In the franchise's story, Hayato Hayasugi, the train-loving son of a train museum curator, accidentally stumbles into his dad's secret research lab one day. Inside he finds the E5 bullet train. As soon as he enters, he hears an announcement that a mysterious enemy, the Bachigami ("bee god"), is attacking the city of New Saitama. Luckily, with the touch of his father's Shinca ("evolve") card, the bullet train he's in transforms into a mighty robot — the Shinkalion E5 Hayabusa. 

In the anime's story, Hayato and other children will serve as conductors to pilot the Shinkalion. The children must work together with the adults of the "Shinkansen Ultra Evolution Institute" (SUEI) to defeat a monster that looks like a jet black bullet train.
 
(Source: Anime News Network)

The second Shinkansen Henkei Robo Shinkalion television anime series based on Takara Tomy's toy line.

In the year 2015, the Angels, huge, tremendously powerful, alien war machines, appear in Tokyo for the second time. The only hope for Mankind's survival lies in the Evangelion, a humanoid fighting machine developed by NERV, a special United Nations agency. Capable of withstanding anything the Angels can dish out, the Evangelion's one drawback lies in the limited number of people able to pilot them. Only a handful of teenagers, all born fourteen years ago, nine months after the Angels first appeared, are able to interface with the Evangelion. One such teenager is Shinji Ikari, whose father heads the NERV team that developed and maintains the Evangelion. Thrust into a maelstrom of battle and events that he does not understand, Shinji is forced to plumb the depths of his own inner resources for the courage and strength to not only fight, but to survive, or risk losing everything. 
(Source: AniDB) 
 
 Note: Later releases include edited versions of Episodes 21-24 called the "Director's Cut" with some visual editing and adding extra scenes that appeared in the theatrical recap 'Death'.

A group called the Shinkansen Ultra Evolution Institute was investigating a recent rash of monster attacks happening in Japan after the appearance of a mysterious Black Shinkansen. The SUEI had a major weapon for the fight - Shinkalions, bullet trains that can transform into giant mecha. One boy, Hayato Hayasugi, was a huge fan of trains and stumbled upon his father’s secret work for the SUEI. Surprisingly, Hayato soon became a Shinkalion driver! As perhaps Japan’s best chance of survival, Hayato and other kids take on the great responsibility of fighting otherworldly enemies. 

Now, a new giant enemy has come from space looking to conquer the planet. Although the SUEI have a new prototype Shinkalion known as the ALFA-X to take up the fight, Hayato’s father, Hokuto, disappears. A 9-year-old version of Hokuto leaps through time to the present to help fight the alien attackers and drives the ALFA-X! 

(Source: Tokyo Otaku Mode)

"Unknown" is a mysterious enemy that suddenly appeared a long time ago. As a countermeasure, the "Evolutionary Railway Development Agency" (ERDA) has developed the "Shinkalion" robot that transform into bullet trains, to prepare for the threat.
 
"I want to be a cool person who can protect something..." Taisei Oonari, a second-year junior high school student, transfers to Shinkai Gakuen Middle School in search of clues about his older sister who disappeared two years ago.
 
Just then, the Unknown appears for the first time in 10 years. Taisei happens to have a high aptitude value as a Shinkalion pilot, and is forced to make a decision to fight it. What is the true nature of the Unknown and what is its purpose? What is the truth that comes to light at the end of the fight? The story of the boys' determination and growth begins now. 
(Source: Official Website, translated) 
Note: Relations are provisional and will be updated when more info is announced.

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