Fig. 1.

Fig. 2.

Fig. 3.

Fig. 4.

Fig. 5.

Fig. 6.

Fig. 7.
![Y25 railway bogie [own development], 1 – frame, 2 – bogie axle, 3 – pivot pin, 4 – suspension (springs, friction dampers), 5 – side slides (mechanical vibration damper)](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/694828ee7c29e05adc524c36/j_ama-2025-0077_fig_007.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKISKFYITU%2F20260221%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260221T210441Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEOj%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIQCySd1L9yAJPQ7UvaNmL8lA74x2ED%2BXD3DQdGLIAwLtHAIgW0XytHRIqeW28YvAqtCtf2fi59fTRe4n0S55vf3uyUoqxgUIsf%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDJB%2BMCeKD2ss%2F6FzmyqaBc7yAoqzxOuJJpcwUp004K2Ob2iuAT%2FO5VQc6SOH%2B5t1WJHrX2ZrlO%2B6EYPRh8UF8VYEMnYEXiuZdzwy1ru6xlRVAyuZxxvf21Q1u10Dk6ubJr1ZBAv9JKEDobQxzAsTTqE4adj%2BDbA5hL7kJ3U%2F8KISjGvhwU6kwkIIaj8jYfwZ2wTOjWRR56USk5j4AZcSM7Job5olz7cM9HxLh2OskEo%2BZndjFgMLz%2BFD0Bi2iKKS3Aqo%2BUZ4do0NzoXetz64tULqvCNpAsk%2Fs%2Fu79YioE17thbN0fI2sAV3yZ0%2BVOfqpY0BAagIgP74M2iP26Tf9sL6boKy%2FwUwozrmxYM5ol%2BEvI%2FF7D%2B%2F%2BFjN%2BffbZl8dPbin0GORG2D%2B3hL1awmqrVmljtJ4XcluHJcl%2BLZZXJTZm6eXZz%2BWyFf6ga9gLVh7FvX3PxaCcLEOX%2BqlEekOoaTorNHZH5hDg5uog8MGO9erKXVeVPlbJzkMVQ7O8ONNShpM2zcGmAcHGWEMK9ffMir1yw0ro9fSqYF%2Fx547lYnEGdaefS9gcyP8b0a3sxKuAsJEj3ltkDnl84hz5jmOQY0uNswnOvjWbCinFf02aO1f%2FMiaB3JZSimc3cQXeS14vp6FSUZ%2FH%2FtuH3eYalfqLOKQriJcqd6NJuvnFCbLqyV1%2F2R3ETxH43ol14jbLlMuHq21ReE68BD%2Bsur5iy%2BZM3OcquG5TqhKNQscU8Q5Mpr8%2BiBdt8%2FhH2bN4Q9pNNxOcyEBAshGH8KA5JlG3fy6bXF2Nu3NQjiZNhAT0F7Hbii5NlntzrxSj4uLSetjLHHcMDx6X2ZvEo%2BsvO0cntDmiDKYVheeSPM11R49hVW4a4cXy4E5VeeARev5epJrszE0R5n314NGc%2F4SvaDCto%2BfMBjqxATRfbRzKZQraQG5us2TwRmhyXMllVtWUAqlvJw%2BTERUUG1dnSZ7ij%2BEJv%2BNLu1UzfC0JFDRFKk3RlmQdp4%2FzGr1g15LSx%2FYveUSfJHhEWkZa%2FsJHJtL3TTW6Fn%2FDU0yMgtP1RSL0AYHgkLNzcNqK2eu7EqFXEqXnTtNuHrt4jSHC7TfVSWIY0PkV98eajOv%2BzCTOJBNaIydMMkSxPZmkXx43XFbY5XNgwqySiCXY2nGxQQ%3D%3D&X-Amz-Signature=699c2c127ff3befaf5d47978f7814b1bfae127b4bc1d4cb70c448057a43b56d5&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Fig. 8.

Fig. 9.

Fig. 10.

