SQL Query product variations by parent category

global $wpdb;

$sql = "
     SELECT p.ID, p.post_parent
     FROM {$wpdb->posts} as p
     INNER JOIN {$wpdb->term_relationships} AS tr ON ( p.post_parent = tr.object_id)
     WHERE tr.term_taxonomy_id IN ( 51, 52 )
     AND p.post_type = 'product_variation' AND p.post_status = 'publish' ORDER BY p.ID ASC
     ";

$variations = $wpdb->get_results( $sql );