Force Estimation of an Asymmetrical Pantograph for Different Damper Positions

Different pantographs are currently used in train vehicles around the world. With the exception of the Shinkansen 500 series telescopic pantograph, all high-speed railway pantographs are of the two-stage type1. The main characteristic of a pantograph is to assure a good current collecting, without interruptions of the current regardless of the height of the pantograph. For this, it is necessary for the pantograph to have a contact plan irrespective of the movement of the mechanical articulated system, a small inertia, a good lateral and transversal stability, to obtain in static and dynamic regime a contact pressure irrespective of the string height, and have a low sensibility at the aerodynamics effects. More of this, the pantograph needs to have a crosshead slipper with an adequate shape and way of suspension for the contact characteristics. Its shape, size and fixation depend on the characteristics of the electric current, on the geometrical characteristics of the contact line2 especially on the catenary irregularities which may cause serious fluctuation of contact force, even leading to the pantograph coming off the catenary3. In the general nonlinear model, the pantograph model is represented in terms of the following kinematic linkages: a lower frame arm, an upper frame arm and a head link. The entire mechanism is raised by a torque applied to a link of the arm. A frame suspension model provides an uplift force to the pantograph. The input force is assured by a suspension, usually a resort or pneumatic system (actuator) which acts horizontally, applying a torque to the lower arm. This input force may vary in time and has to overcome the weight of the mechanism but also must provide the uplift force against the wire4. In some cases there are used only dampers (resorts) to assure the uplift force, as for the pantograph for the Korean high speed train5. The model of the pantograph can be realized with two masses6 with accent on the active control of the pantograph but also a model in three dimensions with the advantages to consider many hypothesizes7. Low contact forces may lead to loss of contact, Abstract


Introduction
Different pantographs are currently used in train vehicles around the world. With the exception of the Shinkansen 500 series telescopic pantograph, all high-speed railway pantographs are of the two-stage type 1 . The main characteristic of a pantograph is to assure a good current collecting, without interruptions of the current regardless of the height of the pantograph. For this, it is necessary for the pantograph to have a contact plan irrespective of the movement of the mechanical articulated system, a small inertia, a good lateral and transversal stability, to obtain in static and dynamic regime a contact pressure irrespective of the string height, and have a low sensibility at the aerodynamics effects. More of this, the pantograph needs to have a crosshead slipper with an adequate shape and way of suspension for the contact characteristics. Its shape, size and fixation depend on the characteristics of the electric current, on the geometrical characteristics of the contact line 2 especially on the catenary irregularities which may cause serious fluctuation of contact force, even leading to the pantograph coming off the catenary 3 .
In the general nonlinear model, the pantograph model is represented in terms of the following kinematic linkages: a lower frame arm, an upper frame arm and a head link. The entire mechanism is raised by a torque applied to a link of the arm. A frame suspension model provides an uplift force to the pantograph. The input force is assured by a suspension, usually a resort or pneumatic system (actuator) which acts horizontally, applying a torque to the lower arm. This input force may vary in time and has to overcome the weight of the mechanism but also must provide the uplift force against the wire 4 . In some cases there are used only dampers (resorts) to assure the uplift force, as for the pantograph for the Korean high speed train 5 . The model of the pantograph can be realized with two masses 6 with accent on the active control of the pantograph but also a model in three dimensions with the advantages to consider many hypothesizes 7 .
Low contact forces may lead to loss of contact, 2 Force Estimation of an Asymmetrical Pantograph for Different Damper Positions resulting in electric arcing and power interruptions. On the other hand, too large contact forces may cause rapid wear of the carbon skates. Moreover, the pantograph may exhibit unexpected motions even when the contact-force variation is kept within a reasonable range. Thus, vertical dynamics of the carbon-strip suspension is also studied with an aim of improving the reliability and safety of running trains 8 . The variation on the head suspension resort stiffness reflects factors related to operation conditions, maintenance and material degradation. The variation on the lower damper of the pantograph represents factors related to usage in service, degradation and lack of maintenance 9 . The pneumatic actuator is working typically at 3.5-4.5 barr and in order to obtain a constant transmission ratio from air pressure to static force between sliding surfaces, the geometry of coupling between the actuator and pantograph is optimized 10 . To improve the dynamical response of the pantograph are used different solutions according to the position of the active suspension stage of the pantograph: a) active suspension system between sliding bows and mobile frame and b) active actuator on the mobile frame, with a passive suspension system placed under sliding bows. The layout b is preferred usually because their shape has less effect on the aerodynamic behavior of the pantograph 10 , has lesser limitation concerning shape, weight and is better protected from the harsh environmental conditions.
There are also studies regarding unconventional methods to supply the electric traction vehicles 11 . All these studies have to be considered having into attention the environmental friendly aspects of the different types of transportation systems, considering the large efforts to improve the quality of the emissions and to reduce the pollution over the medium 12 .
With these considerations it is useful to study the resort/damper position according to the frame of the pantograph, in order to estimate the pantograph dynamics and forces.

