On the influence of wheel-rail combination on active wheelset steering control with wheelset angular velocity feedback and countermeasures

Abstract

Active wheelset steering using wheelset angular velocity feedback has been proposed and proven effective in achieving one of the goals for perfect steering condition, i.e. minimising longitudinal creep forces and thus wear. This control strategy relies on the contact parameters of wheel-rail pairs to generate a desired angular velocity by using the wheel rolling radii. Some wheel-rail combinations give a non-monotonic function of the average rolling radius with respect to curve radius, which therefore poses a difficulty in controlling active steering with the angular velocity feedback. This study aims to investigate the effect of different wheel-rail combinations and wheel wear. Worn wheels in general tend to cause a non-unique function whereas the original profile gives a monotonic one. Two countermeasures are then investigated to cope with the raised challenges. First, the reference signal generated from the approximated average rolling radius method has proven to be effective for both the original and the least worn profile; however, a wheel with higher wear depths would require a new tuned scaling factor. The control strategy based on equal wheelset angular velocity is then investigated with two schemes: equal wheelset angular velocity within the same running gear and equal angular velocity of all wheelsets within the vehicle. Both schemes provide significant wear number reduction, but the second approach results in better distribution of wheel-rail lateral forces among all wheelsets. This control strategy can also relax the demanded knowledge of wheel-rail contact properties and vehicle travelling speed.

Introduction

A mechatronic solution for solid-axle wheelsets is one of the active primary suspensions of railway vehicles that resolves the contradiction between running stability and curving performance in passive suspension designs by using active stability and active steering control.^1,2 Active wheelset steering (AWS) steers a wheelset in curves into a position where curving performance is improved.^3–5 Several studies point at the benefits of this mechatronic running gear solution on wheel-rail wear reductions. Active wheelset steering can be implemented via a wide range of control strategies. One of the most widely utilised classes of control strategies for this active solution is the so-called perfect steering control.^2,3 This class of control strategy aims to minimise longitudinal creep forces and obtain equal lateral forces in all wheelsets while negotiating a curve. This can be achieved through, for instance, perfect wheelset lateral displacement and perfect angle of attack which are mainly relative movements between wheel and rail. The relative movements between wheel and rail are costly to be measured in operations though.

The control strategy of active wheelset steering based on wheelset angular velocity feedback is proposed by the authors to achieve a perfect steering condition. ⁶ This control strategy is proven to be realisable for an active wheelset steering system. It utilises practically measurable wheelset angular velocity which changes due to changes in average wheel rolling radii in curves when a wheelset moves laterally from the track centreline. The mechanism of wheelset angular velocity changes in curves is also revealed by Endo et al. from experiments and validated with multibody dynamic simulations (MBS). ⁷ The most effective method to determine the targeted wheelset angular velocity is to have accurate wheel-rail contact parameters. Thus, this control strategy relies on accurate knowledge of a wheel-rail geometry which can be attained from field measurements, i.e. wheel profile measurement system (WPMS), ⁸ or monitoring systems. Then, the measured profiles can be used to determine the wheel-rail contact to obtain left and right wheel rolling radii. The previous study on this control strategy also pointed out challenges due to non-unique desired wheelset angular velocity, i.e., non-monotonic functions between average rolling radius and magnitude of curve radius.

Wheel profiles evolve due to wear and plastic deformation. Worn profiles cause changes in wheel-rail contact geometry and heavily affect running performance such as derailment risk, ride comfort and running stability. ⁹ Wheel wear can be critical and lead to maintenance efforts to ensure acceptable dynamic running behaviour. ¹⁰ Giossi et al., ¹¹ and Fu et al., ¹² studied wheel wear evolutions in case of active wheelset steering for two-axle and bogie-based vehicles respectively and demonstrated the substantial wheel wear reduction. Hur et al. ¹³ conducted tests of the vehicle with a steering bogie and highlighted flange wear reduction in comparison to the passive one. Wheel wear of a vehicle with active steering in most cases mainly occurs on wheel treads. This type of wheel wear can potentially be challenging to control active wheelset steering with wheelset angular velocity feedback. Thus, the recognition of possible wheel-rail combinations is important for implementation of the proposed control strategy.

