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Development of a program for determining losses in a CVT
Objective
Calculating of losses in a pushbelt CVT.
Methodology for the calculation of losses
1. evaluation of the corrent state of research regarding simulation and calculation
of losses in pushbelt CVT;
2. development of an alternative approach to determine losses in a pushbelt CVT;
3. implementation of the model in a Matlab routine;
4. results.
Development of a program for determining losses in a CVT
INPUT DATA
Manufacturer: Bosch Transmission Technology B.V.
Product name: 24/12/1,50/208,8
Design: push belt
Centre distance: 155 mm
Conical angle: 11属
Contact surfaces pro wheel: 432
Length: 656 mm
Segment width: 1,50 mm
Width: 34,3 mm
Height: 13,1 mm
Mass: 1050 g
Transmission ratio. 2,37
RPMIN:1500 1/min
RPMOUT: 633 1/min
TorqueIN: 120 Nm
TorqueOUT: 284 Nm
Development of a program for determining losses in a CVT
The changes made over the traditional model concern:
- the friction coefficient model;
- the influence of the transversal speed of the belt;
- the mathematical model used for the calculation of the absolute and relative
speeds of the belt;
-the adhesive friction between the various layers forming the transmission belt.
FRICTION COEFFICIENT
I used a mathematical model that approximates the behavior of a CVT with V-
belts: these particular kinds of belts have a section with an isosceles trapezoid
shape. They operate on pulleys that have the outer surface on which is a groove
also trapezoidal in shape. The friction coefficient becomes:
ALGORITHM FOR CALCULATING THE ABSOLUTE AND RELATIVE
SPEED
The hypothesis behind such mathematical model for calculating speeds is to
approximate the motion of the belt around the pulley with a chain transmission.
This model considers:
-transversal dynamics;
-longitudinal dynamics;
-contact between elements: it is modeled in one dimension, since there is no
relative velocity in radial and axial direction;
-the polygonal frequency: I approximate the operation of a CVT with a chain
transmission, because neighboring elements possess a certain distance to each
other depending on the specific design of the belt. Therefore the chain (or belt)
does not enter (or leave) the pulley continuously but in a discrete way.
Development of a program for determining losses in a CVT
Development of a program for determining losses in a CVT
TRANSVERSE FORCE AND SPEED
The friction force FR should be smaller than the maximum static friction force:
FR<FS=袖KFN. For rolling contact, the maximum friction force is determined using
the kinetic friction coefficient FS=袖KFN, because it deals with the transition from
partial to complete sliding. It is possible calculating the transverse force acting on
the belt.
Force and velocity components of a
sliding wheel that is actuated by a
small transverse force F
Development of a program for determining losses in a CVT
ADHESIVE CONTACT BETWEEN BANDS
Adhesion plays an essential role in rubber friction and is therefore an important
phenomenon that must be accounted. In the first model, it is assumed that the
contacting surfaces did not adhere. Actually, there are relatively weak
interactive forces between two bodies: it decrease very quickly as the distance
between the bodies increases. These forces lead, in most cases, to mutual
attraction and are known as adhesive forces.
Traditional model Own model
Primary pulley Secondary
pulley
Primary pulley Secondary
pulley
Torque loss due to segment
sliding relative to a pulley (Nm)
0,0094 0,0094 0,0082 0,0082
Pulley penetration loss (Nm) 0,2408 0,0416 0,2180 0,0376
Pulley wedge loss (Nm) 0,3112 0,1268 0,3110 0,0855
Losses (Nm)
(Watt)
0,5614
88,184
0,1778
11,785
0,5372
84,383
0,1313
8,7030
Transversal speed of the belt
(Nm)
0,2260 0,3094
Losses (Nm)
(Watt)
0,5614
88,184
0,1778
11,785
0,7632
119,88
0,4407
29,211
Total losses (Nm)
(Watt)
0,7393
99,969
1,2039
149,091
Development of a program for determining losses in a CVT
RESULTS

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Nicola Galluzzi - Research project presentation

  • 1. Development of a program for determining losses in a CVT Objective Calculating of losses in a pushbelt CVT. Methodology for the calculation of losses 1. evaluation of the corrent state of research regarding simulation and calculation of losses in pushbelt CVT; 2. development of an alternative approach to determine losses in a pushbelt CVT; 3. implementation of the model in a Matlab routine; 4. results.
