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MF_lateral.py
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'''
Pacejka Tire Model
Calculate parameters and forces of lateral dynamics ONLY
B: Stiffness factor
C: Shape factor
D: Peak factor
E: Curvature factor
Sh: Horizontal shift
Sv: Vertical shift
'''
import numpy as np
import os
import warnings
import yaml
import math
class MF_lateral:
def __init__(self, filename, data_path):
self.param_tires = {}
for ele in filename:
self.param_tires[ele] = self.load_params(ele, data_path)
self.epsilon = 1e-6
self.zeta = 1
def online_params(self, Fz, p, gamma, kappa, alpha, Vcx, tire_select):
self.params = self.param_tires[tire_select]
self.Fz = Fz
self.p = p
self.gamma = gamma
self.kappa = kappa
self.alpha = alpha
self.Vcx = Vcx
self.Vsx = -self.kappa * np.abs(self.Vcx)
self.Vsy = np.tan(self.alpha) * np.abs(self.Vcx)
self.Vs = np.sqrt(np.power(self.Vsx,2) + np.power(self.Vsy,2))
self.LMUY_star = self.params['LMUY'] / (1 + self.params['LMUY'] * self.Vs / self.params['LONGVL'])
self.LMUY_prime = self.LMUY_star / (1 * self.LMUY_star)
self.Fz0_prime = self.params['LFZO'] * self.params['FNOMIN']
# Unpack Parameters
self.dfz = (self.Fz - self.Fz0_prime) / self.Fz0_prime
self.dpi = (self.p - self.params['NOMPRES']) / self.params['NOMPRES']
def load_params(self, filename, data_path):
data_ls = [data for data in os.listdir(data_path)]
idx_ls = [idx for idx, ltr in enumerate(data_ls) if filename in ltr]
name = data_ls[idx_ls[0]]
with open(data_path + name, 'r') as stream:
try:
parsed_yaml = yaml.safe_load(stream)
except yaml.YAMLError as exc:
print(exc)
return parsed_yaml
def calculateFy0(self):
Fz = self.Fz
# [SCALING_COEFFICIENTS]
LCY = self.params['LCY'] # Scale factor of Fy shape factor
LEY = self.params['LEY'] # Scale factor of Fy curvature factor
LKY = self.params['LKY'] # Scale factor of Fy cornering stiffness
LHY = self.params['LHY'] # Scale factor of Fy horizontal shift
LVY = self.params['LVY'] # Scale factor of Fy vertical shift
LKYC = self.params['LKYC'] # Scale factor of camber force stiffness
# [LATERAL_COEFFICIENTS]
PCY1 = self.params['PCY1'] #Shape factor Cfy for lateral forces
PDY1 = self.params['PDY1'] #Lateral friction Muy
PDY2 = self.params['PDY2'] #Variation of friction Muy with load
PDY3 = self.params['PDY3'] #Variation of friction Muy with squared camber
PEY1 = self.params['PEY1'] #Lateral curvature Efy at Fznom
PEY2 = self.params['PEY2'] #Variation of curvature Efy with load
PEY3 = self.params['PEY3'] #Zero order camber dependency of curvature Efy
PEY4 = self.params['PEY4'] #Variation of curvature Efy with camber
PEY5 = self.params['PEY5'] #Variation of curvature Efy with camber squared
PKY1 = self.params['PKY1'] #Maximum value of stiffness Kfy./Fznom
PKY2 = self.params['PKY2'] #Load at which Kfy reaches maximum value
PKY3 = self.params['PKY3'] #Variation of Kfy./Fznom with camber
PKY4 = self.params['PKY4'] #Curvature of stiffness Kfy
PKY5 = self.params['PKY5'] #Peak stiffness variation with camber squared
PKY6 = self.params['PKY6'] #Fy camber stiffness factor
PKY7 = self.params['PKY7'] #Vertical load dependency of camber stiffness
PHY1 = self.params['PHY1'] #Horizontal shift Shy at Fznom
PHY2 = self.params['PHY2'] #Variation of shift Shy with load
PVY1 = self.params['PVY1'] #Vertical shift in Svy./Fz at Fznom
PVY2 = self.params['PVY2'] #Variation of shift Svy./Fz with load
PVY3 = self.params['PVY3'] #Variation of shift Svy./Fz with camber
PVY4 = self.params['PVY4'] #Variation of shift Svy./Fz with camber and load
PPY1 = self.params['PPY1'] #influence of inflation pressure on cornering stiffness
PPY2 = self.params['PPY2'] #influence of inflation pressure on dependency of nominal tyre load on cornering stiffness
PPY3 = self.params['PPY3'] #linear influence of inflation pressure on lateral peak friction
PPY4 = self.params['PPY4'] #quadratic influence of inflation pressure on lateral peak friction
PPY5 = self.params['PPY5'] #Influence of inflation pressure on camber stiffness