Estimation of the Lifting Force of the Pantograph
First it is to estimate the vertical force F developed due to the resort R of the pantograph over the contact line CL depending on the high of the pantograph. To simplify, the pantograph is considered as a bar T with the weight G, length l, and jointed in the point O ( Figure 1). In the point O 2 the bar is linked to the upper arm of the pantograph ( Figure 2). The resort R with a length of l R = a + (b + x) + c drives the bar, where x is a variable. It is considered that there is no friction into the joints of the pantograph. The pantograph will have a vertical motion v v. (Figure 1) where OO 1 = r. Considering F ro and Replacing the value (k 1 +x) into (5) it results the intermediate relation: The force of the resort is given by a relation as: where k 0 is a constant of the resort and x is the elongation of the resort. Thus: Replacing the value of x in (8): Considering by notation m r A = + Summing the torques M r and M g : The force due to the torque M R into the point O 3 (Figure 3): Replacing 0 k Ar l with k 2 it results:

Resort Position for the Pantograph Drive System
The equation (17) shows the link between the force F of the pantograph acting on the contact line and the angle α, and the link between the force F and the height of the pantograph skate l h because of the relation: The equation (17) has three elements: where: ( ) For a variation of the angle α = 0…90 0 , the first and the second expressions vary in different ways, that is the vertical force F is not constant and depend on the high of the skate. Thus, it is not possible to have a perfect constant force by using a resort.
Thus, it is important to know which the best options to obtain a constant force are. In this situation, it is important to analyze the modalities to attach the resort on the bar of the pantograph related to a fixed point.

Possibilities for the Resort Drive System Attachment
In this chapter there are presented some solutions for the resort position which is attached between the pantograph bar and a fixed point. There are also presented the equations accordingly to every solution. The pantograph is considered as a simplified system with a bar supported by the roof of the locomotive and used to collect energy from the contact line. With the above conditions, it results different situations to attach the resort and the bar and we consider for the analysis 12 cases.
In the first case, in extension of the bar T, in the point O 1 , there is a pull bar on length r. One of the resort ends is jointed in the point O 1 , and the other end is fixed in the point O 4 , at the distance A, in the same plane with the inferior arm r, which is, in the same time, the support and the joint point O of the bar of the pantograph. Considering the movement direction of the train (the direction of the speed of the vehicle V), we consider that the resort is placed "in front" of the pantograph.
In the second case, the pull bar r is in the same position as the in the first case, but the support and the joint point of the pantograph bar is the point O 1 , in the extension of the bar T with the bar r. The resort is "behind" the pantograph.   Figure 4.
(a) 3rd case: the resort is horizontal and "in front" of the pantograph. (b) 4th case: the resort is horizontal and "behind" of the pantograph.
In the 3 rd case the pull bar r is in the same position as in the first case, but the resort is jointed in horizontal plane "in front" of the pantograph. One of its ends is on the point O 1 and the other in the point O 4 , at the distance A. In the 4 th case the pull bar r is as in the second case, but the resort is horizontal and "behind" the pantograph, at the distance A from the support in O 1 . Considering the (a) 5 th case: the pull bar r is "in front" and above of the pantograph, at an angle γ, (b) 6 th case: the pull bar r is "in front" and below of the pantograph, at an angle γ.
In case 5 the pull bar r is rigid fixed on the inferior part of the bar T, in the point O 1 (a joint point for the bar T) "in front" of the pantograph at an angle γ (which is considered as constant) from the normal position of the pantograph (Figure 5(a)). At the other end of the bar r, in point O, is fixed an end of the resort R. The other end of the resort is fixed in point O 4 .
In case 6 ( Figure 5(b)) the pull bar r is in extension of the bar T, but at the angle γ.  Figure 6. (a) 7 th case: the pull bar is "in front" of the pantograph, at an angle γ, with horizontal resort, (b) 8 th case: the pull bar is "behind" of the pantograph, at an angle γ, with horizontal resort.
In case 7 (Figure 6(a)) the bar r is as in the case 5, but the resort is horizontally placed "in front" of the pantograph between the point O and O 4 , at a distance a + b + x.
In case 8 ( Figure 6(b)) the bar r is as in the case 6, but the resort is horizontally placed "below" the pantograph, between the point O and O 4 , at a distance a + b + x.
In case 9 the bar r is fixed in the point O 1 , "behind" the pantograph and at the angle g from the normal position of the pantograph, as seen in Figure 7(a). In the point O is fixed one of the ends of the resort and the other is fixed in point O 4 , "in front" of the pantograph, at distance A.  case: the pull bar is "in front" of the pantograph, at angle γ with horizontal resort.
In case 11 (Figure 8(a)), the bar is placed as in the case 9, and the resort is placed horizontally "in front" of the pantograph. In case 12 (Figure 8(b)) the bar is placed as in the case 10 and the resort is placed horizontally "below" the pantograph. case:11

