When rolling helical gears (including helical gears), a reasonable selection of the helical direction of the hob has a certain influence on the precision of the hobbed gear. When cutting teeth, it is desirable to install the hob with a smaller mounting angle (the hob thread is in the same direction as the spiral shaft of the gear being cut, and its mounting angle is small). Because of this, the hob rotates in the direction of the tangential force of the tangential gear opposite to that of the machine table. That is, the hobbing machine indexing worm gear to the worm gear in the opposite direction, this can eliminate the worm gear pair gap, not easy to cause vibration, thereby improving the cutting accuracy, reducing the surface roughness, while allowing the hob to participate in the cutting more teeth , Cutting conditions are good, and the quality of the cut gear is relatively high. If the installation angle of the hob is large, the number of teeth participating in the cutting is reduced, the cutting load is concentrated, the teeth of the cutter are easily worn, vibration is easily generated, and the quality of the cut gear is poor. Therefore when machining a right-handed gear, a right-hand hob should be used: when machining a left-handed gear, a left-hand hob should be used, which can reduce the installation angle of the hob. As for the processing of spur gears, either left or right rotary hobs can be used. Their mounting angle is always equal to the pitch angle of their spirals. It is just different when the wheel blanks are turned. When a standard hob is used for hobbing a standard gear, it is equivalent to meshing the rack with the gear. At this time, the centerline of the hob tooth is tangent to the sub-circle of the gear. Because the tooth thickness of the gear is misaligned, the hob will inevitably generate a small amount of diameter. Displacement causes the centerline of the hob tooth to separate from the gear, which changes the installation angle of the hob: When the hobbing gear is hobbed by a standard hob, the hob must be in accordance with the product of displacement coefficient and gear module specified in the drawing. To adjust (actually to measure the displacement of the gear tooth thickness), it will also cause changes in the installation angle of the hob: the hob bluntly grinds the rake face, not only the outer diameter will decrease, but also the pitch circle diameter It will decrease, and the pitch and mounting angle of the hob will also change. This article details the selection of the hob rounding, the change of the hob mounting angle when the center distance between the hob and the gear to be cut is different, the compensation adjustment of the hob mounting angle when using different angle hobs, and the method of accurately adjusting the installation angle. 1 The selection of the diameter of the hob sub-circle In the production practice, the installation angle of the hob is adjusted only according to the spiral angle of engraved by the new hob, and the hob is not adjusted according to the spiral angle after the hob regrind. The installation angle. In fact, it is annoying to do so, which will bring great inconvenience to production. Therefore, the hob diameter should be selected in consideration of the change of the spiral angle caused by the new hob sharpening. From the new hob sharpening to the last time it cannot be used, the pitch circle of the hob causes the difference between the pitch angle and the rounding angle to rise to a small value, which reduces the tooth profile error and tooth thickness variation. Using the formula for calculating the pitch of the helical gear, the diameter of the hob can be calculated: da=ms·z=mn·z/cosba=mn·z/cos (p/2-la)=mn·z/sina (1) Where: da - the diameter of the gear or hob sub-circular ms - the modulus of the gear face mn - the normal modulus of the gear or hob z - the number of gear teeth or the number of hob ba - the gear sub-round helix angle Or hob round spiral angle la - gear spiral angle or hob spiral angle
