curves can be specified using the Suspension: Spring (Extended) screen. In the particular case of air springs, the pressure in the spring is altered to set the vehicle at a specific trim height regardless of load, preventing large variations in the attitude of the vehicle between empty and laden conditions. The force in the spring is proportional to pressure, and the change in pressure as the spring deflects is proportional to the change in volume due to deflection. The higher initial pressure associated with higher static loading thus produces a higher rate (larger changes in force per unit deflection) for the spring.
Air systems on trucks typically use a simple control valve to adjust air pressure as static load changes. TruckSim and CarSim use the load at initialization of the run, including payloads, to determine the spring characteristics to be used. Also, many air spring installations connect the left and right side springs so that they use a common air volume, hence the same pressure in both springs. When springs are connected like this, they don’t make a contribution to the roll stiffness. Springs in TruckSim and CarSim always contribute to roll stiffness, so you must define an auxiliary roll moment that removes the spring effects when simulating an interconnected air system.
Suspension: Spring
The screen shown in Figure 2 is used to specify the force-displacement properties of the suspension springs, using the hysteretic VehicleSim model described in the previous subsection.
upper and lower curves are defined with a and a friction value defined as ? the force separating the two curves. For example, the difference in forces shown in Figure 1 at the deflection of 96.5 mm is 1200 N, which corresponds to a friction level of 600 N. (The upper curve has friction added, the lower curve has friction subtracted, leading to the factor of two between the friction level and the separation of the curves.)
for defining the upper
Table field for envelope of spring compression force as a function of spring compression during the loading process. The root keyword for the table is FS_COMP. Indices IUNIT, IAXLE, and ISIDE are used to specify the unit, axle, and side.)
Table field for envelope of spring force as a function of compression during the unloading
The spring model would be numerically unstable if the upper envelope (loading) were ever less than the lower envelope (unloading). This is also true when the tables are extrapolated.
To guard against this potential source of error, the VS solvers check the spring data during initialization, and will stop with an error message if there is a violation. There are four checks made of the data.
2323
4
Figure 2. Suspension: Spring
screen.
Figure 3. Simplified version of hysteretic spring.
1. All values of compressive force in the table must be higher than the values of
extension force that are calculated for the deflections used in the compression table.
2. All values of extension force in the table must be lower than the values of
compressive force that are calculated for deflections used in the extension table.
3. The first gradient (spring rate) for the upper envelope must be less than the first
gradient for the lower envelope, to ensure that extrapolated forces calculated for
deflections less than the ranges covered in the tables are compatible.
4.The last gradient (spring rate) for the upper envelope must be greater than the last
gradient for the lower envelope, to ensure that extrapolated forces calculated for
deflections higher than the ranges covered in the tables are compatible.
Beta parameters. One handles the transition up to the compression curve, and the other handling the transition down to the extension curve (shown between the vertical red lines in Figure 1). (Keywords = SPRING_EXT_BETA([IUNIT,] IAXLE, ISIDE)and SPRING_COMP_BETA([IUNIT,] IAXLE, ISIDE)).
As noted in the previous section, these are approximately 1/3 the distance needed to travel through a spring hysteresis (friction) loop.
Suspension: Ride Rate (Spring + Tire)
Use this screen (see Figure 4) to provide measurements of the overall suspension ride stiffness as measured in the laboratory. This is an alternative to the Suspension: Spring screen described in the previous section.
2
3
4
5
Figure 4. The Suspension: Ride Rate (Spring + Tires) screen.
Discussion
Spring properties are sometimes measured as installed in the vehicle by fixing the vehicle body (sprung mass) in a laboratory and moving the wheels up and down with vertical actuators under the tires. In this test condition, changes in vertical tire force are due to compression of both the tire and the suspension spring. This screen is intended perform calculations automatically to remove the tire effects, leaving the nonlinear spring behavior.
This screen has similar controls to the basic spring screen, with a few differences:
1. The tables of force vs. position values you provide are measured at the ground (under the
tires), rather than for the spring in isolation.
2. The screen does not have a control to specify a form of interpolation: it will create a table
with linear interpolation to send to the vehicle solver program.
3. It includes two extra parameters (unsprung mass and tire spring rate), used to calculate
the spring properties from the measured movement and force at the tire/actuator contact.
The graph shows four plots. The two plots shown in the colors green and black correspond to measurements of tire force in response to movement of the actuators under the tires. The two shown in the colors red and blue are calculated by removing the tire effects, and correspond to the behavior of the suspension springs alone.
The numbers for the springs alone are stored in the associated parsfile and can be viewed with the text editor. However, they are not shown on this screen because they are re-calculated whenever a change is made to any of the information on the screen.
You should view the red and blue plots to confirm their validity. If tire properties that are specified are not representative of the properties as they existed when the measurements were made, the calculated points in the red and blue plots can show unusual results, such as a negative spring rate.
User Settings
Table field for envelope of measured ground force as a function of compression (keyword = RIDE_COMP_ENVELOPE). This represents the force vs. deflection that would be measured while the spring is moving in compression (jounce).
The values in this table are used, along with other properties specified on the screen, to define spring compression force as a function of spring compression. The calculated numbers are stored in the same Parsfile (keyword = FS_COMP([IUNIT,] IAXLE, ISIDE)).
Table field for envelope of measured ground force as a function of extension (keyword = RIDE_EXT_ENVELOPE). This represents the force vs. deflection that would be measured while the spring is moving in the extension (rebound) direction.
The values in this table are used, along with other properties specified on the screen, to define spring force as a function of spring extension. The calculated numbers are stored in the same parsfile (keyword = FS_EXT([IUNIT,] IAXLE, ISIDE)).
The spring model would be numerically unstable if the upper envelope (compression) were ever less than the lower envelope (extension). This is also true when the tables are extrapolated. To guard against this potential source of error, the VS solvers check the spring data during initialization, and will stop with an error message if there is a violation. The checks made by the VS solvers are described in the previous secton.
Beta parameters for compression and extension (keywords =
Tire spring rate for the tire that was on the vehicle when the ground force was measured.
You can use a different tire spring rate on the vehicle for your runs—this coefficient is used only to convert the measured ground force to a spring force.
Unsprung mass (both wheels) of the suspension as it was on the vehicle when the ground
Use this screen to provide laboratory measurements of the overall suspension roll stiffness. This is an alternative to the Suspension: Auxiliary Roll Moment screen.
Discussion
Axle roll is resisted by the vertical suspension springs and also by a torsional spring that accounts for the difference between the roll moment as predicted by the spring effects alone and the roll moment that is measured with a laboratory test rig. The properties of the torsional spring can be specified either with this screen or with the Suspension: Auxiliary Roll Moment screen.
Note Although it is called a torsional spring for convenience, the roll moment
can be due to other factors such as twisting of linkages, bending of sheet
metal, binding of linkages, etc. The auxiliary roll moment accounts for
all roll moment effects other than the main suspension springs.
23
4
567
Figure 5. The Suspension: Measured Total Roll Stiffness screen.
the only data values from this screen that are actually transferred to the VS solver. The numbers are stored in the associated parsfile and can be viewed with the text editor. (They are not shown on this screen because they are re-calculated whenever a change is made to any of the information on the screen.)
View the red plot to determine the validity of the measured data and associated suspensions and tire properties. If the spring or tire properties that are specified are not representative of the properties as they existed when the measurements were made, the calculated points in the red plot can show unusual results, such as a negative spring rate.
The measurement is typically made by fixing the vehicle body and rolling the “ground” under the tires, where the “ground” is defined by vertical hydraulic actuators. To provide roll, the actuator on one side is raised while the actuator on the other side is lowered. The actuators are typically controlled to maintain a constant total vertical force and zero lateral force during the test. The vertical movements of the actuators are combined with their lateral spacing to define a “ground angle.” The vertical force measured at each actuator is combined with the lateral spacing to define a “ground roll moment.”
User Settings
Two-column table of values of measured roll moment applied from the vehicle to the ground as a function of vehicle roll relative to the ground (keyword = MX_TOTAL_TABLE). A positive ground angle (where the label “roll angle” is short for “vehicle roll relative to the ground) occurs when the right wheel is higher than the left wheel.
The values in this table are used, along with other properties specified on the screen, to define auxiliary roll moment as a function of suspension roll. The calculated numbers are stored in the same parsfile (keyword = MX_AUX_CARPET([IUNIT,] IAXLE)). Values from this table are interpolated linearly by the vehicle math model, and are extrapolated for roll angles outside the range of the table.
