KISSsys 03/ Template

Transcription

1 KISSsys 03/ Template Calculation of the gear and bearing frequencies 01/04/2015 KISSsoft AG Rosengartenstrasse 4 88 Bubikon Switerland Tel: Fax: info@kisssoft.ag

2 Contents 1 Using the template Setting up calculations Gear meshing frequencies Calculating the gear meshing frequencies Meshing order analysis Output of the results Bearing defect frequencies Calculating the bearing defect frequencies Frequency order analysis Output of the results Frequency calculation formulas Rolling element pass frequency outer race (BPFO) Rolling element pass frequency inner race (BPFI) Rolling element frequencies (BSF) and (BPF) Fundamental train frequency (FTF) Meshing functionality verification Verifying formulas Example Frequency calculation formulas Helical gear pair Planetary gear set Epicyclic gear set Result check / 11

3 General Information Are you interested to know, what are all the meshing frequencies in your transmission? Gear meshing frequency is defined as the number of gear teeth that enter in the mesh per unit of time or on the other words; Gear meshing frequency is the number of teeth multiplied by the rotational frequency of the gear. Meshing frequency is one of the potential noise sources in the transmission. Gear meshing creates a vibration in its meshing frequency, because of transmission error, machining errors, stiffness variation, torque fluctuation and other reasons. Are you also interested to check if some of your bearings may be reason for the noise or vibration. Most important bearing frequencies are rotational frequencies and possible defect frequencies in races or in rolling elements. Frequency is defined as Hert (H) [cycles / sec.]. For the gear meshing it can be calculated by number of teeth * rotational speed [rpm] /. Gear meshing frequency is a harmonic phenomenon and its harmonics can be found by multiplying fundamental meshing frequency by whole numbers (1, 2, 3 ). Different bearing frequencies are calculated in similar manner from the inner geometry of the bearings using formulas with number of contacts in possible place of defect. In KISSsys it will be now possible to calculate meshing frequencies of the gear pairs and possible bearing defects frequencies for the whole transmission very easily. There is a special template available for that. The fundamental meshing frequencies and selected number of harmonics can be calculated, results in the operational point will be shown in one table and it is also possible to do order analysis over the selected speed range. Results will be shown in Hert. Selected bearing with all of the calculated frequencies can be also show in graphical presentation over the selected speed range / 11

4 1 Using the template 1.1 Setting up calculations The table is available in the default templates and has to be entered into the tree structure of a finished gearbox model. Figure 1. Selection of the table in the default templates There will be one table named FrequencyTemplate containing two sub tables called MeshingFrequencies BearingFrequencies with their 2DPlot. You may change names of these components if you want to. 2 Gear meshing frequencies 2.1 Calculating the gear meshing frequencies Use the function GetFrequencies from the sub table MeshingFrequencies (right click on MeshingFrequencies ) to do the calculation for the gear meshing frequencies. You may select how many harmonics will be calculated. Figure 2. Dialog for meshing frequency calculations When number of the harmonics is selected in the dialog and OK is pressed a table with the number of meshing harmonics is created, showing also the power of the mesh, because this can be then used to check which meshes are active and will really have some effect. Figure 3. Gear meshing frequency table / 11

5 First Line P Harmonic_X Names of the gear pairs Power in the mesh Meshing harmonic, X number of the harmonic. 2.2 Meshing order analysis When you want to plot order analysis of the meshing frequencies and its harmonics, use the function SetPlot from the sub table MeshingPlot. A dialog will then appear to make selections for the order analysis. Here you can select which gear calculation you want to display or all, you can select the harmonic number to plot (up to number of calculated harmonics) or all. Select minimum and maximum speeds you want to see (use only positive speed values). Select also, which ksysspeedorforce - component will be the reference speed component. After pressing OK a picture of order analysis will appear. Only meshing frequencies and selected harmonics will be drawn for the meshes which are active. Figure 4. Order analysis definition dialog Figure 5. Order analysis of the meshing frequencies / 11

6 2.3 Output of the results An external file MeshingFrequencies.csv is also created containing the same information as the meshing frequency table. This file is located in the project folder and can be opened e.g. with excel. The gear meshing frequencies are always calculated at the operational point. Figure 6. Output file of calculated gear meshing frequencies 3 Bearing defect frequencies 3.1 Calculating the bearing defect frequencies Use the function GetFrequencies from the sub table BearingFrequencies (right click on BearingFrequencies ) to do the calculation for the bearing frequencies. You may select how many harmonics will be calculated as for the gears. Figure 7. Dialog for bearing frequency calculations When OK is pressed a table with the bearing information and the first harmonic calculated for each category (BPFO, BPFI ) and each bearing is shown. Figure 8. Bearing frequency table / 11

7 Bearing frequencies are based on the formulas for internal geometry of the bearings. This data is not available automatically and therefore these values are needed to be added manually for every bearing. Needful information is described in the following table. These information can be entered directly to the BearingFrequencies - table. User can open it manually from the tree structure using BearingFrequencies - Show. Data in the table Parent n BType D d D Dwe alfa BPFO BPFI BSF FTF BPF Parent of the bearing (shaft or group if connection element) Speed of the bearing (relative speed if connection element) Bearing type Bearing outer diameter (mm) Bearing inner diameter (mm) Number of rolling elements in assembly. (USER DEFINED VALUE) Reference diameter/cage assembly diameter (mm) (USER DEFINED VALUE) Rolling element diameter (mm) (USER DEFINED VALUE) Nominal contact angle (deg) (USER DEFINED VALUE) Rolling element pass frequency outer race (H) Rolling element pass frequency inner race (H) Rolling element rotational frequency (H) Fundamental train frequency (H) Rolling element contact frequency (H) 3.2 Frequency order analysis When you want to plot order analysis of the bearing frequencies and its harmonics, use the function SetPlot from the sub table BearingPlot. A dialog will then appear to make selections for the order analysis. As for the gears, you may select what to display (one bearing or all, on harmonic or all, reference speeds ), but here you can also select which frequency category. Figure 9. Order analysis definition dialog / 11

8 Figure 10. Order analysis of the meshing frequencies Note! Frequency values are not automatically updated when any values for the bearings, or kinematics is changed. User need to run the function GetFrequencies and/or SetPlot again to update the values and meet the new operational conditions. 3.3 Output of the results An external file BearingFrequencies.csv is also created containing more information than the table (all the harmonics for each category and each bearing). This file is located to the project folder and can be opened e.g. with excel. All frequencies are calculated at the operational point. Figure 11. External file created Figure 12. Output file of calculated gear meshing frequencies / 11

9 3.4 Frequency calculation formulas Following formulas are used to calculate the bearing frequencies Rolling element pass frequency outer race (BPFO) n D BPFO D we 2D cos( ) Rolling element pass frequency inner race (BPFI) n D BPFI D we 2D cos( ) Rolling element frequencies (BSF) and (BPF) n D BSF 2 D 2 D 2 we Fundamental train frequency (FTF) we n D FTF D 2 cos ( ) D we 2D, BPF = 2*BSF cos( ) / 11

10 4 Meshing functionality verification 4.1 Verifying formulas In the template formulas number of teeth * rotational speed [rpm] / are used to find out meshing frequency for the helical and bevel gears. In case of epicyclical gear arrangement different formulas are needed to find out correct meshing frequency. In KISSsys, if normal epicyclical arrangement is used (sun-planet-ring), then given formula is used (speed of the sun speed of the carrier) * sun gear number of the teeth /. In all other cases basic formula for the meshing frequency calculation can be used because gear calculations are made with helical gear module, which already takes in the account the relative speed between gears. 4.2 Example Following example is used to verify the formulas. Helical planetary type gearbox configuration is created with one helical gear pair, one normal planetary gear pair and special planetary gear configuration. Input speed is given as 1000 rpm. Figure 13. Schematic view of the example model 4.3 Frequency calculation formulas Helical gear pair 2 Ratio i and meshing frequency 1 f 1 n Planetary gear set Ratio when carrier is input, sun is output and ring is fixed i s and meshing frequency s r r n f c / 11

11 4.3.3 Epicyclic gear set Ratio when sun1 is input, sun2 is fixed and carrier is output meshing frequency f s1 c s1p1, ns1 n f p2 p3 p2 i s1 n p1 s1 p2 p4 p1 s2 p3 and s1 n c s1 and p2 f s2p4 p4 s2 n c 4.4 Result check Given formulas were used to calculate meshing frequencies of the example model. These results are proved to be equal to the results obtained form with KISSsys meshing frequency template. Input speed 1000 rpm Input frequency H i Speed Mesh frequency (H) Input freq. Harmonic Assemply Input Output Output s p Fix r Input carrier Input s Fix s2 16 p1 42 p p3 40 p4 48 Output carrier Figure 14. Gear meshing frequencies calculated with given formulas Figure 15. Gear meshing frequencies calculated with KISSsys / 11