Fig. 11.
![The influence of damping changes on the vibrations of the front bogie caused by the force impulse on the wagon with the semi-trailer. Graphs of vertical displacement as a function of time for two different damping values with marked vibration periods for suspension with different damping variants Cmin = 170 [N·s/mm] and Cmax = 17000 [N·s/mm]](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/694828ee7c29e05adc524c36/j_ama-2025-0077_fig_011.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKISKFYITU%2F20260221%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260221T210441Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEOj%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIQCySd1L9yAJPQ7UvaNmL8lA74x2ED%2BXD3DQdGLIAwLtHAIgW0XytHRIqeW28YvAqtCtf2fi59fTRe4n0S55vf3uyUoqxgUIsf%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDJB%2BMCeKD2ss%2F6FzmyqaBc7yAoqzxOuJJpcwUp004K2Ob2iuAT%2FO5VQc6SOH%2B5t1WJHrX2ZrlO%2B6EYPRh8UF8VYEMnYEXiuZdzwy1ru6xlRVAyuZxxvf21Q1u10Dk6ubJr1ZBAv9JKEDobQxzAsTTqE4adj%2BDbA5hL7kJ3U%2F8KISjGvhwU6kwkIIaj8jYfwZ2wTOjWRR56USk5j4AZcSM7Job5olz7cM9HxLh2OskEo%2BZndjFgMLz%2BFD0Bi2iKKS3Aqo%2BUZ4do0NzoXetz64tULqvCNpAsk%2Fs%2Fu79YioE17thbN0fI2sAV3yZ0%2BVOfqpY0BAagIgP74M2iP26Tf9sL6boKy%2FwUwozrmxYM5ol%2BEvI%2FF7D%2B%2F%2BFjN%2BffbZl8dPbin0GORG2D%2B3hL1awmqrVmljtJ4XcluHJcl%2BLZZXJTZm6eXZz%2BWyFf6ga9gLVh7FvX3PxaCcLEOX%2BqlEekOoaTorNHZH5hDg5uog8MGO9erKXVeVPlbJzkMVQ7O8ONNShpM2zcGmAcHGWEMK9ffMir1yw0ro9fSqYF%2Fx547lYnEGdaefS9gcyP8b0a3sxKuAsJEj3ltkDnl84hz5jmOQY0uNswnOvjWbCinFf02aO1f%2FMiaB3JZSimc3cQXeS14vp6FSUZ%2FH%2FtuH3eYalfqLOKQriJcqd6NJuvnFCbLqyV1%2F2R3ETxH43ol14jbLlMuHq21ReE68BD%2Bsur5iy%2BZM3OcquG5TqhKNQscU8Q5Mpr8%2BiBdt8%2FhH2bN4Q9pNNxOcyEBAshGH8KA5JlG3fy6bXF2Nu3NQjiZNhAT0F7Hbii5NlntzrxSj4uLSetjLHHcMDx6X2ZvEo%2BsvO0cntDmiDKYVheeSPM11R49hVW4a4cXy4E5VeeARev5epJrszE0R5n314NGc%2F4SvaDCto%2BfMBjqxATRfbRzKZQraQG5us2TwRmhyXMllVtWUAqlvJw%2BTERUUG1dnSZ7ij%2BEJv%2BNLu1UzfC0JFDRFKk3RlmQdp4%2FzGr1g15LSx%2FYveUSfJHhEWkZa%2FsJHJtL3TTW6Fn%2FDU0yMgtP1RSL0AYHgkLNzcNqK2eu7EqFXEqXnTtNuHrt4jSHC7TfVSWIY0PkV98eajOv%2BzCTOJBNaIydMMkSxPZmkXx43XFbY5XNgwqySiCXY2nGxQQ%3D%3D&X-Amz-Signature=a4e57aa008adafae174bc711e302404b2be9702158990c07939f4ffbac82574d&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Fig. 12.

Fig. 13.

Fig. 14.