Link to a Suspension: Spring dataset or a Suspension: Ride Rate (Spring + Tire) dataset for the springs that were on the vehicle when the roll moment was measured. You can use a different spring for your runs—the spring data from this link is used only to convert the measured ground roll moment to an auxiliary roll moment.
Tire spring rate for the tires that were on the vehicle when the roll moment was measured.
Unsprung mass (both wheels) of the suspension as it was on the vehicle when the ground force was measured. You can use a different unsprung mass for your runs—this mass is used only to determine the spring loads at zero roll during the measurement.
Axle load during test. Specify the mass supported by the tires during the test. This is used to
Lateral spacing of tire centers (track width) when the roll moment was measured. You can use a different track width for your runs—this track width is used only to determine the moment arm associated with the tire forces.
Lateral spacing of springs when the roll moment was measured. For a solid-axle suspension,
Non-linear Compliances and Mechanical Ratios
The suspension compliance screens Suspension: Independent Compliance, Springs, and Dampers, Suspension: Solid Axle Compliance, Springs, and Dampers. Suspension: Twist Beam Compliance, Springs, and Dampers each include several fields to supply coefficients describing the various compliance properties and mechanical ratios for each type of suspension. Internally, the suspension compliances and mechanical ratios are supported by table functions. This means that special applications requiring very detailed information for these properties can use non-linear tables to describe them. On each compliance screen, right-clicking a compliance or
mechanical ratio field displays some notes, including the table root keyword (for example, CT_FX for toe change due to longitudinal force).
When you type a number in a one of these fields, the associated table function is directed to use a coefficient, by writing the root keyword with the suffix _COEFFICENT. To use the non-linear table representation for a compliance or mechanical ratio property, leave the field blank, and create and link a table using a Generic Table and specify the root keyword. You must also supply index information (e.g., iaxle, iside) for each table.
Independent Suspension Systems
Two methods are available to describe independent suspension systems, available from the drop-down lists from the vehicle screen for selecting suspension types:
1.With Independent,two screens are used to provide more detailed kinematical and
compliance properties: Suspension: Independent System Kinematics and Suspension: Independent Compliance, Springs, and Dampers.
2.With Independent (simple), a single screen Suspension: Independent System is used to
describe suspensions using linearized representations of pitch and roll motion and track and wheelbase change. Springs and dampers are the same on the left and right sides.
These three screens are described in the following sections.
Independent Suspension Kinematics
The kinematical properties of an independent suspension are described on the Suspension: Independent System Kinematics screen, shown in Figure 6.
2
356
7
101112131410111213
14
Figure 6. The Suspension: Independent System Kinematics screen.
Discussion
The kinematics of the suspension linkages are described by the lateral and longitudinal motions of the wheel as the suspension deflects vertically. The lateral movement primarily affects the transfer of tire lateral force to the body and the resulting body roll. The longitudinal movement primarily affects the transfer of tire longitudinal force to the body and the resulting body pitch. These effects are sometimes described using concepts such as roll centers and “side view swing arms,” particularly when performing simple analyses. The VS solver models do not use fixed roll center points or swing arms—the motion of the wheels is defined by the positions of the wheel center and by camber and caster changes as each wheel moves in jounce. A simplified, linearized representation is provided on the Suspension: Independent System screen (see page 20), in which the direction of the line of motion is specified with a roll center height and simple ratios, for compatibility with other models and datasets.
User Settings
Unsprung mass (keyword = M_US([IUNIT,] IAXLE)). This mass includes the wheels,
tires, brakes, and all parts that move vertically with the wheel as the suspension deflects. For parts such as driveline components and suspension linkages that have one end attached to
the moving wheel and the other to the sprung mass, you can add about half of their masses to the overall unsprung mass. This value includes both wheels in the suspension.
Fraction Steered (keyword = R_US_STR(IAXLE)) is the portion of the unsprung mass that rotates about the kingpin axis when the wheels are steered. Typically, it includes the wheel, tire, brake and steering knuckle, but not the control arms, springs or dampers. For an independent suspension, values are normally around 0.8. If the field is blank, a value of 1.0 is used.
Wheel spin moment of inertia (keyword = IW([IUNIT,] IAXLE, ISIDE)). The total
spin inertia for each wheel is the sum of this value plus the inertia due to the tire, as specified on the Tire screen.
Track width (keyword = L_TRACK([IUNIT,] IAXLE)). Lateral distance between centers of tire contact at the design load condition.
Height of the wheel spin axes above the sprung mass origin at the design load condition
(keyword = H_WC([IUNIT,] IAXLE)). This defines the relationship between the location of the wheel relative to the sprung mass and the jounce used to define toe and camber effects.
Wheel center height also appears on the Vehicle: Sprung Mass screen where other dimensions and coordinates in the sprung mass coordinate system are specified. The data field exists on this screen to provide backward compatibility with data from older versions of CarSim and TruckSim. If the wheel heights are specified both here and on the Vehicle: Sprung Mass screen, the data from the Vehicle: Sprung Mass screen takes priority.
Lateral coordinate of the suspension center (keyword = Y_CL_SUSP([IUNIT,]
IAXLE)). Normally zero, this can be given a non-zero value if the wheels are not located symmetrically about the longitudinal centerline of the vehicle sprung mass.
Static camber offset for each wheel (keyword = ISIDE)). This
Static toe offset for each wheel (keyword = ISIDE)). This angle is
Pull-down control for choosing between two jounce definitions:
When the first option is chosen, the jounce at the design load condition is defined as the jounce in the spring table that corresponds to the spring force needed to support the sprung mass in the design load condition.
jounce on each side when the vehicle is in the design condition (keyword = OPT_JNC_DESIGN).
The significance of this setting is in the interpretation of the toe and camber effects, which are both defined as nonlinear functions of jounce. Any change in the system that affects the definition of where zero jounce is located will require that the toe and camber tables be modified.
The first option links the camber, toe, and spring datasets. It is convenient if you do not change those datasets much. In this case you can change the sprung mass properties without worrying about the nonlinear effects of jounce.
The second option links the camber, toe, and sprung mass properties. It is convenient if you do not change the sprung mass properties much. In this case, you can change spring properties without making corresponding adjustments to the toe and camber tables.
Jounce at design load condition (keyword = JNC_DESIGN(IAXLE, ISIDE)).
fields appear when the second option under the pull down control described in is selected.
Links to Suspension: Dive Angle datasets describing the rotation of the unsprung mass
Note: Caster angle is defined to be positive when the upper end of the steering
axis is inclined to the rear. “Dive” is not the same as caster change. The
term “dive” was chosen because it applies to all axles, not just steerable
ones. A positive right hand rotation maintains consistency with other
parts of the models.
Links to Suspension: Longitudinal Position datasets describing the longitudinal (horizontal) translation of the wheel center as a function of suspension compression.
Separate links are provided for the left and right sides. Positive longitudinal motion occurs when the axle moves forward.
Links to Suspension: Camber Angle datasets describing how camber angle varies as a
Link to a Suspension: Lateral Position dataset describing how lateral position of the wheel
Link to a Suspension: Toe Angle dataset describing how toe angle varies as a function of
The compliance properties of an independent suspension are described on the Suspension: Independent Compliance, Springs, and Dampers screen, shown in Figure 7.
Figure 7. The Suspension: Independent Compliance, Springs and Dampers screen. Discussion
displacement of the wheel to tire forces and moments (see fields
each wheel. For example, side force applied to the right wheel would not cause any steer of the left wheel due to the toe vs. Fx coefficient on this screen. (Coupling between left and right wheels is caused by steering system compliance, specified on the Steering screen.)
The use of terms to describe suspension compliance effects (toe or steer, camber or inclination) has been chosen so that for a vehicle with symmetric suspension properties, the numerical signs on the left side and right side coefficients are the same. For example toe for a wheel is defined as positive when the wheel steers inward, toward the vehicle longitudinal axis, while steer is defined to be positive when the wheel undergoes a positive rotation about the Z axis (to the left). Fx is defined as a toe effect, because the two wheels on a symmetric suspension will both either steer in or out due to the applied force. Fy is a steer effect, because the applied force will cause wheels of a symmetric suspension to steer both to the left or both to the right.
Camber is defined to be positive when a wheel leans outward at the top, and positive inclination means the wheel leans to the right, a positive rotation about the X axis that points forward.
Therefore, coefficients that involve camber (e.g. Fx) and have positive sign mean that an applied
positive force causes the wheel to lean out at the top. Coefficients that involve inclination (e.g., Fy) and have positive sign mean that an applied positive force causes the wheel to lean to the right.