  • 2. Development of a program for determining losses in a CVT INPUT DATA Manufacturer: Bosch Transmission Technology B.V. Product name: 24/12/1,50/208,8 Design: push belt Centre distance: 155 mm Conical angle: 11属 Contact surfaces pro wheel: 432 Length: 656 mm Segment width: 1,50 mm Width: 34,3 mm Height: 13,1 mm Mass: 1050 g Transmission ratio. 2,37 RPMIN:1500 1/min RPMOUT: 633 1/min TorqueIN: 120 Nm TorqueOUT: 284 Nm
  • 3. Development of a program for determining losses in a CVT The changes made over the traditional model concern: - the friction coefficient model; - the influence of the transversal speed of the belt; - the mathematical model used for the calculation of the absolute and relative speeds of the belt; -the adhesive friction between the various layers forming the transmission belt. FRICTION COEFFICIENT I used a mathematical model that approximates the behavior of a CVT with V- belts: these particular kinds of belts have a section with an isosceles trapezoid shape. They operate on pulleys that have the outer surface on which is a groove also trapezoidal in shape. The friction coefficient becomes:
  • 4. ALGORITHM FOR CALCULATING THE ABSOLUTE AND RELATIVE SPEED The hypothesis behind such mathematical model for calculating speeds is to approximate the motion of the belt around the pulley with a chain transmission. This model considers: -transversal dynamics; -longitudinal dynamics; -contact between elements: it is modeled in one dimension, since there is no relative velocity in radial and axial direction; -the polygonal frequency: I approximate the operation of a CVT with a chain transmission, because neighboring elements possess a certain distance to each other depending on the specific design of the belt. Therefore the chain (or belt) does not enter (or leave) the pulley continuously but in a discrete way. Development of a program for determining losses in a CVT
  • 5. Development of a program for determining losses in a CVT TRANSVERSE FORCE AND SPEED The friction force FR should be smaller than the maximum static friction force: FR<FS=袖KFN. For rolling contact, the maximum friction force is determined using the kinetic friction coefficient FS=袖KFN, because it deals with the transition from partial to complete sliding. It is possible calculating the transverse force acting on the belt. Force and velocity components of a sliding wheel that is actuated by a small transverse force F
  • 6. Development of a program for determining losses in a CVT ADHESIVE CONTACT BETWEEN BANDS Adhesion plays an essential role in rubber friction and is therefore an important phenomenon that must be accounted. In the first model, it is assumed that the contacting surfaces did not adhere. Actually, there are relatively weak interactive forces between two bodies: it decrease very quickly as the distance between the bodies increases. These forces lead, in most cases, to mutual attraction and are known as adhesive forces.
  • 7. Traditional model Own model Primary pulley Secondary pulley Primary pulley Secondary pulley Torque loss due to segment sliding relative to a pulley (Nm) 0,0094 0,0094 0,0082 0,0082 Pulley penetration loss (Nm) 0,2408 0,0416 0,2180 0,0376 Pulley wedge loss (Nm) 0,3112 0,1268 0,3110 0,0855 Losses (Nm) (Watt) 0,5614 88,184 0,1778 11,785 0,5372 84,383 0,1313 8,7030 Transversal speed of the belt (Nm) 0,2260 0,3094 Losses (Nm) (Watt) 0,5614 88,184 0,1778 11,785 0,7632 119,88 0,4407 29,211 Total losses (Nm) (Watt) 0,7393 99,969 1,2039 149,091 Development of a program for determining losses in a CVT RESULTS