This study aims to investigate the influence of different wheel-rail combinations including original and worn wheel profiles on active wheelset steering control. Insights and practicalities are also discussed considering the feasibility to realise the control system for active steering wheelset based on angular velocity feedback to provide confidence for a real world implementation of the control strategy. As the reference signal generated from the theory demands prior knowledge of wheel-rail contacts, two approaches will be studied as potential solutions to relax the required accurate wheel-rail profiles. First, a control strategy based on an approximated average rolling radius is investigated to evaluate the effectiveness of this method against worn wheels. This would be one of the possible solutions to lower the essential requirements. Finally, an alternative control strategy based on equal wheelset angular velocity will be evaluated. This alternative control strategy aims to not only ease the necessity of prior knowledge of wheel-rail pairs but also relax critical requirements for this control strategy.

Control strategy and influence of wheel-rail pairs

In the control strategy of AWS via angular velocity feedback, the target wheelset angular velocity to obtain pure rolling conditions is highly dependent on wheel-rail pairs. The reference angular velocity of wheelsets in a curve ( $R$ ) is given as

${\mathrm{\Omega }}_{ws}^{ref}=-\frac{1}{2}\left(\frac{v_v}{r_L}\left(1+\frac{b_0}{R}\right)+\frac{v_v}{r_R}\left(1-\frac{b_0}{R}\right)\right).$

(1)

where $v_v$ is vehicle forward speed, $r_{L,R}$ are rolling radii of left and right wheels, $b_0$ is half the distance between left and right contacts, and wheelset angular velocity is negative when moving forward. It also assumes that the distances between left/right contact point to wheelset’s centre of gravity ( $b_L$ and $b_R$ ) are approximately the same as half the distance between left and right contact points ( $b_0$ ). Moreover, a condition to be satisfied in order to achieve minimised longitudinal creepages is

$\frac{r_L}{r_R}=\frac{R+b_0}{R-b_0}=\kappa .$

(2)

Equation (1) can be simplified using an equivalent rolling radius ( $r_e$ ) and the reference is written as

${\mathrm{\Omega }}_{ws}^{ref}=-\frac{v_v}{r_e},$

(3)

where $r_e$ is the equivalent rolling radius of a wheelset as a function of track curve radius ( $R$ ). The equivalent rolling radius can be approximated as average rolling radius ( $r_{ave}$ ) of left and right rolling radius in which a ratio of wheel rolling radii satisfies equation (2). Figure 1(a) is provided for an intuitive illustration for all variables and coordinates of a wheelset negotiating a right-hand curve.

Figure 1.

A wheelset negotiating a right-hand curve with left, right and average rolling radii of S1002 wheel with flange thickness of 31 mm (S1002t31) and 1:40 inclined UIC60 rail (UIC60i40) (a) and reference signal generations using equation (1) (b).

To generate the reference signal, track curvature is first estimated using realisable measurements, e.g. $R^{-1}={\dot{\psi }}_b·v_v^{-1}$ . Then, the ratio of the right-hand side of equation (2) is calculated. This ratio ( $\kappa \left(R^{-1}\right)$ ) is used to interpolate wheel rolling radii from a lookup table with stored wheel rolling radii ( $r_L,r_R$ ) and ratio ( $\kappa \left(r_L,r_R\right)$ ) according to equation (2). The wheel rolling radii are pre-calculated using the wheel-rail contact model in SIMPACK. Both desired wheelset angular velocity signal generation and curvature estimation require an accurate estimate of vehicle travelling speed ( $v_v$ ). This can be obtained by using estimators or sensor fusion techniques. Mei and Li, for instance, proposed a technique of estimating vehicle travelling speed by using a time shift between two wheelsets extracted from the dynamic response of wheelsets due to irregularities.^14,15 The overall reference signal generation method is presented in Figure 1(b).

This derivation assumes a small yaw angle between wheel and rail which holds due to perfect steering condition. Moreover, it assumes that contacts are on the wheel tread so that the contact point angle is small. The locations of contact are mostly on the wheel tread when the perfect steering condition is satisfied. These conditions result in negligible longitudinal displacement of contact points and therefore lead to a relationship between wheelset angular velocity and lateral displacement. ^{9 , 16} Hence, the reference signal generation method shown in Figure 1(b) can be obtained through the knowledge of wheel rolling radii with respect to lateral displacement from the contact model shown in Figure 1(a).