Lateral and longitudinal displacements are measured at the wheel centers. Longitudinal force compliance is measured with equal, parallel longitudinal forces applied at the tire contact patches of both wheels on a suspension. Lateral force compliance is measured with equal but oppositely directed lateral forces applied at the tire contact patches of both wheels on a suspension.
User Settings
Pull-down control for choosing between three options for spring definitions:
Suspension: Spring dataset or a
hysteretic spring model. Selecting it causes the links
The second option specifies that internal spring model is used with an external (Simulink) spring. (See Figure 8 on page 20.) It causes the links
dataset or a Suspension: Ride Rate (Spring + Tire)and to define the initial force carried by the external springs to be displayed.
to define the initial compression of the external springs.
Link to a Suspension: Spring dataset or a Suspension: Ride Rate (Spring + Tire) dataset.
Separate links are provided for the left and right sides.
Upper spring seat height adjustment (keyword = L_SPG_ADJ([IUNIT,] IAXLE,
Link to a Suspension: Shock Absorber dataset. Separate links are provided for the left and right sides.
Link to a Suspension: Jounce and Rebound Stops dataset. Separate links are provided for
displacement. The most common example is of jounce and rebound stops incorporated into a damper that has a motion ratio not equal to 1. The compression values in the table would reflect actual damper displacements.
Motion ratios for the springs. These are the ratios of spring compression to suspension jounce measured at the wheel center (keyword = R_SPRING([IUNIT,] IAXLE, ISIDE)). The ratio is the mechanical advantage of the suspension with respect to the spring. This value is typically between 0.5 (for some SLA suspensions) and 1.0 (for some MacPherson strut suspensions).
Motion ratios for the shock absorbers. These are the ratios of damper stroke to suspension
jounce measured at the wheel center (keyword = R_DAMPER([IUNIT,] IAXLE, ISIDE)). This is the mechanical advantage of the suspension with respect to the shock absorber. This value is typically between 0.5 (for some SLA suspensions) and 1.0 (for some MacPherson strut suspensions).
Motion ratios for the jounce stops. These are the ratios of jounce stop compression to suspension jounce measured at the wheel center (keyword = R_JNC_STOP([IUNIT,] IAXLE, ISIDE)). This is the mechanical advantage of the suspension with respect to the stop bumper.
Motion ratios for the rebound stops. These are the ratios of rebound stop compression to
suspension jounce measured at the wheel center (keyword = R_JNC_STOP([IUNIT,] IAXLE, ISIDE)). This is the mechanical advantage of the suspension with respect to the stop bumper. Note that the signs on rebound stop compression and force are negative, as the suspension is in extension.
Link to a Suspension: Auxiliary Roll Moment dataset or a Suspension: Measured Total Roll Stiffness dataset. The linked dataset accounts for the difference between the overall roll stiffness and the stiffness provided by the springs alone.
Auxiliary roll damping (keyword = DAUX([IUNIT,] IAXLE)). This parameter accounts
for the difference between the overall roll damping and the roll damping provided by the shock absorbers alone.
Coefficient for change in toe per change of tire longitudinal force (keyword = CT_FX([IUNIT,] IAXLE, ISIDE)). A forward tractive force tends to bend a suspension forward, steering the wheel inward (positive toe). Therefore this parameter is likely to have a small but positive value.
Coefficient for change of steer angle per change of tire lateral force (keyword =
CS_FY([IUNIT,] IAXLE, ISIDE)). For wheels that can be steered, the steer axis is usually inclined to intersect the ground in front of the center of tire contact. Thus, a positive lateral force (to the left), acting behind the steer axis usually causes some steer to the right (negative). Therefore, this coefficient is likely to have a small negative value for a steered wheel. For un-steered rear wheels, it should have a value close to zero.
Coefficient for change of steer angle per change of tire aligning torque (keyword = CS_MZ([IUNIT,] IAXLE, ISIDE)). The suspension elements usually deflect when a
steering torque is applied to the wheel. Because the steer and moment have the same sign convention, the compliance coefficient is nearly always positive.
Steering as a result of aligning torque is due both to compliance in the suspension and compliance in the steering system. The effect of this coefficient leads to a steering angle that is added to the steering due to other factors, including the steering system compliance as described in the Steering screen.
Coefficient for change in camber per change of tire longitudinal force (keyword =
CC_FX([IUNIT,] IAXLE, ISIDE)). This parameter is likely to have a value close to zero.
Coefficient for change of inclination angle per change of tire lateral force (keyword = CI_FY([IUNIT,] IAXLE, ISIDE)). A positive lateral force (to the left) tends to bend the suspension and let the wheel incline to the right (positive inclination). Therefore, this parameter is expected to have a small positive value.
Coefficient for change of inclination angle per change of tire aligning torque (keyword =
CI_MZ([IUNIT,] IAXLE, ISIDE)). This parameter is likely to have a value close to zero.
Coefficient for longitudinal displacement of the wheel center per change of tire longitudinal force (keyword = C_LONG([IUNIT,] IAXLE, ISIDE)). Displacement almost always occurs in the same direction as the force, and displacements and forces have the same convention, so this parameter almost always has a small positive value. Longitudinal force compliance is measured with equal, parallel longitudinal forces applied at the tire contact patches of both wheels on a suspension.
Coefficient for lateral displacement of the wheel center per change of tire lateral force
(keyword = C_LAT([IUNIT,] IAXLE, ISIDE)). Displacement almost always occurs in the same direction as the force, and displacements and forces have the same convention, so this parameter almost always has a small positive value. Lateral force compliance is measured with equal but oppositely directed lateral forces applied at the tire contact patches of both wheels on a suspension.
Initial force in an external spring (keyword = FS_OFFSET([IUNIT,] IAXLE, ISIDE)
Simulink or code, along with internal springs from the hysteretic model. (See Figure 8.) If there are no external springs, it is hidden. It indicates the initial force carried by the outside component (springs or other load bearing components). The deflection of the internal spring is initialized based on the remaining load.
Figure 8. The Suspension: Independent Compliance screen with internal + external springs.
Initial compression of an external spring (keyword = CMP_OFFSET([IUNIT,] IAXLE,
are present, these fields are hidden. The spring compression is used to initialize the position of the suspension and can be exported for use by the external model.
Figure 9. The Suspension: Independent Compliance screen with external springs.
Suspension: Independent System (Simplified, Symmetric)
Figure 10 shows the simplified independent suspension screen. When it is used, the suspension is specified as symmetric, with linearized representations of the roll and pitch kinematics.
Unsprung mass (keyword = M_US([IUNIT,] IAXLE)). This mass includes the wheels,
Fraction Steered (keyword = R_US_STR(IAXLE)) is the portion of the unsprung mass that rotates about the kingpin axis when the wheels are steered. Typically, it includes the wheel, tire, brake and steering knuckle, but not the control arms, springs or dampers. For an independent suspension, values are normally around 0.8. If the field is blank, a value of 1.0 is used.
