api update variation

Hi people! I am fighting with a rest problem. I ve an script that ve to update stocks of a woocommerce. Simple product there is no problem but variation products.. I can’t update them, I ve this:

...
    $is_variation = $product instanceof WC_Product_Variation;

    $data = [
        'id' => $product->id,
        //'regular_price' => $search_item['price'],
        'stock_quantity' => $units,
        'manage_stock' => true
    ];

    if($is_variation){
        $result = $woocommerce->put('products/'.$product->parent_id.'/variations/'.$variation_id, $data);
    }
...

Can someone help me in this? thanks! ??