**A&D Technology , Inc.**  4622 Runway Blvd., Ann Arbor, MI 48108 PH: 734 -973 - 1111 FAX: 734 -973 - 1103

www.aanddtech.com 

### Vehicle Road Load Module

1 /2 R.Evans, R.Skinner 8/15/2011 **1.1 VEH.RO**  **AD.LO AD (** **VEH1)** The Veh1 is a utility module that contains the vehicle model for road load calculation. This module takes as an input the shaft speed and outputs the respective torque equivalent of road load that is used in the Dm1 module for the torq ue setpoint. **1.1.1 Road Load Model**  The model used to calculate the road load force , F RL [N], is given by:
J f RL 

### F F F F     (1) where F

f [N] is the friction, F  [N] the banking and F J [N] inertial forces , respectively. These load com ponents are defined as: 

### A Bv Cv F f 

###    2 (2) 

###   

### sin mg F  (3) 

### dt dv m F J 

###  (4) where A [N] , B [ [N·h/km ] and C [ N·h 2/(km) 2] are vehicle specific constants, v [ km/h ] is vehicle speed, m [kg] is the vehicle mass , g [m/s 2] is the acceleration due to gravity , and  is the road grade . E quation (2) can also be expressed as:
0 1 2 

### 2 1 R R air d f f 

### mgC v mgC v C A F 

   ( 5 ) Wh ere A f [m 2] is the frontal area of the vehicle, Cd [ ] is the coefficient of drag, ρ air [kg/m 3] is the density of air , CR2 [h 2/( km ) 2] is the second order coefficient of rolling friction for the vehicle, CR1 [h/km] is the first order coefficient of rolling friction , and CR0 [ ] is the zeroth order coeffici ent of rolling friction
. The vehicle speed is related to the engine shaft speed, n e [min - 1 ] , transmission ratio, k t [ ] , differential ratio, k d [ ], and loaded wheel radius, r [m] , by:



#     

      1000

1 60 1 2 e

d t 

### n k k r v 

d

t e 

### k k n r  12 . 0  (6 ) For a partial powertrain consisting only of an engine and transmission, the output shaft of the transmission is connected to a dynamometer. In this case, the dyno measures the speed and torque on the driveshaft. Since the driveshaft speed, n ds [rpm], is equal to:**A&D Technology , Inc.**  4622 Runway Blvd., Ann Arbor, MI 48108 PH: 734 -973 - 1111 FAX: 734 -973 - 1103

www.aanddtech.com 

### Vehicle Road Load Module

2/2 R.Evans, R.Skinner 8/15/2011 t e ds 

### k n n  Then equation (6) can be rewritten as:

d ds 

### k n r v  12 . 0  (7 ) The road load torque at the driveshaft , T RL [N], is related to the road load force F RL by :

d RLs RL 

### k F r T  (8 ) 

### 1.1.2 Dy**no Control** The Dyno control can b e realized by controlling the torque (based on RL and vehicle mass) and allowing the speed to be a result. The Dyno can also be controlled in speed (the integral of acceleration) according to a=F/m (F=ma) where F is the imbalanced force, m is the vehicle m ass and a is the calculated acceleration. The imbalanced torque is calculated according to:
RL dyno i 

### T T T
  (9 ) 

### Wh ere T

i 

### is the imbalanced torque and T dyno 

### is the torque measured by the inline torque meter of the dyno. The addition of requeste d brake torque ( T brake 

### ) from the driver model yields the following: brake RL dyno ib 

### T

T T T


  (10 ) 

### This imbalanced force should lead to an acceleration of the dyno according to: vehilce ib dyno 

### J T /   (11 ) 

### The mass of the vehicle translated into a rotational inertia Jvehicle 

### is calculated as: ) 2 /( 2 d t vehilce vehilce 

### k

k d m J   (12 ) 

### The Jvehicle 

### is a constant for a given vehicle arrangement