Figure 1(a) shows the rolling radii of left and right wheel and the mean value with respect to wheelset lateral displacement. Left and right wheel rolling radii are pre-calculated using FASTSIM ¹⁷ with a vertical wheel force (Q) at the nominal value on tangent track and zero wheelset yaw angle according to small angle assumptions. Distribution of vertical wheel loads changes in curves due to non-compensated lateral acceleration in quasi-static conditions. Despite the change of rolling radii from varying vertical wheel forces, the relation of rolling radii and curvature evaluated at tangent track conditions can be used within the whole range of curve radii and it is proven to be effective according to the previous study. Moreover, the wheel load variation of the passenger vehicle is in a narrow range and the current load measuring system such e.g. estimation from air spring pressure can provide quite an accurate estimate of loads.

The lookup table of wheel rolling radii with respect to ratio $\kappa$ as shown in Figure 1(b) can be reconstructed to a function between average wheel rolling radius and magnitude of curve radius. This is the simplified approach using an equivalent rolling radius according to equation (3). This graph can be used to determine the monotonicity of the function. Wheel-rail pairs with a monotonic function are feasible to utilise in the control system for active wheelset steering.

In this study, symmetric rails and wheels are considered. Standardised S1002 with 32.5 mm flange thickness specified in EN13715 ¹⁸ and UIC60 rail with 1:40 and 1:30 are evaluated in the previous study by the authors. ⁶ These wheel-rail combinations have monotonic functions and are therefore possible to apply for active wheelset steering. To elaborate on the importance of a wheel-rail combination in realising the control strategy based on wheelset angular velocity feedback, original S1002 wheels with two different flange thicknesses, 32.5 and 31 mm, on a curve track with UIC60 and S49 rails are considered. In the previous study by the authors, 1:40 inclined S49 rail with standardised S1002 wheels resulted in a non-unique function between the average rolling radius and magnitude of curve radius. Nevertheless, the same rail with S1002 wheels, 31-mm flange thickness has a monotonic function as shown in Figure 2 (right). This highlights the crucial role of wheel-rail combination. Figure 2 illustrates the function between the average rolling radius and curve radius for all combinations mentioned above.

Figure 2.

Function between curve radius and average rolling radius of S1002 wheel with UIC60 rail (left) and S49 rail (right) under different flange thickness and rail inclination (i).

Table 1 summarises the monotonicity of each wheel-rail combination. It is monotonic if $\nabla f\left(R\right)<0$ for the whole range of curve radii. Apart from the effect of different flange thicknesses in changing the monotonicity of the function, the range of curve radius is also important. It can be seen from S1002t31/UIC60i40 and S1002t31/S49i30 that their functions are monotonic with the range of interest of 100-5,000 m, but it is non-unique if we expand the upper range to 10 km. Nevertheless, this combination is expected to be possible to use for active wheelset steering with wheelset angular velocity feedback as the range of non-unique average rolling radius is small and in a larger curve radius. This will be investigated in a later step.

Table 1.

Monotonicity of a function between curve radius and average rolling radius with different wheel-rail combinations.

Rail	Flange thickness S1002 wheel	Curve radius range (m)
		100-10,000	100-5,000
S49i40	31 mm	✓	✓
	32.5 mm	×	×
S49i30	31 mm	×	✓
	32.5 mm	✓	✓
UIC60i40	31 mm	×	✓
	32.5 mm	✓	✓
UIC60i30	31 mm	✓	✓
	32.5 mm	✓	✓

Influence of worn wheels

Focus in this section is on wheel-rail combinations with worn wheel profiles. As mentioned earlier, the wheels of a vehicle with an active steering wheelset tend to wear mainly at the wheel tread. Tread wear can dramatically change the contact situation between wheel and rail. This type of wear is caused by forces between wheel tread and rail surface including creepages and creep forces, ¹⁹ and large creepages and creep forces due to traction and braking. ²⁰ To analyse worst-case scenarios, worn wheels from a passive vehicle are employed based on data available from both measurement and wear evolution simulations. Patterns of worn wheels in general are affected by several factors such as wheel-rail pairs, vehicle running behaviour and track geometry. Two worn wheel patterns illustrated in Figure 3 are employed in this study, Set A and Set B. Set A profiles are from measurements whereas Set B profiles are from long-term wheel wear simulation. These profiles are smoothened and aligned with the original profile S1002t31. Both sets of profiles reflect wear of wheels with approximately vehicle mileage of 35-195 kkm. These two sets are used because they have two distinguished wear patterns where the peaks of wear depth on the wheel thread are in different locations.