Kya = PKY1 * self.Fz0_prime * (1 + PPY1 * self.dpi) * (1 - PKY3 * abs(self.gamma)) * np.sin(PKY4 * np.arctan((Fz / self.Fz0_prime) /
((PKY2+PKY5 * np.power(self.gamma,2)) * (1+PPY2 * self.dpi)))) * self.zeta * LKY
SVyg = Fz * (PVY3 + PVY4 * self.dfz) * self.gamma * LKYC * self.LMUY_prime * self.zeta
# MF6.1 and 6.2 equatons
Kyg0 = Fz * (PKY6 + PKY7 * self.dfz) * (1 + PPY5 * self.dpi) * LKYC
signKya = np.sign(Kya)
SHy = (PHY1 + PHY2 * self.dfz) * LHY + ((Kyg0 * self.gamma - SVyg) / (Kya + self.epsilon * signKya)) * self.zeta + self.zeta - 1 # (4.E27)
SVy = Fz * (PVY1 + PVY2 * self.dfz) * LVY * self.LMUY_prime * self.zeta + SVyg # (4.E29)
# low speed mode
Wvlow = 0.5 * (1 + np.cos(np.pi * (self.Vcx / self.params['VXLOW'])))
self.rdctSmth = 1 - Wvlow
if self.Vcx < self.params['VXLOW']:
SVy *= self.rdctSmth
SHy *= self.rdctSmth
alphay = self.alpha + SHy # (4.E20)
Cy = PCY1 * LCY # (4.E21)
muy = (PDY1 + PDY2 * self.dfz) * (1 + PPY3 * self.dpi + PPY4 * np.power(self.dpi,2)) * (1 - PDY3 * np.power(self.gamma,2)) * self.LMUY_star # (4.E23)
Dy = muy * Fz * self.zeta # (4.E22)
signAlphaY = np.sign(alphay)
Ey = (PEY1 + PEY2 * self.dfz) * (1 + PEY5 * np.power(self.gamma,2) - (PEY3 + PEY4 * self.gamma) * signAlphaY) * LEY # (<=1)(4.E24)
# Limits check
if Ey>1:
warnings.warn("Warning CoeffChecks: Ey over limit (>1), Eqn(4.E14)")
Ey = 1
signDy = np.sign(Dy) # If [Dy = 0] then [sign(0) = 0]. This is done to avoid [Kya / 0 = NaN] in Eqn 4.E26
By = Kya / (Cy * Dy + self.epsilon * signDy) # (4.E26) [sign(Dy) term explained on page 177]
Fy0 = Dy * np.sin(Cy * np.arctan(By * alphay - Ey * (By * alphay - np.arctan(By * alphay))))+ SVy # (4.E19)
muy = 0 if Fz == 0 else muy
params = {
'By': By,
'Cy': Cy,
'Dy': Dy,
'Ey': Ey,
'SVy': SVy,
'SHy': SHy,
'muy': muy
}
return Fy0, params
def calculateFy(self):
Fz = self.Fz
kappa = self.kappa
alpha_star = self.alpha
gamma_star = self.gamma
Fy0, params = self.calculateFy0()
muy = params['muy']
# [SCALING_COEFFICIENTS]
LYKA = self.params['LYKA'] # Scale factor of alpha influence on Fx
LVYKA = self.params['LVYKA'] # Scale factor of kappa induced Fy
# [LATERAL_COEFFICIENTS]
RBY1 = self.params['RBY1'] # Slope factor for combined Fy reduction
RBY2 = self.params['RBY2'] # Variation of slope Fy reduction with alpha
RBY3 = self.params['RBY3'] # Shift term for alpha in slope Fy reduction
RBY4 = self.params['RBY4'] # Influence of camber on stiffness of Fy combined
RCY1 = self.params['RCY1'] # Shape factor for combined Fy reduction
REY1 = self.params['REY1'] # Curvature factor of combined Fy
REY2 = self.params['REY2'] # Curvature factor of combined Fy with load
RHY1 = self.params['RHY1'] # Shift factor for combined Fy reduction
RHY2 = self.params['RHY2'] # Shift factor for combined Fy reduction with load
RVY1 = self.params['RVY1'] # Kappa induced side force Svyk./Muy.*Fz at Fznom
RVY2 = self.params['RVY2'] # Variation of Svyk./Muy.*Fz with load
RVY3 = self.params['RVY3'] # Variation of Svyk./Muy.*Fz with camber
RVY4 = self.params['RVY4'] # Variation of Svyk./Muy.*Fz with alpha
RVY5 = self.params['RVY5'] # Variation of Svyk./Muy.*Fz with kappa
RVY6 = self.params['RVY6'] # Variation of Svyk./Muy.*Fz with atan(kappa)
DVyk = muy * Fz * (RVY1 + RVY2 * self.dfz + RVY3 * gamma_star) * np.cos(np.arctan(RVY4 * alpha_star)) * self.zeta # (4.E67)
SVyk = DVyk * np.sin(RVY5 * np.arctan(RVY6 * kappa)) * LVYKA # (4.E66)
SHyk = RHY1 + RHY2 * self.dfz # (4.E65)
Eyk = REY1 + REY2 * self.dfz # (<=1) (4.E64)
Cyk = RCY1 # (4.E63)
Byk = (RBY1 + RBY4 * np.power(gamma_star,2)) * np.cos(np.arctan(RBY2 * (alpha_star - RBY3))) * LYKA # (> 0) (4.E62)
kappas = kappa + SHyk # (4.E61)
if Eyk>1:
warnings.warn("Warning CoeffChecks: Ey over limit (>1), Eqn(4.E14)")
Eyk = 1
Gyk0 = np.cos(Cyk * np.arctan(Byk * SHyk - Eyk * (Byk * SHyk - np.arctan(Byk * SHyk)))) # (4.E60)
Gyk = np.cos(Cyk *np.arctan(Byk * kappas - Eyk * (Byk * kappas - np.arctan(Byk * kappas)))) / Gyk0 # (> 0)(4.E59)
# Low speed model
Vx = self.Vcx
if Vx <= self.params['VXLOW']:
SVyk *= self.rdctSmth
Fy = Gyk * Fy0 + SVyk # (4.E58)
return Fy, Gyk