主动悬架系统 主动悬架是用一个有自身能源的力发生器来代替被动悬架中的弹簧和减振器。根据作动器响应带宽的不同，主动悬架又分为宽带主动悬架和有限带宽主动悬架，也被叫做全主动悬 架和慢主动悬架。 全主动悬架系统所采用的作动器具有较宽的响应频带，以便对车轮的高频共振也加以控制。作动器多采用电液或液气伺服系统，控制带宽一般应至少覆盖0～15Hz，有的作动器响应带宽甚至高达100Hz。结构示意图见上图。从减少能量消耗的角度考虑，也可保留一个与作动器并联的传统弹簧，以用来支持车身静载。 主动悬架的一个重要特点就是，它要求作动器所产生的力能够很好地跟踪任何力控制信号。因此，它为控制律的选择提供了一个广泛的设计空间，即如何确定控制律以使系统能够让车辆达到最佳的总体性能。近二十年来，有大量关于主动悬架的研究论文及专题回顾文献发表。研究结果表明，主动悬架能够在不同路面情况及行驶条件下显著地提高车辆性能。 主动悬架的研制工作起始于八十年代。Lotus 制造了第一辆装有主动悬架的样车。其系统的响应可达30Hz，它可使乘坐舒适性和转弯及制动时的车身姿态控制提高约35%。还有一些主动悬架实施的例子，如Lotus Turbo Esprit、Damlar Benz的试验样机系统、BMW 和Ford等。然而，由于这些主动悬架系统具有的高成本、高能耗、增加的重量及复杂程度，使主动悬架仅限于样车及一些赛车等有限的应用上。 结构上，有限带宽主动悬架通常由作动器与一个普通弹簧串联后，再与一个被动阻尼器并联构成，见上图。这种系统在低频时（一般小于5或6赫兹）采用主动控制，而高于这个频率时，控制阀不再响应，系统特性相当于传统的被动悬架，而被动悬架在高频时的效果也 比较好。 由于有限带宽主动悬架作动器仅需在一窄带频率范围内工作，所以它降低了系统的成本及复杂程度，比全主动悬架便宜得多。尽管如此，它的主动控制仍然覆盖了主要的车身振动，包括纵向、俯仰、侧倾以及转向控制等要求的频率范围，改善了车身共振频率附近的行驶性能，提高了对车身姿态的控制，性能可达到与全主动系统很接近的程度。 就实用性及商业竞争力而言，有限带宽主动悬架的应用前景较好。专家普遍认为采用气液控制慢主动系统在商用领域最有发展前途，但若想在今后几年内有重大的发展，还得要求在电液阀技术方面有大的突破来降低成本。已有一些装有该类悬架的车辆投入市场，如Nissan Infiniti Q45和Toyato Celica等。两个有限带宽主动悬架系统实施方案见下图。
底盘-10-麦弗逊式悬架的构造及拆装实训
汽修专业理实一体教案 课题项目七麦弗逊式悬架的结构、工作原理及拆装实训 教学目标一、知识目标 了解麦弗逊式悬架的工作原理原理二、技能目标 拆卸安装悬架 三、情感目标 培养团队合作能力 培养不怕脏不怕累的劳动精神 教学重点一、实训车间的行为规范 二、悬架及减震的工作原理 教学难点一、悬架的运动原理 二、规范的使用各种工具 教学准备一、转向系统实训台 二、拆装作业台 三、120件套工具箱 作业布置一、作业 二、实训报告 教学考核一、现场提问（30%） 二、现场实践操作（70%）
教学反思 教学内容或教学流程教法设计 一、课前三分钟 1.强调车间内不允许玩手机，督促班干部收缴手机 2.保持车间干净整洁，不准带入饮料零食等物 3.未经老师允许，不得擅自操作各个机械 4.检查教材、笔记本、笔 二、复习旧知与导入新课 1.复习旧知 底盘构成 2.导入新课 颠簸路面上，车辆如何减少震动，吸收能量？ （1）弹簧延时，缓冲 （2）减震吸收能量 三、悬架的结构
『悬挂在汽车底盘安放位置的示意 图』 ●悬挂的概念和分类 首先让我们来了解一下什么 是悬挂：悬挂是汽车的车架与车桥或车轮之间的一切传力连接装置的总称，悬架的主要作用是传递作用在车轮和车身之间的一切力和力矩，比如支撑力、制动力和驱动力等，并且缓和由不平路面传给车身的冲击载荷、衰减由此引起的振动、保证乘员的舒适性、减小货物和车辆本身的动载荷。典型的汽车悬挂结构由弹性元件、减
震器以及导向机构等组成，这三部分分别起缓冲，减振和力的传递作用。绝大多数悬挂多具有螺旋弹簧和减振器结构，但不同类型的悬挂的导向机构差异却很大，这也是悬挂性能差异的核心构件。根据结构不同可分为非独立悬挂和独立悬挂两种。 『奥迪S4前后均采用了独立悬挂』 非独立悬挂由于是用一根杆件直接刚性地连接在两侧车轮上，一侧车轮受到的冲击、振动必然要影响另一侧车轮，这样自然不会得到较好的操纵稳定性及舒适性，同时由于左
汽车悬挂系统结构原理图解 Post by：2010-10-419:48:00 什么是悬挂系统 舒适性是轿车最重要的使用性能之一。舒适性与车身的固有振动特性有关，而车身的固有振动特性又与悬架的特性相关。所以，汽车悬架是保证乘坐舒适性的重要部件。同时，汽车悬架做为车架(或车身)与车轴(或车轮)之间作连接的传力机件，又是保证汽车行驶安全的重要部件。因此，汽车悬架往往列为重要部件编入轿车的技术规格表，作为衡量轿车质量的指标之一。 汽车车架（或车身）若直接安装于车桥（或车轮）上，由于道路不平，由于地面冲击使货物和人会感到十分不舒服，这是因为没有悬架装置的原因。汽车悬架是车架（或车身）与车轴（或车轮）之间的弹性联结装置的统称。它的作用是弹性地连接车桥和车架（或车身），缓和行驶中车辆受到的冲击力。保证货物完好和人员舒适；衰减由于弹性系统引进的振动，使汽车行驶中保持稳定的姿势，改善操纵稳定性；同时悬架系统承担着传递垂直反力，纵向反力（牵引力和制动力）和侧向反力以及这些力所造成的力矩作用到车架（或车身）上，以保证汽车行驶平顺；并且当车轮相对车架跳动时，特别在转向时，车轮运动轨迹要符合一定的要求，因此悬架还起使车轮按一定轨迹相对车身跳动的导向作用。 悬架结构形式和性能参数的选择合理与否，直接对汽车行驶平顺性、操纵稳定性和舒适性有很大的影响。由此可见悬架系统在现代汽车上是重要的总成之一。
一般悬架由弹性元件、导向机构、减振器和横向稳定杆组成。弹性元件用来承受并传递垂直载荷，缓和由于路面不平引起的对车身的冲击。弹性元件种类包括钢板弹簧、螺旋弹簧、扭杆弹簧、油气弹簧、空气弹簧和橡胶弹簧。减振器用来衰减由于弹性系统引起的振动，减振器的类型有筒式减振器，阻力可调式新式减振器，充气式减振器。导向机构用来传递车轮与车身间的力和力矩，同时保持车轮按一定运动轨迹相对车身跳动，通常导向机构由控制摆臂式杆件组成。种类有单杆式或多连杆式的。钢板弹簧作为弹性元件时，可不另设导向机构，它本身兼起导向作用。有些轿车和客车上，为防止车身在转向等情况下发生过大的横向倾斜，在悬架系统中加设横向稳定杆，目的是提高横向刚度，使汽车具有不足转向特性，改善汽车的操纵稳定性和行驶平顺性。 悬挂系统的分类 现代汽车悬架的发展十分快，不断出现，崭新的悬架装置。按控制形式不同分为被动式悬架和主动式悬架。目前多数汽车上都采用被动悬架，如下图所示，也就是汽车姿态（状态）只能被动地取决于路面及行驶状况和汽车的弹性元件，导向机构以及减振器这些机械零件。20世纪80年代以来主动悬架开始在一部分汽车上应用，并且目前还在进一步研究和开发中。主动悬架可以能动地控制垂直振动及其车 身姿态，根据路面和行驶工况自动调整悬架刚度和阻尼。
目录 一 : 主动悬架简介 二：电子技术控制 三：主动控制技术——三类典型的液力主动控制系统。 1）A类由 Lotus(莲花 )公司开发 2）B类由 AP公司发展的气液悬架 3）C类液力主动控制系统由 Nissan公司开发四：主动悬架的最优控制方法 五：智能控制系统 六：作动器－蓄能式减震器 七：主动式液压悬架 八：主动式空气悬架 九：电机蓄能式主动悬架 十：双重控制空气悬架系统－奔驰公司研发
一：主动悬架 汽车的主动悬架系统是在普通悬架系统中附加一个可以控制阻尼作用力的装置，由执行机构、测量系统、反馈控制系统和能源系统四部分组成。主动悬架能够根据汽车的运动状态和路面状况，适时地调节悬架的刚度和阻尼，使悬架系统处于最佳减振状态，使车辆在各种路面状况下都会有良好的舒适性。主动悬架的关键部位是其执行机构，也就是可以调节的悬架阻尼系统。 主动悬架有作为直接力发生器的动作器，可以根据输入与输出进行最优的反馈控制，使悬架有最好的减震特性，以提高汽车的平顺性和操纵稳定性。主动悬架的一个重要特点就是，它要求作动器所产生的力能够很好地跟踪任何力控制信号。因此，它为控制律的选择提供了一个广泛的设计空间，即如何确定控制律以使系统能够让车辆达到最佳的总体性能。 针对悬架系统的非线性特点，研究适宜的悬架系统电控技术是汽车悬架系统振动性能改进的方向。悬架位于车身与轮胎之间，对车辆的运动性能、乘坐舒适性有重大的影响。按照路面行驶工况最优控制，悬架性能以确保车辆行驶性能与乘坐舒适性，电子控制悬架将进一步向高性能方向发展。作为实现这种对悬架的优化控制的方式之一，是利用“预知传感器”进行预知控制的“预知控制悬架” 二：电子控制技术 电子技术控制汽车悬架系统主要由（车高、转向角、加速度、路况预测）传感器、电子控制ECU、悬架控制的执行器等组成。系统的控制功能通常有以下三个： 1）车高调整：当汽车在起伏不平的路面行驶时，可以使车身抬高，以便于通过；在良好路面高速行驶时，可以降低车身，以减少空气助
