Gear tooth profile simulation apparatus and method, and machining tool edge surface simulation apparatus and method

A simulation method for performing a simulation of a tooth profile of a gear to be formed by gear machining, the gear machining involving:

• causing a central axis of a workpiece and a central axis of a machining tool including on its outer periphery a plurality of tool edges to incline relative to each other;
• synchronizing rotation of the workpiece around the central axis of the workpiece and rotation of the machining tool around the central axis of the machining tool;
• and
• rectilinearly moving, in this state, the machining tool relative to the workpiece along the central axis of the workpiece, and forming the gear on the workpiece,
• the simulation method comprising:
• a) storing info illation on a shape of the workpiece, information on a shape of a cross section of a portion of the workpiece that is necessary for the simulation and is to be machined into the gear, and information on a plurality of definition points indicating a shape of an edge surface of each tool edge of the machining tool;
• b) performing, in accordance with the information stored in step a), a calculation to obtain a plurality of passage points in a three-dimensional coordinate system where the definition points will pass through the cross section during the gear machining;
• c) causing the cross section in the three-dimensional coordinate system to be disposed parallel to a plane defined by predetermined two of axes of the three-dimensional coordinate system, and converting the passage points in the three-dimensional coordinate system obtained in step b) into passage points in a two-dimensional coordinate system;
• and
• d) deciding, in accordance with the passage points in the two-dimensional coordinate system obtained in step c), a shape of the tooth profile to be formed on the workpiece in the two-dimensional coordinate system.

A simulation apparatus for performing a simulation of an edge surface of each of a plurality of tool edges on an outer periphery of a machining tool for gear machining, the gear machining involving:

• causing a central axis of a workpiece and a central axis of the machining tool to incline relative to each other;
• synchronizing rotation of the workpiece around the central axis of the workpiece and rotation of the machining tool around the central axis of the machining tool;
• and
• rectilinearly moving, in this state, the machining tool relative to the workpiece along the central axis of the workpiece, thus forming a gear on the workpiece,
• the simulation apparatus comprising:
• a memory to store information on a shape of the workpiece, information on a shape of a cross section of the tool edge of the machining tool that is necessary for the simulation, and information on a plurality of definition points indicating a shape of a tooth profile of the gear;
• a first calculator to perform, in accordance with the information stored in the memory, a calculation to obtain a plurality of passage points in a three-dimensional coordinate system where the definition points will pass through the cross section during the gear machining;
• a second calculator to cause the cross section in the three-dimensional coordinate system to be disposed parallel to a plane defined by predetermined two of axes of the three-dimensional coordinate system, thus converting the passage points in the three-dimensional coordinate system obtained by the first calculator into passage points in a two-dimensional coordinate system;
• and
• a third calculator to decide a shape of the edge surface in the two-dimensional coordinate system in accordance with the passage points in the two-dimensional coordinate system obtained by the second calculator.

A simulation method for performing a simulation of an edge surface of each of a plurality of tool edges on an outer periphery of a machining tool for gear machining, the gear machining involving:

• causing a central axis of a workpiece and a central axis of the machining tool to incline relative to each other;
• synchronizing rotation of the workpiece around the central axis of the workpiece and rotation of the machining tool around the central axis of the machining tool;
• and
• rectilinearly moving, in this state, the machining tool relative to the workpiece along the central axis of the workpiece, and forming a gear on the workpiece,
• the simulation method comprising:
• a) storing information on a shape of the workpiece, information on a shape of a cross section of the tool edge of the machining tool that is necessary for the simulation, and information on a plurality of definition points indicating a shape of a tooth profile of the gear;
• b) performing, in accordance with the information stored in step a), a calculation to obtain a plurality of passage points in a three-dimensional coordinate system where the definition points will pass through the cross section during the gear machining;
• c) causing the cross section in the three-dimensional coordinate system to be disposed parallel to a plane defined by predetermined two of axes of the three-dimensional coordinate system, and converting the passage points in the three-dimensional coordinate system obtained in step b) into passage points in a two-dimensional coordinate system;
• and
• d) deciding a shape of the edge surface in the two-dimensional coordinate system in accordance with the passage points in the two-dimensional coordinate system obtained in step c).