Method and apparatus to estimate automotive alternator belt slip as a function of battery voltage
An embodiment contemplates a method for determining belt slip in a vehicle. The vehicle includes an engine and an alternator rotatably coupled by an accessory drive belt. The accessory drive belt engaging a rotating member of the engine for driving a rotating member of the alternator. A battery voltage is measured. An estimated battery voltage is determined as a function of engine speed. The belt slip of the alternator is detected in response to a comparison of the estimated battery voltage and the measured battery voltage.
1. A method for determining belt slip in a vehicle, the vehicle including an engine and an alternator rotatably coupled by an accessory drive belt, the accessory drive belt engaging a rotating member of the engine for driving a rotating member of the alternator, the method comprising the steps of:
measuring a battery voltage;
determining an estimated battery voltage as a function of engine speed; and
detecting belt slip in response to a comparison of the estimated battery voltage and the measured battery voltage.
2. The method of claim 1 wherein the estimated battery voltage is determined as a function of an alternator voltage set point.
3. The method of claim 2 wherein the estimated battery voltage is determined by the following formula:
V b-est =−c 1 F dc +c 2
where V b-est is the estimated battery voltage, F dc is an alternator field duty cycle; c 1 is value based on a function of the engine speed, and c 2 is a value based on a function of the alternator voltage set point.
4. The method of claim 3 wherein c 1 and c 2 are retrieved from a look-up table.
5. The method of claim 4 wherein c 1 is determined by the following formula:
c
1
=
-
3
3
π
L
af
R
l
r
ω
egn
2
R
a
+
3
π
r
ω
egn
L
s
where L af is the mutual inductance between a single phase winding and the field winding, L s is the synchronous inductance, R l is the alternator to battery cable resistance, R a is the alternator internal resistance, r is the radius of the pulley of the alternator, and ω egn is the engine speed.
6. The method of claim 5 wherein c 2 is determined by the following formula:
c
2
=
(
2
R
a
-
3
π
r
ω
egn
L
s
+
R
l
)
V
set
2
R
a
+
3
π
r
ω
egn
L
s
where L s is the is the synchronous inductance, R l is the alternator to battery cable resistance, R a is the alternator internal resistance, r is the radius of the pulley of the alternator, ω egn is the engine rpm, and V set is the voltage set point.
7. The method of claim 6 wherein each combination of values for c 1 and c 2 are determined for a respective voltage set point V set and engine RPM ω egn .
8. The method of claim 7 wherein each of the combination values c 1 and c 2 are determined using a recursive least square function.
9. The method of claim 8 wherein determining each of the combination values c 1 and c 2 using the recursive least square function comprises the steps of:
(a) recording an engine rpm and voltage set point combination;
(b) calculating values c 1 and c 2 using the recursive least square function;
(c) fixing the values c 1 and c 2 when recursively updated values c 1 and c 2 converge; and
(d) storing the fixed values c 1 and c 2 in the look-up table in combination with the recorded engine rpm and voltage set point if the determined values c 1 and c 2 converge, otherwise returning to step (a).
10. The method of claim 1 wherein an indicator is actuated on the vehicle for providing notification of the belt slip condition when a difference between the measured voltage and estimated voltage is greater than a threshold for a predetermined period of time.
11. A belt slip detection system for detecting a slippage of an accessory drive belt, the accessory drive belt engaging a rotatable member of an engine for driving a rotatable member of an alternator, the belt slip detection system comprising:
a control module configured for determining a belt slip of the alternator as a function of a measured battery voltage and an estimated battery voltage, wherein the estimated battery voltage determined as a function an engine speed, wherein the control module determines whether the estimated battery voltage is greater than the measured battery voltage, and wherein the control module is configured to enable a driver-perceptible warning of the belt slip.
12. The belt slip detection system of claim 11 wherein the control module estimates the battery voltage using the following formula:
V b-est =−c 1 F dc +c 2
where V b-est is the estimated battery voltage, F dc is an alternator field duty cycle; c 1 is value based on a function of the engine rpm, and c 2 is a value based on a function of the alternator voltage set point.
13. The belt slip detection system of claim 12 further comprising a look-up table for storing a combination of values for c 1 and c 2 , wherein the combination of values for c 1 and c 2 are stored in relation to an associated voltage set point V set and an engine RPM ω egn .
14. The belt slip detection system of claim 13 wherein the control module determines the value c 1 using the following formula:
c
1
=
-
3
3
π
L
af
R
l
r
ω
egn
2
R
a
+
3
π
r
ω
egn
L
s
where L af is the mutual inductance between a single phase winding and the field winding, L s is the synchronous inductance, R l is the alternator to battery cable resistance, R a is the alternator internal resistance, r is the radius of the pulley of the alternator, and ω egn is the engine rpm.
15. The belt slip detection system of claim 14 wherein the control module determines the value c 2 using the following formula:
c
2
=
(
2
R
a
-
3
π
r
ω
egn
L
s
+
R
l
)
V
set
2
R
a
+
3
π
r
ω
egn
L
s
where L s is the synchronous inductance, R l is the alternator to battery cable resistance, R a is the alternator internal resistance, r is the radius of the pulley of the alternator, ω egn is the engine rpm, and V set , is the voltage set point determined by the engine control module.
16. The belt slip detection system of claim 15 wherein the control module determines the values c 1 and c 2 using a recursive least square function.
17. The belt slip detection system of claim 16 wherein the values c 1 and c 2 stored in the lookup table are determined by a learning program, the learning program identifies a respective voltage set point V set and engine RPM ω egn combination at which values c 1 and c 2 are determined, the learning program uses the recursive least square function to calculate the values c 1 and c 2 , the learning program identifies the values c 1 and c 2 when the recursively updated values c 1 and c 2 converge, the values c 1 and c 2 identified at convergence are stored in the lookup table along with the associated voltage set point V set and engine RPM ω egn .
18. The belt slip detection system of claim 11 wherein the control module is a battery control module.
19. The belt slip detection system of claim 11 further comprising a warning indictor for providing a notification of a determined belt slip condition when a difference between the measured voltage and estimated voltage is greater than a threshold for a predetermined period of time.
20. A method for determining belt slip in a vehicle, the vehicle including an engine and an alternator rotatably coupled by an accessory drive belt, the accessory drive belt engaging a rotating member of the engine for driving a rotating member of the alternator, the method comprising the steps of:
measuring an engine speed;
determining an expected alternator speed as a function of engine speed;
measuring a battery voltage;
determining a calculated alternator speed as a function of the measured battery voltage; and
detecting belt slip in response to a comparison of the calculated alternator speed and the expected alternator speed.