Parking Brake Effectiveness Calculations

This section details how the parking brake effectiveness of railway vehicles is determined, including holding capacity and gradient calculations. This information is taken from UIC Leaflet 544-1 [1].

1. Definition of Parking Brake Effectiveness

The effectiveness of the parking brake is expressed as the braked weight [t] corresponding to the braking of a vehicle starting from low speed [1, 2]. The braked weight, whether calculated or determined, is always expressed as whole numbers; values of 0.5 are rounded down while values ≥ 0.5 are rounded up [Glossary].

Where:

• Bh: Braked weight of hand brake [t] [3].
• ΣFdyn: Total dynamic force acting on blocks or shoes when parking brake is applied with nominal force [kN] [4]. (See Appendix F, item F.2.5 to determine ΣFdyn [4]).
• μ1: Friction coefficient at 50 km/h for the relevant friction materials [-] [4].
  • Cast iron blocks: 0.19 [4]
  • Composite blocks: 0.20 [4]
  • Sintered blocks: 0.20 [4]
  • LL blocks: 0.17 [4]
  • Composite pads: 0.35 [3]
  • Sintered pads: 0.30 [3]
• rm: Mean friction radius (rm=rh for block brakes) [m] [3].
• rh: Half-worn wheel radius [m] [3].

2. Applied Nominal Force

In parking brake calculations, the applied nominal force is as follows [3, 5]:

• For screw brake: 0.5 kN force at wheel or lever handle [3, 5].
• For spring-loaded brake: Load applied by spring at nominal stroke when brake is applied and no neutralizing spring force exists [3, 5].

3. Calculation Methods

3.1. Manual Control with Screw Brake

3.1.1. Block Brakes

For vehicles equipped with block brakes, the Fb block brake force is calculated with the following equation [5, 6]:

Where:

• Fb: Total static force applied on blocks on braked axles by screw brake [kN] [6].
• FK: Force at handwheel or lever (0.5 kN) [kN] [6].
• FF: Force applied by brake shoe pull spring (typically 1.5 kN) [kN] [6].
• FR: Opposing force of adjuster (typically 2 kN) [kN] [6].
• iH: Total multiplication ratio for screw brake [-] [7].
• iP: Total multiplication ratio for air brake [-] [7].
• iR: Multiplication ratio behind brake rod adjuster. Normally iR is twice the number of axles braked using screw brake [-] [7].
• ηH: Factor representing static efficiency of force transfer from handwheel or lever to brake blocks (= 0.19) [-] [7].
• ηP: Factor representing static efficiency of air brake axle brake rod (= 0.8) [-] [7].
• ηR: Factor representing static efficiency of axle brake rod behind adjuster (= 0.9) [-] [7].

In this case, ΣFdyn for Bh is 9/8 of Fb [8].

3.1.2. Disc Brakes

For vehicles equipped with disc brakes, the Fb shoe force is calculated with the following general equation [8]:

Where:

• Fb: Total force applied on shoes [kN] [8].
• FK: Total force at handwheel or lever (0.5 kN) [kN] [8].
• FR: Counterbalance force of brake cylinder [kN] [8].
• ns: Number of disc brake units [-] [8].
• iH: Total multiplication ratio of screw brake [-] [8].
• iR: Multiplication ratio of air brake shoe [-] [8].
• ηH1: Factor representing static efficiency of screw (= 0.25) [-] [9].
• ηH2: Factor representing static efficiency of force transfer between screw and shoes or shoe housings [-] [9].
• ηR: Factor representing static efficiency of air brake axle brake rod (= 0.9) [-] [9].

In this case, ΣFdyn for Bh equals Fb [9].

3.2. Spring-Loaded Brakes

For spring-loaded brakes, Fb is calculated similarly [10]:

Where:

• Fb: Total static force applied on brake blocks or pads [kN] [10].
• Fsp: Net force applied by spring cylinder at output when spring brake is applied [kN] [10].
• isp: Multiplication ratio between spring brake cylinder and blocks or pads [-] [10].
• ηfi: Factor representing static efficiency of force transfer between spring brake cylinder and blocks or pads [-] [10].
  • ηfi = 1 if spring brake is applied directly to blocks [10]
  • ηfi = 0.9 if spring brake is applied to disc through lining [11]
  • Smaller value if force transfer is more complex and must be determined by measurement [11]
• nFed: Number of spring brake cylinders [-] [11].

In this case, ΣFdyn for Bh equals Fb [11].

4. Calculation of Maximum Gradient for Vehicle Retention with Parking Brake

The maximum gradient on which a vehicle with a specific parking brake type can be safely held stationary is calculated with the following equation [11]:

Where:

• ims: Gradient steepness [‰] [12].
• Fb: Calculated total static force applied on wheel blocks or pads by handwheel [kN] [12].
• μstat: Friction coefficient at 0 km/h for specific friction material [-] [12].
  • Cast iron blocks: 0.35 [12]
  • Composite blocks: 0.20 [13]
  • Sintered blocks: 0.20 [13]
  • LL blocks: 0.17 [13]
  • Composite pads: 0.35 [13]
  • Sintered pads: 0.30 [13]
• rm: Mean friction radius (rm=rh for block brakes) [m] [12].
• rh: Half-worn wheel radius [m] [12].
• m: Vehicle weight [t] [12].
• g: Gravitational acceleration [9.81 m/s²] [12].

5. Required Maximum Adhesion

The braking force generated at the wheel tread (Fb × μstat × rm / rh) is only valid up to the maximum adhesion level (τ_wheel/rail = 0.12) for each axle in a wagon with parking brake applied [13]. If the calculated braking force exceeds this value, the holding force for required maximum adhesion can be considered [13].

When braking load and vehicle load are evenly distributed across all wheelsets, the adhesion requirement at each calculation step or deceleration section (despite running resistance) can be checked using the following formula [14, 15]. The adhesion requirement must not exceed the 0.15 limit under any load condition [14].

Where:

• τi: Adhesion coefficient between wheel and rail at time "i" [-] [15].
• Fc: Braking force at calculation step "i" [kN] [15].
• m: Test vehicle mass [t] [15].
• ai: Deceleration at time "i" [m/s²] [15].
• g: Gravitational acceleration [9.81 m/s²] [15].

Source: UIC Leaflet 544-1, 4th Edition, October 2004.

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