Fig. 1 In formula (1), if z = 1 is a single-head hob, and Fig. 1 shows a new hob end projection, it will be discarded after being sharpened to the OC surface. If the circle diameter is taken in the OB profile, the circle diameter of the single-head hob is related to the tooth height and the amount of backlash. The elevation angle is sin la=mn/da (2) and the pitch angle on the new hob pitch circle is Sin l1=mn/d1 (3) The angle of elevation on the pitch of the old hob sharpened to be unusable is sin l2=mn/d2 (4) ∵ d1>da>d2 ∴sin l2>sin la>sin l1 L2>la>l1. If the sub-circle is taken within the OA profile, the sub-circular diameter is only related to the tooth height, and the spiral angle of the new hob sub-circle is sin l1a=mn/d1a (5) When using the old hob pitch spiral angle sin l2a = mn/d2a (6) ∵ l1a = l1: l2a> la ∴ l2a-l1a> la-l1 ∵ l2a = l2: l1a> la ∴ l2a-l1a> l2 -la As long as we consider the hob of the circle diameter determined by the top height and the hob that considers both the top height and the circle diameter determined by the amount of backlash, the former is due to the pitch angle of the pitch circle and the diameter of the circled circle. The difference is greater than the latter, so the design hob to select the sub-circle diameter should press the latter, in order to ensure that the new and old hob installation angle change is reduced, improve the gear tooth accuracy, thereby reducing the change in tooth thickness. 2 When the center distance between the hob and the gear to be cut is different, the installation angle of the hob is changed. When a standard hob is used to hob the standard gear, it is equivalent to the mesh between the rack and the gear. At this time, the centerline of the cutter is tangent to the gear, and the cutter tooth The center line is the pitch line, and the gear segmentation is the purely rolling pitch circle on the hob line. After the hobbing is completed, theoretically speaking: the tooth thickness on the pitch circle of the gear is equal to that of the hob tooth. Slot Width: The circumference of the gear face (helical gear or helical gear) is equal to the circumference of the hob. In fact, there are errors in the thickness of the hob and the tooth thickness of the teeth. Therefore, the centerline of the hob tooth is not tangent to the gear and is separated. The amount of separation depends on the amount of radial displacement caused by the gear thickness deviation. When the standard hob is used to cut the gear, when the center distance between the gear to be cut and the hob increases, the hob pitch increases. When the center distance between the cut gear and the hob decreases, the hob pitch decreases. When hobbing a standard gear, the pitch circle diameter of the hob is daw, so daw=da+Esi/2sina0. Where Esi is the lower deviation of the gear normal length tooth thickness. If the work diagram gives the deviation of the thickness of the sub-chord tooth and the thickness of the fixed chord tooth, the deviation from the length of the common normal can be calculated. Esi symbols should be substituted for calculations. Let a0 be the gear minuteness pressure angle: change the pitch angle of the hob due to gear tooth thickness deviation to law, then sin law=mn/daw=mn/(da+Esi/2sina0)=sin la/(1 +Esisin la/2mnsina0) (7) The actual mounting angle of the hob is G=ba±law (8) When hobbing the translating gear with a standard hob, set the pitch circle diameter of the hob to dawe, then dawe= Da+2mne+Esi/2sina0. In the equation, e is the displacement coefficient (e>0 or e<0), and the symbol of e should be substituted into the calculation. The change of the pitch angle of the hob due to the number of bits changed to lawe can be simplified after finishing. sin lawe=mn/dawe=mn/(da+2mne+Esi/2sina0) Simplification can be achieved after sin lawe= Sin la/(1+2esin la+Esisin la/2mn·sina0) (9) The actual mounting angle of the hob is Ge=ba±lawe (10) 3 Compensation of the actual mounting angle of the hob Adjustment of the hobbing precision standard gear In the case of gear change and gear change, if the tooth profile accuracy is high and the change in tooth thickness is small, the installation angle of the reel cannot be adjusted according to the engraving of the reel, and it should be in accordance with equations (7), (8), (9) And (10) Calculate the actual angle to adjust the hob mounting angle to reduce the tooth profile error and tooth thickness variation. When using equation (7) for calculations, such as |law-la |>4', adjust the actual installation angle of the reel and adjust it according to the formula (8) G=ba±law. Installation: Use equation (9) for calculation If, for example, |lawe-la|>4', adjust the actual mounting angle of the reel, and adjust it according to the formula (10) Ge=ba±la±lawe.
