Temperature models for grinding system state monitoring

Abstract

The grinding temperature limits the productivity of this operation and is an important parameter for assessing the state of the grinding system. However, there is no information about the current grinding temperature in the existing computer systems for monitoring and process diagnostics on CNC grinding machines. This is due to the difficulty of measuring this parameter directly or indirectly. In the first case – difficulty with the installation of temperature sensors, in the second – there are no acceptable mathematical models for determining the grinding temperature. The objective of the study is development of a simpler temperature model which is acceptable for the modern grinding with large values of the workpiece velocity relative to the grinding wheel. To reach the study objective a classification of solutions of three-, two-, and one-dimensional differential equations of heat conduction with the same initial and boundary conditions was made to research the grinding temperatures with the help of these solutions under otherwise equal conditions. The conditions of results close agreement of the solutions are established depending on the geometrical configuration of the contact zone between the grinding wheel and the workpiece: H/L <1 and H >4, where H and L are half width and half length of the contact zone, respectively. The above three solutions of differential heat conduction equations obtained under boundary conditions of the second kind and were converted to a uniform dimensionless form, in which the dimensionless temperature depends on the coordinate and dimensionless time multiplicity of the Peclet number, which characterizes this time, the dimensionless half and velocity of the moving heat source. A comparative analysis of surface and deep temperatures was performed for the above three solutions depending on the Peclet number. The possibility of determining the grinding temperature on modern highspeed CNC machines with a one-dimensional solution with H > 4 on the basis of computer subsystems of designing, monitoring and diagnosing of grinding operations is shown