| The double arc harmonic reducer has many characters such as the high transmission accuracy,large bearing capacity and small return difference.So the double arc harmonic reducer is widely used in precision transmission fields such as radar,satellites,medical equipment and robots.The design and manufacture technology of the double arc harmonic reducer rigid gear shape cutter are complex.So the harmonic reducer is difficult to product.The paper establishes a mathematical model for the simulation of slotting machining of rigid gears,deduces the tooth profile of the double-arc gear-shaping cutter,and explores the relationship between the key parameters of the gear-shaping cutter.What's more the effective length of the cutter is calculated,and the tooth shape of the cutter is optimized.On the basis,the influence of run-out errors,gear-shaping cutter parameters and processing parameters on the cutter machining precision is calculated.Finally,the influence of cutter tooth number on the cutter machining precision is verified by experiments.The main contents of this paper are as follows:(1)Based on the tooth profile of the double-Circular-arc rigid gear,the paper establishes the mathematical model of cutting by the precise kinematic method.What's more,the paper obtains the original section tooth profile of the cutter,studies the relationship between the front angle of the top edge and the back angle of the top edge,explores the relationship between the front angle of the side edge and the back angle of the side edge.(2)By establishing the mathematical model of cutting after grinding,the paper deduces the gear-shaping cutter's cutting edge tooth profile after grinding,and calculates the effective length of the cutter,prolongs the effective length of the cutter by optimizing the tooth shape of the cutter.(3)The paper establishes the mathematical model of cutting containing the run-out error,studies the influence of the run-out error on the tooth-profile error of rigid gear,and explores the influence of the machine tool run-out error and gear-shaping cutter run-out error on the machining accuracy of the cutter.(4)By establishing the mathematical model of cutting containing the number of gear-shaping cutter and process parameters,the paper analyzes the influence of the cutter tooth number on the rigid gear tooth error,studies the influence of the cutter tooth number on the effective length and machining accuracy of the cutter.And the influence of slotting rings on the machining accuracy of the cutter is studied.(5)The experiment measures the pitch error and cumulative pitch error of the left and right tooth surfaces of the rigid gear processed by the 55 tooth cutter and 69 tooth cutter,.And then,the paper analyzes the rigid gear's transmission error component by the above two kinds of errors.It is proved that the gear-shaping cutter with more tooths numbers have higer machining accuracy than cutter with less tooths numbers. |
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