SRT Calculator

1
SRT Calculator

• Certifiers and Users Course

2
Course Outline (morning)

• Regulating Size and Weight
• Stability related Performance Measures
• Derivation of SRT Calculator
• Basic Use of SRT Calculator
• Test on Basic Use of the Calculator

3
Course Outline (afternoon)

• SRT Calculator Advanced Topics in Loading
• SRT Calculator Advanced Topics in Suspensions
• Review
• Advanced Users Test

4
Dimensions and Mass Rules Why?

• To promote safety
• Stability
• Manouevrability
• Fit on the road
• To protect the infrastructure
• Road damage
• Bridge damage
• Fit on the road

5
Dimensions and Mass Rules How?

• Prescriptive Limits
• Maximum or minimum mass values
• Maximum or minimum dimensions
• Specify what a vehicle must look like rather than
  what it needs to be able to do

6
Prescriptive Limits Pros

• Simple to regulate
• Easy to enforce
• Relatively straightforward compliance
• Relatively low cost
• Usually unambiguous

7
Prescriptive Limits Cons

• Not directly linked to the safety or
  infrastructure protection outcome that is
  intended
• Less safe vehicles may still be legal
• Cumbersome lots of rules
• Relatively inflexible
• Inhibits innovation

8
Performance Based Standards

• Performance Standard Performance Measure
  Acceptance Level
• Performance Measure - Some quantity that is
  measured (or calculated) during a specified set
  of test conditions.
• Acceptance Level Minimum or maximum level
  required to pass. This may vary with operating
  environment
• Specify what a vehicle must be able to do rather
  than what it must look like

9
Performance Based StandardsExamples

• Basic concept is not new
• Braking requirements Stopping distance from
  30km/h or a dry sealed surface shall be less than
  7m
• Turning circle requirements a vehicle must be
  able to complete a 360 turn inside a 25m wall-to
  wall circle

10
Performance Based StandardsPros

• Directly related to the factors that are to be
  controlled
• Allow for innovation and flexibility in vehicle
  design
• Improve industry understanding of vehicle factors
  that contribute to safety

11
Performance Based StandardsCons

• More complicated and expensive to assess for
  compliance
• More complex to regulate
• Risk of reducing safety by encouraging vehicles
  to the minimum standard
• Risk that the set of PBS is not complete

12
Performance Measures for Stability and Safety

• RTAC Study in 1980s to characterise the Canadian
  HV fleet
• Range of measures relating to stability and
  safety
• Static Roll Threshold (SRT)
• Dynamic Load Transfer Ratio (DLTR)
• Rearward Amplification (RA)
• Yaw Damping Ratio (YDR)
• High Speed Transient Offtracking (HSTO)
• High Speed Steady Offtracking (HSO)
• Low Speed Offtracking (LSO)

13
Rollover Related PMs

• SRT steady speed cornering
• Maximum lateral acceleration that a vehicle can
  withstand before wheel liftoff
• DLTR evasive manouevre stability
• Load transfer from one side of the vehicle to the
  other during a high speed lane change

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Fleet Distribution of SRT
SRT Distribution of Fleet
20
15
Percent
10
5
0
0.3
0.35 0.4
0.45 0.5
0.55 0.6
0.65 0.7
0.75 0.8
0.85 0.9
0.95 1
1.05 1.1
Static Roll Threshold (g)
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Crashed Vehicles Distribution of SRT
SRT Distribution of Crashed Vehicles
35
30
25
20
Percent
15
10
5
0
0.3
0.35 0.4
0.45 0.5
0.55 0.6
0.65 0.7
0.75 0.8
0.85 0.9
0.95 1
1.05 1.1
Static Roll Threshold (g)
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Relative Crash Rate as a Function of SRT
Relative Crash Rate vs SRT
5
4
3
Relative Crash Rate
2
1
0
0.3
0.35 0.4
0.45 0.5
0.55 0.6
0.65 0.7
0.75 0.8
0.85 0.9
Static Roll Threshold (g)
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SRT Conclusions

• Fleet distribution bi-modal
• 15 fleet have SRT lt 0.35g
• 40 crashed vehicles have SRT lt 0.35g
• Improving performance of the worst vehicles will
  have a significant impact on crash rates

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Fleet Distribution of DLTR
DLTR Distribution of the Fleet
18
16
14
12
10
8
6
4
2
0
0.05
0.15
0.25
0.35
0.45
0.55
0.65
DLTR
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Crashed Vehicles Distribution of DLTR
DLTR Distribution of Crashed Vehicles
30
25
20
15
10
5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
DLTR
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Relative Crash Rate as a Function of DLTR
Relative crash rate vs DLTR
3.5
3
2.5
2
1.5
1
0.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
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DLTR Conclusions

