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The Design for the Precision of Cylindrical Gear Transmission

Posted: 2014-04-11 04:28:53  Hits: 1188
 
I. The operating requirements of transmission gear
Gear is one of the most important parts of machines and equipments. To a certain extent, the precision of gear affects the quality of the whole machine or equipment. Because tooth shapes are relatively complex and have more parameters, the accuracy evaluation is quite intricacy.
The demands that modern industry requires gear transmission mainly consist of the following four items:
1. The change ratio of transmission for a lap must be as minor as possible to guarantee the accuracy of transfer motion. 
2. The change ratio of instantaneous transmission must be as minor as possible to guarantee transmission steady, small shock & vibration and low noise. 
3. Working flank must have good contact under loading conditions to guarantee enough bearing capacity and service life. 
4. Gear pairs must have appropriate backlash in circular tooth (Clearance between the meshing teeth of non-working surface).
For gears or gear pairs, emphasis on the above four requirements are different according to various uses and working conditions. For example, the control system or dividing transmission of servo system puts emphasis on transfer precision to guarantee the coordination of driving and driven gear motor. Automobile and tractor speed gear transmission puts emphasis on working steady to reduce noise. Low speed and heavy loading gear transmission puts emphasis on tooth surface contact accuracy to guarantee good tooth surface contact. High speed heavy machinery gear transmission in turbines have high requirement which needs a big backlash to guarantee large flow of oil. 
 
II. Gear error evaluation indicators
In order to check and accept gears, following evaluation indicators toward spur gears are established: 
1. Motion precision evaluation
(1) The tangential position error ΔFi"
Definition: When the measured gear and ideal gear turn with single mesh, relative to the rotation angle of the master gear in a lap of the measured gear, the maximum difference between the measured gear’s actual rotation angle and theory rotation angle. It is an overall metrics.
(2) Accumulative pitch error, K accumulative pitch error ΔFpk
Definition: On the reference circle of the measured gear, the maximum difference of any two corresponding flanks between actual and nominal arc length. It is an overall metrics.  
A. The radial runout of tooth ring ΔFr 
Definition: Within a lap of gear, when probe is on the tooth or tooth groove and double contact in the middle of depth of tooth, measuring head relative to the maximum change of gear axis. It is a one-way metrics.   
B. The changes of common normal ΔFw
Definition: Within a lap of the gear, the maximum difference of common normal between actual and nominal length. It is a tangential property one-way metrics.  
(3) Radial composite error ΔFi″
Definition: When the measured gear and ideal gear turned with double mesh, the maximum difference of the double mesh center distance in a lap of the measured gear. It is a radial direction property one-way metrics.  
In conclusion, we can use a comprehensive metrics or two one-way individual metrics to assess the errors of the transfer motion accuracy for gears. It should get one radial direction property and one tangential property to fully reflect the nature of the processing factors on the movement precision. 
 
2. Operation stability evaluation
(1) The tangential position error ΔFi"
Definition: On the tangential composite error record curve, the biggest value of little ripples. It is a overall metrics.    
(2) Radial composite error ΔFi″
Definition: On the radial composite error record curve, the biggest value of little ripples. In batch production, Δfi″ is a proxy indicator for Δfi". It is comprehensive metrics.
(3) Tooth profile error Δff and base pitch deviation Δfpb
A. Tooth profile error Δff: On the tooth face and in the working part of tooth profile, including two recent normal distance of the actual tooth form, except the addendum chamfering part. It is a one-way metrics.
B. Base pitch deviation Δfpb: The difference between the measured gear’s actual base pitch and the nominal base pitch. It is a one-way metrics.  
(4) Tooth profile error Δff and circular pitch deviation Δfpt: On the reference circle, the difference between the actual circular pitch and nominal circular pitch. It is a one-way metrics.    
(5) Circular pitch deviation Δfpt and base pitch deviation Δfpb
 In conclusion, Δfi" is a comprehensive metrics used for evaluate the gear working stability. For spur gear, Δfi' is caused by the base pitch deviation and tooth profile error. When using single indicators to assess the precision of the spur gear, no matter what kind of gear cutting method, it both can be used Δff and ΔFPB in principle. For larger diameter or below level 7 precision of gear, because the involute tester measuring range is limited and the price is more expensive, Δfpt and Δfpb should be chosen.
 
