Sure, parts to ASME specifications cost less than MIL-SPEC parts.  They should!  It costs more to produce parts that conform to military requirements.  Know for sure that you are supplying parts that meet MIL-SPEC call outs for material, hardness, plating, testing and certification.  For tooth, helical and Belleville washers and metallic and non-metallic flat washers that meet those specifications, rely on the MIL-SPEC specialist:

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Mil-Spec

Mil-Spec Fasteners

AN—Air Force—Navy Aeronautical
Standards

AN901
AN940
AN960
AN961
AN970
AN8013
AN122576 thru
AN122600
AN212588

NAS—National Aerospace Standards
NAS460
NAS513
NAS549
NAS620
NAS1070
NAS1149
NAS1169
NAS1193
NAS1195
NAS1197
NAS1252
NAS1515
NAS1587
NAS1598
NAS1640
NAS1676

NASM Standards
NASM15795
NASM20002
NASM35333
NASM35338
NASM45595

MS—Military Standards
MS9276
MS9320
MS9321
MS9482
MS9549
MS9581
MS9582
MS9768
MS9880
MS14151
MS14155
MS14177
MS14183
MS14198
MS14226
MS15795
MS15820
MS16212
MS16213
MS17811
MS17973

MIL—W—Standards
M12133/1
M12133/2
M38527/09
M45595/1
M45595/2
M45595/8
M45595/9

MS—Military Standards
MS20002
MS21206
MS21258
MS21299
MS21306
MS21307
MS25081
MS25440
MS27111
MS27183
MS28777
MS35333
MS35334
MS35335
MS35336
MS35337
MS35338
MS35340
MS35790
MS45904
MS51412
MS51413
MS51414
MS51415
MS51416
MS51496
MS51848
MS51859
MS51867
MS51936
MS75009
MS122026 thru
MS122075