• Fleet distribution tri-modal
• increase in crash rate for DLTR gt 0.7
• limited evidence for significant effect of crash
  rate for lower DLTR
• Note that DLTR and SRT are not independent

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Levels for PBS

• SRT
• From crash data 0.4g-0.45g is desirable
• Internationally 0.35g minimum is widely suggested
• Higher targets affect too many vehicles and have
  too big an effect on productivity
• DLTR
• Internationally 0.6 maximum has been suggested
  but some debate
• From crash data 0.67 approximately equivalent
  effect to 035g SRT in New Zealand

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Potential Impact on Crash Rate

• 15 of vehicles below 0.35g SRT involved in 40
  of rollover crashes
• Reducing their crash rate to the average could
  reduce rollover crashes by more than 25
• SRT and DLTR are related. Improving one will
  improve the other

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SRT CalculatorDerivation and Validation

• Static Roll Threshold (SRT)
• Maximum lateral acceleration that a vehicle can
  withstand during steady speed cornering before
  the wheels on one side lift off.

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Static Roll Threshold Determination

• Experimentally through a tilt-table test
• Analytically by computer simulation
• SRT Calculator

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Tilt-Table Test

• Pros
• No vehicle instrumentation reqd
• No vehicle parameters reqd
• Cons
• Facility cost
• Testing cost
• Accuracy depends on good test procedures

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SRT by Computer Simulation

• Pros
• Cheaper than physical testing
• No instrumentation or measurements required
• Cons
• Detailed vehicle parameters needed
• Too costly for routine use
• Skilled analysts required to ensure accuracy

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2D Model Horizontal Forces
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2D Model Vertical Forces
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Simple 2D Rollover Model
Solving force and moment balance equations gives
a simple equation for SRT
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2D Model Complications

• Roll angle, ?, is the result of all the
  compliances in the vehicle. It is not simple to
  determine
• Two ends of the vehicle are not necessarily the
  same. Need to consider the interaction between
  them

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Graphical Method(Winkler et al)
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Graphical Method with Lash (Winkler et al)
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SRT Calculator Basic Assumptions

• Applied to a single vehicle unit with no more
  than two axle groups
• Two axle groups are connected by a rigid body
  i.e. chassis flex is not taken into account
• Suspension stiffnesses are approximated as linear
  i.e. constant rate but suspension lash is taken
  into account

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SRT Calculator Basic Method

• Develop equations for graphical method (see
  Schedule 1 in Dimensions and Mass Rule 41001)
• Equations are piecewise linear. Solve for
  transition points, checking for validity.
• SRT is maximum lateral acceleration for which a
  valid solution exists.

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Vehicle Parameters in Equations

• Sprung mass by axle group and Cg height
• Unsprung mass by axle group and Cg height
• Tyre vertical stiffness
• Tyre track width
• Suspension vertical stiffness
• Suspension roll stiffness
• Suspension track width
• Suspension roll centre height
• Suspension lash

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SRT Calculator Software Specifications

• User inputs known or easily obtained
• Web-based software
• Three versions
• Public on internet
• Level 1 Certifier generates compliance
  certificates for relatively standard vehicles
• Level 2 Certifier generates compliance
  certificates

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SRT Calculator Implementation

• Aim to minimise user data input requirements but
  maintain enough flexibility to represent key
  vehicle parameters accurately enough
• Assumptions on default parameter values are
  conservative so that actual SRT will be at least
  as high as calculator result

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Calculator Implementation -continued

• Vehicle width is assumed to be 2.5m tyre track
  width is back-calculated from tyre size and
  configuration
• Generic tyre properties based on size and
  configuration are used
• Standard axle and wheel masses for each vehicle
  type are assumed
• Empty sprung mass Cg height is assumed based on
  vehicle type
• Generic suspension parameters are embedded so
  that in many cases actual data are not needed

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Calculator Validation

• Tilt table test on a 4-axle trailer
• Comparison with results from Yaw-Roll simulations
  for a selection of vehicles

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Validation resultsTilt-table tests
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Validation resultsGeneric Suspensions
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Validation results User-Defined Suspensions
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Rollover Example
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SRT Requirements in Rule 41001

• Principle of Safety at Reasonable Cost
• SRT level 0.35g
• All heavy vehicles of Class NC and Class TD have
  to comply except for those on the exempt list

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SRT Requirements in Rule 41001Continued

• Distinction between compliance and certification
• All vehicles listed above must comply
• Only vehicles of Class TD with a load height
  greater than 2.8m need to be certified

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Using the SRT CalculatorBasics

• Start the calculator either
• On the internet at the LTSA site
  www.ltsa.govt.nz/srt-calculator
• Or for certifiers from the Start menu or the
  desktop icon SRT Calculator