Figure 3.

Two sets of worn profiles: set A (left) and set B (right) where each set consists of five profiles ranging from 35 to 195 kkm approximately.

According to Figure 4, most of the wheel-rail pairs can maintain the monotonicity of the average rolling radius for the least worn profile except for UIC60i40/S1002t31 set A. The functions for UIC60i30 with all of Set B profiles are monotonic. A larger wear depth than the profile B5 with UIC60i30 would cause a non-monotonic function. Some wheel-rail combinations are more sensitive to become non-unique when a wheel wears. The function for UIC60i40 with B1 profile is unique if we consider the curve radius below 4,800 m. The effect of the non-unique average rolling radius is small which can be seen from Figure 4 and is thus expected not to influence the control algorithm significantly. This highlights the importance of wheel-rail combinations in the application of active wheelset steering via angular velocity feedback.

Figure 4.

Function between average rolling radius and magnitude of curve radius with different wheel-rail combinations.

According to Giossi et al., ¹¹ volume losses due to wear of the active wheelset steering using feedforward control are decreased by more than 60% compared to the passive two-axle vehicle. The studies also revealed a strong relation between actual volume losses and wear number ( $T\gamma$ ). Hence, a vehicle with active steering capability and in turn lower wear number, has much lower wear in comparison to a passive one. The previous study of the control strategy based on wheelset angular velocity showed a wear reduction of up to 90% using $T\gamma$ as indicator for wear. ⁶ This would significantly extend the running mileage until the wheel-rail contact situation becomes non-monotonic. Moreover, the most preferable active wheelset steering goal is to equally distribute wear along the profile. This approach would maintain the profiles and their monotonicity and also the dynamic behaviour of the vehicle.

One of the foreseen challenges is the need for frequent profile measurements to obtain accurate wheel-rail contact parameters. This is crucial in the calculation of target wheelset angular velocity for a perfect steering condition. Potential solutions to deal with this challenge will be proposed and analysed in the proceeding sections.

Use of approximated average rolling radius

According to the previous section, the reference signal generation using equation (1) needs an analysis for a new set of wheel-rail pair when a wheel profile changes. This would require frequent measurements of wheel-rail profiles. In this section, a control strategy using an approximated equivalent rolling radius is applied to investigate the effectiveness of this approach when a wheel is worn out. Instead of using the theoretically derived reference signal generation method, our previous study proposed an approximation of equivalent rolling radius. Derived from equation (3), the average rolling radius can be approximated using

${\stackrel{\sim }{\mathrm{\Omega }}}_{ws}^{ref}=-\frac{v_v}{r_0+\alpha r_0{b}_0{R}^{-1}},$

(4)

where $\alpha$ is a scaling factor for curve fitting and $r_0$ is the nominal rolling radius at zero wheelset lateral displacement. This nominal rolling radius can be changed due to wear and vertical wheel load ( $Q$ ). It can be determined from the vehicle speed ( $v_v$ ) and angular velocity ( ${\mathrm{\Omega }}_{ws}$ ) on tangent track. In this section, we investigate the effect of approximated average rolling radii on the wear number when the wheel profiles change due to wear. Two wheel-rail pairs including original S1002t31 and B1 profile with UIC60i30 rail are used in this section. According to preliminary investigations, a scaling factor ( $\alpha$ ) of 0.8 can be used for both the original and B1 profiles which gives a decent approximation of the average rolling radius. The scaling factor of 0.8 is selected as it provides the best fit to the average rolling radius ( $r_{ave}$ ) for the original wheel profile with a UIC60i30 rail shown in Figure 5 (left). This scaling factor value also produces decent approximation of the average rolling radius for B1/UIC60i30 wheel-rail combination. It should be noted that the nominal rolling radii of these profiles are different. Figure 5 (left) shows the functions of the average rolling radius and curve radius as well as their approximations using equation (4) and a scaling factor of 0.8.

Figure 5.

Wear number of the vehicle with AWS with approximation of average rolling radius.

