MS4031 – Teknik Kendaraan (Rel)

Modul-6: Longitudinal Train DynamicsTRACTION FORCE & ROLLING RESISTANCE

Yunendar Aryo Handoko ST., PhD

Fakultas Teknik Mesin dan Dirgantara

TRAIN RUNING PERFORMANCE• Transport capacity

• Train composition

• Number of passenger or tonnage of freight

• Headway• Acceleration

• Maximum speed

• Dwelling time• Loading unloading

• Affect Total travelling time

• Redundancy - Realibility• Minimum requirement

2

Acc Coast Dec Dwel

TRANSFORMASI ENERGI MENJADI GAYA GERAK

Lokomotif Diesel & KRD Lokomotif Listrik & KRL

DE

DH

TRAIN RUNING PERFORMANCE – KONSUMSI ENERGI

POWER AND TRACTIVE EFFORT

𝑇𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝐸𝑓𝑓𝑜𝑟𝑡 =𝑃𝑜𝑤𝑒𝑟 𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑓𝑜𝑟 𝑇𝑟𝑎𝑐𝑡𝑖𝑜𝑛

𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦

Gross power generated by diesel engine

Locomotive power available for traction

(Torque x rpm)

Electrical Power to Motors

(volts x amp)

Power at rail (tractive effort at

wheel rim x speed)

85 % Power left for hauling train

W

POWER AND TRACTIVE EFFORT

POWER AND TRACTIVE EFFORT

TYPICAL TRACTIVE EFFORT DIAGRAM OF LOCOMOTIVE

Tractive Effort – Notch & Adhesion Limit

GAYA-GAYA LONGITDINAL YANG BEKERJA PADA KERETA SAAT TRAKSI

TOTAL GAYA YANG MELAWAN ARAH TRAKSI DISEBUT SEBAGAI ROLLING RESISTANCE

ROLLING RESISTANCE

Fundamental Formula (Davis Equation)

• A quadratic formula has been used for over 80 years to approximate rail vehicle resistance

• Von Borries Formel, Leitzmann Formel, Barbier and Davis worked on this equation:

R = A + BV + CV2

where R is the rail vehicle resistance (N), V is the velocity of the vehicle (m/s), and A (N), B (N s/m) and

C (Ns2 / m2 ) are regression coefficients obtained by fitting test data to the Davis equation.

NOTE:

The coefficients A and B in the Davis equation account for mass and mechanical resistance

The coefficient C accounts for air resistance (proportional to the square of the speed)

The Davis equation has been modified over the years for various rail systems and configurations

Example of Rolling Resistance Formula Derived from Davis Equation

where:RG is the resistance (kN) due to gradients, M is the mass of the train in tons g is the acceleration due to gravity (m/s2) X is the gradient in the form 1 in X (for example: a grade of 3% is expressed as X = 1/0.03 = 33.33 in the formula above)

Additional Terms to the Davis Equation(Gradient Forces)

Additional Terms to the Davis Equation(Resistance due to Curvature)

where:rc is the resistance due to curvature (kN/ton)k is dimensionless parameter depending upon the train (varies from 500 to 1200)RC is the curve radius in a horizontal plane (meters).

EXAMPLE PLOT OF ROLLING RESISTANCE AND TRACTIVE EFFORT VS SPEED

LOCOMOTIVE PERFORMANCE 2200 HP (1700 KW)

LOK CC 300 - INKA LOK CC 201 - GE

LOK CC 300 - INKA LOK CC 201 - GE

LOCOMOTIVE PERFORMANCE 2200 HP (1700 KW) – Hauling Load

HIYDRAULIC LOCOMOTIVE CC 300TRACTIVE EFFORT VS ROLLING RESISTANCE

Contoh Tugas Kasus PerhitunganTraction Performance

21

• Condition• Power available for traction = 1000 kW• Car Weight: MC=50 ton, TC=48 ton• Wheel-Rail adhesion = 0.22 (for traction performance calculation)• Running resistance formula (in kgf):

• R = (1.65 + 0.0247 x V) x Wm + (0.78 + 0.0028 x V) x Wt + (0.028 + 0.0078 x (n-1)) x V2

• Starting resistance 4 kgf/ton• V = train speed (km/h)• Wm = weight of motor car (ton)• Wt = weight of trailer car (ton)• n = number of car per trainset

TC TC TC MCMC

Konfigurasi Rangkaian Kereta

Profil Trek

A

B

C

𝛼

𝛽

Rangkaian kereta menempuh perjalanan dari A ke C melewati 2 petak jalan AB dan BC yang mempunyaigradien berbeda (𝛼 = 4 %0 , 𝛽= 10 %0 )

Tugas:1. Buatlah traction performance diagram (TE vs Kecepatan dan Pecepatan vs Kecepatan) dari rangkaian kereta

tersebut.2. Hitung kecepatan maksimum yang dapat dicapai rangkaian kereta pada lintas datar (gradien =0) dan pada

gradien 15 %0.

3. Jika kereta berangkat dari titik A, hitung kecepatan pada titik B dan C, serta waktu yang diperlukan untukmenempuh A ke C – asumsi kereta selalu berjalan dengan kondisi traksi maksimum.

Problem: