The constant coincidence of the indexing circle and pitch circle of gear and rack mesh is also a prerequisite. The pressure angle of the indexing circle of the gear is 20 degrees. For the rack with a pressure angle of 20 degrees, their pitch circle coincides with the indexing circle. However, if the pressure angle of the indexing circle of the gear is 20 degrees, but we use a rack with a pressure angle of 15 degrees to match, then the pitch circle of the gear does not coincide with the indexing circle. At present, most of the rack design data that customers can find requires that the rack pressure angle is equal to the gear indexing circle pressure angle. But there are also many occasions where we will use a rack that is not equal to the pressure angle of the gear indexing circle. At this time, the pitch circle of the gear is the diameter of the corresponding gear circle when the gear pressure angle is the same as the rack pressure angle.
Part of the formula required for the calculation of gear and rack fit: acceleration: a=vt (v is the maximum speed when the load is moving)
Driving force (vertical): F=mg+ma (vertical transmission does not need to consider friction)
Driving force (horizontal): F=mg+ma (safety factor)
Acceleration torque: T=Fr (r is the radius of gear indexing circle)
Rack module and pitch calculation
Algorithm for the modulus and pitch of straight rack
1. Model m=pitch p pi
2. Pitch p=modulus m pi
3. Intermeshing center line Ho=rack height HK modulus m
Algorithm of the module and pitch of the helical rack
1. Module m=pitch p (pi trigonometric function cosB)
2. Pitch p=modulus m (pi trigonometric function cosB)
3. Meshing center line Ho=rack height Hk modulus m Note that the standard diagonal rack angle is 19.5283 degrees (19 degrees, 31 minutes, 42 seconds), and the trigonometric function cosB=0.9424764995.
Algorithm of spur gear module and pitch
1. Dividing circle diameter technology Do=number of teeth Z modulus m
2. Diameter calculation Dk=(number of teeth Z modulus m) (modulus m2)
3. Calculation of gear circumference after one revolution Z=diameter of indexing circle Do pi
Note: The installation center distance from the gear center point to the bottom surface of the rack is Hb=(diameter of the indexing circle Do2)+the meshing center line Ho.
Calculation of module and pitch of helical gear
1. Calculation of diameter of indexing circle Do=(number of teeth Z modulus m) trigonometric function cosB
2. Diameter calculation Dk=((number of teeth Z module m) trigonometric function cosB)+(module m2)
3. The calculation of the circumference of the gear after one revolution Z=the diameter of the indexing circle Do the circumference Note the installation center distance from the gear center point to the bottom surface of the rack The installation center distance Hb=(the diameter of the indexing circle Do2)+the meshing center line Ho.
The above is the calculation formula for the module and pitch of gear and rack, which is only for reference, because the technical personnel will assist in handling the specific product selection.
Calculation of gear ratio
Transmission ratio t=Z2Z1=n1n2
Speed of driving gear n1=800rpm
Speed of driven gear n2=400rpm
Number of teeth of driving gear Z1=20
Number of teeth of driven gear Z2=40
Transmission ratio t=Z2Z1=n1n2=4020=800400=2
That is to say, the transmission ratio is equal to the ratio of the number of teeth of the passive gear to the driving gear, and also equal to the ratio of the speed of the driving gear to the driven gear
Gear rack meshing center distance:
1. There is a fixed formula for calculating the center distance of gear and rack mesh:
Straight teeth are as follows: straight tooth indexing circle radius+rack indexing line, formula: a=h+d2, h is the height of the indexing line, take the rack of module 2 as an example: rack height x rack width=24mmx24mm, indexing line height=24mm2mm=22.
2 is the rack modulus, 22 is the height from the indexing line to the bottom of the rack, straight tooth indexing circle diameter=number of teeth x modulus, such as M2Z20, indexing circle diameter is d=2x20=40, 402=20, center distance 22+20=42.
2. Finding the right gear rack is an important part of designing the machine. We provide a complete product portfolio. We can select the gear rack suitable for the application according to our requirements for smooth operation, positioning accuracy, feed force, convenient installation, etc. We have economic and precision series linear system selection, and the parameters perfectly match your system, such as the maximum torque that the gear rack can bear and the mesh clearance of the gear rack, etc.
3. When designing the gear rack structure, the center distance is an important parameter, which needs to be continuously corrected by the later commissioning engineer to meet the required accuracy of our equipment. During the design, the mounting plate should be left with commissioning allowance.
4. Take the straight tooth as an example, the distance of movement on the rack when it rotates for one cycle, such as mold 2, 20 teeth, and the distance of gear rotation for one cycle is 40mm.
Module calculation of rack: pitch=module 3.14
The moving speed of moving parts can be calculated by the rolling speed of the gear on the rack.
V=3.14mz.n。
Match the moving speed of the device through the moving speed V.
The processing technology of precision rack is divided into: gear milling, gear grinding, etc.
The accuracy levels are respectively, 6, 6S, 8 and 9. The overall pitch line error of grinding rack is less than 0.025mm. The thrust of gear grinding rack varies from 10000N-200000 N. The tooth surface roughness of the grinding rack is less than Ra0.8, so the moving noise is very small, less than 45 decibels. The tooth pitch error of the grinding rack is less than 0.005mm. The movement is very stable without abnormal vibration. The tooth surface of the grinding rack moves stably at high speed. The grinding rack has high strength and high acceleration, and the rack surface is subject to anti-rust treatment. Precision grinding rack is widely used in machine tools, laser cutting machines, gantry processing, robot automation.
Source: maintenance automation
