Tooth Geometry for Headstock Gear for Feed System of a Shearer Loader

TECHNICAL FIELD

The present invention pertains to a headstock gear for a feed system of a shearer loader, comprising a plurality of teeth, wherein each tooth has a tooth geometry. The present invention further pertains to a system comprising such a headstock gear and a gear rack. The present invention further pertains to a method for dimensioning a geometry profile of a headstock gear.

Technological Background

Headstock gears are commonly used in underground feed systems of shearer loaders. In the case of shearer loaders, gear racks are used in the feed system. During operation, the teeth of the headstock gear engage in tooth gaps between the gear rack teeth to convert a rotational movement of the headstock gear into a translational movement of the shearer loader.

The gear rack is usually composed of several individual gear rack segments, the length of which corresponds substantially to the length of a respective pan section of an associated scraper chain conveyor so that the scraper chain conveyor and in this respect also the gear rack can conform to an undulating course of a winning longwall face with synclines, anticlines and curves. Due to the segmental construction of the gear rack on account of the individual gear rack segments, a shearer loader can also follow a curved course of a face conveyor and the horizontal and/or vertical bends without obstruction.

When the headstock gear engages a gear rack segment in a middle section, the gear rack pitch is constant, providing a smooth operation of the feed system without gear jumps and without excessive forces acting on the headstock gear. However, at intersections between individual gear rack segments, the gear rack frequently exhibits mechanically noticeable changes in distance between an end tooth of a first gear rack segment and another, adjacent, end tooth of a second gear rack segment. To this end, a variation in gear rack pitch occurs, causing substantial stresses in the headstock gear travelling over said gear rack pitch variation. Such sudden stress fluctuations can wear off the headstock gear and/or the flanks of the gear rack teeth and/or brake off a tooth of the headstock gear. If the gear rack pitch variation reaches a critical variation, gear jumps occur, leading to further wear and shortened lifespan of the headstock gear.

Therefore, a need exists to prevent load peaks in the headstock gear when travelling over an intersection of two gear rack segments, thus increasing lifespan of the headstock gear.

SUMMARY OF THE INVENTION

Starting from the prior art, it is an objective to provide an improved headstock gear for a feed system of a shearer loader. In particular, it may be an objective to provide a feed system which allows smooth travelling over an intersection of two adjacent gear racks comprising a gear rack pitch variation.

This objective is solved by means of a headstock gear with the features of claim 1, by means of a system according to claim 10 and by a method according to claim 15. Preferred embodiments are set forth in the present specification, the Figures as well as the dependent claims.

Accordingly, a headstock gear for a feed system of a shearer loader is suggested, comprising a plurality of teeth, each tooth having a tooth geometry. Further, for each tooth, the tooth geometry consists of two symmetric S-shaped tooth profiles which are arranged line symmetrically regarding a radius line, as seen from a view along an axis of rotation.

Furthermore, a system is suggested, which comprises such a headstock gear and a gear rack comprising several gear rack segments which are arranged next to each other such that a track is provided. The gear rack comprises two different gear rack pitches.

Further, a method for dimensioning a tooth geometry of a headstock gear for a shearer loader is suggested, comprising a plurality of teeth, the method comprising the steps of identifying all relevant engagement conditions during operation of the headstock gear together with the gear rack; and selecting a tooth geometry on the basis of the identified relevant engagement conditions by minimizing a tooth root tension.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure will be more readily appreciated by reference to the following detailed description when being considered in connection with the accompanying drawings in which:

FIG. 1 schematically shows a side view of a headstock gear,

FIG. 2 schematically shows an isolated tooth geometry of a tooth of the headstock gear shown in FIG. 1;

FIG. 3 schematically shows a schematic side view of a headstock gear together with a gear rack;

FIG. 4 illustrates an outer limitation of an envelope fitting for one of the S-shaped profiles in a non-dimensional representation;

FIG. 5 illustrates an envelope for one of the S-shaped profiles in a non-dimensional representation;

FIG. 6 illustrates an envelope for one of the S-shaped profiles in a non-dimensional representation;

FIG. 7 is a flow chart of a method for dimensioning a tooth geometry according to a first embodiment;

FIG. 8 shows a flow chart of a method for dimensioning a tooth geometry according to a second embodiment;

FIG. 9A illustrates an outer limitation of an envelope fitting for one of the S-shaped profiles in a dimensional representation;

FIG. 9B illustrates an envelope for one of the S-shaped profiles in a dimensional representation; and

FIG. 10 depicts a tooth geometry of a headstock gear as an output of the method for dimensioning a tooth geometry.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In the following, the invention will be explained in more detail with reference to the accompanying Figures. In the Figures, like elements are denoted by identical reference numerals and repeated description thereof may be omitted in order to avoid redundancies.

In FIG. 1, the headstock gear 10 for a feed system of a shearer loader is depicted in a side view, comprising a plurality of teeth 1, each tooth 1 having a tooth geometry 2. For each tooth 1, the tooth geometry 2 consists of two symmetric S-shaped tooth profiles S1, S2 which are arranged line symmetrically regarding a radius line, as seen from a view along an axis of rotation A.

In the context of the present disclosure, the term tooth geometry 2 refers to the entire outer geometry of a given tooth. Likewise, the term profile, or S-shaped profile, refers to the outline of the tooth geometry as seen from a view along an axis of rotation A of the headstock gear 10.

The tooth geometry is suitable for engaging a gear rack (not shown in FIG. 1). The tooth geometry 2 is designed such that an engagement with at least two different gear rack pitches (not shown in FIG. 1) is enabled.

Enabling the headstock gear 10 to operate at at least two different gear rack pitches is achieved by the specific desing of the tooth geometry 2. Such tooth geometry 2 may deviate from involent tooth geometries as known in the state of the art in that it may not be the optimal geometry for combing either one of the different gear rack pitches alone. However, despite potentially operating at a sub-optimal engagement conditions, a headstock gear having a tooth geometry 2 according to the present disclosure is surprisingly longer lasting compared to a tooth geometry 2 optimized for a single gear rack pitch. That is because the tooth geometry 2 according to the present disclosure leads to less fluctuating stress impacts when operated at varying gear rack pitches.

According to the embodiment shown in FIG. 1, the headstock gear 10 is rotatable around a rotational axis A and comprises eleven teeth 1. Alternatively, the number of teeth may be different. Further, each tooth 1 of the headstock gear 10 has a tooth geometry 2 comprising a flat section at its tooth tip. In addition thereto, as indicated by reference numeral 12, each tooth 1 of the plurality of teeth is hardened the case hardening and/or inductive hardening at the root 12 of each of the teeth 1. Alternatively, hardening may be optional, depending on the expected variation of gear rack pitches. According to the embodiment shown in FIG. 1, hardening is not provided at the tip of each of the teeth 1.

The tooth geometry 2 of the headstock gear 10 is designed such that root stresses of each tooth 1 are minimized. Additionally, the tooth geometry 2 of the headstock gear 10 is designed such that a product of Hertzian stress and a relative slip component is minimized when engaged with the gear rack (not shown). It has been shown by experiment that after taking into consideration all potential gear rack pitch variations, optimizing the tooth geometry by the criterion of minimizing said product may lead to a tooth geometry 2 providing a particularly durable headstock gear 10.

FIG. 2 schematically shows an isolated tooth geometry 2 of a tooth 1 of a headstock gear 10 according to FIG. 1. The tooth geometry 2 consists of two symmetric S-shaped tooth profiles S1, S2 which are arranged line symmetrically regarding a radius line, as seen from a view along an axis of rotation A. The radius line is indicated by the dashed line and travels through the axis of rotation A. The axis of rotation refers to a rotation of the headstock gear 10 during operation.

FIG. 3 shows a schematic side view of a headstock gear 10 together with a gear rack 4 where the teeth 1 of the headstock gear 10 are combing with rack teeth 8 of the gear rack 4. To this end, the tooth geometry 2 is designed such that an engagement with at least two different gear rack pitches 6, 6′ is enabled. The headstock gear 10 shown in FIG. 2 can be identical to the headstock gear 10 disclosed in FIG. 1. In this case, the plurality of teeth 1 of the headstock gear 10 comprises eleven teeth.

Alternatively, according to an embodiment not shown in FIG. 2, a different headstock gear 10 may be used, in particular a headstock gear 10 having a different number of teeth 1, in particular ten teeth 1. In the shown embodiment, a system comprising the headstock gear 10 in a gear rack 4 comprising two gear rack segments 4′ is shown. The gear rack segments 4′ are arranged next to each other such that a track is provided along which the headstock gear 10 may engage during operation.

Each of the two different gear rack segments 4, 4′ comprise several rack teeth 8 arranged equidistantly on each gear rack segment 4′ such that each of the gear rack segments 4′ have the same constant gear rack pitch 6′. However, at the intersection between the two gear rack segments 4 and 4′, a change or variation in gear rack pitch 6 occurs. According to the illustration shown in FIG. 2, the headstock gear 10 engages with the gear rack 4 precisely at a location where the gear rack pitch 6 differs from the nominal gear rack pitch 6′. As an example, the nominal gear rack pitch 6′ may be 147 mm.

FIG. 4 illustrates an outer limitation of an envelope fitting for one of the S-shaped profiles S2 in a non-dimensional representation. To this end, one of the S-shaped profiles S2 comprises an envelope fitting into a frame with the non-dimensional outer limitations L2 defined by x-y coordinates set forth in all of the following columns:

Column 1
Column 2
Column 3
Column 4

x
y
x
y
x
y
x
y

0.0561
0.9984
0.1172
0.8987
0.1223
0.6948
0.0975
0.8947

0.0562
0.9983
0.1173
0.8982
0.1220
0.6957
0.0973
0.8951

0.0565
0.9980
0.1175
0.8977
0.1217
0.6966
0.0972
0.8955

0.0568
0.9977
0.1176
0.8973
0.1214
0.6974
0.0970
0.8960

0.0572
0.9974
0.1178
0.8968
0.1211
0.6983
0.0969
0.8964

0.0575
0.9970
0.1179
0.8963
0.1208
0.6992
0.0968
0.8968

0.0578
0.9967
0.1181
0.8959
0.1205
0.7001
0.0966
0.8972

0.0581
0.9964
0.1182
0.8954
0.1202
0.7010
0.0965
0.8976

0.0584
0.9961
0.1184
0.8950
0.1199
0.7019
0.0963
0.8981

0.0587
0.9958
0.1185
0.8945
0.1196
0.7027
0.0962
0.8985

0.0590
0.9955
0.1186
0.8940
0.1194
0.7036
0.0960
0.8989

0.0594
0.9952
0.1188
0.8936
0.1191
0.7045
0.0959
0.8993

0.0597
0.9948
0.1189
0.8931
0.1188
0.7054
0.0957
0.8997

0.0600
0.9945
0.1190
0.8926
0.1186
0.7063
0.0956
0.9001

0.0603
0.9942
0.1192
0.8922
0.1183
0.7072
0.0954
0.9006

0.0606
0.9939
0.1193
0.8917
0.1180
0.7081
0.0953
0.9010

0.0609
0.9935
0.1194
0.8912
0.1178
0.7090
0.0951
0.9014

0.0612
0.9932
0.1196
0.8908
0.1175
0.7099
0.0950
0.9018

0.0615
0.9929
0.1197
0.8903
0.1173
0.7108
0.0948
0.9022

0.0619
0.9926
0.1198
0.8898
0.1170
0.7116
0.0947
0.9026

0.0622
0.9923
0.1200
0.8894
0.1168
0.7125
0.0945
0.9031

0.0625
0.9919
0.1201
0.8889
0.1165
0.7134
0.0944
0.9035

0.0628
0.9916
0.1202
0.8884
0.1163
0.7143
0.0942
0.9039

0.0631
0.9913
0.1204
0.8879
0.1161
0.7152
0.0941
0.9043

0.0634
0.9910
0.1205
0.8875
0.1158
0.7161
0.0939
0.9047

0.0637
0.9906
0.1206
0.8870
0.1156
0.7170
0.0937
0.9051

0.0640
0.9903
0.1207
0.8865
0.1154
0.7179
0.0936
0.9055

0.0643
0.9900
0.1209
0.8861
0.1152
0.7188
0.0934
0.9059

0.0646
0.9896
0.1210
0.8856
0.1149
0.7197
0.0933
0.9063

0.0649
0.9893
0.1211
0.8851
0.1147
0.7206
0.0931
0.9068

0.0652
0.9890
0.1212
0.8846
0.1145
0.7215
0.0929
0.9072

0.0655
0.9886
0.1214
0.8842
0.1143
0.7225
0.0928
0.9076

0.0658
0.9883
0.1215
0.8837
0.1141
0.7234
0.0926
0.9080

0.0661
0.9880
0.1216
0.8832
0.1139
0.7243
0.0925
0.9084

0.0664
0.9876
0.1217
0.8827
0.1137
0.7252
0.0923
0.9088

0.0667
0.9873
0.1218
0.8823
0.1135
0.7261
0.0921
0.9092

0.0670
0.9870
0.1220
0.8818
0.1133
0.7270
0.0920
0.9096

0.0673
0.9866
0.1221
0.8813
0.1131
0.7279
0.0918
0.9100

0.0676
0.9863
0.1222
0.8808
0.1129
0.7288
0.0916
0.9104

0.0679
0.9860
0.1223
0.8804
0.1127
0.7297
0.0915
0.9108

0.0682
0.9856
0.1224
0.8799
0.1125
0.7306
0.0913
0.9112

0.0685
0.9853
0.1225
0.8794
0.1124
0.7315
0.0911
0.9116

0.0688
0.9849
0.1226
0.8789
0.1122
0.7324
0.0909
0.9120

0.0691
0.9846
0.1227
0.8785
0.1120
0.7334
0.0908
0.9125

0.0694
0.9843
0.1229
0.8780
0.1119
0.7343
0.0906
0.9129

0.0697
0.9839
0.1230
0.8775
0.1117
0.7352
0.0904
0.9133

0.0700
0.9836
0.1231
0.8770
0.1115
0.7361
0.0903
0.9137

0.0703
0.9832
0.1232
0.8765
0.1114
0.7370
0.0901
0.9141

0.0706
0.9829
0.1233
0.8761
0.1112
0.7379
0.0899
0.9145

0.0709
0.9825
0.1234
0.8756
0.1111
0.7388
0.0897
0.9149

0.0712
0.9822
0.1235
0.8751
0.1109
0.7398
0.0896
0.9153

0.0715
0.9819
0.1236
0.8746
0.1108
0.7407
0.0894
0.9157

0.0718
0.9815
0.1237
0.8741
0.1106
0.7416
0.0892
0.9161

0.0721
0.9812
0.1238
0.8737
0.1105
0.7425
0.0890
0.9165

0.0723
0.9808
0.1239
0.8732
0.1103
0.7434
0.0889
0.9169

0.0726
0.9805
0.1241
0.8725
0.1102
0.7444
0.0887
0.9173

0.0729
0.9801
0.1242
0.8716
0.1101
0.7453
0.0885
0.9177

0.0732
0.9798
0.1244
0.8708
0.1099
0.7462
0.0883
0.9181

0.0735
0.9794
0.1246
0.8699
0.1098
0.7471
0.0881
0.9184

0.0738
0.9791
0.1247
0.8690
0.1097
0.7480
0.0879
0.9188

0.0741
0.9787
0.1249
0.8680
0.1096
0.7490
0.0878
0.9192

0.0744
0.9784
0.1251
0.8671
0.1095
0.7499
0.0876
0.9196

0.0746
0.9780
0.1253
0.8662
0.1093
0.7508
0.0874
0.9200

0.0749
0.9776
0.1254
0.8653
0.1092
0.7517
0.0872
0.9204

0.0752
0.9773
0.1256
0.8644
0.1091
0.7526
0.0870
0.9208

0.0755
0.9769
0.1257
0.8634
0.1090
0.7536
0.0868
0.9212

0.0758
0.9766
0.1259
0.8625
0.1089
0.7545
0.0867
0.9216

0.0761
0.9762
0.1260
0.8616
0.1088
0.7554
0.0865
0.9220

0.0763
0.9759
0.1262
0.8607
0.1087
0.7563
0.0863
0.9224

0.0766
0.9755
0.1263
0.8598
0.1087
0.7573
0.0861
0.9228

0.0769
0.9752
0.1265
0.8588
0.1086
0.7582
0.0859
0.9232

0.0772
0.9748
0.1266
0.8579
0.1085
0.7591
0.0857
0.9236

0.0775
0.9744
0.1267
0.8570
0.1084
0.7600
0.0855
0.9239

0.0778
0.9741
0.1269
0.8561
0.1083
0.7610
0.0853
0.9243

0.0780
0.9737
0.1270
0.8551
0.1083
0.7619
0.0851
0.9247

0.0783
0.9733
0.1271
0.8542
0.1082
0.7628
0.0849
0.9251

0.0786
0.9730
0.1272
0.8533
0.1081
0.7637
0.0847
0.9255

0.0789
0.9726
0.1273
0.8523
0.1081
0.7647
0.0846
0.9259

0.0791
0.9723
0.1274
0.8514
0.1080
0.7656
0.0844
0.9263

0.0794
0.9719
0.1275
0.8505
0.1079
0.7665
0.0842
0.9267

0.0797
0.9715
0.1277
0.8496
0.1079
0.7674
0.0840
0.9270

0.0800
0.9712
0.1278
0.8486
0.1078
0.7684
0.0838
0.9274

0.0802
0.9708
0.1278
0.8477
0.1078
0.7693
0.0836
0.9278

0.0805
0.9704
0.1279
0.8468
0.1077
0.7702
0.0834
0.9282

0.0808
0.9701
0.1280
0.8458
0.1077
0.7712
0.0832
0.9286

0.0811
0.9697
0.1281
0.8449
0.1077
0.7721
0.0830
0.9290

0.0813
0.9693
0.1282
0.8440
0.1076
0.7730
0.0828
0.9293

0.0816
0.9690
0.1283
0.8431
0.1076
0.7739
0.0826
0.9297

0.0819
0.9686
0.1283
0.8421
0.1076
0.7749
0.0824
0.9301

0.0821
0.9682
0.1284
0.8412
0.1075
0.7758
0.0822
0.9305

0.0824
0.9678
0.1285
0.8403
0.1075
0.7767
0.0820
0.9309

0.0827
0.9675
0.1286
0.8393
0.1075
0.7777
0.0818
0.9313

0.0829
0.9671
0.1286
0.8384
0.1075
0.7786
0.0816
0.9316

0.0832
0.9667
0.1287
0.8375
0.1075
0.7795
0.0814
0.9320

0.0835
0.9664
0.1287
0.8365
0.1075
0.7804
0.0811
0.9324

0.0837
0.9660
0.1288
0.8356
0.1074
0.7814
0.0809
0.9328

0.0840
0.9656
0.1288
0.8347
0.1074
0.7823
0.0807
0.9331

0.0843
0.9652
0.1289
0.8337
0.1074
0.7832
0.0805
0.9335

0.0845
0.9648
0.1289
0.8328
0.1074
0.7842
0.0803
0.9339

0.0848
0.9645
0.1289
0.8319
0.1075
0.7851
0.0801
0.9343

0.0851
0.9641
0.1290
0.8309
0.1075
0.7860
0.0799
0.9346

0.0853
0.9637
0.1290
0.8300
0.1075
0.7869
0.0797
0.9350

0.0856
0.9633
0.1290
0.8291
0.1075
0.7879
0.0795
0.9354

0.0858
0.9630
0.1290
0.8281
0.1075
0.7888
0.0793
0.9358

0.0861
0.9626
0.1291
0.8272
0.1075
0.7897
0.0791
0.9361

0.0864
0.9622
0.1291
0.8263
0.1076
0.7907
0.0788
0.9365

0.0866
0.9618
0.1291
0.8253
0.1076
0.7916
0.0786
0.9369

0.0869
0.9614
0.1291
0.8244
0.1076
0.7925
0.0784
0.9373

0.0871
0.9610
0.1291
0.8235
0.1077
0.7934
0.0782
0.9376

0.0874
0.9607
0.1291
0.8225
0.1077
0.7944
0.0780
0.9380

0.0877
0.9603
0.1291
0.8216
0.1077
0.7953
0.0778
0.9384

0.0879
0.9599
0.1291
0.8207
0.1078
0.7962
0.0776
0.9387

0.0882
0.9595
0.1291
0.8197
0.1078
0.7971
0.0773
0.9391

0.0884
0.9591
0.1291
0.8188
0.1079
0.7981
0.0771
0.9395

0.0887
0.9587
0.1290
0.8179
0.1079
0.7990
0.0769
0.9398

0.0889
0.9584
0.1290
0.8169
0.1080
0.7999
0.0767
0.9402

0.0892
0.9580
0.1290
0.8160
0.1081
0.8009
0.0765
0.9406

0.0894
0.9576
0.1290
0.8151
0.1081
0.8018
0.0762
0.9409

0.0897
0.9572
0.1289
0.8141
0.1082
0.8027
0.0760
0.9413

0.0899
0.9568
0.1289
0.8132
0.1083
0.8036
0.0758
0.9417

0.0902
0.9564
0.1289
0.8122
0.1083
0.8045
0.0756
0.9420

0.0904
0.9560
0.1288
0.8113
0.1084
0.8054
0.0754
0.9424

0.0907
0.9556
0.1288
0.8104
0.1085
0.8063
0.0751
0.9428

0.0909
0.9552
0.1287
0.8095
0.1085
0.8071
0.0749
0.9431

0.0912
0.9548
0.1287
0.8085
0.1086
0.8080
0.0747
0.9435

0.0914
0.9544
0.1286
0.8076
0.1087
0.8088
0.0745
0.9438

0.0917
0.9541
0.1286
0.8067
0.1087
0.8097
0.0742
0.9442

0.0919
0.9537
0.1285
0.8057
0.1088
0.8106
0.0740
0.9446

0.0921
0.9533
0.1284
0.8048
0.1088
0.8114
0.0738
0.9449

0.0924
0.9529
0.1283
0.8039
0.1088
0.8123
0.0735
0.9453

0.0926
0.9525
0.1283
0.8029
0.1089
0.8131
0.0733
0.9456

0.0929
0.9521
0.1282
0.8021
0.1089
0.8140
0.0731
0.9460

0.0931
0.9517
0.1281
0.8012
0.1089
0.8148
0.0729
0.9464

0.0934
0.9513
0.1281
0.8004
0.1090
0.8157
0.0726
0.9467

0.0936
0.9509
0.1280
0.7995
0.1090
0.8166
0.0724
0.9471

0.0938
0.9505
0.1280
0.7986
0.1090
0.8174
0.0722
0.9474

0.0941
0.9501
0.1279
0.7978
0.1090
0.8183
0.0719
0.9478

0.0943
0.9497
0.1279
0.7969
0.1091
0.8191
0.0717
0.9481

0.0946
0.9493
0.1278
0.7961
0.1091
0.8200
0.0715
0.9485

0.0948
0.9489
0.1278
0.7952
0.1091
0.8208
0.0712
0.9488

0.0950
0.9485
0.1277
0.7944
0.1091
0.8217
0.0710
0.9492

0.0953
0.9481
0.1277
0.7935
0.1091
0.8226
0.0708
0.9496

0.0955
0.9477
0.1276
0.7926
0.1091
0.8234
0.0705
0.9499

0.0957
0.9473
0.1276
0.7918
0.1091
0.8243
0.0703
0.9503

0.0960
0.9469
0.1276
0.7909
0.1091
0.8251
0.0701
0.9506

0.0962
0.9465
0.1276
0.7901
0.1091
0.8260
0.0698
0.9510

0.0964
0.9460
0.1275
0.7892
0.1091
0.8268
0.0696
0.9513

0.0967
0.9456
0.1275
0.7883
0.1090
0.8277
0.0693
0.9517

0.0969
0.9452
0.1275
0.7875
0.1090
0.8286
0.0691
0.9520

0.0971
0.9448
0.1275
0.7866
0.1090
0.8294
0.0689
0.9523

0.0973
0.9444
0.1275
0.7858
0.1090
0.8303
0.0686
0.9527

0.0976
0.9440
0.1275
0.7849
0.1089
0.8311
0.0684
0.9530

0.0978
0.9436
0.1274
0.7840
0.1089
0.8320
0.0681
0.9534

0.0980
0.9432
0.1274
0.7832
0.1089
0.8329
0.0679
0.9537

0.0983
0.9428
0.1274
0.7823
0.1088
0.8337
0.0677
0.9541

0.0985
0.9424
0.1274
0.7815
0.1088
0.8346
0.0674
0.9544

0.0987
0.9420
0.1275
0.7806
0.1088
0.8354
0.0672
0.9548

0.0989
0.9415
0.1275
0.7797
0.1087
0.8363
0.0669
0.9551

0.0992
0.9411
0.1275
0.7789
0.1087
0.8371
0.0667
0.9555

0.0994
0.9407
0.1275
0.7780
0.1086
0.8380
0.0664
0.9558

0.0996
0.9403
0.1275
0.7772
0.1085
0.8388
0.0662
0.9561

0.0998
0.9399
0.1275
0.7763
0.1085
0.8397
0.0659
0.9565

0.1000
0.9395
0.1276
0.7755
0.1084
0.8406
0.0657
0.9568

0.1003
0.9391
0.1276
0.7746
0.1083
0.8414
0.0655
0.9572

0.1005
0.9387
0.1276
0.7737
0.1083
0.8423
0.0652
0.9575

0.1007
0.9382
0.1276
0.7729
0.1082
0.8431
0.0650
0.9578

0.1009
0.9378
0.1277
0.7720
0.1081
0.8440
0.0647
0.9582

0.1011
0.9374
0.1277
0.7712
0.1080
0.8448
0.0645
0.9585

0.1013
0.9370
0.1278
0.7703
0.1079
0.8457
0.0642
0.9588

0.1016
0.9366
0.1278
0.7694
0.1079
0.8465
0.0640
0.9592

0.1018
0.9361
0.1278
0.7686
0.1078
0.8474
0.0637
0.9595

0.1020
0.9357
0.1279
0.7677
0.1077
0.8482
0.0635
0.9598

0.1022
0.9353
0.1279
0.7669
0.1076
0.8491
0.0632
0.9602

0.1024
0.9349
0.1280
0.7660
0.1075
0.8500
0.0629
0.9605

0.1026
0.9345
0.1281
0.7652
0.1074
0.8508
0.0627
0.9608

0.1028
0.9340
0.1281
0.7643
0.1073
0.8517
0.0624
0.9612

0.1030
0.9336
0.1282
0.7634
0.1072
0.8525
0.0622
0.9615

0.1033
0.9332
0.1283
0.7626
0.1070
0.8534
0.0619
0.9618

0.1035
0.9328
0.1283
0.7617
0.1069
0.8542
0.0617
0.9622

0.1037
0.9323
0.1284
0.7609
0.1068
0.8551
0.0614
0.9625

0.1039
0.9319
0.1285
0.7600
0.1067
0.8559
0.0612
0.9628

0.1041
0.9315
0.1286
0.7592
0.1066
0.8568
0.0609
0.9632

0.1043
0.9311
0.1286
0.7583
0.1064
0.8576
0.0606
0.9635

0.1045
0.9306
0.1287
0.7574
0.1063
0.8585
0.0604
0.9638

0.1047
0.9302
0.1288
0.7566
0.1062
0.8593
0.0601
0.9641

0.1049
0.9298
0.1289
0.7557
0.1060
0.8601
0.0599
0.9645

0.1051
0.9294
0.1290
0.7549
0.1059
0.8610
0.0596
0.9648

0.1053
0.9289
0.1291
0.7540
0.1057
0.8618
0.0593
0.9651

0.1055
0.9285
0.1292
0.7532
0.1056
0.8627
0.0591
0.9654

0.1057
0.9281
0.1293
0.7523
0.1054
0.8635
0.0588
0.9658

0.1059
0.9276
0.1294
0.7515
0.1053
0.8644
0.0586
0.9661

0.1061
0.9272
0.1295
0.7506
0.1051
0.8652
0.0583
0.9664

0.1063
0.9268
0.1296
0.7498
0.1049
0.8661
0.0580
0.9667

0.1065
0.9264
0.1298
0.7489
0.1048
0.8669
0.0578
0.9670

0.1067
0.9259
0.1299
0.7481
0.1046
0.8677
0.0575
0.9674

0.1069
0.9255
0.1300
0.7472
0.1045
0.8684
0.0572
0.9677

0.1071
0.9251
0.1301
0.7464
0.1043
0.8691
0.0570
0.9680

0.1073
0.9246
0.1302
0.7455
0.1042
0.8695
0.0567
0.9683

0.1075
0.9242
0.1304
0.7447
0.1041
0.8700
0.0564
0.9686

0.1077
0.9238
0.1305
0.7438
0.1040
0.8704
0.0562
0.9690

0.1079
0.9233
0.1306
0.7430
0.1039
0.8709
0.0559
0.9693

0.1081
0.9229
0.1308
0.7421
0.1039
0.8713
0.0556
0.9696

0.1082
0.9225
0.1309
0.7413
0.1038
0.8718
0.0554
0.9699

0.1084
0.9220
0.1311
0.7404
0.1037
0.8722
0.0551
0.9702

0.1086
0.9216
0.1312
0.7396
0.1036
0.8726
0.0548
0.9705

0.1088
0.9211
0.1314
0.7387
0.1035
0.8731
0.0546
0.9709

0.1090
0.9207
0.1315
0.7379
0.1034
0.8735
0.0543
0.9712

0.1092
0.9203
0.1317
0.7370
0.1033
0.8740
0.0540
0.9715

0.1094
0.9198
0.1318
0.7362
0.1032
0.8744
0.0538
0.9718

0.1096
0.9194
0.1320
0.7354
0.1031
0.8748
0.0535
0.9721

0.1097
0.9189
0.1322
0.7345
0.1029
0.8753
0.0532
0.9724

0.1099
0.9185
0.1323
0.7337
0.1028
0.8757
0.0529
0.9727

0.1101
0.9181
0.1325
0.7328
0.1027
0.8762
0.0527
0.9730

0.1103
0.9176
0.1327
0.7320
0.1026
0.8766
0.0524
0.9733

0.1105
0.9172
0.1329
0.7311
0.1025
0.8770
0.0521
0.9736

0.1107
0.9167
0.1330
0.7303
0.1024
0.8775
0.0518
0.9740

0.1108
0.9163
0.1332
0.7295
0.1023
0.8779
0.0516
0.9743

0.1110
0.9159
0.1334
0.7286
0.1022
0.8784
0.0513
0.9746

0.1112
0.9154
0.1336
0.7278
0.1021
0.8788
0.0510
0.9749

0.1114
0.9150
0.1338
0.7269
0.1020
0.8792
0.0507
0.9752

0.1115
0.9145
0.1340
0.7261
0.1019
0.8797
0.0505
0.9755

0.1117
0.9141
0.1342
0.7253
0.1018
0.8801
0.0502
0.9758

0.1119
0.9136
0.1344
0.7244
0.1016
0.8805
0.0499
0.9761

0.1121
0.9132
0.1346
0.7236
0.1015
0.8810
0.0496
0.9764

0.1122
0.9127
0.1348
0.7228
0.1014
0.8814
0.0493
0.9767

0.1124
0.9123
0.1350
0.7219
0.1013
0.8818
0.0491
0.9770

0.1126
0.9118
0.1352
0.7211
0.1012
0.8823
0.0488
0.9773

0.1128
0.9114
0.1354
0.7203
0.1011
0.8827
0.0485
0.9776

0.1129
0.9109
0.1356
0.7194
0.1009
0.8831
0.0482
0.9779

0.1131
0.9105
0.1359
0.7186
0.1008
0.8836
0.0479
0.9782

0.1133
0.9100
0.1361
0.7178
0.1007
0.8840
0.0477
0.9785

0.1134
0.9096
0.1363
0.7169
0.1006
0.8844
0.0474
0.9788

0.1136
0.9091
0.1365
0.7161
0.1005
0.8849
0.0471
0.9791

0.1138
0.9087
0.1368
0.7153
0.1003
0.8853
0.0468
0.9794

0.1139
0.9082
0.1370
0.7145
0.1002
0.8857
0.0465
0.9797

0.1141
0.9078
0.1372
0.7136
0.1001
0.8862
0.0462
0.9800

0.1143
0.9073
0.1375
0.7128
0.1000
0.8866
0.0460
0.9803

0.1144
0.9069
0.1377
0.7120
0.0998
0.8870
0.0457
0.9805

0.1146
0.9064
0.1380
0.7112
0.0997
0.8875
0.0454
0.9808

0.1147
0.9060
0.1382
0.7103
0.0996
0.8879
0.0451
0.9811

0.1149
0.9055
0.1385
0.7095
0.0995
0.8883
0.0448
0.9814

0.1151
0.9051
0.1387
0.7087
0.0993
0.8887
0.0445
0.9817

0.1152
0.9046
0.1390
0.7079
0.0992
0.8892
0.0442
0.9820

0.1154
0.9042
0.1393
0.7071
0.0991
0.8896
0.0440
0.9823

0.1155
0.9037
0.1395
0.7062
0.0989
0.8900
0.0437
0.9826

0.1157
0.9032
0.1398
0.7054
0.0988
0.8904
0.0434
0.9829

0.1158
0.9028
0.1401
0.7046
0.0987
0.8909
0.0431
0.9831

0.1160
0.9023
0.1403
0.7038
0.0986
0.8913
0.0428
0.9834

0.1161
0.9019
0.1406
0.7030
0.0984
0.8917
0.0425
0.9837

0.1163
0.9014
0.1409
0.7022
0.0983
0.8921
0.0422
0.9840

0.1165
0.9010
0.1412
0.7014
0.0981
0.8926
0.0422
0.9841

0.1166
0.9005
0.1414
0.7005
0.0980
0.8930
0.0561
0.9984

0.1168
0.9000
0.1417
0.6997
0.0979
0.8934

0.1169
0.8996
0.1229
0.6930
0.0977
0.8938

0.1171
0.8991
0.1226
0.6939
0.0976
0.8943

FIG. 5 illustrates an envelope for one of the S-shaped profiles S2 in a non-dimensional representation. The envelope of the S-shaped profile shown in FIG. 5 represents only a part of the envelope of the total S-shaped profile S2. The term envelope refers to the section of the S-shaped profile that is actually designed or covered by the disclosed data. Hence, FIG. 5 shows an envelope of the S-shaped profile S2. The part shown in FIG. 5 covers the same range covered by the envelope fitting into a frame with the non-dimensional outer limitations L2 as disclosed in FIG. 4 and the columns below. To this end, one of the S-shaped profiles S2 (not shown in FIG. 5) has an envelope including all of the non-dimensional x-y-coordinates in all following columns:

Column 1
Column 2
Column 3
Column 4

x
y
x
y
x
y
x
y

0.1404
0.6794
0.1190
0.8288
0.1144
0.8696
0.1070
0.8978

0.1361
0.6873
0.1189
0.8315
0.1144
0.8696
0.1048
0.9039

0.1326
0.6955
0.1188
0.8351
0.1144
0.8696
0.1024
0.9104

0.1287
0.7074
0.1186
0.8378
0.1144
0.8696
0.0998
0.9168

0.1255
0.7186
0.1184
0.8413
0.1144
0.8696
0.0972
0.9226

0.1227
0.7308
0.1182
0.8440
0.1143
0.8705
0.0943
0.9288

0.1205
0.7431
0.1178
0.8476
0.1143
0.8705
0.0912
0.9348

0.1190
0.7547
0.1175
0.8503
0.1143
0.8705
0.0882
0.9403

0.1179
0.7671
0.1171
0.8538
0.1143
0.8705
0.0848
0.9461

0.1175
0.7796
0.1167
0.8565
0.1143
0.8705
0.0813
0.9518

0.1176
0.7912
0.1162
0.8600
0.1143
0.8705
0.0778
0.9569

0.1183
0.8037
0.1157
0.8627
0.1143
0.8705
0.0740
0.9623

0.1185
0.8064
0.1151
0.8662
0.1141
0.8711
0.0701
0.9676

0.1187
0.8100
0.1146
0.8688
0.1141
0.8711
0.0663
0.9724

0.1189
0.8127
0.1146
0.8688
0.1141
0.8711
0.0621
0.9774

0.1190
0.8163
0.1146
0.8688
0.1141
0.8711
0.0578
0.9822

0.1191
0.8190
0.1146
0.8688
0.1126
0.8780
0.0537
0.9866

0.1191
0.8225
0.1144
0.8696
0.1110
0.8844

0.1191
0.8252
0.1144
0.8696
0.1090
0.8912

FIG. 6 illustrates an envelope for one of the S-shaped profiles S2 in a non-dimensional representation. The envelope of the S-shaped profile shown in FIG. 6 represents the entire envelope of the total S-shaped profile S2. To this end, one of the S-shaped profiles S2 has an envelope comprising all of the non-dimensional x-y-coordinates in all of the following columns:

Column 1
Column 2
Column 3
Column 4

x
y
x
y
x
y
x
y

0.1887
0.6427
0.1191
0.8252
0.1143
0.8705
0.0740
0.9623

0.1802
0.6456
0.1190
0.8288
0.1143
0.8705
0.0701
0.9676

0.1721
0.6495
0.1189
0.8315
0.1143
0.8705
0.0663
0.9724

0.1645
0.6542
0.1188
0.8351
0.1143
0.8705
0.0621
0.9774

0.1573
0.6597
0.1186
0.8378
0.1143
0.8705
0.0578
0.9822

0.1514
0.6652
0.1184
0.8413
0.1143
0.8705
0.0537
0.9866

0.1456
0.6720
0.1182
0.8440
0.1143
0.8705
0.0492
0.9912

0.1404
0.6794
0.1178
0.8476
0.1141
0.8711
0.0482
0.9921

0.1361
0.6873
0.1175
0.8503
0.1141
0.8711
0.0471
0.9929

0.1326
0.6955
0.1171
0.8538
0.1141
0.8711
0.0459
0.9937

0.1287
0.7074
0.1167
0.8565
0.1141
0.8711
0.0447
0.9943

0.1255
0.7186
0.1162
0.8600
0.1126
0.8780
0.0435
0.9948

0.1227
0.7308
0.1157
0.8627
0.1110
0.8844
0.0422
0.9953

0.1205
0.7431
0.1151
0.8662
0.1090
0.8912
0.0409
0.9956

0.1190
0.7547
0.1146
0.8688
0.1070
0.8978
0.0395
0.9958

0.1179
0.7671
0.1146
0.8688
0.1048
0.9039
0.0382
0.9959

0.1175
0.7796
0.1146
0.8688
0.1024
0.9104
0.0340
0.9961

0.1176
0.7912
0.1146
0.8688
0.0998
0.9168
0.0296
0.9962

0.1183
0.8037
0.1144
0.8696
0.0972
0.9226
0.0254
0.9963

0.1185
0.8064
0.1144
0.8696
0.0943
0.9288
0.0213
0.9964

0.1187
0.8100
0.1144
0.8696
0.0912
0.9348
0.0169
0.9965

0.1189
0.8127
0.1144
0.8696
0.0882
0.9403
0.0127
0.9966

0.1190
0.8163
0.1144
0.8696
0.0848
0.9461
0.0086
0.9966

0.1191
0.8190
0.1144
0.8696
0.0813
0.9518
0.0042
0.9967

0.1191
0.8225
0.1144
0.8696
0.0778
0.9569
0.0000
0.9967

FIG. 7 shows a flow chart of a method for dimensioning a tooth geometry according to a first embodiment. Thereto, FIG. 7 discloses a method for dimensioning a tooth geometry 2 of a headstock gear 10 for a shearer loader, comprising a plurality of teeth 1, the method comprising the steps of identifying S10 all relevant engagement conditions during operation of the headstock gear 10 together with the gear rack 4 and selecting S20 a tooth geometry 2 on the basis of the identified relevant engagement conditions by minimizing a tooth root tension.

Instead of optimizing a headstock gear 10 for a given gear rack pitch, which would usually result in a tooth geometry of the involent shape as only normal forces are acting on engaging tooth flanks, the method according to the present disclosure may deliberately deviate therefrom. Quite the contrary, a non-optimal engagement between tooth flanks is accepted. It was found that adverse effects resulting from a non-optimal engagement are outweighed by the benefits from avoiding sudden stress fluctuations due to sudden gear rack pitch variations.

FIG. 8 shows a flow chart of a method for dimensioning a tooth geometry according to a first embodiment. Thereto, FIG. 8 discloses a further development of the method for dimension a tooth geometry as disclosed in FIG. 7. Accordingly, further optimization strategies may be considered in order to select a suitable tooth geometry among a range of possible tooth geometries. The steps S30, S40 and S50 may be applied exclusively or in any combination thereof. To this end, the method according to FIG. 8 comprises the step of maximizing S30 a tooth root strength by exploiting the available distance between the outline of the gear rack teeth 8 and the headstock gear 10.

Additionally, the method optionally comprises the step of minimizing S40 the occurrence of a gear jump. According to the present disclosure, a gear jump refers to an incident where an engagement between a headstock gear tooth and a gear rack tooth fails and a roll-over occurs. Alternatively or additionally, the method comprises the step of minimizing S50 the product of Hertzian stress and a relative slip component when engaged with the gear rack 4.

FIG. 9A illustrates an outer limitation of an envelope fitting for one of the S-shaped profiles S2 in a dimensional representation. To this end, one of the S-shaped profiles S2 comprises an envelope fitting into a frame with the non-dimensional outer limitations L2 defined by x-y coordinates. According to the example shown in FIG. 9A, the coordinates disclosed in the context of FIG. 4 above are multiplied by a dimension of 300 mm, in order to obtain a dimensional tooth geometry. The x-y-coordinates comprise all of the following columns:

Column 1
Column 2
Column 3
Column 4

x
y
x
y
x
y
x
y

16.830
299.520
35.160
269.598
36.680
208.440
29.238
268.407

16.860
299.492
35.204
269.459
36.589
208.703
29.197
268.533

16.957
299.396
35.248
269.321
36.499
208.967
29.154
268.660

17.052
299.303
35.292
269.182
36.410
209.231
29.112
268.786

17.147
299.209
35.335
269.043
36.321
209.495
29.069
268.913

17.242
299.115
35.378
268.905
36.234
209.760
29.027
269.039

17.337
299.020
35.421
268.766
36.148
210.024
28.983
269.165

17.431
298.926
35.463
268.626
36.062
210.290
28.940
269.291

17.526
298.831
35.506
268.487
35.978
210.555
28.897
269.416

17.620
298.736
35.548
268.348
35.894
210.821
28.853
269.542

17.714
298.641
35.589
268.208
35.812
211.087
28.809
269.668

17.808
298.545
35.631
268.069
35.730
211.353
28.765
269.793

17.902
298.449
35.672
267.929
35.649
211.620
28.720
269.918

17.996
298.354
35.713
267.789
35.569
211.887
28.676
270.043

18.090
298.257
35.754
267.649
35.490
212.154
28.631
270.168

18.183
298.161
35.794
267.509
35.412
212.421
28.586
270.293

18.276
298.065
35.835
267.369
35.335
212.689
28.540
270.418

18.369
297.968
35.875
267.229
35.259
212.957
28.495
270.543

18.462
297.871
35.914
267.088
35.184
213.225
28.449
270.667

18.555
297.774
35.954
266.948
35.109
213.494
28.403
270.791

18.648
297.677
35.993
266.807
35.036
213.763
28.357
270.916

18.740
297.579
36.032
266.666
34.963
214.032
28.310
271.040

18.833
297.481
36.071
266.525
34.892
214.301
28.264
271.164

18.925
297.383
36.109
266.384
34.821
214.570
28.217
271.288

19.017
297.285
36.147
266.243
34.752
214.840
28.170
271.411

19.109
297.187
36.185
266.102
34.683
215.110
28.122
271.535

19.200
297.088
36.223
265.960
34.615
215.380
28.075
271.658

19.292
296.989
36.260
265.819
34.548
215.651
28.027
271.781

19.383
296.890
36.297
265.677
34.482
215.922
27.979
271.905

19.475
296.791
36.334
265.535
34.417
216.193
27.931
272.028

19.566
296.692
36.371
265.393
34.353
216.464
27.882
272.151

19.657
296.592
36.407
265.252
34.290
216.735
27.834
272.273

19.747
296.492
36.443
265.109
34.228
217.007
27.785
272.396

19.838
296.392
36.479
264.967
34.167
217.279
27.736
272.518

19.929
296.292
36.515
264.825
34.107
217.551
27.687
272.641

20.019
296.191
36.550
264.682
34.047
217.823
27.637
272.763

20.109
296.090
36.585
264.540
33.989
218.095
27.587
272.885

20.199
295.990
36.620
264.397
33.931
218.368
27.537
273.007

20.289
295.888
36.654
264.255
33.875
218.641
27.487
273.129

20.378
295.787
36.689
264.112
33.819
218.914
27.437
273.250

20.468
295.686
36.723
263.969
33.765
219.187
27.386
273.372

20.557
295.584
36.757
263.826
33.711
219.460
27.335
273.493

20.646
295.482
36.790
263.682
33.658
219.734
27.284
273.615

20.735
295.380
36.823
263.539
33.607
220.008
27.233
273.736

20.824
295.278
36.856
263.396
33.556
220.281
27.182
273.857

20.913
295.175
36.889
263.252
33.506
220.556
27.130
273.977

21.001
295.072
36.921
263.108
33.457
220.830
27.078
274.098

21.089
294.969
36.953
262.965
33.409
221.104
27.026
274.219

21.178
294.866
36.985
262.821
33.362
221.379
26.974
274.339

21.266
294.763
37.017
262.677
33.316
221.654
26.921
274.459

21.353
294.659
37.048
262.533
33.271
221.929
26.869
274.579

21.441
294.555
37.079
262.389
33.227
222.204
26.816
274.699

21.528
294.451
37.110
262.244
33.184
222.479
26.762
274.819

21.616
294.347
37.141
262.100
33.142
222.754
26.709
274.939

21.703
294.243
37.171
261.956
33.100
223.030
26.656
275.058

21.790
294.138
37.215
261.742
33.060
223.306
26.602
275.178

21.877
294.034
37.267
261.490
33.021
223.581
26.548
275.297

21.963
293.929
37.318
261.238
32.982
223.857
26.494
275.416

22.050
293.823
37.372
260.963
32.945
224.133
26.439
275.535

22.136
293.718
37.425
260.688
32.908
224.410
26.384
275.654

22.222
293.612
37.477
260.413
32.873
224.686
26.330
275.772

22.308
293.507
37.528
260.137
32.838
224.962
26.275
275.891

22.394
293.401
37.578
259.861
32.804
225.239
26.219
276.009

22.479
293.295
37.626
259.585
32.772
225.516
26.164
276.128

22.565
293.188
37.674
259.309
32.740
225.792
26.108
276.246

22.650
293.082
37.721
259.033
32.709
226.069
26.052
276.364

22.735
292.975
37.767
258.756
32.680
226.346
25.996
276.481

22.820
292.868
37.811
258.479
32.651
226.624
25.940
276.599

22.904
292.761
37.855
258.203
32.623
226.901
25.884
276.716

22.989
292.653
37.897
257.926
32.596
227.178
25.827
276.834

23.073
292.546
37.939
257.648
32.570
227.455
25.770
276.951

23.157
292.438
37.979
257.371
32.545
227.733
25.713
277.068

23.241
292.330
38.019
257.094
32.521
228.011
25.656
277.185

23.325
292.222
38.057
256.816
32.498
228.288
25.598
277.301

23.409
292.113
38.094
256.538
32.476
228.566
25.540
277.418

23.492
292.005
38.130
256.260
32.455
228.844
25.482
277.534

23.575
291.896
38.166
255.982
32.435
229.122
25.424
277.651

23.658
291.787
38.200
255.704
32.415
229.400
25.366
277.767

23.741
291.678
38.233
255.426
32.397
229.678
25.307
277.883

23.824
291.569
38.265
255.147
32.380
229.956
25.249
277.999

23.907
291.459
38.295
254.869
32.364
230.234
25.190
278.114

23.989
291.349
38.325
254.590
32.348
230.512
25.131
278.230

24.071
291.240
38.354
254.311
32.334
230.790
25.071
278.345

24.153
291.129
38.382
254.032
32.320
231.068
25.012
278.460

24.235
291.019
38.408
253.753
32.308
231.347
24.952
278.575

24.316
290.909
38.434
253.474
32.296
231.625
24.892
278.690

24.398
290.798
38.459
253.195
32.286
231.904
24.832
278.805

24.479
290.687
38.482
252.916
32.276
232.182
24.772
278.919

24.560
290.576
38.504
252.636
32.268
232.460
24.711
279.034

24.641
290.465
38.526
252.357
32.260
232.739
24.650
279.148

24.722
290.353
38.546
252.077
32.254
233.018
24.590
279.262

24.802
290.242
38.565
251.798
32.248
233.296
24.528
279.376

24.883
290.130
38.583
251.518
32.243
233.575
24.467
279.490

24.963
290.018
38.600
251.238
32.239
233.853
24.406
279.604

25.043
289.905
38.616
250.959
32.237
234.132
24.344
279.717

25.122
289.793
38.631
250.679
32.235
234.410
24.282
279.830

25.202
289.680
38.645
250.399
32.234
234.689
24.220
279.944

25.281
289.568
38.658
250.119
32.234
234.968
24.158
280.057

25.360
289.455
38.670
249.839
32.235
235.246
24.095
280.169

25.439
289.341
38.681
249.559
32.237
235.525
24.032
280.282

25.518
289.228
38.690
249.279
32.240
235.803
23.970
280.395

25.597
289.115
38.699
248.999
32.244
236.082
23.907
280.507

25.675
289.001
38.706
248.718
32.249
236.361
23.843
280.619

25.753
288.887
38.713
248.438
32.255
236.639
23.780
280.731

25.831
288.773
38.718
248.158
32.262
236.918
23.716
280.843

25.909
288.658
38.722
247.878
32.269
237.196
23.652
280.955

25.987
288.544
38.725
247.598
32.278
237.475
23.588
281.066

26.064
288.429
38.728
247.317
32.288
237.753
23.524
281.178

26.142
288.314
38.729
247.037
32.299
238.031
23.460
281.289

26.219
288.199
38.729
246.757
32.310
238.310
23.395
281.400

26.295
288.084
38.728
246.476
32.323
238.588
23.330
281.511

26.372
287.969
38.725
246.196
32.337
238.866
23.265
281.621

26.449
287.853
38.722
245.916
32.351
239.145
23.200
281.732

26.525
287.737
38.718
245.636
32.367
239.423
23.135
281.842

26.601
287.621
38.713
245.356
32.383
239.701
23.069
281.953

26.677
287.505
38.706
245.075
32.401
239.979
23.004
282.063

26.752
287.389
38.699
244.795
32.419
240.257
22.938
282.173

26.828
287.272
38.690
244.515
32.439
240.535
22.872
282.282

26.903
287.156
38.681
244.235
32.459
240.813
22.805
282.392

26.978
287.039
38.670
243.955
32.480
241.091
22.739
282.501

27.053
286.922
38.658
243.675
32.502
241.363
22.672
282.611

27.128
286.804
38.646
243.395
32.523
241.625
22.605
282.720

27.202
286.687
38.632
243.115
32.543
241.882
22.538
282.829

27.277
286.569
38.617
242.835
32.561
242.138
22.471
282.937

27.351
286.451
38.601
242.555
32.579
242.395
22.404
283.046

27.425
286.334
38.584
242.276
32.596
242.652
22.336
283.154

27.498
286.215
38.566
241.996
32.611
242.909
22.268
283.262

27.572
286.097
38.546
241.716
32.626
243.166
22.200
283.371

27.645
285.978
38.526
241.437
32.640
243.423
22.132
283.478

27.718
285.860
38.505
241.157
32.652
243.680
22.064
283.586

27.791
285.741
38.483
240.883
32.664
243.937
21.995
283.694

27.863
285.622
38.462
240.621
32.675
244.194
21.927
283.801

27.936
285.503
38.442
240.364
32.685
244.452
21.858
283.908

28.008
285.383
38.423
240.107
32.693
244.709
21.789
284.015

28.080
285.264
38.405
239.850
32.701
244.966
21.720
284.122

28.152
285.144
38.388
239.592
32.708
245.224
21.650
284.229

28.224
285.024
38.372
239.335
32.714
245.481
21.581
284.335

28.295
284.904
38.357
239.078
32.719
245.738
21.511
284.442

28.366
284.783
38.342
238.820
32.723
245.996
21.441
284.548

28.437
284.663
38.329
238.563
32.726
246.253
21.371
284.654

28.508
284.542
38.316
238.305
32.728
246.511
21.301
284.760

28.579
284.422
38.305
238.048
32.729
246.768
21.230
284.865

28.649
284.301
38.294
237.790
32.729
247.025
21.159
284.971

28.719
284.179
38.284
237.533
32.728
247.283
21.089
285.076

28.789
284.058
38.275
237.275
32.726
247.540
21.018
285.181

28.859
283.937
38.267
237.017
32.723
247.798
20.946
285.286

28.928
283.815
38.260
236.760
32.719
248.055
20.875
285.391

28.998
283.693
38.253
236.502
32.714
248.312
20.804
285.496

29.067
283.571
38.248
236.244
32.708
248.570
20.732
285.600

29.136
283.449
38.243
235.986
32.701
248.827
20.660
285.705

29.205
283.326
38.240
235.729
32.693
249.084
20.588
285.809

29.273
283.204
38.237
235.471
32.684
249.342
20.516
285.913

29.341
283.081
38.235
235.213
32.675
249.599
20.443
286.016

29.409
282.958
38.234
234.955
32.664
249.856
20.371
286.120

29.477
282.835
38.234
234.697
32.652
250.113
20.298
286.223

29.545
282.712
38.235
234.439
32.639
250.370
20.225
286.326

29.612
282.588
38.236
234.182
32.626
250.627
20.152
286.430

29.679
282.465
38.239
233.924
32.611
250.884
20.079
286.532

29.746
282.341
38.242
233.666
32.595
251.141
20.005
286.635

29.813
282.217
38.247
233.408
32.579
251.398
19.932
286.738

29.880
282.093
38.252
233.151
32.561
251.655
19.858
286.840

29.946
281.969
38.258
232.893
32.542
251.912
19.784
286.942

30.012
281.845
38.265
232.635
32.523
252.168
19.710
287.044

30.078
281.720
38.273
232.377
32.502
252.425
19.636
287.146

30.144
281.595
38.282
232.120
32.481
252.681
19.561
287.247

30.209
281.470
38.292
231.862
32.458
252.938
19.487
287.349

30.274
281.345
38.302
231.605
32.435
253.194
19.412
287.450

30.339
281.220
38.314
231.347
32.410
253.451
19.337
287.551

30.404
281.095
38.326
231.089
32.385
253.707
19.262
287.652

30.469
280.969
38.340
230.832
32.358
253.963
19.186
287.753

30.533
280.843
38.354
230.575
32.331
254.219
19.111
287.853

30.597
280.717
38.369
230.317
32.302
254.475
19.035
287.954

30.661
280.591
38.385
230.060
32.273
254.730
18.960
288.054

30.725
280.465
38.402
229.803
32.243
254.986
18.884
288.154

30.789
280.339
38.420
229.545
32.211
255.241
18.808
288.254

30.852
280.212
38.438
229.288
32.179
255.497
18.731
288.353

30.915
280.085
38.458
229.031
32.146
255.752
18.655
288.453

30.978
279.958
38.478
228.774
32.112
256.007
18.578
288.552

31.040
279.831
38.500
228.517
32.077
256.262
18.502
288.651

31.103
279.704
38.522
228.261
32.040
256.517
18.425
288.750

31.165
279.577
38.545
228.004
32.003
256.772
18.348
288.848

31.227
279.449
38.569
227.747
31.965
257.026
18.270
288.947

31.288
279.322
38.594
227.490
31.926
257.281
18.193
289.045

31.350
279.194
38.620
227.234
31.886
257.535
18.115
289.143

31.411
279.066
38.646
226.977
31.845
257.789
18.038
289.241

31.472
278.938
38.674
226.721
31.803
258.043
17.960
289.339

31.533
278.809
38.702
226.465
31.760
258.297
17.882
289.437

31.593
278.681
38.732
226.209
31.716
258.551
17.804
289.534

31.654
278.552
38.762
225.953
31.671
258.804
17.725
289.631

31.714
278.424
38.793
225.697
31.626
259.057
17.647
289.728

31.774
278.295
38.825
225.441
31.579
259.311
17.568
289.825

31.833
278.165
38.858
225.185
31.531
259.564
17.489
289.922

31.893
278.036
38.892
224.930
31.482
259.816
17.410
290.018

31.952
277.907
38.926
224.674
31.433
260.066
17.331
290.115

32.011
277.777
38.962
224.419
31.387
260.297
17.252
290.211

32.070
277.648
38.998
224.164
31.339
260.531
17.173
290.307

32.128
277.518
39.036
223.909
31.298
260.730
17.093
290.403

32.187
277.388
39.074
223.654
31.270
260.863
17.013
290.498

32.245
277.257
39.113
223.399
31.241
260.997
16.933
290.593

32.302
277.127
39.153
223.144
31.213
261.130
16.853
290.689

32.360
276.997
39.194
222.890
31.184
261.263
16.773
290.784

32.417
276.866
39.235
222.635
31.155
261.395
16.693
290.878

32.475
276.735
39.278
222.381
31.126
261.528
16.612
290.973

32.531
276.604
39.321
222.127
31.097
261.661
16.531
291.067

32.588
276.473
39.366
221.873
31.067
261.793
16.451
291.162

32.644
276.342
39.411
221.619
31.037
261.926
16.370
291.256

32.701
276.211
39.457
221.365
31.007
262.058
16.289
291.349

32.757
276.079
39.504
221.112
30.977
262.190
16.207
291.443

32.812
275.947
39.552
220.859
30.946
262.322
16.126
291.537

32.868
275.815
39.601
220.605
30.915
262.454
16.044
291.630

32.923
275.683
39.651
220.352
30.884
262.586
15.963
291.723

32.978
275.551
39.701
220.100
30.853
262.718
15.881
291.816

33.033
275.419
39.752
219.847
30.821
262.850
15.799
291.908

33.087
275.287
39.805
219.594
30.789
262.981
15.717
292.001

33.142
275.154
39.858
219.342
30.757
263.113
15.634
292.093

33.196
275.021
39.912
219.090
30.725
263.244
15.552
292.185

33.250
274.888
39.967
218.838
30.693
263.375
15.469
292.277

33.303
274.755
40.023
218.587
30.660
263.506
15.387
292.369

33.357
274.622
40.079
218.335
30.627
263.637
15.304
292.461

33.410
274.489
40.137
218.084
30.593
263.768
15.221
292.552

33.463
274.356
40.195
217.833
30.560
263.899
15.137
292.643

33.515
274.222
40.254
217.582
30.526
264.030
15.054
292.734

33.568
274.088
40.314
217.331
30.492
264.161
14.971
292.825

33.620
273.954
40.375
217.080
30.458
264.291
14.887
292.915

33.672
273.820
40.437
216.830
30.424
264.421
14.803
293.006

33.723
273.686
40.500
216.580
30.389
264.552
14.719
293.096

33.775
273.552
40.564
216.330
30.354
264.682
14.635
293.186

33.826
273.417
40.628
216.081
30.319
264.812
14.551
293.276

33.877
273.283
40.693
215.831
30.283
264.942
14.467
293.365

33.928
273.148
40.760
215.582
30.248
265.072
14.382
293.455

33.978
273.013
40.827
215.333
30.212
265.201
14.298
293.544

34.028
272.878
40.895
215.084
30.176
265.331
14.213
293.633

34.078
272.743
40.963
214.836
30.139
265.461
14.128
293.722

34.128
272.608
41.033
214.588
30.103
265.590
14.043
293.810

34.178
272.472
41.103
214.340
30.066
265.719
13.958
293.899

34.227
272.337
41.175
214.092
30.029
265.848
13.873
293.987

34.276
272.201
41.247
213.845
29.991
265.977
13.787
294.075

34.325
272.065
41.320
213.597
29.954
266.106
13.702
294.163

34.373
271.929
41.394
213.350
29.916
266.235
13.616
294.251

34.421
271.793
41.469
213.104
29.878
266.364
13.530
294.338

34.469
271.657
41.544
212.857
29.840
266.492
13.444
294.425

34.517
271.521
41.621
212.611
29.801
266.621
13.358
294.512

34.565
271.384
41.698
212.365
29.763
266.749
13.272
294.599

34.612
271.248
41.776
212.119
29.724
266.877
13.186
294.686

34.659
271.111
41.856
211.874
29.685
267.006
13.099
294.772

34.706
270.974
41.935
211.629
29.645
267.134
13.013
294.859

34.752
270.837
42.016
211.384
29.606
267.261
12.926
294.945

34.799
270.700
42.098
211.139
29.566
267.389
12.839
295.031

34.845
270.562
42.180
210.895
29.526
267.517
12.752
295.116

34.891
270.425
42.264
210.651
29.485
267.644
12.666
295.200

34.936
270.287
42.348
210.408
29.445
267.772
12.649
295.217

34.981
270.150
42.433
210.164
29.404
267.899
16.830
299.520

35.027
270.012
42.518
209.921
29.363
268.026

35.071
269.874
36.864
207.914
29.322
268.153

35.116
269.736
36.771
208.177
29.280
268.280

FIG. 9B illustrates an envelope L2 for one of the S-shaped profiles S2 in a dimensional representation. According to the example shown in FIG. 9B, the coordinates disclosed in the context of FIG. 6 above are multiplied by a dimension of 300 mm, in order to obtain a dimensional tooth geometry. The envelope of the S-shaped profile shown in FIG. 9B represents the entire envelope of the S-shaped profile S2. To this end, one of the S-shaped profiles S2 (represented in FIG. 9B as envelope of S2) has an envelope including all of the dimensional x-y-coordinates in all following columns:

Column 1
Column 2
Column 3
Column 4

x
y
x
y
x
y
x
y

56.6110
192.7995
35.7255
247.5689
34.2771
261.1364
22.2125
288.7033

54.0681
193.6945
35.7071
248.6441
34.2771
261.1364
21.0318
290.2830

51.6338
194.8529
35.6825
249.4502
34.2771
261.1364
19.8951
291.7189

49.3353
196.2615
35.6354
250.5245
34.2771
261.1364
18.6412
293.2153

47.1982
197.9048
35.5893
251.3297
34.2771
261.1364
17.3516
294.6673

45.4326
199.5693
35.5136
252.4024
34.2771
261.1364
16.1172
295.9818

43.6663
201.6058
35.4461
253.2061
34.2771
261.1364
14.7629
297.3458

42.1246
203.8173
35.3418
254.2764
34.2342
261.3430
14.4530
297.6266

40.8248
206.1791
35.2529
255.0780
34.2342
261.3430
14.1211
297.8803

39.7814
208.6648
35.1201
256.1451
34.2342
261.3430
13.7832
298.0972

38.5993
212.2284
35.0099
256.9441
34.2342
261.3430
13.4144
298.2934

37.6576
215.5853
34.8487
258.0073
33.7708
263.4148
13.0455
298.4523

36.8137
219.2438
34.7172
258.8030
33.2870
265.3267
12.6497
298.5856

36.1483
222.9389
34.5278
259.8616
32.7146
267.3504
12.2599
298.6822

35.6916
226.3953
34.3754
260.6522
32.0873
269.3470
11.8476
298.7491

35.3744
230.1364
34.3754
260.6522
31.4533
271.1848
11.4472
298.7808

35.2391
233.8885
34.3754
260.6522
30.7231
273.1248
10.1978
298.8260

35.2766
237.3748
34.3754
260.6522
29.9412
275.0336
8.8823
298.8680

35.4926
241.1231
34.3268
260.8934
29.1660
276.7856
7.6325
298.9026

35.5539
241.9273
34.3268
260.8934
28.2878
278.6300
6.3826
298.9319

35.6214
243.0005
34.3268
260.8934
27.3617
280.4392
5.0667
298.9571

35.6612
243.8061
34.3268
260.8934
26.4551
282.0950
3.8166
298.9756

35.7001
244.8807
34.3268
260.8934
25.4399
283.8328
2.5664
298.9890

35.7185
245.6870
34.3268
260.8934
24.3805
285.5319
1.2503
298.9974

35.7286
246.7623
34.3268
260.8934
23.3532
287.0820
0.0000
299.0000

FIG. 10 shows one example of a tooth geometry 2 as a result of the method for dimensioning a headstock root geometry 2. The fine lines indicate tooth geometries of headstock gear teeth known from the state of the art.

It will be obvious for a person skilled in the art that these embodiments and items only depict examples of a plurality of possibilities. Hence, the embodiments shown here should not be understood to form a limitation of these features and configurations. Any possible combination and configuration of the described features can be chosen according to the scope of the invention.

This is in particular the case with respect to the following optional features which may be combined with some or all embodiments, items and/or features mentioned before in any technically feasible combination.

A headstock gear for a feed system of a shearer loader may be provided.

The headstock gear for feed system of a shearer loader may comprise a plurality of teeth, each tooth having a tooth geometry. Furthermore, for each tooth, the tooth geometry may consist of two symmetric S-shaped tooth profiles which are arranged line symmetrically regarding a radius line, as seen from a view along an axis of rotation.

The tooth geometry may be suitable for engaging a gear rack. Furthermore, the tooth geometry may be designed such that an engagement with at least two different gear rack pitches is enabled.

Instead of designing the tooth geometry such that the tooth geometry has a classic involute shape, the tooth geometry is adjusted such that an engagement with at least two different gear rack pitches is enabled. This increases service life of the tooth root as well as the service life of the tools flanks as breakage to gear jumps or improper engagement between headstock gear rack segments may be prevented.

The plurality of teeth may comprise 11 teeth.

The tooth geometry may consist, for each tooth, of two symmetric S-shaped tooth profiles which are arranged line symmetrically regarding a radius line, as seen from a view along the axis of rotation of the headstock gear.

One of the S-shaped profiles may comprise an envelope fitting into a frame with the non-dimensional outer limitations defined by the x-y coordinates set forth in all of the columns disclosed above in description of FIG. 4.

One of the S-shaped profiles may have an envelope including all or at least some of the non-dimensional x-y-coordinates set forth in all of the columns disclosed above in description of FIG. 5. The envelope of the S-shaped profile shown represents only a part of the envelope of the total S-shaped profile S2. Said part covers about the same range covered by the envelope fitting into a frame with the non-dimensional outer limitations as disclosed in FIG. 4 above.

One of the S-shaped profiles may have an envelope comprising all of the non-dimensional x-y-coordinates set forth above in the description of FIG. 6.

The coordinates may be multiplied by a dimension, for example 100 mm to 300 mm, in order to obtain a dimensioned tooth geometry, preferably wherein the headstock gear extends over the entire height of a tooth, preferably wherein the S-shaped profile has the length of about 70 mm.

Alternatively, the S-shaped profiles may be expressed by a single continuous polynomic function or by several polynomic functions.

Each tooth of the plurality of teeth may be hardened, preferably case hardened and/or inductive hardened.

The hardening may be provided at the root of each of the teeth, preferably wherein the hardening is not provided at the tip of the teeth.

A system may be provided comprising a headstock gear according to the present disclosure and a gear rack comprising several gear rack segments which are arranged next to each other such that a track is provided. The gear rack may comprise two different gear rack pitches.

Different gear rack pitches may be present for example due to relative displacement of individual gear rack segments. In this case, two gear rack segments may comprise a different gear pitch at their intersection compared to the nominal gear rack pitch. In the case when a headstock gear travels over a gear rack and inconsistent gear rack pitch, the headstock gear may be damaged for example due to gear jumps which may lead to failure or breakage of the headstock gear.

Each of the gear rack segments may comprise several rack teeth, preferably wherein the gear rack teeth have a substantially trapezoid cross-section.

The headstock you may comprise eleven teeth, wherein the gear rack may comprise a nominal gear rack pitch of 147 mm.

The headstock tooth geometry may be designed such that root stresses of each tooth are minimized. Thereby, the resilience of the tooth against wear and gear jumps may be increased.

The headstock gear tooth geometry may be designed such that a product of Hertzian stress and a relative slip component is minimized when engaged with the gear rack.

A method of dimensioning a tooth geometry of a headstock gear for a shearer loader, comprising a plurality of teeth, may comprise the steps of identifying all relevant engagement conditions during operation of the headstock gear together with the gear rack and selecting a tooth geometry on the basis of the identified relevant engagement conditions by minimizing a tooth root tension.

Ideal gear racks have a constant pitch due to equidistant gear rack teeth. However, different gear rack pitches may be present for example due to relative displacement of individual gear rack segments. In this case, the outermost of two gear rack segments may comprise a different gear pitch compared to the nominal gear rack pitch. In the case when a headstock gear travels over a gear rack and inconsistent gear rack pitch, the headstock gear may be damaged for example due to gear jumps which may lead to failure or breakage of the headstock gear.

The method may for example include starting from an ideal tooth geometry, corresponding to a geometry that is optimized for a constant gear rack pitch. On the basis of such an ideal tooth geometry, under consideration of all relevant engagement conditions during operation of the headstock gear together with the gear rack, the tooth geometry can be further optimized according to the present disclosure.

However, deviating from a geometry that is ideal for a constant gear rack pitch for the sake of optimizing the headstock gear for at least two gear rack pitches has the consequence, that the engagement of the headstock gear is not ideal for either of the at least two gear rack pitches. This means that additional stresses are inflicted to the headstock gear throughout operation. Therefore, selecting a tooth geometry on the basis of the identified relevant engagement conditions by minimizing a tooth root tension allows safe dimensioning of the tooth geometry.

The method may further comprise the step of maximizing a tooth root strength by exploiting the available distance between the outline of the gear rack teeth and the headstock gear. As a tooth geometry according to the present disclosure may have a non-ideal engagement for any gear rack pitch, exploiting the available distance between the outline of the gear rack teeth and the headstock gear may increase service lifetime to a reduced tooth root tension.

The method may further comprise the step of minimizing the occurrence of gear jump.

Furthermore, the method may further comprise the step of minimizing the product of Hertzian stress and a relative slip component when engaged with the gear rack.

According to a preferred embodiment, one or more steps of the method for dimensioning a tooth geometry may be calculated by an algorithm. The algorithm may be provided on a non-transient computer readable storage medium.

In general, the result of one or more of method steps may comprise a data range or threshold within which the technical effect of the above-mentioned discloser may be observed. However, although solved according to the present closer may have in common, that the yielded resolved deviates from optimization results focusing on one gear rack pitch.

INDUSTRIAL APPLICABILITY

With reference to the Figures, a headstock gear for a feed system of a shearer loader is suggested. The suggested headstock gear as mentioned above is applicable in any gear rack application. The tooth geometry being designed such that an engagement with at least two different gear rack pitches is enabled provides that, despite potentially operating at a sub-optimal engagement, a headstock gear having such a tooth geometry is longer lasting compare to a tooth geometry optimized for one gear rack pitch.

LIST OF REFERENCE NUMERALS

- A Axis of rotation
- L2 Outer limitation for an envelope fitting
- S1, S2 S-shaped tooth profiles
- S10 Identifying step
- S20 Selecting step
- S30 Maximizing tooth root strength step
- S40 Minimizing gear jump step
- S50 Minimizing product Hertzian stress and a relative slip component step
- 1 Headstock tooth
- 2 Tooth geometry
- 4 Gear rack
- 4′ Gear rack segment
- 6 Gear rack pitch
- 6′ Gear rack pitch (nominal)
- 8 Gear rack teeth
- 10 Headstock gear
- 12 Tooth root

Tooth Geometry for Headstock Gear for Feed System of a Shearer Loader

Information

Publication Number

Date Filed

Date Published

Inventors

Original Assignees

CPC

International Classifications

Abstract

Description

Claims

PCT Information