关于汽车悬架系统 ——简单知识了解 李良 车辆工程 说明： 1、单独的关于悬架的资料太多，将资料简化，尽可能简单些，写的不好，多多批评指正。第二部分对悬架的设计和选型很有参考价值，可以看看。 2、另外搜集了一些关于悬架方面的资料（太多了，提供部分），也很不错。 3、有什么问题或建议多多提，我喜欢～～～～～～～～ 第一部分简单回答您提出的问题 悬架的作用： 1、连接车体和车轮，并用适度的刚性支撑车轮； 2、吸收来自路面的冲击，提高乘坐舒适性； 3、有助于行驶中车体的稳定，提高操作性能； 悬架系统设计应满足的性能要点： 1、保证汽车有良好的行驶平顺性；相关联因素有：振动频率、振动加速度界限值 2、有合适的减振性能；应与悬架的弹性特性很好地匹配，保证车身和车轮在共振区的振幅小，振动衰减快 3、保证汽车具有良好的操纵稳定性；主要为悬架导向机构与车轮运动的协调，一方面悬架要保证车轮跳动时，车轮定位参数不发生很大的变化，另一方面要减小车轮的动载荷和车轮跳动量 4、汽车制动和加速时能保持车身稳定，减少车身纵倾（点头、后仰）的可能性，保证车身在制动、转弯、加速时稳定，减小车身的俯仰和侧倾 5、能可靠地传递车身与车轮之间的一切力和力矩，零部件质量轻并有足够的强度、刚度和寿命 悬架的主要性能参数的确定： 1、前、后悬架静挠度和动挠度； 2、悬架的弹性特性； 3、（货车）后悬架主、副簧刚度的分配； 4、车身侧倾中心高度与悬架侧倾角刚度及其在前、后轴的分配； 5、前轮定位参数的变化与导向机构结构尺寸的选择； 悬架系统与转向系统： 1、悬架机构位移的转向效应，悬架系对操纵性、稳定性的影响之一是悬架机构的位移随弹簧扰度而变所引起的转向效应。轴转向，使用纵置钢板弹簧的车轴式悬架的汽车在转弯时车体所发生侧摆的情况下，转弯外侧车轮由于弹簧被压缩而后退，内侧车轮由于弹簧拉伸而前进，其结果是整个车轴相当原来的车轴中心产生转角，这种现象称为周转向。前轮产生转向不足的效应，后轮产生转向过度的效应。独立悬架外侧成为前束（负前束），而产生轴转向效应。 2、车轮外倾角变化的转向效应，大多数独立悬架的车轮对面外倾角以及轮胎接地负荷都随着车体的倾斜而变化，这时外倾推力也发生变化，车轮被推向转弯的外侧，前轮有转向不足，后轮有转向过度的倾向。在这种情况下，其作用和离心对抗，所以产生相反效应。车轴式悬架在转弯时由于左右的负荷移动，轮胎的扰度不同也产生若干的外倾角的变化，其作用相同。 3、上述都是转弯时的情况，而直进时由于路面凹凸不平使车轮上下振动，也同时会产生这种效应，随着外倾角的变化也有产生轴转向的可能性。一般轴转向或因外倾角变化的转向效应都会改变原来的操纵特性，所以对操纵性，稳定性影响相当大，因此，在设计汽车时往往把这些效应计算在内面修正其操纵特性。
XX大学 现代控制理论 ——汽车半主动悬架系统的建模与分析 姓名：XXX 学号：XXXX 专业：XXXX
一． 课题背景 汽车的振动控制是汽车设计的一个重要研究内容，涉及到汽车的平顺性和操纵稳定性。悬架系统是汽车振动系统的一个重要子系统，其振动传递特性对汽车性能有很大影响。因此设计性能良好的悬架系统以减少路面激励的振动传递，从而提高汽车的平顺性和操纵稳定性是汽车振动控制研究的重要课题。 悬架系统是汽车车身与轮胎间的弹簧和避震器组成整个支撑系统，用于支撑车身，改善乘坐舒适度。而半主动悬架是悬架弹性元件的刚度和减振器的阻尼系数之一可以根据需要进行调节控制的悬架。 目前，半主动悬架研究主要集中在调节减振器的阻尼系数方面，即将阻尼可调减振器作为执行机构，通过传感器检测到汽车行驶状况和道路条件的变化以及车身的加速度，由ECU 根据控制策略发出脉冲控制信号实现对减振器阻尼系数的有级可调和无级可调。 二． 系统建模与分析 1.1 半主动悬架系统的力学模型 以二自由度 1/4半主动悬架模型为例，并对系统作如下假设： (1) 悬挂质量与非悬挂质量均为刚体； (2) 悬架系统具有线性刚度和阻尼； (3) 悬架在工作过程中不与缓冲块碰撞； (4) 轮胎具有线性刚度，且在汽车行驶过程中始终与地面接触。 综上，我们将该系统等效为两个质量块M ，m ；两个弹簧系统Ks ，Kt ；一个可调阻尼器（包含一个 常规阻尼器Cs 和一个变化阻尼力F ），如图1所示。 图1 系统力学模型 1.2 半主动悬架系统的数学模型 由减振器的简化模型得:N S =-+F C V F 对m 进行分析：()211201122()t s s d z dz dz m K z z K z z C F dt dt dt ?? =------ ??? 即：()()1011212()t s s mz K z z K z z C z z F =------ 对M 进行分析：2212122 ()s s d z dz dz M K z z C F dt dt dt ?? =-+-+ ??? 即：()()21212s s Mz K z z C z z F =-+-+
车辆主动悬架的控制研究 悬架就是汽车的重要装置之一,它对汽车的平顺性、操纵稳定性、通过性等多种使用性能有着很大的影响。设计优良的悬架系统,对提高汽车产品质量有着极其重要的意义。目前,汽车上普遍采用的就是弹性元件与减震器组成的常规悬架,从控制力学的角度,将这种悬架称为被动悬架。实践与研究结果都表明,常规悬架受到许多限制,即使采用优化方法来设计也只就是将其性能改善到一定程度。为了克服常规悬架对其性能改善的限制,在汽车中采用与发展了新型的主动悬架。主动悬架能够根据路面情况及汽车运行的实际状态进行最优反馈控制,使汽车整体行驶性能达到最佳。主动悬架的主要特点就是能够主动提供能量,与传统被动悬架相比,其最大的优点在于具有高度的自适应性。 一、 车辆主动悬架系统建模 主动悬架的分析模型如图3、3所示,图中u 为主动悬架执行机构的作用力。 主动悬架的运动微分方程为: ?????---==)(01..11..22x x k u x m u x m t (1) 状态变量、输出向量的选取同被动悬架,且为了便 于与被动悬架的比较分析,选取与被动悬架模型 相同的输入信号,路面激励仍为选白噪声)(t ω, 根据微分方程组(1),建立如下所示的状态方程与 输出方程 ?????+=++=Eu Cx y t D Bu Ax x )(ω。 (2) 式中: ??????????????--=0001000000010101m k A t ;????????????????-=121010m m B ;????????????=0100D ; ??????????=010*********C ;??????????????=0012m E 汽车悬架可认为就是一种连续线性的随机最优控制系统,由最优线性滤波器串接确定性调节器的最优反馈增益系数矩阵组成。这两部分参数可分别加以确定。对于控制要求的性能指标就是二次函数积分型的调节器问题,外界干扰就是高斯白噪声,综合性能指标为: dt t u t R t u t X t Q t X u J T T ?∞+=0)]()()()()()([)( (3) 此处认为汽车主动悬架的最优控制器为一个终端时间无限的线性调节器,问题仍就是寻找最优控制)(t u ,使目标函数J 取极小。线性调节器的主要问题之一就是如何选择Q 、R 阵以获得比较满意的控制过程动态响应,计算机仿真可以解决这个问题。 在悬架设计中,为提高汽车的操纵稳定性与行驶平顺性,应使簧载质量垂直加速度、悬架
毕业设计（论文） 文献综述 题目十九座客车悬架系统设计 专业车辆工程（汽车工程） 班级08级2班 学生 指导教师 2012 年
