Heating device and image forming apparatus with abnormality detection

A heating device comprising:

• a driving member configured to be driven by a driver and to rotate;
• a driven member being in contact with the driving member and configured to rotate with the rotation of the driving member;
• a heater configured to heat a surface of at least one of the driving member and the driven member;
• a first temperature detector configured to measure the temperature of the heated surface;
• a second temperature detector configured to measure the temperature around the heater;
• and
• a controller operable to control heating of the heater, the controller comprising:
• a first calculator operable to calculate a slope of a first temperature difference of a first time point, the first temperature difference being a difference between a first temperature detected by the first temperature detector at the first time point and a second temperature detected by the second temperature detector at the first time point;
• a second calculator operable to calculate a slope of a second temperature difference of a second time point, the second time point being a time point when a predetermined time has elapsed from the first time point, the second temperature difference being a difference between a third temperature detected by the first temperature detector at the second time point and a fourth temperature detected by the second temperature detector at the second time point;
• a third calculator operable to calculate a change ratio of temperature difference slope, based on the slope of the first temperature difference and the slope of the second temperature difference;
• and
• a determiner operable to determine that an abnormality occurs when the change ratio of the temperature difference exceeds a threshold.

A heating device comprising:

• a driving member configured to be driven by a driver and to rotate;
• a driven member being in contact with the driving member and configured to rotate with the rotation of the driving member;
• a heater configured to heat a surface of at least one of the driving member and the driven member;
• a temperature detector configured to measure the temperature of the heated surface;
• and
• a controller operable to control heating of the heater based on the measurement result of the temperature detector, the controller comprising:
• a determiner operable to determine that an abnormality occurs when a second order differential value of change of the temperature detected by the temperature detector with time exceeds a threshold.