3. Contact accuracy evaluation
During gear working, both the tooth surface need to contact well to ensure uniform load distribution on tooth. On the tooth depth direction, tooth profile error will affect both the tooth surface contact. On the tooth width direction, tooth alignment error will affect both the tooth surface contact.      
Tooth alignment error means that tool feed direction and reference axis of gear is not parallel when processing gears. For example, tool slide guide rail tilts along the radial and tangential, tooth beating billet positioning end jumping relatives to the reference axis, etc. In addition, the adjustment error of the machine tool transmission chain is a primary cause to make the tooth alignment error. 
The tooth contact accuracy evaluation:   
(1) Tooth alignment error (ΔFβ) 
On the reference cylinder surface, the effective part of the tooth width (except the end chamfering), tooth alignment error means actual tooth line and the minimum transverse distance between the two lines of tooth alignment.    
Tooth alignment line is an intersecting line of tooth surface and reference cylinder surface. Usually spur gear’s Tooth alignment line is a straight line. The helical gear’s Tooth alignment line is spiral line. Design tooth alignment line can be modified. As high-speed heavy-duty gear is usually amended crowned teeth or tooth tip relief when designing to compensate tooth deformation under the load and improve the gear’s bearing capacity.
Tooth alignment error allows measure in the middle of the depth of tooth, and special tooth alignment inspection tester is usually used.
(2) Contact line error (ΔFb)
When a pair of helical gear meshing, in the meshing plane should be along a straight line to contact, this is the contact line. Contact line error is within the tangent plane of the base cylinder, parallel to the nominal contact line, and contain the normal distance between the two straight lines of the actual contact line. It affects the size of the tooth surface contact spots. Contact line fully reflect the tooth profile errors and tooth alignment error, it is a leading indicator to evaluate the helical gear load distribution is uniformity.
(3) The axial pitch deviation (ΔFPX) 
For wide helical gear, on the straight line that parallel to the gear's reference axis and approximately the tooth depth central, the axial pitch deviation ΔFPX is the difference between the actual distance and the nominal distance of any two tooth surfaces on the same side. The deviation counts value along the normal direction of tooth surface. It directly affects the size of the wide helical gear’s tooth surface contact spots. 
 
4. The backlash of gear evaluation 
In order to make the gear meshing with backlash, it should increase box center distance or make the tooth thin. Considering the machining characteristic of body and the gear, it should adopt the method of thinning tooth thickness to get the gear backlash (The base system of center distance). Reduction in tooth thickness by adjusting the cutting tool and the radial location of blank, the error will affect the size of the backlash. In addition, the geometric eccentricity and movement eccentricity can also make tooth thickness uneven. 
In order to control the tooth thickness thinning and get the necessary backlash, the following evaluation indicators can be used: 
(1) Tooth thickness deviation(ΔES)
Tooth thickness deviation is the difference tooth thickness between the actual value and the nominal value on the gear’s reference cylinder surface. For helical gear, it means normal tooth thickness. In order to guarantee the backlash, the upper deviation (ESS) and lower deviation (ESi) is usually negative.  
Tooth thickness deviation, it can use gear tooth calipers to measure in the middle of the depth of tooth. Addendum circle as the measurement benchmark, addendum is the high of chordal, measured the chordal tooth thickness on the reference circle. 
(2) The average length deviation of common normal line (ΔEWm)
The average length deviation of common normal line is within a lap of gear, the difference length between average value and nominal of the common normal line. ΔEWm = (W1+W2+…+W3)/z — W
In the formula z is an average value. Because the tooth thickness thinning the common normal length also decreased accordingly, the average length of common normal deviation is as an index to reflect the backlash. Tooth thickness deviation is usually checked by across certain number of teeth to measure the common normal length.
 

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