汽车悬架系统文献综述 1.前言 悬架是安装在车桥和车轮之间用来吸收汽车在高低不平的路面上行驶所产生的颠簸力的装置。因此，汽车悬架系统对汽车的操作稳定性、乘坐舒适性都有很大的影响。由于悬架系统的结构在不断改进，其性能及控制技术也得到了迅速提高。尽管一百多年来汽车悬架从结构形式到作用原理一直在不断地演进，但从结构功能而言，它都是由弹性元件、减振装置和导向机构三部分组成。在有些情况下，某一零部件兼起两种或三种作用，比如钢板弹簧兼起弹性元件和导向机构的作用，麦克弗逊悬架中的减振器柱兼起减振器及部分导向机构的作用，有些主动悬架中的作动器则具有弹性元件、减振器和部分导向机构的功能。其作用是传递路面作用在车轮和车架上的支承力、牵引力、制动力和侧向反力以及这些力所产生的力矩，并且缓冲和吸收由不平路面通过车轮传给车架或车身的振动与冲击，抑制车轮的不规则振动，提高车辆平顺性(乘坐舒适性)和安全性(操纵稳定性)，减少动载荷引起的零部件和货物损坏[1]。 2.汽车悬架系统的发展状况 非独立悬架早期广泛应用于轿车及轿车以外的其它车型中，由于其可靠性和简单的特性，现在还被广泛的用于轿车的后桥，轻型货车和越野汽车的后桥，重型货车的前后桥都采用非独立悬架。 独立悬架早期只单纯用于轿车上，目前大部分轻型货车和越野汽车为了提高舒适性也开始采用独立悬架，同时一些中型卡车及客车为了提高驾乘的舒适性和行驶平顺性也开始采用独立悬架，在国外甚至一些轮式工程机械如吊车和重型卡车也开始采用独立悬架。因此对于独立悬架的设计技术，国内外都进行了研究，这些研究主要集中在以下几个方面：独立悬架设计方法，独立悬架参数对汽车行驶平顺性的影响；独立悬架对汽车操纵稳定性的影响。国内的研究主要表现为：独立悬架和转向系的匹配；独立悬架与转向横拉杆长度和断开点的确定；悬架弹性元件的设计分析；导向机构的运动分析；独立悬架对前轮定位参数的影响；独立悬架的优化设计等。国外除上述研究外，还进入了微观领域的研究，如用原子力学显微镜观察悬架材料内部聚合体的原子转化情况，研究悬架作为弹性介质的流变特性[2]等，从而使得独立悬架向着智能化、轻量化、小型化、通用化方向发
目录 1引言1 2汽车悬架系统的类型和应用1 2.1被动悬架1 2.2主动悬架2 2.3半主动悬架2 3主动悬架控制系统国内外研究现状2 4汽车悬架的控制策略3 4.1天棚阻尼与开关阻尼控制3 4.2随机线性二次最优控制3 4.3模糊控制4 4.4神经网络控制4 4.5预测控制4 4.6滑模变结构控制5 4.7复合控制5 5控制方法的展望5 5.1注重控制策略的综合运用5 5.2注重汽车其他系统与主动悬架系统的联合控制研究5 5.3注重悬架系统模型的降阶研究6 6结论6 参考文献：6
汽车主动（半主动）悬架控制系统的 研究发展 1引言 汽车主动悬架目前是国内外研究的热点问题，研究的关键技术主要在控制策略的选择上及执行器的研发方面。国外由于成本问题，一些油气主动悬架也仅限用在一些高级轿车上，国内在此方面还处在研发及试验阶段，离主动悬架系统普遍使用在轿车上的时代还较远。 2汽车悬架系统的类型和应用 悬架是车架与车桥之间一切传力装置的总称，它的主要功用是传递作用在车轮和车架之间的力和力矩，缓冲由不平路面传给车架或车身的冲击力，并衰减由此引起的振动，以保证汽车能平顺行驶。衡量悬架性能好坏的主要指标是汽车行驶的平顺性; 即乘坐舒适性和操纵稳定性，但这两个方面是相互排斥的性能要求。由于被动悬架的刚度和阻尼系数是固定的，无法根据不同的使用要求自适应地改变，在结构设计上只能是满足平顺性和操纵稳定性之间矛盾的折衷。 为服这个缺陷，国外在五十年代提出了“主动悬架”的概念。主动悬架的特点是能根据外界输入或车辆本身状态的变化进行动态自适应调节。主动悬架包控制单元和力发生器，力发生器的作用下使悬架的特性得到控制，如同改变了悬架的刚度和阻尼系数，其中最关键的是控制算法的优劣。 2.1被动悬架 被动悬架, 由弹性元件和不可变参数的减振器组成, 只能在特定工况下达到最优, 缺少对变载荷、变车速、不可预测路况的适应性。被动悬架是传统的机械结构，由弹簧、减震器和导向机构组成。被动悬架的刚度和阻尼系数均不可调，只能在特定的工况下达到最优减振效果，存在明显的共振峰，难以同时获得良好的乘坐舒适性和操纵稳定性，缺乏灵活性。但被动悬架因结构简单、设计容易和制造方便，且无须额外的能量输入，目前在中低档轿车上应用最为广泛[1]。为了进一步改善被动悬架的减振效果,满足现代汽车对悬架提出的更高的性能要求，在桑塔纳、夏利和赛欧等轿车上加强了通过优化寻找最优悬架参数和对悬架导向机构的研究，采用了带有横向稳定杆的多连杆机构悬架系统，在一定程度上改善了被动悬架减振效果。
前言： 悬架是汽车的车架与车桥或车轮之间的一切传力连接装置的总称，其作用是传递作用在车轮和车架之间的力和力扭，并且缓冲由不平路面传给车架或车身的冲击力，并衰减由此引起的震动，以保证汽车能平顺地行驶。典型的悬架结构由弹性元件、导向机构以及减震器等组成，个别结构则还有缓冲块、横向稳定杆等。弹性元件又有钢板弹簧、空气弹簧、螺旋弹簧以及扭杆弹簧等形式，而现代轿车悬架多采用螺旋弹簧和扭杆弹簧，个别高级轿车则使用空气弹簧。悬架是汽车中的一个重要总成，它把车架与车轮弹性地联系起来，因此悬架与车辆的行驶平顺性、操控稳定性具有极大的关系。悬架设计的好坏直接影响到整车的性能。因此开发出高品质的悬架是车辆工程师的一项重要任务。而悬架部分涉及的专业知识也比较高深，本文期望通过对悬架进行初级设计以达到对悬架有进一步了解的目 的。 关键词:悬架；减震器；弹簧计算 1
1悬架 1.1悬架的功用 汽车悬架是车架（或车身）与车轴（或车轮）之间的弹性联结装置的统称。它的作用是弹性地连接车桥和车架（或车身），缓和行驶中车辆受到的冲击力；保证货物完好和人员舒适；衰减由于弹性系统引进的振动，使汽车行驶中保持稳定的姿势，改善操纵稳定性；同时悬架系统承担着传递垂直反力，纵向反力（牵引力和制动力）和侧向反力以及这些力所造成的力矩作用到车架（或车身）上，以保证汽车行驶平顺；并且当车轮相对车架跳动时，特别在转向时，车轮运动轨迹要符合一定的要求，因此悬架还起使车轮按一定轨迹相对车身跳动的导向作用。 1.2 悬架的组成 一般悬架由弹性元件、导向机构、减振器和横向稳定杆组成。 1.弹性元件 弹性元件用来承受并传递垂直载荷，缓和由于路面不平引起的对车身的冲击。弹性元件种类包括钢板弹簧、螺旋弹簧、扭杆弹簧、油气弹簧、空气弹簧和橡胶弹簧等，这里我们选用螺旋弹簧。 2.减振器 减振器用来衰减由于弹性系统引起的振动，减振器的类型有筒式减振器，阻力可调式新式减振器，充气式减振器。 3.导向机构 导向机构用来传递车轮与车身间的力和力矩，同时保持车轮按一定运动轨迹相对车身跳动，通常导向机构由控制摆臂式杆件组成。种类有单杆式或多连杆式的。钢板弹簧作为弹性元件时，可不另设导向机构，它本身兼起导向作用。有些轿车和客车上，为防止车身在转向等情况下发生过大的横向倾斜，在悬架系统中加设横向稳定杆，目的是提高横向刚度，使汽车具有不足转向特性，改善汽车的操纵稳定性和行驶平顺性。
汽车系统半主动减振器的仿真设计 摘要：本文阐述了卡车半主动悬架的设计与使用。半主动悬架设计的主要目的是为了减小路面影响。通过仿真和参数优化设计了半主动减振器的反馈控制规则。通过仿真试验预测的效果在实车上得到了验证。一辆是卡车试验台，一辆是半拖车拖拉机。仿真实验和实际测量值表明半主动阻尼是实现高路面适应性车辆的一个重要思路。 关键词：半主动悬架半主动阻尼卡车悬架路面破坏路面保护车辆 介绍： 电子控制的汽车悬架，尤其是主动与半主动阻尼器的研究已经开展了很长时间了。主动悬架的主要目的就是提高车辆行驶的舒适性。然而，却忽略了汽车悬架的其他工作情况指标，比如，轮胎－路面动载荷、轮胎－桥和轮胎－土壤等其他工况下的动载荷。 路面网络的维护工作对路面主管机构是一项费用很高的工作。而且，受损路面会对车辆和路面自身造成损伤。每个欧洲国家花数十亿欧元修理维护公路系统，维修费用占全部公路费用的40％～80％，约占国民生产总值的0.4％。 尽管我们尚未对路面损伤的机制有清楚的了解。但有一点我们可以证实，即路面损伤很大程度上由重型车辆交通所致，当然还有一些其他的影响因素，如路面结构、气候、环境影响等。人们研究所有这些因素对路面的影响已经多年了。车辆对路面的破坏是由轮胎与路面的作用力所致[8]。计算结果表明，一辆满载卡车对路面的破坏程度是一辆客车的10000倍。目前，国家标准只对轮胎－路面的静力作了限制。然而，最近的DIVINE和SADTS项目研究表明，轮胎－路面的动载荷部分对路面和桥梁的破坏更大。 