Analytical model of a machining centre vertical axis with dynamic weight counterbalancing by a pneumatic proportional valve

High Speed Machining is getting more and more important in order to fulfill the goal of a reduction of manufacturing times and costs, together with an increase of quality. The design of modern Machining Centres is quite a difficult task, as high forces of inertia arise from high speeds. Thus, the development of simulative mathematical models can be of a great support for the designer. This paper deals with the development of a Simulink model of the vertical axis of a machining centre. Full details are provided on the mechanical and pneumatic devices it is composed of, in particular regarding the architecture and the operative behaviour of a pneumatic proportional valve. This is important device has the basic role of dynamically counterbalancing the spindle head weight, maintaining the resulting force at a constant value, independently of the applied motion. Full details on the algebraic and differential equations to be implemented are provided throughout the paper. The results proved the efficiency of the pneumatic device and its short response time. Processing the simulative outcomes led to the identification of an equivalent second-order dynamic system. A simplified Simulink model could therefore be developed accordingly and used to simulate the response to whatever motion law applied to the head.