To evaluate this approach, the vehicle model is the same as used in the previous study by the authors. ⁶ The vehicle runs at balanced speed at six curve radii. The simulations are performed with co-simulation between SIMPACK and MATLAB/Simulink. The curving performance indicator used in this study is wear number ( $T\gamma$ ) which is given as

$T\gamma =|F_{\xi }{\nu }_{\xi }|+|F_{\eta }{\nu }_{\eta }|+|M_{\zeta }\varphi |,$

(5)

where $F$ and $\nu$ are creep forces and creepages in longitudinal ( $\xi$ ) and lateral $\left(\eta \right)$ directions. Spin creep moment ( $M_{\zeta }$ ) and spin creepage ( $\varphi$ ) are neglected. This indicator is based on energy dissipated in the wheel-rail contact which has a strong correlation to wheel-rail wear which is generally affected by creepages and creep forces. ⁹ The total wear number is a summation of energy dissipation in all contact points. Figure 5 (right) shows the total wear number of the vehicle with active wheelset steering with an approximation method. The employed method with a scaling factor of 0.8 can be used for both wheel-rail combinations giving a considerable wear number reduction. Unlike the theoretically derived average rolling radius for each curve radius, the approximation method might result in higher wear number in larger curve radii, which is affected by the accuracy of estimation. Nevertheless, the resulting wear number is still low. The preliminary investigation indicates that the same scaling factor can be used for a couple of wheel profiles in Set B. However, the scaling factor would need to be adjusted when we have larger wear depths. The inaccuracy of approximation will cause difficulties in controlling the wheelset as discussed in the previous study by the authors.

Alternative control strategy based on equal wheelset angulars velocity

According to the previous section, the requirement for prior knowledge of wheel-rail contacts is eased. Still, a measurement for nominal rolling radius and new tuned scaling factors are required when wear depths are higher to maintain its effectiveness in terms of curving performance and controllability of the control system. In this section, an alternative control strategy is proposed as a possible solution to avoid the frequently required profile measurement and nominal wheel radius. First, it is assumed that we have enough information that the function of the average rolling radius and magnitude of the curve radius is monotonic. For instance, the analysis from the previous section shows the confidence range of vehicle mileages from the original profile to the least worn one in maintaining monotonicity of this function. In this alternative control strategy, if the average rolling radius function is monotonic, wheelsets can be steered to result in the same wheelset angular velocity. It is mentioned by Fu et al. ⁵ that one possible control strategy is to control all wheelsets so that they have the same relative movements between wheel-rail, including wheelset lateral displacement and angle of attack; however, there are limited studies on this control approach as well as the mechanism for this strategy.

This approach would help to improve curving performance because the rear wheelset in each running gear usually has substantially better curving performance in terms of wear. Front wheelsets, especially in the leading running gear, are more critical in curve negotiation with high creep forces and wear. ⁹ With this understanding of the dynamic behaviour of rail vehicle running gears, the leading wheelset could therefore be steered to have the same movement as the trailing one to improve the performance. A similar concept of partially controlled running gear was studied by Togami et al. ²¹ for asymmetric link-type forced steering bogies. ²² The preliminary investigation is performed using the approach that the angular velocity of the front wheelset is controlled to reach the same as the rear wheelset of its respective running gear instead of determining the desired angular velocity. This results in substantial improvements in wear number in quasi-static curving; however, this causes large wear when entering and exiting a curve since the steering force of a front wheelset also affects the movement of the bogie frame and there is no counterbalance from the steering force from a rear wheelset.

Hence, two possible control schemes are investigated in this study:

(1) Leading and trailing wheelset in the same running gear are controlled to have the same wheelset angular velocity.

(2) Additional controllers are incorporated to control angular velocity of all wheelsets within the vehicle to be the same.

The schematics for both control schemes are given in Figure 6. One of the foreseen problems is that the performance on tangent track can be deteriorated with the steered wheelset for equal movements. In this case, wheelsets are kept at the same angular velocity but not at the nominal wheelset position, i.e. non-zero wheelset lateral displacements relative to the track. However, this effect can be eliminated by using an additional controller to keep the suspension deflections in longitudinal direction the same when operating in a larger curve radius than 10,000 m. This additional controller, illustrated in Figure 6(c), is added to each wheelset which is similar to the approach in the previous study. Alternatively, the steering control can only be activated in a certain range of curve radii. A wheelset will then naturally be steered itself at the nominal position due to its self-centring mechanism.^7,18 For scheme 2, i.e. controllers keeping wheelset angular velocity between two running gears equal, less actuation effort should be needed than for the ones that control two wheelsets in running gear to prevent overshooting due to time differences in negotiating the curve for each wheelset. This is caused by the large bogie distance between two running gears. All controllers with angular velocity feedback ( $C_{\mathrm{\Omega }}^{wi}$ ) are PID controllers with the passive adaptation mechanism using nonlinear rate feedback. ²³ This passive adaptation is introduced to guarantee acceptable control performance for all cases which is proven to be effective in the previous study. ⁶

Figure 6.