Simulations and Results
For the simulations there are considered the data 13 : l=0.510        Figure 9 and Table 1.
The pantograph has a movement close to a sinusoid. To avoid large amplitudes and the detachments from the contact wire, the pantograph has to assure the maximum and minimum amplitude of the sinusoid. These values depend on the position of the pull bar and of the resort drive system. Analyzing the simulations in Figure 9  In these situations there are two cases with positive values and two with negative values. In practice, this can be realized by replacing the expansion resort with a compression one, with the same mechanical parameters. In these cases the reaction times are low assuring a good contact between the skate and the contact wire. These solutions are to be recommended for the pantograph drive system. c. The medium value for the maximum forces considering all the twelve cases is 99.42 N, while the medium value for the minimum forces is 66.27 N.

Test bench Experiments
A practical analysis is made considering the force variation on lifting and descending of the pantograph. From the 12 cases presented above we consider two cases, the 4 th case and the 9 th case, because they have the resort horizontal and "behind" the pantograph, at the distance A from the support in O1 (case 4), and the bar r is fixed "behind" the pantograph and at the angle γ from the normal position of the pantograph, but in the point O is fixed one of the ends of the resort and the other is fixed in point O4, "in front" of the pantograph, at distance A (case 9).
For these two extreme situations there are determined the static characteristic F =f(α) of the pantograph for lifting and descending, considering a bench stand as in Figure 10. An asymmetrical pantograph (1) at a scale of ¼ as regarding a real system. The pantograph has two graphite skates (2) and the classical mechanical lifting (resort) system (3) used for the main lifting force. The pull bar r could be placed in different positions, (4) and (5), "in front" and "behind" of the pantograph in order to analyze the considered positions.
The pantograph model has a low inertia, a good lateral stability, a constant contact pressure for a specific high and a low wear of the graphite skate.    Figure 11. The static characteristic F =f(α) for the 4th case.  Figure 12. The static characteristic F =f(α) for the 9th case. Figure 12 presents the static characteristics F =f(α) for the 9 th case. The experimental characteristic has a maximum of 78 N for lifting and 77 N for descending, while the minimum values are 60 N for lifting and 59.5 N for descending. The difference between the lifting force and descending force is maximum 1N. Comparing with the simulations, the difference is about 4.28 N for the maximum force and 3.56 N for the minimum force.
It is to say that these analyses can be used to identify the optimal position of the pull bar from the main axle of the pantograph, in order to find the optimal work area of the pantograph, with small variation of the contact force and with a better contact between the pantograph and the contact line.

Conclusions
One of the current collecting problems is to assure a permanent contact between the pantograph and the contact line but without using too high forces. Knowing the relation between the contact force and the high of the skate of the pantograph gives the possibility to estimate the place to attach the resort on the pantograph's bar.
In the cases 1, 2, 5, 6, 9, 10 the resort is attached in a slanting way. In the cases 3, 4, 7, 8, 11, 12 the resort is horizontal attached for every high of the pantograph. To estimate the influence of the resort position related to the oscillation point in the cases 1, 3, 5, 7, 9, 11 the resort is attached above of the oscillation point and in cases 2, 4, 6, 8, 10, 12 it is attached below the oscillation point. Analyzing the 12 cases we can conclude: • If the resort is attached above of the oscillation point all the coefficient of the trigonometrically functions are the same; • The contact force variation depends strongly by the position of the resort: if the resort is horizontal (above or below of the oscillation point) the variation curve is the same. • For the situations when the resort is attached by a crank (above or below of the oscillation point), in the relation of the force it appears a new expression. • The 9 th case offers a low variation of the force, assuring a better power collecting for the vehicle. It is to mention that the pantograph is droved by a resort, but it could be used any other mechanism, like pneumatic or hydraulic drive system.