伴随着价格低廉、功能强大的电子元件和作动器技术，人们对设计要求的提高促使了可控悬架的广泛研究。很多情况下，半主动作动器取代了全主动。半主动悬架不可能取得像全主动悬架一样的性能提高，但是，它具有实用和价格优势。 1.1 半主动阻尼： 半主动悬架因为其与主动悬架相比有很多的优点而倍受推崇，尤其是它相对于现有系统应用方便，而且能耗低。半主动系统中的一个代表就是半主动阻尼器（SAD），它可以根据一些输入信号（通常是电信号）来调节阻尼比。 半主动悬架不需要昂贵、笨重的元件，比如液压泵、储能器、液压管路和作动器等，而仅仅只需要一个可调的半主动阻尼器。这些半主动系统不能像全主动作动器一样提供相同的力规则；然而，其效果则非常接近于全主动悬架，并且能节省很大的作动能量。在许多应用中，当前的被动阻尼器很可能被半主动取代，这些可以通过可控孔口和电流变流液或磁流变流液实现。 变阻尼孔半主动阻尼器就是通过在原有被动液压阀上增加一个可变阀孔的螺旋阀，其阻尼比的变化液依赖于螺旋阀的输入电流。 研究的阻尼比连续可变的半主动阻尼器Mannesmanm Sachs CDCN 50/55。所需输入电流的变化范围为0.6A～2A。0.6A反映了最小阻尼曲线，而2A对应了最大阻尼曲线。半主动阻尼器结构拥有先进的失效安全功能：当输入电流为0时，比如外部线路断了，阻尼值自动设置为中间值。所谓的失效－安全保障特性参见图1。 由图1，很明显，半主动阻尼器有一个很有限的动作区域，最大阻尼曲线和最小阻尼曲线限定在第一和第三象限。控制单元将所需的输入力转化为可以实现的作用力，这个例在特性区域范围内并和电流值相对应。比如，实际速度所需的力大于系统可以提供的最大力，则输出力就取系统可以提供的最大力；若需要的输入力比比系统的最小输出力小，则输出最小的输出力。如果所需的力和实际速度符号相反，即需要产生能量（可以证明这种情况对半主动阻尼器是不可能的），输出力就由最小耗散能确定。
附录Ⅰ：外文资料 Automotive Suspension System Overview The impact of the Vehicle in many aspects, Suspension plays a very important role . The components of the suspension system perform six basic functions: 1.Maintain correct vehicle ride height. 2.Reduce the effect of shock forces. 3.Maintain correct wheel alignment. 4.Support vehicle weight. 5.Keep the tires in contact with the road. 6.Control the vehicle’s direction of travel. Most suspension systems have the same basic parts and operate basically in the same way. They differ, however, in the way the parts are arranged. The vehicle wheel is attached to a steering knuckle. The steering knuckle is attached to the vehicle frame by two control arms, which are mounted so they can pivot up and down. A coil spring is mounted between the lower control arm and the frame. When the wheel rolls over a bump, the control arms move up and compress the spring. When the wheel rolls into a dip, the control arms move down and the springs expand. The spring force brings the control arms and the wheel back into the normal position as soon as the wheel is on flat pavement. The idea is to allow the wheel to move up and down while the frame, body, and passengers stay smooth and level. The unequal length control arm or short, long arm (SLA) suspension system has been common on American vehicles for many years. Because each wheel is independently connected to the frame by a steering knuckle, ball joint assemblies, and upper and lower control arms, the system is often described as an independent suspension. The short, long arm suspension system gets its name from the use of two control arms from the frame to the steering knuckle and wheel assembly. The two control arms are of unequal length with a long control arm on the bottom and a short control arm on the top. The control arms are sometimes called A arms because in the top view they are shaped like the letter A. In the short, long arm suspension system, the upper control arm is attached to a cross shaft through two combination rubber and metal bushings. The cross shaft, in turn, is bolted to the frame. A ball joint, called the upper ball joint, is attached to the outer end of the upper arm and connects to the steering knuckle through a tapered stud held in position with a nut. The inner ends of the lower control arm have pressed-in