Fig. 2 4 Accurate adjustment of the mounting angle of the hob The adjustment of the accuracy of the mounting angle of the hob on the hobbing machine affects the change in tooth profile accuracy and tooth thickness of the cut gear. Normally, the adjustment method is that the operator adjusts the tool holder dial scale and the vernier scale as shown in Fig. 2. The vernier scale is generally 6' in each cell, so the adjustment angle of the mounting angle of the reel is 6'. When finishing the bevel gear tooth profile, the hob mounting angle needs to be accurately adjusted to 1', or even to the second. At this time, the vernier scale obviously cannot meet the needs, thus making it difficult to precisely adjust the hob mounting angle. We use a dial gauge to adjust the number of cells on the cursor to the number of cells on the dial gauge. This allows the hob's mounting angle to be accurately adjusted to a second. Adjust the installation angle of the hob as shown in Fig. 2. Ba±la=5° 56'38". Precise adjustment method: first adjust the angle of the tool holder to 5°54', and then use a dial indicator to install the deflection plate. Rotate the center of any position and let the tool holder turn 6'. Look at the dial indicator as 540 grids. The number of 1 points is 540÷6=90 grids. The number of grids in 1" is 90÷60=1.5 grids. From this, when the 2'38" is obtained, the indicator of the dial gauge should be 2x90+38x1.5=237 grids. The tool rest should be reset to 5°54', and the tool rest should be adjusted by 237 grids. The required installation angle of the hob is 5°56'38"accurate to seconds. 4 Conclusion When hobbing a gear with a standard hob, whether it is a hobbing standard gear or a hobbing transformation gear, the mounting angle of the hob will change: After the new hob is sharpened, the pitch angle on the pitch circle will change and Causes the hob installation angle to change. The change of the angle of advance after hob sharpening can be controlled by reasonably selecting the diameter of the hob to make the installation angle of the hob after the hob sharpened smaller, so as to improve the accuracy of the tooth profile and reduce the change of the tooth thickness. The use of a standard hob to roll standard gears and shift gears means the final fine-tooth gear tooth profile: Only when the hob mounting angle is adjusted by the reel angle engraved by the reel to achieve tooth profile accuracy, press ( 7) (8) (9) (10) Adjust the formula. If it is not the last fine tooth shape but rough or semi-finish tooth shape, pre-machining grinding, rake, shaving, etc., it is not necessary to adjust the installation angle of the reel by law or lawe.
Fig. 1 In formula (1), if z = 1 is a single-head hob, and Fig. 1 shows a new hob end projection, it will be discarded after being sharpened to the OC surface. If the circle diameter is taken in the OB profile, the circle diameter of the single-head hob is related to the tooth height and the amount of backlash. The elevation angle is sin la=mn/da (2) and the pitch angle on the new hob pitch circle is Sin l1=mn/d1 (3) The angle of elevation on the pitch of the old hob sharpened to be unusable is sin l2=mn/d2 (4) ∵ d1>da>d2 ∴sin l2>sin la>sin l1 L2>la>l1. If the sub-circle is taken within the OA profile, the sub-circular diameter is only related to the tooth height, and the spiral angle of the new hob sub-circle is sin l1a=mn/d1a (5) When using the old hob pitch spiral angle sin l2a = mn/d2a (6) ∵ l1a = l1: l2a> la ∴ l2a-l1a> la-l1 ∵ l2a = l2: l1a> la ∴ l2a-l1a> l2 -la As long as we consider the hob of the circle diameter determined by the top height and the hob that considers both the top height and the circle diameter determined by the amount of backlash, the former is due to the pitch angle of the pitch circle and the diameter of the circled circle. The difference is greater than the latter, so the design hob to select the sub-circle diameter should press the latter, in order to ensure that the new and old hob installation angle change is reduced, improve the gear tooth accuracy, thereby reducing the change in tooth thickness. 2 When the center distance between the hob and the gear to be cut is different, the installation angle of the hob is changed. When a standard hob is used to hob the standard gear, it is equivalent to the mesh between the rack and the gear. At this time, the centerline of the cutter is tangent to the gear, and the cutter tooth The center line is the pitch line, and the gear segmentation is the purely rolling pitch circle on the hob line. After the hobbing is completed, theoretically speaking: the tooth thickness on the pitch circle of the gear is equal to that of the hob tooth. Slot Width: The circumference of the gear face (helical gear or helical gear) is equal to the circumference of the hob. In fact, there are errors in the thickness of the hob and the tooth thickness of the teeth. Therefore, the centerline of the hob tooth is not tangent to the gear and is separated. The amount of separation depends on the amount of radial displacement caused by the gear