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Vehicle Type Choice

• Affects default no of axles and tyre
  configurations but these can be changed
• Affects axle mass values and empty sprung mass Cg
  height which are embedded values
• For a semi-trailer only the rear bogey is
  analysed and it is treated as if it were an
  independent vehicle (like a simple trailer)

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No of Axles

• Choosing a vehicle type inserts a default number
  of front and rear axles. These should be changed
  if necessary
• Some basic error checking is done. Eg a
  semi-trailer must have zero front axles

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Main Data Entry Page

• Schematic showing vehicle type and axle
  configuration selected. If wrong go back.
• Data entry boxes have pop-up help on labels (not
  functioning on Netscape 4)

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Main Data Entry Page - Tyres

• For each axle tyre size and configuration should
  be selected
• Selection affects unsprung mass (standard wheel
  masses) value and Cg height
• Selection determines track width
• Calculator does not allow for the effects of low
  profile tyres as they are not significant

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Main Data Entry Page Axle Loads

• For each axle group, gross mass and tare mass
  must be entered
• Calculator automatically calculates payload mass
  and total mass as numbers are entered
• Payloads and totals are not correct until all
  data have been entered

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Main Data Entry Page Axle Loads continued

• Tare mass values should come from a weighbridge
  docket or from the manufacturer
• The gross mass should be based on either the
  current RUC value or a higher value specified by
  the operator
• Gross mass should not be the vehicle GVM unless
  requested by the operator
• Distribution of gross mass between axle groups is
  normally in proportion to the axle group load
  limits

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Main Data Entry Page Load Categories

• This is used to determine the payload Cg height
• Mixed Freight Assumes 70 of load mass is in
  bottom half of load space and 30 in the top half
• Uniform Density Assumes the payload Cg is at
  the vertical midpoint of the load space. Expects
  the load space to be symmetric about a horizontal
  axis.
• Other Requires the user to calculate the
  vertical position of the payload Cg. This option
  is not available to level 1 certifiers

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Main Data Entry Page Load Geometry

• For load types Mixed and Uniform, the load bed
  and load height are used to calculate the payload
  Cg
• Implicit assumption that the values are constant
  along the vehicle but
• Sloping decks/roofs use values at longitudinal
  midpoint (level 1 certifier)
• Step decks can use a weighted average of values
  based on load mass carried at each level (level 2
  certifier)
• Anything more complex use load category Other
  (level 2 certifier)

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Main Data Entry Page Load Geometry contd

• For load type Other the payload Cg height must be
  calculated by the user and entered explicitly
• A load height value must also be entered but this
  is only for inclusion on the certificate. It is
  not used in the calculations

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Main Data Entry Page Suspension Data

• Suspension type selection
• generic suspension data come from reported
  measurement results and are at the compliant end
  of the spectrum, i.e. resultant SRT will be lower
• user defined requires the user to input
  suspension parameters. These data must be
  obtained from the supplier or by measurement and
  documentary support should be kept.
• The user defined option is not available to
  level 1 certifiers

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Main Data Entry Page Suspension Data contd

• Suspension track width and lash can be easily
  measured
• Values can be entered for both generic and
  user defined suspension types
• NB Lash is the movement at the axle not at the
  spring hanger
• Ensure correct units are used

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Main Data Entry Page Suspension Data contd

• Generic displays the embedded suspension
  parameter values. These cannot be changed by the
  user
• Two types of generic air suspension
• Low roll stiffness type
• High roll stiffness type
• High roll stiffness type uses the axle as an
  anti-roll bar. This requires that
• Suspension has beam axle(s)
• Trailing arms are rigidly connected to the beam
  axle(s)
• If in doubt assume low roll stiffness type

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High roll stiffness type air suspension
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Main Data Entry Page Suspension Data for User
defined

• User defined requires suspension parameters to
  be entered.
• Care is required to ensure
• Correct units
• Roll stiffness is per axle
• Spring stiffness is per spring assuming two
  springs per axle
• Roll centre height is measured from the axle
  centre with ve upwards

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Main Data Entry Page Calculate SRT

• Some error checking is done on data entry but
  most is done when calculation is initiated
• Masses are limited to a maximum Vehicle Axle
  Index of 1.1.
• All input data is checked against upper and lower
  limits
• Equation solver assumes small roll angles (lt20)
  and this is checked
• If SRT is less than 0.35g, the calculator
  determines the reduced load height or reduced
  mass needed to achieve 0.35g

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SRT Results

• Calculated SRT is shown
• If below 0.35g reduced mass and reduced height to
  pass is shown
• Can use back button to return, modify inputs
  and recalculate or
• Certifiers can login to generate certificate

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SRT Greater than 0.35g
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SRT Less than 0.35g
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Certificate Pages

• After login certificate data page
• Info required for certificate has no effect on
  calculations
• Certifier details embedded in personalized copy
  of software
• Generate Certificate button creates a
  certificate in a format suitable for A4 printing
• Certificate includes all input data and hence can
  be used to replicate results
• Attach SRT Cert to LT 400

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Advanced topics in loading Removable bodies

• Eg stock-crates
• Option 1 Consider body as part of payload
• Option 2 Consider body as part of tare mass
• With load category Other option 1 is best
• Otherwise need to consider overall effect. Empty
  sprung mass Cg is assumed to be 0.56m above axle
  centre for a truck and 1.25m above the axle
  centre for a trailer. Which option is more
  realistic?