悬架是汽车的重要装置之一，它对汽车的平顺性、操纵稳定性、通过性等多种使用性能有着很大的影响。设计优良的悬架系统，对提高汽车产品质量有着极其重要的意义。目前，汽车上普遍采用的是弹性元件和减震器组成的常规悬架，从控制力学的角度，将这种悬架称为被动悬架。实践和研究结果都表明，常规悬架受到许多限制，即使采用优化方法来设计也只是将其性能改善到一定程度。为了克服常规悬架对其性能改善的限制，在汽车中采用和发展了新型的主动悬架。主动悬架能够根据路面情况及汽车运行的实际状态进行最优反馈控制，使汽车整体行驶性能达到最佳。主动悬架的主要特点是能够主动提供能量，与传统被动悬架相比，其最大的优点在于具有高度的自适应性。 一、车辆主动悬架系统建模 主动悬架的分析模型如图所示，图中u为主动悬架执行机构的作用力。 主动悬架的运动微分方程为： (1) 状态变量、输出向量的选取同被动悬架，且为了便于与被动悬架的比较分析，选取与被动悬架模型相同的输入信号，路面激励仍为选白噪声， 根据微分方程组（1），建立如下所示的状态方程和输出方程 （2） 式中： ；；；； 汽车悬架可认为是一种连续线性的随机最优控制系统，由最优线性滤波器串接确定性调节器的最优反馈增益系数矩阵组成。这两部分参数可分别加以确定。对于控制要求的性能指标是二次函数积分型的调节器问题，外界干扰是高斯白噪声，综合性能指标为： (3) 此处认为汽车主动悬架的最优控制器为一个终端时间无限的线性调节器，问题仍是寻找最优控制，使目标函数J取极小。线性调节器的主要问题之一是如何选择Q、R阵以获得比较满意的控制过程动态响应，计算机仿真可以解决这个问题。 在悬架设计中，为提高汽车的操纵稳定性和行驶平顺性，应使簧载质量垂直加速度、悬架动扰度及轮胎动变形较小。此外，从实现控制的角度来看，应使所需的控制能量较小。因此式(3)可写为 (4) 或写为 (5) 其中 这里，q——轮胎动变形加权系数1 q——悬架动扰度加权系数2式中第一、二项为误差指标，表示在～∞整个时间内系统实际状态与平衡之间的误差总和。这一积分越小，说明控制误差越小，性能越好。积分式中第三项为能量指标，表示在～∞整个时间内支付能量的总和。系统状态转移是考控制u(t)来进行的，为要使系统误差很小，则需要支付很大的能量代价。最优反馈 增益系数矩阵式可写成 (6) 式中，增益值k~k有明确的物理意义。k可等效于一放置于簧载和非簧载质量间的弹簧，114改变 k则影响簧载质量的固有频率；k作用于簧载质量的绝对速度上，影响其悬挂阻尼；k312大小涉及轮胎变形，对车轮的垂直弹跳频率产生影响；k作用于非簧载质量的速度上，影响4其非悬挂阻尼。 主动悬架系统的能控性，能观测性二、．
长城汽车悬架系统 目录 一、悬架系统基础知识 二、弹性元件 三、减振器 四、导向装置及套筒 五、横向稳定杆 六、常见故障 一、悬架系统基础知识 悬架系统概述:舒适性是乘用车最重要的使用性能之一。舒适性与车身的固有振动特性有关，而车身的固有振动特性又与悬架的特性相关。所以，汽车悬架是保证乘坐舒适性的重要部件。同时，汽车悬架做为车架 ( 或车身 ) 与车轴 ( 或车轮 ) 之间作连接的传力机件，又是保证汽车行驶安全的重要部件。由于人体所习惯的垂直振动频率约为1~1.6Hz, 所以车身振动的固有频率应接近或处于人体所适应的范围。 悬架的功用:1、连接车桥和车架（车身）； 2、传递各种力和力矩； 3、缓冲、减振、导 向及稳定。 悬架的结构组成: 弹性元件:承受垂直载荷，缓和冲击； 减振器:减振； 导向装置:传力、导向； 横向稳定器：辅助弹性元件，以防横向倾斜。
悬架的分类: 1.主动式悬架与被动式悬架:目前多数汽车上都采用被动悬架，也就是汽车姿态 （状态）只能被动地取决于路面及行驶状况和汽车的弹性元件，导向机构以及减振器这些机械零件。主动悬架可以自动地控制垂直振动及其车身姿态，根据路面和行驶工况自动调整悬架刚度和阻尼。采用主动式悬架后，汽车对侧倾、俯仰、横摆跳动和车身的控制都能更加迅速、精确，汽车高速行驶和转弯的稳定性提高，车身侧倾减少。制动时车身前俯小，启动和急加速可减少后仰。 即使在坏路面，车身的跳动也较少，轮胎对地面的附着力提高。 1) 主动式液压悬架:电子控制的主动式液压悬架能根据悬架的质量和加速度 等，利用液压部件主动地控制汽车的振动。主动式液压悬架在汽车重心附近安装有纵向、横向加速度和横摆陀螺仪传感器，用来采集车身振动、车轮跳动、车身高度和倾斜状态等信号，这些信号被输入到控制单元ECU，ECU根据输入信号和预先设定的程序发出控制指令，控制伺服电机并操纵前后四个执行油缸 工作。 2) 主动式空气悬架:在电子控制的主动式空气悬架系统中，微机根据传感器送 来的信号和驾驶员给予的控制模式经过运算分析后向悬架发出指令，悬架可以根据微机给出的指令改变悬架的刚度和阻尼系数，使车身在行驶过程中保持良好的稳定性能，并且将车身的振动响应控制在允许的范围内。一般说来，主动式空气悬架的控制内容包括车身高度、减振器衰减力、弹簧弹性系数等三项。 2.非独立悬架与独立悬架：非独立悬架特点是两侧车轮安装于一整体式车桥上，
前轮最常见悬挂形式麦弗逊独立悬挂详解 2010年10月14日 15:11:14 来源： Che168 麦弗逊悬挂(macphersan)，是现在非常常见的一种独立悬挂形式，大多应用在车辆的前轮。简单地说，麦弗逊式悬挂的主要结构即是由螺旋弹簧加上减震器以及A字下摆臂组成，减震器可以避免螺旋弹簧受力时向前、后、左、右偏移的现象，限制弹簧只能作上下方向的振动，并且可以通过对减震器的行程、阻尼以及搭配不同硬度的螺旋弹簧对悬挂性能进行调校。麦弗逊悬挂最大的特点就是体积比较小，有利于对比较紧凑的发动机舱布局。不过也正是由于结构简单，对侧向不能提供足够的支撑力度，因此转向侧倾以及刹车点头现象比较明显。下面就为大家详细的介绍一下麦弗逊悬挂的构造以及性能表现。 麦弗逊悬挂的历史： 麦弗逊式悬挂是应前置发动机前轮驱动(ff)车型的出现而诞生的。ff车型不仅要求发动机要横向放置，而且还要增加变速箱、差速器、驱动机构、转向机，以往的前悬挂空间不得不加以压缩并大幅删掉，因此工程师才设计出节省空间、成本低的麦弗逊式悬挂，以符合汽车需求。
麦弗逊（Macphersan）是这套悬挂系统发明者的名字，他是美国伊利诺伊州人，1891年生。大学毕业后他曾在欧洲搞了多年的航空发动机，并于1924年加入通用汽车公司的工程中心。30年代，通用的雪佛兰公司想设计一种真正的小型汽车，总设计师就是麦弗逊。他对设计小型轿车非常感兴趣，目标是将这种四座轿车的质量控制在0．9吨以内，轴距控制在2．74米以内，设计的关键是悬挂。麦弗逊一改当时盛行的板簧与扭杆弹簧的前悬挂方式，创造性地将减振器和螺旋弹簧组合在一起，装在前轴上。实践证明这种悬架形式的构造简单，占用空间小，而且操纵性很好。后来，麦弗逊跳槽到福特，1950年福特在英国的子公司生产的两款车，是世界上首次使用麦弗逊悬架的商品车。 麦弗逊悬挂的构造： 麦弗逊悬挂构造图 麦弗逊式悬挂由螺旋弹簧、减震器、A字形下摆臂组成，绝大部分车型还会加上横向稳定杆。麦弗逊式独立悬架的物理结构为支柱式减震器兼作主销，承受来自于车身抖动和地面冲击的上下预
《现代控制理论及其应用》课程小论文 基于Matlab的汽车主动悬架控制器设计与仿真 学院：机械工程学院 班级：ＸＸＸＸ（XX） 姓名：X X X 2015年6月3号 河北工业大学
目录 1、研究背景 (3) 2、仿真系统模型的建立 (4) 2.1被动悬架模型的建立 (4) 2.2主动悬架模型的建立 (5) 3、LQG控制器设计 (6) 4、仿真输出与分析 (7) 4.1仿真的输出 (7) 4.2仿真结果分析 (9) 5、总结 (10) 附录：MATLAB程序源代码 (11) （一）主动悬架车辆模型 (11) （二）被动悬架车辆模型 (12) （三）均方根函数 (13)
1、研究背景 汽车悬架系统由弹性元件、导向元件和减振器组成,是车身与车轴之间连接的所有组合体零件的总称,也是车架(或承载式车身)与车桥(或车轮)之间一切力传递装置的总称,其主要功能是使车轮与地面有很好的附着性,使车轮动载变化较小,以保证车辆有良好的安全性,缓和路面不平的冲击,使汽车行驶平顺,乘坐舒适,在车轮跳动时,使车轮定位参数变化较小,保证车辆具有良好的操纵稳定性。 (a)被动悬架系统(b)半主动悬架系统(c)主动悬架系统 图1 悬架系统 汽车的悬架种类从控制力学的角度大致可以分为被动悬架、半主动悬架、主动悬架3种（如图1所示）。目前,大部分汽车使用被动悬架,这种悬架在路面不平或汽车转弯时,都会受到冲击,从而引起变形,这时弹簧起到了减缓冲击的作用,同时弹簧释放能量时,产生振动。为了衰减这种振动,在悬架上采用了减振器,这种悬架作用是外力引起的,所以称为被动悬架。半主动悬架由可控的阻尼及弹性元件组成,悬架的参数在一定范围内可以任意调节。主动悬架是在控制环节中安装了能够产生上下移动力的装置,执行元件针对外力的作用产生一个力来主动控制车身的移动和车轮受到的载荷,即路面的反作用力。随着电控技术的发展，微处理器在车辆中的应用已经日趋普遍,再加上作动器、可调减振器和变刚度弹簧等重大技术的突破,使人们更加注对主动悬架系统的研究。 车辆悬架的特性可以从车身垂直加速度,悬架动行程以及轮胎动位移来研究。本文对主动悬架采用LQG最优设计策略,利用MATLAB/Simulink软件进行仿真,分别对被动悬架与主动悬架建立动力学模型,并对两种悬架的仿真结果做了详细的比较分析与说明。