Fig. 15.
![The influence of damping changes on the vibrations of the front bogie caused by the force impulse on the wagon with the semi-trailer. Graphs of vertical displacement as a function of time for two different damping values with marked amplitudes for calculating the logarithmic vibration damping decrement for suspensions with different damping variants Cmin = 170 [N·s/mm] and Cmax = 17000 [N·s/mm]](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/694828ee7c29e05adc524c36/j_ama-2025-0077_fig_015.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKISKFYITU%2F20260221%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260221T210441Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEOj%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIQCySd1L9yAJPQ7UvaNmL8lA74x2ED%2BXD3DQdGLIAwLtHAIgW0XytHRIqeW28YvAqtCtf2fi59fTRe4n0S55vf3uyUoqxgUIsf%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDJB%2BMCeKD2ss%2F6FzmyqaBc7yAoqzxOuJJpcwUp004K2Ob2iuAT%2FO5VQc6SOH%2B5t1WJHrX2ZrlO%2B6EYPRh8UF8VYEMnYEXiuZdzwy1ru6xlRVAyuZxxvf21Q1u10Dk6ubJr1ZBAv9JKEDobQxzAsTTqE4adj%2BDbA5hL7kJ3U%2F8KISjGvhwU6kwkIIaj8jYfwZ2wTOjWRR56USk5j4AZcSM7Job5olz7cM9HxLh2OskEo%2BZndjFgMLz%2BFD0Bi2iKKS3Aqo%2BUZ4do0NzoXetz64tULqvCNpAsk%2Fs%2Fu79YioE17thbN0fI2sAV3yZ0%2BVOfqpY0BAagIgP74M2iP26Tf9sL6boKy%2FwUwozrmxYM5ol%2BEvI%2FF7D%2B%2F%2BFjN%2BffbZl8dPbin0GORG2D%2B3hL1awmqrVmljtJ4XcluHJcl%2BLZZXJTZm6eXZz%2BWyFf6ga9gLVh7FvX3PxaCcLEOX%2BqlEekOoaTorNHZH5hDg5uog8MGO9erKXVeVPlbJzkMVQ7O8ONNShpM2zcGmAcHGWEMK9ffMir1yw0ro9fSqYF%2Fx547lYnEGdaefS9gcyP8b0a3sxKuAsJEj3ltkDnl84hz5jmOQY0uNswnOvjWbCinFf02aO1f%2FMiaB3JZSimc3cQXeS14vp6FSUZ%2FH%2FtuH3eYalfqLOKQriJcqd6NJuvnFCbLqyV1%2F2R3ETxH43ol14jbLlMuHq21ReE68BD%2Bsur5iy%2BZM3OcquG5TqhKNQscU8Q5Mpr8%2BiBdt8%2FhH2bN4Q9pNNxOcyEBAshGH8KA5JlG3fy6bXF2Nu3NQjiZNhAT0F7Hbii5NlntzrxSj4uLSetjLHHcMDx6X2ZvEo%2BsvO0cntDmiDKYVheeSPM11R49hVW4a4cXy4E5VeeARev5epJrszE0R5n314NGc%2F4SvaDCto%2BfMBjqxATRfbRzKZQraQG5us2TwRmhyXMllVtWUAqlvJw%2BTERUUG1dnSZ7ij%2BEJv%2BNLu1UzfC0JFDRFKk3RlmQdp4%2FzGr1g15LSx%2FYveUSfJHhEWkZa%2FsJHJtL3TTW6Fn%2FDU0yMgtP1RSL0AYHgkLNzcNqK2eu7EqFXEqXnTtNuHrt4jSHC7TfVSWIY0PkV98eajOv%2BzCTOJBNaIydMMkSxPZmkXx43XFbY5XNgwqySiCXY2nGxQQ%3D%3D&X-Amz-Signature=c37725790b341137105644f4c3ef4c963b336e1a96c4bee9142e4ea9bc812545&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Fig. 16.

Fig. 17.

Fig. 18.

Fig. 19.

Fig. 20.

Fig. 21.

Fig. 22.

Summary of the maximum and minimum reactions in the wheelrail contact for various conditions of the wagon motion simulation
| Straight track | Curved track | ||
|---|---|---|---|
| Speed V [km/h] | 100 | 100 | 120 |
| Reaction of the front right wheel – RPPmax[kN] | 163.8 | 264 | 283 |
| Reaction of the front right wheel – RPPmin [kN] | 138.2 | -4 | -6 |
| Reaction of the rear left wheel – RTLmax[kN] | 119 | 217.9 | 308 |
| Reaction of the rear left wheel - RTLmin [kN] | 87.4 | ~0 | 10 |
Summary of parameters describing the wagon’s natural vibrations
| WAGON WITHOUT SEMI-TRAILER | WAGON WITH SEMI-TRAILER AND LOAD | |||
|---|---|---|---|---|
| DAMPING | Cmin | Cmax | Cmin | Cmax |
| Vibration period – T | 0.2 s | 0.116 s | 0.232 s | 0.172 s |
| Vibration frequency – ϑ | 5 Hz | 8.6 Hz | 4.3 Hz | 5.8 Hz |
| Amplitude after releasing vibrations – Amax | 3.5 mm | 2.8 mm | 1.5 mm | 2.7 mm |
| Logarithmic damping decrement – δ | 0.07 | 1.5 | 0.51 | 1.69 |