Schematics of active wheelset steering based on equal wheelset angular velocity with Scheme 1 (a) and Scheme 2 (b) control architectures, and additional control layer for suspension deflection control (c).

To evaluate this proposed control system, the vehicle operates on a curved track of 600-2500 m radius. Operation conditions include non-compensated lateral acceleration of −0.65, 0 and 0.65 $m·s^{-2}$ . The passive vehicle has primary longitudinal stiffnesses of 37.5 MN/m. These stiffnesses are reduced to 8 MN/m in the vehicle with active wheelset steering to decrease actuation forces. Yaw actuation is used in this active wheelset steering configuration which is demonstrated to be feasible due to coupled dynamics between lateral and yaw direction. S1002t31 wheel and UIC60i30 rail with two inclinations of 1:30 and 1:40 are employed in the investigation. The functions between the average rolling radius and magnitude of curve radius of this wheel-rail pairs for both combinations are monotonic when evaluating in the curve radius range of 100-50 km. However, S1002t31/UIC60i40 in the curve radius range of 100-100 km is non-monotonic, but it is expected to be possible to control with this control strategy.

First, wheelset movements of a S1002t31/UIC60i40 wheel-rail combination in a 600 m curve at balanced speed are presented in Figure 7 in comparison to the uncontrolled active vehicle. This is to observe how the control system based on equal wheelset movement performs in comparison to the uncontrolled case. It can be seen from the wheelset angular velocity for both controlled and not controlled wheelsets that the control system with scheme 1 tries to find a balance between front and rear wheelsets. Control scheme 2 also finds a balance between front and rear running gears. Wheelset lateral displacements are also being controlled which demonstrates that the assumptions are fulfilled. Despite the non-monotonicity of the function of these wheel-rail pairs, this combination is possible to control as predicted. The effect of non-monotonicity reflects on the wheelset angular velocity begin at slightly higher magnitude when entering the curve and at the end of exiting the curve compared to the one on tangent sections.

Figure 7.

Wheelset movements including wheelset angular velocity and lateral displacement at balance speed on R600 curved track for the uncontrolled active vehicle (left) and the vehicle with active wheelset steering using both control schemes (right).

As mentioned earlier, the total wear number ( $T\gamma$ ) can represent curving performance. Figure 8 shows the wear number of the passive vehicle and the vehicle with both control schemes. On average Scheme 2 is slightly better than Scheme 1. Nevertheless, both schemes give a significant reduction in wear number. The reduction of wear numbers ranges between 79 and 98% for all 18 cases. However, Scheme 2 is preferred as the lateral wheel-rail forces are more distributed among all wheelsets compared to Scheme 1 which is one of the performance targets of a perfect steering condition. Nevertheless, both schemes are proven to be safe to operate for all employed running cases.

Figure 8.

Total wear number of the vehicle with S1002t31/UIC60i40 including Passive suspension with original stiff longitudinal suspension; (a), AWS Scheme 1; (b) and AWS Scheme 2; (c) with corresponding percentage of total wear number reduction compared to the passive one.

Scheme 2, as preferred compared to Scheme 1, is then applied to wheel-rail combinations used in the previous section, i.e., UIC60i30 rail with two wheel profiles including original S1002t31 and least worn B1 profiles. Figure 9 shows the wear number of the active vehicle with control Scheme 2 for both wheel-rail pairs. The results show the effectiveness of both control schemes where wear number reduction ranges between 67 and 99% in comparison to the passive vehicle for each wheel-rail combination. It can be seen from Figure 9 (right) for worn S1002t31 B1/UIC60i30 wheel-rail combination that a larger curve radius has a higher wear number at balanced speed and cant deficiency. This is potentially an effect of the tread wear as the contact location for perfect steering in large curve radii is at the wheel tread. Nevertheless, this control approach is effective in curving performance improvement for B1/UIC60i30 wheel-rail combination as it provides a monotonic function between average rolling radius and curve radius for this wheel-rail pair which is shown in Figure 4. Despite the change of wheel profile, the results show the effectiveness of the control strategy based on the equal wheelset angular velocity feedback approach. This control strategy is therefore applicable to a wide range of wheel profiles if the wheel-rail combination gives a monotonic function between average rolling radius and curve radius. However, the control system for each wheel-rail combination is specifically tuned to achieve adequate performance, especially in quasi-static curving. A robust control system would be needed to accommodate the change of wheel profile which leads to wheel-rail contact parameter variations.^24–26

Figure 9.