thickness deviation. When the standard hob is used to cut the gear, when the center distance between the gear to be cut and the hob increases, the hob pitch increases. When the center distance between the cut gear and the hob decreases, the hob pitch decreases. When hobbing a standard gear, the pitch circle diameter of the hob is daw, so daw=da+Esi/2sina0. Where Esi is the lower deviation of the gear normal length tooth thickness. If the work diagram gives the deviation of the thickness of the sub-chord tooth and the thickness of the fixed chord tooth, the deviation from the length of the common normal can be calculated. Esi symbols should be substituted for calculations. Let a0 be the gear minuteness pressure angle: change the pitch angle of the hob due to gear tooth thickness deviation to law, then sin law=mn/daw=mn/(da+Esi/2sina0)=sin la/(1 +Esisin la/2mnsina0) (7) The actual mounting angle of the hob is G=ba±law (8) When hobbing the translating gear with a standard hob, set the pitch circle diameter of the hob to dawe, then dawe= Da+2mne+Esi/2sina0. In the equation, e is the displacement coefficient (e>0 or e<0), and the symbol of e should be substituted into the calculation. The change of the pitch angle of the hob due to the number of bits changed to lawe can be simplified after finishing. sin lawe=mn/dawe=mn/(da+2mne+Esi/2sina0) Simplification can be achieved after sin lawe= Sin la/(1+2esin la+Esisin la/2mn·sina0) (9) The actual mounting angle of the hob is Ge=ba±lawe (10) 3 Compensation of the actual mounting angle of the hob Adjustment of the hobbing precision standard gear In the case of gear change and gear change, if the tooth profile accuracy is high and the change in tooth thickness is small, the installation angle of the reel cannot be adjusted according to the engraving of the reel, and it should be in accordance with equations (7), (8), (9) And (10) Calculate the actual angle to adjust the hob mounting angle to reduce the tooth profile error and tooth thickness variation. When using equation (7) for calculations, such as |law-la |>4', adjust the actual installation angle of the reel and adjust it according to the formula (8) G=ba±law. Installation: Use equation (9) for calculation If, for example, |lawe-la|>4', adjust the actual mounting angle of the reel, and adjust it according to the formula (10) Ge=ba±la±lawe.
Fig. 2 4 Accurate adjustment of the mounting angle of the hob The adjustment of the accuracy of the mounting angle of the hob on the hobbing machine affects the change in tooth profile accuracy and tooth thickness of the cut gear. Normally, the adjustment method is that the operator adjusts the tool holder dial scale and the vernier scale as shown in Fig. 2. The vernier scale is generally 6' in each cell, so the adjustment angle of the mounting angle of the reel is 6'. When finishing the bevel gear tooth profile, the hob mounting angle needs to be accurately adjusted to 1', or even to the second. At this time, the vernier scale obviously cannot meet the needs, thus making it difficult to precisely adjust the hob mounting angle. We use a dial gauge to adjust the number of cells on the cursor to the number of cells on the dial gauge. This allows the hob's mounting angle to be accurately adjusted to a second. Adjust the installation angle of the hob as shown in Fig. 2. Ba±la=5° 56'38". Precise adjustment method: first adjust the angle of the tool holder to 5°54', and then use a dial indicator to install the deflection plate. Rotate the center of any position and let the tool holder turn 6'. Look at the dial indicator as 540 grids. The number of 1 points is 540÷6=90 grids. The number of grids in 1" is 90÷60=1.5 grids. From this, when the 2'38" is obtained, the indicator of the dial gauge should be 2x90+38x1.5=237 grids. The tool rest should be reset to 5°54', and the tool rest should be adjusted by 237 grids. The required installation angle of the hob is 5°56'38"accurate to seconds. 4 Conclusion When hobbing a gear with a standard hob, whether it is a hobbing standard gear or a hobbing transformation gear, the mounting angle of the hob will change: After the new hob is sharpened, the pitch angle on the pitch circle will change and Causes the hob installation angle to change. The change of the angle of advance after hob sharpening can be controlled by reasonably selecting the diameter of the hob to make the installation angle of the hob after the hob sharpened smaller, so as to improve the accuracy of the tooth profile and reduce the change of the tooth thickness. The use of a standard hob to roll standard gears and shift gears means the final fine-tooth gear tooth profile: Only when the hob mounting angle is adjusted by the reel angle engraved by the reel to achieve tooth profile accuracy, press ( 7) (8) (9) (10) Adjust the formula. If it is not the last fine tooth shape but rough or semi-finish tooth shape, pre-machining grinding, rake, shaving, etc., it is not necessary to adjust the installation angle of the reel by law or lawe.
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