Involute Position Determination in Asymmetrical Gear Cutting
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Solution Overview
Problem
Existing methods for determining the position of involutes in gear wheels with asymmetrical or conical tooth shapes are inaccurate, as they rely on averaging methods suitable for symmetrical gears, failing to account for the geometric properties of asymmetrical and conical toothing, which leads to incorrect results and potential gear damage due to improper machining.
Innovation Solution
A method that involves generating relative movements between the workpiece and tool to detect contact points on both tooth flanks, calculating angles of rotation, feeds, center distance, and cross-axis positions, and using kinematic chains to determine the position of involutes based on known geometric properties of the tool and workpiece, allowing for precise positioning even in asymmetrical and conical gearing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If averaging methods are used to determine involute positions, then the process is simple and fast, but the measurement precision is insufficient for asymmetrical and conical gearing
Solution Approach 1:
The measurement process is segmented into multiple discrete contact point detections across different tooth flanks and positions. Instead of a single averaged measurement, the system performs segmented measurements at specific locations (e.g., left and right flanks, different radial positions) and uses these individual data points to calculate precise involute positions through coordinate transformation and kinematic chain calculations.
2Device complexity
If conventional touching methods are used, then the device complexity is low, but the manufacturing precision deteriorates for asymmetrical and conical toothing
Solution Approach 1:
A coordinate transformation system and kinematic chain calculation model serve as intermediaries between the simple contact detection and the final precise position determination. The intermediary layer processes the raw contact coordinates through mathematical transformations that account for asymmetrical and conical geometry, enabling high precision without requiring complex measurement hardware.
3Measurement precision
If multiple measuring points are taken for conical and asymmetrical gearing, then the measurement precision improves, but the loss of time increases due to multiple measurements
Solution Approach 1:
The system performs preliminary actions by pre-calculating transformation matrices and kinematic chain parameters based on known gear geometry (asymmetrical and conical properties). These preliminary calculations enable rapid processing of multiple contact points during actual measurement, reducing the time penalty of taking multiple measurements while maintaining high precision.
4Ease of operation
If automated centering is implemented for asymmetrical gearing, then the ease of operation improves, but the device complexity increases
Solution Approach 1:
The measurement system performs self-service by automatically calculating involute positions and determining optimal centering based on the measured contact points and known gear geometry. The system uses the measured coordinates and kinematic chain models to autonomously determine the correct positioning without requiring external intervention or complex manual adjustment procedures.
Data Source
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AI summary
Method for determining the position of the involutes of a pre-cut workpiece within a gear cutting machine using a toothed tool, comprising the following steps: generating a first relative movement between the workpiece and the tool, detecting the resulting first contact between a first tooth flank of the tool and a first tooth flank of the workpiece and acquiring a first set of coordinates to represent the relative movement of the workpiece and the tool; generating a second relative movement between the workpiece and the tool, detecting the resulting second contact between a second tooth flank of the tool and a second tooth flank of the workpiece and acquiring a second set of coordinates to represent the relative movement of the workpiece and the tool; and determining the angles of rotation and the feed rates.of the center distance and the axis cross angle of tool and workpiece based on the first and second coordinate sets and subsequent calculation of the position of the involutes based on the rotation angles, the feeds, the center distance and the axis cross angle.