Total wear number of the vehicle with UIC60i30 rail and original S1002t31; (a) and worn S1002t31 B1; (b) wheel profiles.

Both proposed control schemes with a strategy based on equal wheelset angular velocity provide remarkable wheel-rail wear reduction evaluated as wear number. Results from both wheel-rail combinations, which to some extent provide monotonic functions in the range of 100-5,000 m, confirm the effectiveness of these approaches. More importantly, these approaches not only relax the requirements of accurate knowledge of wheel-rail contact parameters but also require signals of an absolute vehicle travelling speed and curvature. Moreover, wheel-rail contact parameters especially in wheel rolling radius are also influenced by wheel load and running condition in curves as mentioned earlier. The studied vehicle is a of long-range type normally with a low passenger load compared to the tare weight. For vehicle with larger load variations, the load will have an influence on the wear. Hence, this provides a suitable solution for the active wheelset steering based on angular velocity feedback especially when wheel-rail profiles might not be measured frequently or are only partially known. The estimation of curvature through on-board measurements is only used to set the threshold for additional controllers to keep left and right suspension deflections the same in tangent sections which might require less accuracy than the estimation used for reference signal generation.

Conclusions

This study investigates the influence of different wheel-rail combination on the control strategy of active wheelset steering using angular velocity feedback by considering the function between average rolling radius and magnitude of track curve radius. Results of different wheel-rail combinations highlight its impact on the monotonicity of the function, which is crucial for realising the active wheelset steering with angular velocity feedback.

The effect of worn wheels is investigated to observe how the function changes when the wheel wear. It reveals that wheel wear can lead to non-monotonic functions of average rolling radius; however, some sets of worn wheels can maintain the monotonicity of the function at higher vehicle mileages than the least worn profile. Hence, the selection of wheel-rail pairs is crucial for the practicality of the control strategy based on wheelset angular velocity feedback. The right combination should be considered in both the original and worn profiles.

From the perspective of the mechatronic solution, active wheelset steering technology can manipulate the wheel-rail contact points in curves; thus, the control scheme with strategic manipulation and equal distribution of wear would be preferred. The strategy that distributes the wear along the profiles instead of reaching the minimum level should be further studied. This will not only maintain the monotonic function of the desired wheelset angular velocity but also reduce the maintenance need. The wheel-rail monitoring and profile measurement systems would help to enable this.

The demanded prior understanding of wheel-rail contact situations and accurate vehicle travelling speed are crucial for the generation of targeted wheelset angular velocity. Despite the possibility of obtaining these parameters in practice, the realisation of this control strategy in operations can still be challenging. Hence, the study evaluates alternative control schemes also based on equal wheelset angular velocity strategy. This control strategy does not require accurate wheel-rail contact situation to calculate the targeted wheelset angular velocity which can reduce the requirement for frequent profile measurements. This is possible from the fact that trailing wheelsets perform relatively well in curves and leading wheelsets usually have a larger angle of attack when negotiating the curve. Two control schemes investigated in this study provide evidence of curving performance improvements in terms of wear number while diminishing the need for both wheel-rail pair information and vehicle speed. Scheme 1 is to control the angular velocity of wheelsets within the same running gear to be the same. Scheme 2 where additional controllers are used to control wheelset angular velocity for both front and rear running gears the same is preferred as it also provides better distribution of wheel-rail lateral forces compared to Scheme 1. Scheme 2 is also proven to be effective for both original S1002t31 and least worn wheel profile (B1) with UIC60i30 rail. Lastly, this control strategy based on equal wheelset angular velocity should be further studied with field experiments.

This study uses symmetric wheels and rails to conduct all analyses. The effect of worn rails should be further investigated as high and low rails are worn out differently. This will cause asymmetric rail profiles in the curve and therefore directly affect the control strategy with wheelset angular velocity feedback.