Railway Design - Curves and Cant Connections - PDF

Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway layout (b) Andrea Baliello | Engineer 5b. Railway design 1 ...

Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway layout (b) Andrea Baliello | Engineer 5b. Railway design 1  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Curves and cant connections Introduction For a better comfort, in the design of railway lines, it is expected the inclusion of: ▪ Cant connections between the straight and the curve (where there is a cant) or between two circular curve (composed curves) ▪ Transition curves (variable radius) between the straight and the circular curve or between two circular curve (composed curves) The parameters taken into account for the design of cant connections are: a) the recoil r b) the roll velocity ω c) the lifting velocity Vl. Andrea Baliello | Engineer 5b. Railway design 2  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Curves and cant connections a) Recoil As in the case of roads, there is a design parameter that links the kinematic characteristics with the geometrical characteristics of the planimetric layout: the recoil r, occurring when the vehicle passes from the straight trajectory to the curvilinear trajectory, and vice versa. ▪ When the train passes from one infinite radius to a finished one, due to the brusque application of the centrifugal force, a variation of transversal not- compensated centrifugal acceleration happens in the time t: anc r= [m/s3] t *** This value influences the ride comfort of the passengers Andrea Baliello | Engineer 5b. Railway design 3  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Curves and cant connections a) Recoil Assuming that the connection with length l is covered with a constant speed v: l t= L [km/h] v [m/s] t [s] v anc  v V in [km/h] anc  V r= [m/s3] r= [m/s3] l 3,6  l Andrea Baliello | Engineer 5b. Railway design 4  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Curves and cant connections a) Recoil Basing on experimental experience, comfort can be put in relation with the recoil: → r ≤ 0.30 m/s3 excellent comfort → 0.30 < r ≤ 0.45 m/s3 good comfort → 0.45 < r ≤ 0.70 m/s3 acceptable comfort → 0.70 < r ≤ 0.85 m/s3 exceptionally acceptable comfort Andrea Baliello | Engineer 5b. Railway design 5  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Curves and cant connections b) Roll velocity The roll velocity ω is the angular velocity of a railway vehicle (considered rigid and with a negligible length), that rotates around the support point on the inner rail in the perpendicular plane with respect to the motion direction : h = [rad/s] d t where: h: cant [mm] d: distance of the two rails ≈ 1500 mm t: travel time during the connection [s] Andrea Baliello | Engineer 5b. Railway design 6  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Curves and cant connections b) Roll velocity Assuming that the connection with length l is covered with a constant speed v: l t= L [km/h] v [m/s] t [s] v hv V in [km/h] h V = [rad/s] = [rad/s] d l 3,6  d  l Andrea Baliello | Engineer 5b. Railway design 7  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Curves and cant connections c) Lifting speed The lifting speed Vl is equal to the vertical component of the outer wheel speed, when the train drives during the cant connection: h V Vl = [mm/s] 3,6  l where: h: cant [mm] V: speed [km/h]mm l: length of cant connection [m] ▪ The French railways have identified in the range 60 ÷ 117 mm/s the sensitivity limit of lifting speed, corresponding to a recoil equal to 0.80 m/s3 Andrea Baliello | Engineer 5b. Railway design 8  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Curves and cant connections Limit values for c, ω and Vl On the ordinary Italian network, the limit values of r, ω and Vl are fixed for different rank speed, i.e. for different anc anc [m/s2] r [m/s2] ω [rad/s] Vl [mm/s] 0.60 0.25 0.036 54 0.80 0.35 0.038 57 ** Exceptionally or 1.00 0.40** 0.040 60 temporarily 0.6 m/s3 ▪ In Italian high speed system, recoil r is set equal to 0.15 m/s3 (exceptionally it can reach up to 0.25 m/s3) and the lifting speed Vl is equal to 23.4 mm/s ▪ Once chosen the situation, cant length can be determined: anc  V h V h V l= [m] l= [m] l= [m] 3,6  r 3,6  d   3,6  Vl Andrea Baliello | Engineer 5b. Railway design 9  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Curves and cant connections Cant connection In some network (Swiss, Portuguese, Japanese) the cant is achieved, for half space, raising linearly the outer rail and, for the other half space, lowering linearly the inner rail. Rounding ▪ Practical difficulties in the Linear connection realization of a similar geometry have induced Rounding almost all of the railway networks to realize the connection by varying linearly the height of the outer rail (with a constant slope) and rounding at the beginning and the end of the same Andrea Baliello | Engineer 5b. Railway design 10  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Curves and cant connections Cant connection Otherwise, despite the simplicity of linear cant connection construction and maintenance, it is desirable to use a cant connection with the biquadratic or sinusoidal cant connection. These types of cant connection involve an increase of maximum slope, but avoid the abrupt changes of r and ω both at the beginning and at the end of the cant connection (more comfort) ▪ Experiments have demonstrated the advantages of sinusoidal cant connection (with regard to the vertical accelerations, especially at curve exits) ▪ Also in the high speed lines, it is used the linear cant connection for the construction and maintenance simplicity Andrea Baliello | Engineer 5b. Railway design 11  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Curves and cant connections Cant connection Bi-quadratic connection Sinusoidal connection Andrea Baliello | Engineer 5b. Railway design 12  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Curves and cant connections Cant connection During the cant connection: Slope Recoil Roll velocity Lifting velocity Constants Slope of vertical connection Railway allowable speed p = 3.0 ‰ v ≤ 50 Km/h Examples: p = 1.25 ‰ v ≥ 125 Km/h Andrea Baliello | Engineer 5b. Railway design 13  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Curves and cant connections Planimetric transition curve The planimetric connection is introduced in the transition between straight line and circular curve (or between two circular curve) to overcome some problems: ▪ the occurrence of abnormal motions for the instantaneous application/end of centrifugal force (the higher the force amount, the higher the abnormal motion); ▪ the vehicle approach to the inner rail in the straight line (cant connection) and the subsequent abrupt wheel shift on the outer rail on the curve beginning. The connection are intended to define a gradual change of: ▪ the curvature ▪ the transversal acceleration ▪ the cant → Time by time, the centrifugal force is balanced with the weight components Andrea Baliello | Engineer 5b. Railway design 14  Department of Civil, Architectural and Environmental Engineering Course: Railways and Airports Railway design Curves and cant connections Planimetric transition curve The planimetric connection must: ▪ start at the same point of cant connection ▪ have the same length of cant connection ▪ produce a linear centrifugal acceleration application The transition curves (variable radius of curvature) are inserted: ▪ between the straight line and the circular curve with radius R ▪ between two circular curves with different radius (called compound curves) Andrea Baliello | Engineer 5b. Railway design 15