68
Advanced topics in loading Sloping Load Beds

• Determine longitudinal position of Cg
• Measure (or calculate) load bed height and load
  height at this location

69
Advanced topics in loading Variable height decks

• Load bed height Weighted average of the
  different heights using the proportion of payload
  mass carried as the weighting
• Alternatively can use load category Other and
  calculate the Cg of the payload explicitly

70
Advanced topics in loading No horizontal axis of
symmetry

• Use load category Other and calculate payload
  Cg height

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Advanced topics in loading Unit Loads

• Use load category Other and calculate payload
  Cg height
• Use worst case typical load
• Possible approaches include
• Obtain Cg heights from equipment suppliers
• Obtain maximum cross-slope capabilityfrom
  suppliers and calculate Cg height

72
Advanced topics in suspensions Generic
suspensions

• Parameter values derived from UMTRI factbook and
  based on measurements but do not represent any
  actual suspension
• Parameters selected to be at the more compliant
  end of the spectrum and thus give conservative
  estimates of SRT
• Provision for users to enter measured values for
  suspension track width and axle lash

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Generic Total Roll Stiffness

• Generic steer axle 130000 Nm/radian
• Generic steel 520000 Nm/radian
• Generic air (high stiffness) 780000
  NM/radian
• Generic air (low stiffness) 280000
  NM/radian

74
Generic Suspension Vertical Stiffness

• Generic steer axle 185000 N/m
• Generic steel 1000000 N/m
• Generic air 350000 N/m

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Generic Roll Centre Heights

• These are from the ground
• Standard wheel approx 0.5m radius
• Generic steer axle 0.48m
• Generic steel 0.7m
• Generic air 0.7m

76
Advanced topics in suspensions User defined
suspensions

• Must enter suspension make and model for
  traceability
• Three key parameters needed
• Composite roll stiffness
• Spring vertical stiffness
• Roll centre height
• To determine these requires sophisticated
  measurement techniques and analysis
• Thus the key data must be provided by the
  suspension supplier who must take responsibility
  for its accuracy and validity

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User defined suspensionsConversions

• Composite roll stiffness auxiliary roll
  stiffness roll stiffness from springs
• Any two of the above (with spring track width)
  can be used to calculate the third

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User defined suspensionsConversions continued

• For steel suspensions (with no anti-roll bar)
  auxiliary roll stiffness is usually relatively
  small (5-10 of total)
• For low roll stiffness air suspensions (trailing
  arms bushed on axle or no beam axle), the
  auxiliary roll stiffness is also relatively small
• For high roll stiffness air suspensions (trailing
  arms rigidly clamped or welded to the axle), the
  auxiliary roll stiffness is high (80 or more of
  the total roll stiffness)

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Composite Roll Stiffness

• Input value is per axle assuming all axles in the
  group of equal stiffness
• Manufacturer value may be per axle group. If
  this is the case, halve the value for a tandem
  and one-third it for a tridem.
• Roll stiffness is required in Nm/radian. It may
  be supplied in in-lb/degree. To convert multiply
  by 6.47
• Input value is per radian. Supplied data may be
  per degree. Make sure and convert if necessary.

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Spring Stiffness

• Input value is per spring assuming two
  springs/axle and all springs of equal stiffness
• For one spring/axle suspensions (eg camelback
  type) halve the spring stiffness values
• For unequal stiffness springs, average the spring
  stiffness. If unequal load share, use load share
  weightings to calculate weighted average
• Vertical stiffness is required in N/m. It may be
  provided in lb/in. To convert multiply by 175.13

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Roll Centre Height

• Input value measured from axle centre not the
  ground, i.e. independent of tyre size.
• Influenced by all linkages in suspension
• Determination by measurement is quite complex

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Advanced topics in suspensions Effects of
Parameter Changes

• Increased roll stiffness improves SRT
• If roll stiffness (relative to load) differs
  between ends of vehicle, increasing the stiffness
  of the softer one has more effect
• Large axle lash values have a negative impact on
  SRT
• Higher roll centres lead to a better SRT
• Improvements of the order of 10-15 are possible
  with suspension improvements