Yii, relation model filter search

I am battling with CGridView filtering using the related model column, I have two models Cars and Colour, so Colour has_many Car and Car belongs_to Colour. The grid column from related model displays fine, I'm just not able to filter with it. I am getting mysql error

Column not found: 1054 Unknown column 'carName'

Colour model HAS_MANY - Cars

I declaired the variable $carName from the Car model, so this model can see it.

public $carName;
public function rules()
{
   return array(
          array('id, carName, colourName', 'safe', 'on'=>'search'),
               )
}
public function relations()
{

    return array(
                'CarsObj'=>array(self::HAS_MANY, 'Cars', 'colourID')
    );
}

public function search()
{ 

    $criteria=new CDbCriteria;
    $criteria->with = "CarsObj";
    $criteria->compare('carName', $this->carName, true);

    $criteria->compare('id',$this->id);
    $criteria->compare('colourName',$this->colourName,true);


    return new CActiveDataProvider($this, array(
        'criteria'=>$criteria,
    ));
}

Car Model BELONGS_TO - Colour

public function relations()
{ 
 return array( 
   'ColourObj'=>array(self::BELONGS_TO, 'Colour', 'colourID')
 );
}

CGridView, i am using the Colour Model search as my dataProvider

 $model = new Colour('search');
 $data = $model->search(); 
 $this->widget('zii.widgets.grid.CGridView', array(
           'dataProvider'=>$data
           ,'filter'=>$model 
           ,'pager'=>array('header'=>'')  
           ,'columns'=>array( //related model column
                    'id',
                     'colourName',
                      array(
                            'header' => 'carName',
                            'type' => 'raw', 
                            'name' => 'carName',
                            'value' => function($data, $row) { //$data is item of DataProvider, $row is number of row (starts from 0)
                                $carNames= CHtml::listData((array)$data->ColourObj, 'id', 'carName');
                                return implode(', ', $carNames);
                            }
                            )

By default CActiveRecord using lazy load. You need to set attribute together true. Also it's a good practice to set table alias when you using with.

public function search(){ 
    $criteria=new CDbCriteria;
    $criteria->together = true;
    $criteria->with = 'CarsObj';
    $criteria->compare('CarsObj.carName',$this->carName,true);
    $criteria->compare('t.id',$this->id);
    $criteria->compare('t.colourName',$this->colourName,true);

    return new CActiveDataProvider($this, array(
        'criteria'=>$criteria,
    ));
}